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",[99,1040,1042,1071],{"className":1041},[102],[99,1043,1045],{"className":1044},[106],[108,1046,1047],{"xmlns":110},[112,1048,1049,1069],{},[115,1050,1051,1053,1067],{},[118,1052,121],{"stretchy":120},[123,1054,1055,1057,1059],{},[126,1056,128],{},[126,1058,131],{},[115,1060,1061,1063,1065],{},[126,1062,136],{},[118,1064,140],{"separator":139},[142,1066,144],{},[118,1068,147],{"stretchy":120},[149,1070,152],{"encoding":151},[99,1072,1074],{"className":1073,"ariaHidden":139},[156],[99,1075,1077,1080,1083,1143],{"className":1076},[160],[99,1078],{"className":1079,"style":165},[164],[99,1081,121],{"className":1082},[169],[99,1084,1086,1089],{"className":1085},[173],[99,1087,128],{"className":1088},[173,177],[99,1090,1092],{"className":1091},[181],[99,1093,1095,1135],{"className":1094},[185,186],[99,1096,1098,1132],{"className":1097},[190],[99,1099,1101,1112],{"className":1100,"style":195},[194],[99,1102,1103,1106],{"style":198},[99,1104],{"className":1105,"style":203},[202],[99,1107,1109],{"className":1108},[207,208,209,210],[99,1110,131],{"className":1111},[173,177,210],[99,1113,1114,1117],{"style":216},[99,1115],{"className":1116,"style":203},[202],[99,1118,1120],{"className":1119},[207,208,209,210],[99,1121,1123,1126,1129],{"className":1122},[173,210],[99,1124,136],{"className":1125,"style":229},[173,177,210],[99,1127,140],{"className":1128},[233,210],[99,1130,144],{"className":1131},[173,210],[99,1133,241],{"className":1134},[240],[99,1136,1138],{"className":1137},[190],[99,1139,1141],{"className":1140,"style":248},[194],[99,1142],{},[99,1144,147],{"className":1145},[254],[99,1147,1149,1178],{"className":1148},[102],[99,1150,1152],{"className":1151},[106],[108,1153,1154],{"xmlns":110},[112,1155,1156,1176],{},[115,1157,1158,1160,1174],{},[118,1159,121],{"stretchy":120},[123,1161,1162,1164,1166],{},[126,1163,128],{},[126,1165,131],{},[115,1167,1168,1170,1172],{},[126,1169,506],{},[118,1171,140],{"separator":139},[510,1173,512],{},[118,1175,147],{"stretchy":120},[149,1177,517],{"encoding":151},[99,1179,1181],{"className":1180,"ariaHidden":139},[156],[99,1182,1184,1187,1190,1253],{"className":1183},[160],[99,1185],{"className":1186,"style":527},[164],[99,1188,121],{"className":1189},[169],[99,1191,1193,1196],{"className":1192},[173],[99,1194,128],{"className":1195},[173,177],[99,1197,1199],{"className":1198},[181],[99,1200,1202,1245],{"className":1201},[185,186],[99,1203,1205,1242],{"className":1204},[190],[99,1206,1208,1219],{"className":1207,"style":549},[194],[99,1209,1210,1213],{"style":198},[99,1211],{"className":1212,"style":203},[202],[99,1214,1216],{"className":1215},[207,208,209,210],[99,1217,131],{"className":1218},[173,177,210],[99,1220,1221,1224],{"style":216},[99,1222],{"className":1223,"style":203},[202],[99,1225,1227],{"className":1226},[207,208,209,210],[99,1228,1230,1233,1236],{"className":1229},[173,210],[99,1231,506],{"className":1232,"style":575},[173,177,210],[99,1234,140],{"className":1235},[233,210],[99,1237,1239],{"className":1238},[173,582,210],[99,1240,512],{"className":1241},[173,586,210],[99,1243,241],{"className":1244},[240],[99,1246,1248],{"className":1247},[190],[99,1249,1251],{"className":1250,"style":248},[194],[99,1252],{},[99,1254,147],{"className":1255},[254],".",[1258,1259,1260],"h3",{"id":1260},"表达形式一",[67,1262,1263,1264,1293,1294,1322,1323,1351,1352,1380,1381,1479,1480,1581,1582,1610],{},"对于多元两相体系，包含",[99,1265,1267,1281],{"className":1266},[102],[99,1268,1270],{"className":1269},[106],[108,1271,1272],{"xmlns":110},[112,1273,1274,1279],{},[115,1275,1276],{},[126,1277,1278],{},"n",[149,1280,1278],{"encoding":151},[99,1282,1284],{"className":1283,"ariaHidden":139},[156],[99,1285,1287,1290],{"className":1286},[160],[99,1288],{"className":1289,"style":282},[164],[99,1291,1278],{"className":1292},[173,177],"个组元，以及",[99,1295,1297,1310],{"className":1296},[102],[99,1298,1300],{"className":1299},[106],[108,1301,1302],{"xmlns":110},[112,1303,1304,1308],{},[115,1305,1306],{},[126,1307,136],{},[149,1309,272],{"encoding":151},[99,1311,1313],{"className":1312,"ariaHidden":139},[156],[99,1314,1316,1319],{"className":1315},[160],[99,1317],{"className":1318,"style":282},[164],[99,1320,136],{"className":1321,"style":229},[173,177],"和",[99,1324,1326,1339],{"className":1325},[102],[99,1327,1329],{"className":1328},[106],[108,1330,1331],{"xmlns":110},[112,1332,1333,1337],{},[115,1334,1335],{},[126,1336,506],{},[149,1338,617],{"encoding":151},[99,1340,1342],{"className":1341,"ariaHidden":139},[156],[99,1343,1345,1348],{"className":1344},[160],[99,1346],{"className":1347,"style":627},[164],[99,1349,506],{"className":1350,"style":575},[173,177],"两个相。假设",[99,1353,1355,1368],{"className":1354},[102],[99,1356,1358],{"className":1357},[106],[108,1359,1360],{"xmlns":110},[112,1361,1362,1366],{},[115,1363,1364],{},[126,1365,136],{},[149,1367,272],{"encoding":151},[99,1369,1371],{"className":1370,"ariaHidden":139},[156],[99,1372,1374,1377],{"className":1373},[160],[99,1375],{"className":1376,"style":282},[164],[99,1378,136],{"className":1379,"style":229},[173,177],"相的成分为",[99,1382,1384,1410],{"className":1383},[102],[99,1385,1387],{"className":1386},[106],[108,1388,1389],{"xmlns":110},[112,1390,1391,1407],{},[115,1392,1393],{},[123,1394,1395,1397,1399],{},[126,1396,306],{},[126,1398,131],{},[115,1400,1401,1403,1405],{},[126,1402,136],{},[118,1404,140],{"separator":139},[142,1406,144],{},[149,1408,1409],{"encoding":151},"x_i^{\\alpha, 0}",[99,1411,1413],{"className":1412,"ariaHidden":139},[156],[99,1414,1416,1419],{"className":1415},[160],[99,1417],{"className":1418,"style":165},[164],[99,1420,1422,1425],{"className":1421},[173],[99,1423,306],{"className":1424},[173,177],[99,1426,1428],{"className":1427},[181],[99,1429,1431,1471],{"className":1430},[185,186],[99,1432,1434,1468],{"className":1433},[190],[99,1435,1437,1448],{"className":1436,"style":195},[194],[99,1438,1439,1442],{"style":198},[99,1440],{"className":1441,"style":203},[202],[99,1443,1445],{"className":1444},[207,208,209,210],[99,1446,131],{"className":1447},[173,177,210],[99,1449,1450,1453],{"style":216},[99,1451],{"className":1452,"style":203},[202],[99,1454,1456],{"className":1455},[207,208,209,210],[99,1457,1459,1462,1465],{"className":1458},[173,210],[99,1460,136],{"className":1461,"style":229},[173,177,210],[99,1463,140],{"className":1464},[233,210],[99,1466,144],{"className":1467},[173,210],[99,1469,241],{"className":1470},[240],[99,1472,1474],{"className":1473},[190],[99,1475,1477],{"className":1476,"style":248},[194],[99,1478],{},"，而新相的成分为",[99,1481,1483,1509],{"className":1482},[102],[99,1484,1486],{"className":1485},[106],[108,1487,1488],{"xmlns":110},[112,1489,1490,1506],{},[115,1491,1492],{},[123,1493,1494,1496,1498],{},[126,1495,306],{},[126,1497,131],{},[115,1499,1500,1502,1504],{},[126,1501,506],{},[118,1503,140],{"separator":139},[510,1505,512],{},[149,1507,1508],{"encoding":151},"x_i^{\\beta, \\textrm{new}}",[99,1510,1512],{"className":1511,"ariaHidden":139},[156],[99,1513,1515,1518],{"className":1514},[160],[99,1516],{"className":1517,"style":527},[164],[99,1519,1521,1524],{"className":1520},[173],[99,1522,306],{"className":1523},[173,177],[99,1525,1527],{"className":1526},[181],[99,1528,1530,1573],{"className":1529},[185,186],[99,1531,1533,1570],{"className":1532},[190],[99,1534,1536,1547],{"className":1535,"style":549},[194],[99,1537,1538,1541],{"style":198},[99,1539],{"className":1540,"style":203},[202],[99,1542,1544],{"className":1543},[207,208,209,210],[99,1545,131],{"className":1546},[173,177,210],[99,1548,1549,1552],{"style":216},[99,1550],{"className":1551,"style":203},[202],[99,1553,1555],{"className":1554},[207,208,209,210],[99,1556,1558,1561,1564],{"className":1557},[173,210],[99,1559,506],{"className":1560,"style":575},[173,177,210],[99,1562,140],{"className":1563},[233,210],[99,1565,1567],{"className":1566},[173,582,210],[99,1568,512],{"className":1569},[173,586,210],[99,1571,241],{"className":1572},[240],[99,1574,1576],{"className":1575},[190],[99,1577,1579],{"className":1578,"style":248},[194],[99,1580],{},"。根据Gibbs-Duhem关系，",[99,1583,1585,1598],{"className":1584},[102],[99,1586,1588],{"className":1587},[106],[108,1589,1590],{"xmlns":110},[112,1591,1592,1596],{},[115,1593,1594],{},[126,1595,136],{},[149,1597,272],{"encoding":151},[99,1599,1601],{"className":1600,"ariaHidden":139},[156],[99,1602,1604,1607],{"className":1603},[160],[99,1605],{"className":1606,"style":282},[164],[99,1608,136],{"className":1609,"style":229},[173,177],"相相成分的能量切面可以表示为",[99,1612,1615],{"className":1613},[1614],"katex-display",[99,1616,1618,1678],{"className":1617},[102],[99,1619,1621],{"className":1620},[106],[108,1622,1624],{"xmlns":110,"display":1623},"block",[112,1625,1626,1675],{},[115,1627,1628,1636,1638,1655,1661],{},[1629,1630,1631,1634],"msup",{},[126,1632,1633],{},"f",[126,1635,136],{},[118,1637,313],{},[1639,1640,1641,1644,1653],"munderover",{},[118,1642,1643],{},"∑",[115,1645,1646,1648,1650],{},[126,1647,131],{},[118,1649,313],{},[142,1651,1652],{},"1",[126,1654,1278],{},[302,1656,1657,1659],{},[126,1658,306],{},[126,1660,131],{},[123,1662,1663,1665,1667],{},[126,1664,128],{},[126,1666,131],{},[115,1668,1669,1671,1673],{},[126,1670,136],{},[118,1672,140],{"separator":139},[142,1674,144],{},[149,1676,1677],{"encoding":151},"f^\\alpha=\\sum_{i=1}^n x_i \\mu_i^{\\alpha, 0}",[99,1679,1681,1729],{"className":1680,"ariaHidden":139},[156],[99,1682,1684,1688,1720,1723,1726],{"className":1683},[160],[99,1685],{"className":1686,"style":1687},[164],"height:0.9088em;vertical-align:-0.1944em;",[99,1689,1691,1695],{"className":1690},[173],[99,1692,1633],{"className":1693,"style":1694},[173,177],"margin-right:0.1076em;",[99,1696,1698],{"className":1697},[181],[99,1699,1701],{"className":1700},[185],[99,1702,1704],{"className":1703},[190],[99,1705,1708],{"className":1706,"style":1707},[194],"height:0.7144em;",[99,1709,1711,1714],{"style":1710},"top:-3.113em;margin-right:0.05em;",[99,1712],{"className":1713,"style":203},[202],[99,1715,1717],{"className":1716},[207,208,209,210],[99,1718,136],{"className":1719,"style":229},[173,177,210],[99,1721],{"className":1722,"style":398},[397],[99,1724,313],{"className":1725},[402],[99,1727],{"className":1728,"style":398},[397],[99,1730,1732,1736,1810,1814,1854],{"className":1731},[160],[99,1733],{"className":1734,"style":1735},[164],"height:2.9291em;vertical-align:-1.2777em;",[99,1737,1741],{"className":1738},[1739,1740],"mop","op-limits",[99,1742,1744,1801],{"className":1743},[185,186],[99,1745,1747,1798],{"className":1746},[190],[99,1748,1751,1773,1786],{"className":1749,"style":1750},[194],"height:1.6514em;",[99,1752,1754,1758],{"style":1753},"top:-1.8723em;margin-left:0em;",[99,1755],{"className":1756,"style":1757},[202],"height:3.05em;",[99,1759,1761],{"className":1760},[207,208,209,210],[99,1762,1764,1767,1770],{"className":1763},[173,210],[99,1765,131],{"className":1766},[173,177,210],[99,1768,313],{"className":1769},[402,210],[99,1771,1652],{"className":1772},[173,210],[99,1774,1776,1779],{"style":1775},"top:-3.05em;",[99,1777],{"className":1778,"style":1757},[202],[99,1780,1781],{},[99,1782,1643],{"className":1783},[1739,1784,1785],"op-symbol","large-op",[99,1787,1789,1792],{"style":1788},"top:-4.3em;margin-left:0em;",[99,1790],{"className":1791,"style":1757},[202],[99,1793,1795],{"className":1794},[207,208,209,210],[99,1796,1278],{"className":1797},[173,177,210],[99,1799,241],{"className":1800},[240],[99,1802,1804],{"className":1803},[190],[99,1805,1808],{"className":1806,"style":1807},[194],"height:1.2777em;",[99,1809],{},[99,1811],{"className":1812,"style":1813},[397],"margin-right:0.1667em;",[99,1815,1817,1820],{"className":1816},[173],[99,1818,306],{"className":1819},[173,177],[99,1821,1823],{"className":1822},[181],[99,1824,1826,1846],{"className":1825},[185,186],[99,1827,1829,1843],{"className":1828},[190],[99,1830,1832],{"className":1831,"style":366},[194],[99,1833,1834,1837],{"style":369},[99,1835],{"className":1836,"style":203},[202],[99,1838,1840],{"className":1839},[207,208,209,210],[99,1841,131],{"className":1842},[173,177,210],[99,1844,241],{"className":1845},[240],[99,1847,1849],{"className":1848},[190],[99,1850,1852],{"className":1851,"style":388},[194],[99,1853],{},[99,1855,1857,1860],{"className":1856},[173],[99,1858,128],{"className":1859},[173,177],[99,1861,1863],{"className":1862},[181],[99,1864,1866,1906],{"className":1865},[185,186],[99,1867,1869,1903],{"className":1868},[190],[99,1870,1872,1883],{"className":1871,"style":195},[194],[99,1873,1874,1877],{"style":198},[99,1875],{"className":1876,"style":203},[202],[99,1878,1880],{"className":1879},[207,208,209,210],[99,1881,131],{"className":1882},[173,177,210],[99,1884,1885,1888],{"style":216},[99,1886],{"className":1887,"style":203},[202],[99,1889,1891],{"className":1890},[207,208,209,210],[99,1892,1894,1897,1900],{"className":1893},[173,210],[99,1895,136],{"className":1896,"style":229},[173,177,210],[99,1898,140],{"className":1899},[233,210],[99,1901,144],{"className":1902},[173,210],[99,1904,241],{"className":1905},[240],[99,1907,1909],{"className":1908},[190],[99,1910,1912],{"className":1911,"style":248},[194],[99,1913],{},[67,1915,1916,1917,1610],{},"同理，",[99,1918,1920,1933],{"className":1919},[102],[99,1921,1923],{"className":1922},[106],[108,1924,1925],{"xmlns":110},[112,1926,1927,1931],{},[115,1928,1929],{},[126,1930,506],{},[149,1932,617],{"encoding":151},[99,1934,1936],{"className":1935,"ariaHidden":139},[156],[99,1937,1939,1942],{"className":1938},[160],[99,1940],{"className":1941,"style":627},[164],[99,1943,506],{"className":1944,"style":575},[173,177],[99,1946,1948],{"className":1947},[1614],[99,1949,1951,2005],{"className":1950},[102],[99,1952,1954],{"className":1953},[106],[108,1955,1956],{"xmlns":110,"display":1623},[112,1957,1958,2002],{},[115,1959,1960,1966,1968,1982,1988],{},[1629,1961,1962,1964],{},[126,1963,1633],{},[126,1965,506],{},[118,1967,313],{},[1639,1969,1970,1972,1980],{},[118,1971,1643],{},[115,1973,1974,1976,1978],{},[126,1975,131],{},[118,1977,313],{},[142,1979,1652],{},[126,1981,1278],{},[302,1983,1984,1986],{},[126,1985,306],{},[126,1987,131],{},[123,1989,1990,1992,1994],{},[126,1991,128],{},[126,1993,131],{},[115,1995,1996,1998,2000],{},[126,1997,506],{},[118,1999,140],{"separator":139},[510,2001,512],{},[149,2003,2004],{"encoding":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\\left.\\Delta G_m^{\\alpha \\rightarrow \\beta}\\right|_{\\mathbf{x}=\\mathbf{x}^{\\beta, \\text { new }}}=\\sum_{i=1}^n x_i^{\\beta, \\text { new }} \\mu_i^{\\alpha, 0}-G_m^{\\beta, \\text { new }} \\\\\n& =\\sum_{i=1}^n\\left(x_i^{\\beta, \\text { new }}-x_i^{\\alpha, 0}\\right) \\mu_i^{\\alpha, 0}-G_m^{\\beta, \\text { new }}+\\sum_{i=1}^n x_i^{\\alpha, 0} \\mu_i^{\\alpha, 0} \\\\\n& =\\sum_{i=1}^n\\left(x_i^{\\beta, \\text { new }}-x_i^{\\alpha, 0}\\right) \\mu_i^{\\alpha, 0}-G_m^{\\beta, \\text { new }}+G_m^{\\alpha, 0} \\\\\n& =G_m^{\\alpha, 0}-G_m^{\\beta, \\text { new }}+\\sum_{i=1}^n\\left(x_i^{\\beta, \\text { new }}-x_i^{\\alpha, 0}\\right)\\left(\\mu_i^{\\alpha, 0}-\\mu_n^{\\alpha, 0}\\right)+\\mu_n^{\\alpha, 0} \\sum_{i=1}^n\\left(x_i^{\\beta, \\text { new }}-x_i^{\\alpha, 0}\\right) \\\\\n& =G_m^{\\alpha, 0}-G_m^{\\beta, \\text { new }}+\\sum_{i=1}^{n-1}\\left(x_i^{\\beta, \\text { new }}-x_i^{\\alpha, 0}\\right) \\tilde{\\mu}_i^{\\alpha, 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shiki shiki-themes material-theme-lighter material-theme material-theme-palenight","# 能量数据为Pandat软件计算结果，Ni-Al体系的fcc与L12_fcc的计算结果，数据库为Pandat的镍基高温合金数据库。\nx_matrix_al = 0.2\nx_matrix_ni = 0.8\nmu_matrix_al = -157793.0\nmu_matrix_ni = -51148.8\ngm_matrix = -72477.6\n\nprint(\"gm: \", gm_matrix, x_matrix_al * mu_matrix_al + x_matrix_ni * mu_matrix_ni)\n\nx_l12_al = 0.24\nx_l12_ni = 0.76\ngm_l12 = -79069.11\nmu_l12_al = -182955.13\nmu_l12_ni = -46263.00\nprint(\"gm: \", gm_l12, x_l12_al * mu_l12_al + x_l12_ni * mu_l12_ni)\nprint(\"dp l12: \", mu_l12_al - mu_l12_ni)\n\ndriving_force_v1 = x_l12_al * (mu_matrix_al - mu_l12_al) + x_l12_ni * (mu_matrix_ni - mu_l12_ni)\nprint(\"driving_force_v1: \", driving_force_v1)\n\ndriving_force_v2 = gm_matrix - gm_l12 + (x_l12_al - x_matrix_al) * (mu_matrix_al - mu_matrix_ni)\nprint(\"driving_force_v2: \", driving_force_v2)\n","python","",[10569,10570,10571,10578,10584,10590,10596,10602,10608,10614,10620,10625,10631,10637,10643,10649,10655,10661,10667,10672,10678,10684,10689,10695],"code",{"__ignoreMap":10567},[99,10572,10575],{"class":10573,"line":10574},"line",1,[99,10576,10577],{},"# 能量数据为Pandat软件计算结果，Ni-Al体系的fcc与L12_fcc的计算结果，数据库为Pandat的镍基高温合金数据库。\n",[99,10579,10581],{"class":10573,"line":10580},2,[99,10582,10583],{},"x_matrix_al = 0.2\n",[99,10585,10587],{"class":10573,"line":10586},3,[99,10588,10589],{},"x_matrix_ni = 0.8\n",[99,10591,10593],{"class":10573,"line":10592},4,[99,10594,10595],{},"mu_matrix_al = -157793.0\n",[99,10597,10599],{"class":10573,"line":10598},5,[99,10600,10601],{},"mu_matrix_ni = -51148.8\n",[99,10603,10605],{"class":10573,"line":10604},6,[99,10606,10607],{},"gm_matrix = -72477.6\n",[99,10609,10611],{"class":10573,"line":10610},7,[99,10612,10613],{"emptyLinePlaceholder":53},"\n",[99,10615,10617],{"class":10573,"line":10616},8,[99,10618,10619],{},"print(\"gm: \", gm_matrix, x_matrix_al * mu_matrix_al + x_matrix_ni * mu_matrix_ni)\n",[99,10621,10623],{"class":10573,"line":10622},9,[99,10624,10613],{"emptyLinePlaceholder":53},[99,10626,10628],{"class":10573,"line":10627},10,[99,10629,10630],{},"x_l12_al = 0.24\n",[99,10632,10634],{"class":10573,"line":10633},11,[99,10635,10636],{},"x_l12_ni = 0.76\n",[99,10638,10640],{"class":10573,"line":10639},12,[99,10641,10642],{},"gm_l12 = -79069.11\n",[99,10644,10646],{"class":10573,"line":10645},13,[99,10647,10648],{},"mu_l12_al = -182955.13\n",[99,10650,10652],{"class":10573,"line":10651},14,[99,10653,10654],{},"mu_l12_ni = -46263.00\n",[99,10656,10658],{"class":10573,"line":10657},15,[99,10659,10660],{},"print(\"gm: \", gm_l12, x_l12_al * mu_l12_al + x_l12_ni * mu_l12_ni)\n",[99,10662,10664],{"class":10573,"line":10663},16,[99,10665,10666],{},"print(\"dp l12: \", mu_l12_al - mu_l12_ni)\n",[99,10668,10670],{"class":10573,"line":10669},17,[99,10671,10613],{"emptyLinePlaceholder":53},[99,10673,10675],{"class":10573,"line":10674},18,[99,10676,10677],{},"driving_force_v1 = x_l12_al * (mu_matrix_al - mu_l12_al) + x_l12_ni * (mu_matrix_ni - mu_l12_ni)\n",[99,10679,10681],{"class":10573,"line":10680},19,[99,10682,10683],{},"print(\"driving_force_v1: \", driving_force_v1)\n",[99,10685,10687],{"class":10573,"line":10686},20,[99,10688,10613],{"emptyLinePlaceholder":53},[99,10690,10692],{"class":10573,"line":10691},21,[99,10693,10694],{},"driving_force_v2 = gm_matrix - gm_l12 + (x_l12_al - x_matrix_al) * (mu_matrix_al - mu_matrix_ni)\n",[99,10696,10698],{"class":10573,"line":10697},22,[99,10699,10700],{},"print(\"driving_force_v2: \", driving_force_v2)\n",[67,10702,10703],{},"验算结果为",[10562,10705,10709],{"className":10706,"code":10708,"language":582},[10707],"language-text","gm:  -72477.6 -72477.64000000001\ngm:  -79069.11 -79069.1112\ndp l12:  -136692.13\ndriving_force_v1:  2325.703199999998\ndriving_force_v2:  2325.7419999999975\n",[10569,10710,10708],{"__ignoreMap":10567},[1258,10712,10713],{"id":10713},"参考说明",[67,10715,10716],{},[91,10717],{"alt":10718,"src":10719},"Hillert, M.","https:\u002F\u002Fppm-sources.oss-cn-hongkong.aliyuncs.com\u002Fwebsites\u002Fmynote\u002Fmaterials\u002Fthermodynamics\u002Fdriving-force-original-note.png",[10721,10722,10723],"style",{},"html .light .shiki span {color: var(--shiki-light);background: var(--shiki-light-bg);font-style: var(--shiki-light-font-style);font-weight: var(--shiki-light-font-weight);text-decoration: var(--shiki-light-text-decoration);}html.light .shiki span {color: var(--shiki-light);background: var(--shiki-light-bg);font-style: var(--shiki-light-font-style);font-weight: var(--shiki-light-font-weight);text-decoration: var(--shiki-light-text-decoration);}html .default .shiki span {color: var(--shiki-default);background: var(--shiki-default-bg);font-style: var(--shiki-default-font-style);font-weight: var(--shiki-default-font-weight);text-decoration: var(--shiki-default-text-decoration);}html .shiki span {color: var(--shiki-default);background: var(--shiki-default-bg);font-style: var(--shiki-default-font-style);font-weight: var(--shiki-default-font-weight);text-decoration: var(--shiki-default-text-decoration);}html .dark .shiki span {color: var(--shiki-dark);background: var(--shiki-dark-bg);font-style: var(--shiki-dark-font-style);font-weight: var(--shiki-dark-font-weight);text-decoration: var(--shiki-dark-text-decoration);}html.dark .shiki span {color: var(--shiki-dark);background: var(--shiki-dark-bg);font-style: var(--shiki-dark-font-style);font-weight: var(--shiki-dark-font-weight);text-decoration: var(--shiki-dark-text-decoration);}",{"title":10567,"searchDepth":10580,"depth":10580,"links":10725},[10726],{"id":18,"depth":10580,"text":18,"children":10727},[10728,10729,10730,10731],{"id":1260,"depth":10586,"text":1260},{"id":3759,"depth":10586,"text":3759},{"id":6960,"depth":10586,"text":6960},{"id":10713,"depth":10586,"text":10713},"2026-09-06","基于 Gibbs-Duhem 关系与扩散势，推导多元两相体系中相变驱动力的两种表达形式及其等价关系，并附 Pandat 计算数据的验算示例。","md",{},{"title":18,"description":10733},"eGgw8vJWCf9PSuev2ZmuWuxpzo6sT35NU6mUkgNFnT4",{"id":10739,"title":10,"author":10740,"body":10742,"date":27077,"description":27078,"extension":10734,"image":27079,"meta":27080,"minRead":10622,"navigation":53,"path":11,"seo":27081,"stem":12,"__hash__":27082},"blog\u002Fblog\u002Fchemical-potential-and-diffusion-potential.md",{"name":60,"avatar":10741},{"src":62,"alt":60},{"type":64,"value":10743,"toc":27068},[10744,10748,10751,10756,10760,10875,11129,11132,11448,11754,11786,12071,12214,12217,12531,12534,13281,13284,13681,13850,13853,14556,14559,15601,15604,16160,16164,16272,16580,16582,16953,16956,17283,17313,17581,17722,17724,18090,18093,18814,18897,18899,19291,19455,19457,20155,20157,21189,21191,21731,21735,21741,22290,22294,22833,22837,22840,22845,22848,23179,23240,23543,23548,23551,23941,23943,24266,24269,24272,24843,24846,25347,25350,25590,25593,25882,25914,26464,26467,26727,26730,27055,27058,27062],[86,10745,10747],{"id":10746},"the-partial-gibbs-energy-and-the-gibbs-energy","The partial Gibbs energy and the Gibbs energy",[67,10749,10750],{},"The partial Gibbs energy, or the chemical potential, is the partial quantity of the Gibbs energy, which means that it is independent of the amount of substance. Generally speaking, the Gibbs energy can be described as a function of temperature, pressure and compositions of components, and thus the chemical potential can be derived from such a mathematical formula. Sometimes, one might feel confused that there exist several different formulas of chemical potential with respect to the Gibbs energy. In this post, two different formulas are to be discussed, respectively.",[67,10752,10753],{},[81,10754,10755],{},"In the following derivation, the temperature and pressure are assumed as constant.",[1258,10757,10759],{"id":10758},"for-gibbs-energy-with-independent-composition","For Gibbs energy with independent composition",[67,10761,10762,10763,10792,10793,10845,10846,10874],{},"In this context, the Gibbs energy is a function of the solute components, denoted as ",[99,10764,10766,10779],{"className":10765},[102],[99,10767,10769],{"className":10768},[106],[108,10770,10771],{"xmlns":110},[112,10772,10773,10777],{},[115,10774,10775],{},[142,10776,1652],{},[149,10778,1652],{"encoding":151},[99,10780,10782],{"className":10781,"ariaHidden":139},[156],[99,10783,10785,10789],{"className":10784},[160],[99,10786],{"className":10787,"style":10788},[164],"height:0.6444em;",[99,10790,1652],{"className":10791},[173]," to ",[99,10794,10796,10814],{"className":10795},[102],[99,10797,10799],{"className":10798},[106],[108,10800,10801],{"xmlns":110},[112,10802,10803,10811],{},[115,10804,10805,10807,10809],{},[126,10806,2266],{},[118,10808,2254],{},[142,10810,1652],{},[149,10812,10813],{"encoding":151},"m-1",[99,10815,10817,10836],{"className":10816,"ariaHidden":139},[156],[99,10818,10820,10824,10827,10830,10833],{"className":10819},[160],[99,10821],{"className":10822,"style":10823},[164],"height:0.6667em;vertical-align:-0.0833em;",[99,10825,2266],{"className":10826},[173,177],[99,10828],{"className":10829,"style":2590},[397],[99,10831,2254],{"className":10832},[2594],[99,10834],{"className":10835,"style":2590},[397],[99,10837,10839,10842],{"className":10838},[160],[99,10840],{"className":10841,"style":10788},[164],[99,10843,1652],{"className":10844},[173],", while the ",[99,10847,10849,10862],{"className":10848},[102],[99,10850,10852],{"className":10851},[106],[108,10853,10854],{"xmlns":110},[112,10855,10856,10860],{},[115,10857,10858],{},[126,10859,2266],{},[149,10861,2266],{"encoding":151},[99,10863,10865],{"className":10864,"ariaHidden":139},[156],[99,10866,10868,10871],{"className":10867},[160],[99,10869],{"className":10870,"style":282},[164],[99,10872,2266],{"className":10873},[173,177],"-th component is regarded as the solvent.",[67,10876,10877,140],{},[99,10878,10880,10939],{"className":10879},[102],[99,10881,10883],{"className":10882},[106],[108,10884,10885],{"xmlns":110},[112,10886,10887,10936],{},[115,10888,10889,10891,10893,10895,10897,10903,10905,10912,10914,10916,10918,10920,10922,10934],{},[126,10890,2263],{},[118,10892,313],{},[126,10894,1633],{},[118,10896,2813],{"stretchy":120},[302,10898,10899,10901],{},[126,10900,1278],{},[142,10902,1652],{},[118,10904,140],{"separator":139},[302,10906,10907,10909],{},[126,10908,1278],{},[142,10910,10911],{},"2",[118,10913,140],{"separator":139},[126,10915,1256],{"mathvariant":2257},[126,10917,1256],{"mathvariant":2257},[126,10919,1256],{"mathvariant":2257},[118,10921,140],{"separator":139},[302,10923,10924,10926],{},[126,10925,1278],{},[115,10927,10928,10930,10932],{},[126,10929,2266],{},[118,10931,2254],{},[142,10933,1652],{},[118,10935,2846],{"stretchy":120},[149,10937,10938],{"encoding":151},"G = f(n_1, n_2, ..., n_{m-1})",[99,10940,10942,10961],{"className":10941,"ariaHidden":139},[156],[99,10943,10945,10949,10952,10955,10958],{"className":10944},[160],[99,10946],{"className":10947,"style":10948},[164],"height:0.6833em;",[99,10950,2263],{"className":10951},[173,177],[99,10953],{"className":10954,"style":398},[397],[99,10956,313],{"className":10957},[402],[99,10959],{"className":10960,"style":398},[397],[99,10962,10964,10967,10970,10973,11014,11017,11020,11060,11063,11066,11070,11073,11076,11126],{"className":10963},[160],[99,10965],{"className":10966,"style":344},[164],[99,10968,1633],{"className":10969,"style":1694},[173,177],[99,10971,2813],{"className":10972},[169],[99,10974,10976,10979],{"className":10975},[173],[99,10977,1278],{"className":10978},[173,177],[99,10980,10982],{"className":10981},[181],[99,10983,10985,11006],{"className":10984},[185,186],[99,10986,10988,11003],{"className":10987},[190],[99,10989,10992],{"className":10990,"style":10991},[194],"height:0.3011em;",[99,10993,10994,10997],{"style":369},[99,10995],{"className":10996,"style":203},[202],[99,10998,11000],{"className":10999},[207,208,209,210],[99,11001,1652],{"className":11002},[173,210],[99,11004,241],{"className":11005},[240],[99,11007,11009],{"className":11008},[190],[99,11010,11012],{"className":11011,"style":388},[194],[99,11013],{},[99,11015,140],{"className":11016},[233],[99,11018],{"className":11019,"style":1813},[397],[99,11021,11023,11026],{"className":11022},[173],[99,11024,1278],{"className":11025},[173,177],[99,11027,11029],{"className":11028},[181],[99,11030,11032,11052],{"className":11031},[185,186],[99,11033,11035,11049],{"className":11034},[190],[99,11036,11038],{"className":11037,"style":10991},[194],[99,11039,11040,11043],{"style":369},[99,11041],{"className":11042,"style":203},[202],[99,11044,11046],{"className":11045},[207,208,209,210],[99,11047,10911],{"className":11048},[173,210],[99,11050,241],{"className":11051},[240],[99,11053,11055],{"className":11054},[190],[99,11056,11058],{"className":11057,"style":388},[194],[99,11059],{},[99,11061,140],{"className":11062},[233],[99,11064],{"className":11065,"style":1813},[397],[99,11067,11069],{"className":11068},[173],"...",[99,11071,140],{"className":11072},[233],[99,11074],{"className":11075,"style":1813},[397],[99,11077,11079,11082],{"className":11078},[173],[99,11080,1278],{"className":11081},[173,177],[99,11083,11085],{"className":11084},[181],[99,11086,11088,11117],{"className":11087},[185,186],[99,11089,11091,11114],{"className":11090},[190],[99,11092,11094],{"className":11093,"style":10991},[194],[99,11095,11096,11099],{"style":369},[99,11097],{"className":11098,"style":203},[202],[99,11100,11102],{"className":11101},[207,208,209,210],[99,11103,11105,11108,11111],{"className":11104},[173,210],[99,11106,2266],{"className":11107},[173,177,210],[99,11109,2254],{"className":11110},[2594,210],[99,11112,1652],{"className":11113},[173,210],[99,11115,241],{"className":11116},[240],[99,11118,11120],{"className":11119},[190],[99,11121,11124],{"className":11122,"style":11123},[194],"height:0.2083em;",[99,11125],{},[99,11127,2846],{"className":11128},[254],[67,11130,11131],{},"or",[67,11133,11134,140],{},[99,11135,11137,11205],{"className":11136},[102],[99,11138,11140],{"className":11139},[106],[108,11141,11142],{"xmlns":110},[112,11143,11144,11202],{},[115,11145,11146,11148,11150,11153,11156,11162,11164,11170,11172,11178,11180,11182,11184,11186,11188,11200],{},[126,11147,2263],{},[118,11149,313],{},[126,11151,11152],{},"N",[118,11154,11155],{},"⋅",[302,11157,11158,11160],{},[126,11159,2263],{},[126,11161,2266],{},[118,11163,2813],{"stretchy":120},[302,11165,11166,11168],{},[126,11167,306],{},[142,11169,1652],{},[118,11171,140],{"separator":139},[302,11173,11174,11176],{},[126,11175,306],{},[142,11177,10911],{},[118,11179,140],{"separator":139},[126,11181,1256],{"mathvariant":2257},[126,11183,1256],{"mathvariant":2257},[126,11185,1256],{"mathvariant":2257},[118,11187,140],{"separator":139},[302,11189,11190,11192],{},[126,11191,306],{},[115,11193,11194,11196,11198],{},[126,11195,2266],{},[118,11197,2254],{},[142,11199,1652],{},[118,11201,2846],{"stretchy":120},[149,11203,11204],{"encoding":151},"G = N \\cdot G_m(x_1, x_2, ..., x_{m-1})",[99,11206,11208,11226,11245],{"className":11207,"ariaHidden":139},[156],[99,11209,11211,11214,11217,11220,11223],{"className":11210},[160],[99,11212],{"className":11213,"style":10948},[164],[99,11215,2263],{"className":11216},[173,177],[99,11218],{"className":11219,"style":398},[397],[99,11221,313],{"className":11222},[402],[99,11224],{"className":11225,"style":398},[397],[99,11227,11229,11232,11236,11239,11242],{"className":11228},[160],[99,11230],{"className":11231,"style":10948},[164],[99,11233,11152],{"className":11234,"style":11235},[173,177],"margin-right:0.109em;",[99,11237],{"className":11238,"style":2590},[397],[99,11240,11155],{"className":11241},[2594],[99,11243],{"className":11244,"style":2590},[397],[99,11246,11248,11251,11292,11295,11335,11338,11341,11381,11384,11387,11390,11393,11396,11445],{"className":11247},[160],[99,11249],{"className":11250,"style":344},[164],[99,11252,11254,11257],{"className":11253},[173],[99,11255,2263],{"className":11256},[173,177],[99,11258,11260],{"className":11259},[181],[99,11261,11263,11284],{"className":11262},[185,186],[99,11264,11266,11281],{"className":11265},[190],[99,11267,11270],{"className":11268,"style":11269},[194],"height:0.1514em;",[99,11271,11272,11275],{"style":369},[99,11273],{"className":11274,"style":203},[202],[99,11276,11278],{"className":11277},[207,208,209,210],[99,11279,2266],{"className":11280},[173,177,210],[99,11282,241],{"className":11283},[240],[99,11285,11287],{"className":11286},[190],[99,11288,11290],{"className":11289,"style":388},[194],[99,11291],{},[99,11293,2813],{"className":11294},[169],[99,11296,11298,11301],{"className":11297},[173],[99,11299,306],{"className":11300},[173,177],[99,11302,11304],{"className":11303},[181],[99,11305,11307,11327],{"className":11306},[185,186],[99,11308,11310,11324],{"className":11309},[190],[99,11311,11313],{"className":11312,"style":10991},[194],[99,11314,11315,11318],{"style":369},[99,11316],{"className":11317,"style":203},[202],[99,11319,11321],{"className":11320},[207,208,209,210],[99,11322,1652],{"className":11323},[173,210],[99,11325,241],{"className":11326},[240],[99,11328,11330],{"className":11329},[190],[99,11331,11333],{"className":11332,"style":388},[194],[99,11334],{},[99,11336,140],{"className":11337},[233],[99,11339],{"className":11340,"style":1813},[397],[99,11342,11344,11347],{"className":11343},[173],[99,11345,306],{"className":11346},[173,177],[99,11348,11350],{"className":11349},[181],[99,11351,11353,11373],{"className":11352},[185,186],[99,11354,11356,11370],{"className":11355},[190],[99,11357,11359],{"className":11358,"style":10991},[194],[99,11360,11361,11364],{"style":369},[99,11362],{"className":11363,"style":203},[202],[99,11365,11367],{"className":11366},[207,208,209,210],[99,11368,10911],{"className":11369},[173,210],[99,11371,241],{"className":11372},[240],[99,11374,11376],{"className":11375},[190],[99,11377,11379],{"className":11378,"style":388},[194],[99,11380],{},[99,11382,140],{"className":11383},[233],[99,11385],{"className":11386,"style":1813},[397],[99,11388,11069],{"className":11389},[173],[99,11391,140],{"className":11392},[233],[99,11394],{"className":11395,"style":1813},[397],[99,11397,11399,11402],{"className":11398},[173],[99,11400,306],{"className":11401},[173,177],[99,11403,11405],{"className":11404},[181],[99,11406,11408,11437],{"className":11407},[185,186],[99,11409,11411,11434],{"className":11410},[190],[99,11412,11414],{"className":11413,"style":10991},[194],[99,11415,11416,11419],{"style":369},[99,11417],{"className":11418,"style":203},[202],[99,11420,11422],{"className":11421},[207,208,209,210],[99,11423,11425,11428,11431],{"className":11424},[173,210],[99,11426,2266],{"className":11427},[173,177,210],[99,11429,2254],{"className":11430},[2594,210],[99,11432,1652],{"className":11433},[173,210],[99,11435,241],{"className":11436},[240],[99,11438,11440],{"className":11439},[190],[99,11441,11443],{"className":11442,"style":11123},[194],[99,11444],{},[99,11446,2846],{"className":11447},[254],[67,11449,11450,11451,11479,11480,11551,11552,11623,11624,11653,11654,11724,11725,11753],{},"where ",[99,11452,11454,11467],{"className":11453},[102],[99,11455,11457],{"className":11456},[106],[108,11458,11459],{"xmlns":110},[112,11460,11461,11465],{},[115,11462,11463],{},[126,11464,11152],{},[149,11466,11152],{"encoding":151},[99,11468,11470],{"className":11469,"ariaHidden":139},[156],[99,11471,11473,11476],{"className":11472},[160],[99,11474],{"className":11475,"style":10948},[164],[99,11477,11152],{"className":11478,"style":11235},[173,177]," is the total amount of all the substances, ",[99,11481,11483,11501],{"className":11482},[102],[99,11484,11486],{"className":11485},[106],[108,11487,11488],{"xmlns":110},[112,11489,11490,11498],{},[115,11491,11492],{},[302,11493,11494,11496],{},[126,11495,2263],{},[126,11497,2266],{},[149,11499,11500],{"encoding":151},"G_m",[99,11502,11504],{"className":11503,"ariaHidden":139},[156],[99,11505,11507,11511],{"className":11506},[160],[99,11508],{"className":11509,"style":11510},[164],"height:0.8333em;vertical-align:-0.15em;",[99,11512,11514,11517],{"className":11513},[173],[99,11515,2263],{"className":11516},[173,177],[99,11518,11520],{"className":11519},[181],[99,11521,11523,11543],{"className":11522},[185,186],[99,11524,11526,11540],{"className":11525},[190],[99,11527,11529],{"className":11528,"style":11269},[194],[99,11530,11531,11534],{"style":369},[99,11532],{"className":11533,"style":203},[202],[99,11535,11537],{"className":11536},[207,208,209,210],[99,11538,2266],{"className":11539},[173,177,210],[99,11541,241],{"className":11542},[240],[99,11544,11546],{"className":11545},[190],[99,11547,11549],{"className":11548,"style":388},[194],[99,11550],{}," is the mole Gibbs energy, ",[99,11553,11555,11573],{"className":11554},[102],[99,11556,11558],{"className":11557},[106],[108,11559,11560],{"xmlns":110},[112,11561,11562,11570],{},[115,11563,11564],{},[302,11565,11566,11568],{},[126,11567,1278],{},[126,11569,131],{},[149,11571,11572],{"encoding":151},"n_i",[99,11574,11576],{"className":11575,"ariaHidden":139},[156],[99,11577,11579,11583],{"className":11578},[160],[99,11580],{"className":11581,"style":11582},[164],"height:0.5806em;vertical-align:-0.15em;",[99,11584,11586,11589],{"className":11585},[173],[99,11587,1278],{"className":11588},[173,177],[99,11590,11592],{"className":11591},[181],[99,11593,11595,11615],{"className":11594},[185,186],[99,11596,11598,11612],{"className":11597},[190],[99,11599,11601],{"className":11600,"style":366},[194],[99,11602,11603,11606],{"style":369},[99,11604],{"className":11605,"style":203},[202],[99,11607,11609],{"className":11608},[207,208,209,210],[99,11610,131],{"className":11611},[173,177,210],[99,11613,241],{"className":11614},[240],[99,11616,11618],{"className":11617},[190],[99,11619,11621],{"className":11620,"style":388},[194],[99,11622],{}," is the amount of the ",[99,11625,11627,11640],{"className":11626},[102],[99,11628,11630],{"className":11629},[106],[108,11631,11632],{"xmlns":110},[112,11633,11634,11638],{},[115,11635,11636],{},[126,11637,131],{},[149,11639,131],{"encoding":151},[99,11641,11643],{"className":11642,"ariaHidden":139},[156],[99,11644,11646,11650],{"className":11645},[160],[99,11647],{"className":11648,"style":11649},[164],"height:0.6595em;",[99,11651,131],{"className":11652},[173,177],"-th component and ",[99,11655,11657,11675],{"className":11656},[102],[99,11658,11660],{"className":11659},[106],[108,11661,11662],{"xmlns":110},[112,11663,11664,11672],{},[115,11665,11666],{},[302,11667,11668,11670],{},[126,11669,306],{},[126,11671,131],{},[149,11673,11674],{"encoding":151},"x_i",[99,11676,11678],{"className":11677,"ariaHidden":139},[156],[99,11679,11681,11684],{"className":11680},[160],[99,11682],{"className":11683,"style":11582},[164],[99,11685,11687,11690],{"className":11686},[173],[99,11688,306],{"className":11689},[173,177],[99,11691,11693],{"className":11692},[181],[99,11694,11696,11716],{"className":11695},[185,186],[99,11697,11699,11713],{"className":11698},[190],[99,11700,11702],{"className":11701,"style":366},[194],[99,11703,11704,11707],{"style":369},[99,11705],{"className":11706,"style":203},[202],[99,11708,11710],{"className":11709},[207,208,209,210],[99,11711,131],{"className":11712},[173,177,210],[99,11714,241],{"className":11715},[240],[99,11717,11719],{"className":11718},[190],[99,11720,11722],{"className":11721,"style":388},[194],[99,11723],{}," is the mole fraction of the ",[99,11726,11728,11741],{"className":11727},[102],[99,11729,11731],{"className":11730},[106],[108,11732,11733],{"xmlns":110},[112,11734,11735,11739],{},[115,11736,11737],{},[126,11738,131],{},[149,11740,131],{"encoding":151},[99,11742,11744],{"className":11743,"ariaHidden":139},[156],[99,11745,11747,11750],{"className":11746},[160],[99,11748],{"className":11749,"style":11649},[164],[99,11751,131],{"className":11752},[173,177],"-th component.",[67,11755,11756,11757,11785],{},"The chemical potential of the ",[99,11758,11760,11773],{"className":11759},[102],[99,11761,11763],{"className":11762},[106],[108,11764,11765],{"xmlns":110},[112,11766,11767,11771],{},[115,11768,11769],{},[126,11770,131],{},[149,11772,131],{"encoding":151},[99,11774,11776],{"className":11775,"ariaHidden":139},[156],[99,11777,11779,11782],{"className":11778},[160],[99,11780],{"className":11781,"style":11649},[164],[99,11783,131],{"className":11784},[173,177],"-th component, is the partial quantity of the Gibbs energy and that is",[67,11787,11788],{},[99,11789,11791,11839],{"className":11790},[102],[99,11792,11794],{"className":11793},[106],[108,11795,11796],{"xmlns":110},[112,11797,11798,11836],{},[115,11799,11800,11806,11808,11834],{},[302,11801,11802,11804],{},[126,11803,128],{},[126,11805,131],{},[118,11807,313],{},[11809,11810,11811,11824],"mfrac",{},[115,11812,11813,11816,11818],{},[126,11814,11815],{"mathvariant":2257},"∂",[126,11817,11152],{},[302,11819,11820,11822],{},[126,11821,2263],{},[126,11823,2266],{},[115,11825,11826,11828],{},[126,11827,11815],{"mathvariant":2257},[302,11829,11830,11832],{},[126,11831,1278],{},[126,11833,131],{},[126,11835,1256],{"mathvariant":2257},[149,11837,11838],{"encoding":151},"\\mu_i = \\frac{\\partial N G_m}{\\partial n_i}.",[99,11840,11842,11898],{"className":11841,"ariaHidden":139},[156],[99,11843,11845,11849,11889,11892,11895],{"className":11844},[160],[99,11846],{"className":11847,"style":11848},[164],"height:0.625em;vertical-align:-0.1944em;",[99,11850,11852,11855],{"className":11851},[173],[99,11853,128],{"className":11854},[173,177],[99,11856,11858],{"className":11857},[181],[99,11859,11861,11881],{"className":11860},[185,186],[99,11862,11864,11878],{"className":11863},[190],[99,11865,11867],{"className":11866,"style":366},[194],[99,11868,11869,11872],{"style":369},[99,11870],{"className":11871,"style":203},[202],[99,11873,11875],{"className":11874},[207,208,209,210],[99,11876,131],{"className":11877},[173,177,210],[99,11879,241],{"className":11880},[240],[99,11882,11884],{"className":11883},[190],[99,11885,11887],{"className":11886,"style":388},[194],[99,11888],{},[99,11890],{"className":11891,"style":398},[397],[99,11893,313],{"className":11894},[402],[99,11896],{"className":11897,"style":398},[397],[99,11899,11901,11905,12068],{"className":11900},[160],[99,11902],{"className":11903,"style":11904},[164],"height:1.3413em;vertical-align:-0.4451em;",[99,11906,11908,11911,12065],{"className":11907},[173],[99,11909],{"className":11910},[169,2336],[99,11912,11914],{"className":11913},[11809],[99,11915,11917,12056],{"className":11916},[185,186],[99,11918,11920,12053],{"className":11919},[190],[99,11921,11924,11983,11994],{"className":11922,"style":11923},[194],"height:0.8962em;",[99,11925,11927,11930],{"style":11926},"top:-2.655em;",[99,11928],{"className":11929,"style":4480},[202],[99,11931,11933],{"className":11932},[207,208,209,210],[99,11934,11936,11940],{"className":11935},[173,210],[99,11937,11815],{"className":11938,"style":11939},[173,210],"margin-right:0.0556em;",[99,11941,11943,11946],{"className":11942},[173,210],[99,11944,1278],{"className":11945},[173,177,210],[99,11947,11949],{"className":11948},[181],[99,11950,11952,11974],{"className":11951},[185,186],[99,11953,11955,11971],{"className":11954},[190],[99,11956,11959],{"className":11957,"style":11958},[194],"height:0.3281em;",[99,11960,11962,11965],{"style":11961},"top:-2.357em;margin-left:0em;margin-right:0.0714em;",[99,11963],{"className":11964,"style":2513},[202],[99,11966,11968],{"className":11967},[207,2517,2518,210],[99,11969,131],{"className":11970},[173,177,210],[99,11972,241],{"className":11973},[240],[99,11975,11977],{"className":11976},[190],[99,11978,11981],{"className":11979,"style":11980},[194],"height:0.143em;",[99,11982],{},[99,11984,11986,11989],{"style":11985},"top:-3.23em;",[99,11987],{"className":11988,"style":4480},[202],[99,11990],{"className":11991,"style":11993},[11992],"frac-line","border-bottom-width:0.04em;",[99,11995,11997,12000],{"style":11996},"top:-3.4101em;",[99,11998],{"className":11999,"style":4480},[202],[99,12001,12003],{"className":12002},[207,208,209,210],[99,12004,12006,12009,12012],{"className":12005},[173,210],[99,12007,11815],{"className":12008,"style":11939},[173,210],[99,12010,11152],{"className":12011,"style":11235},[173,177,210],[99,12013,12015,12018],{"className":12014},[173,210],[99,12016,2263],{"className":12017},[173,177,210],[99,12019,12021],{"className":12020},[181],[99,12022,12024,12045],{"className":12023},[185,186],[99,12025,12027,12042],{"className":12026},[190],[99,12028,12031],{"className":12029,"style":12030},[194],"height:0.1645em;",[99,12032,12033,12036],{"style":11961},[99,12034],{"className":12035,"style":2513},[202],[99,12037,12039],{"className":12038},[207,2517,2518,210],[99,12040,2266],{"className":12041},[173,177,210],[99,12043,241],{"className":12044},[240],[99,12046,12048],{"className":12047},[190],[99,12049,12051],{"className":12050,"style":11980},[194],[99,12052],{},[99,12054,241],{"className":12055},[240],[99,12057,12059],{"className":12058},[190],[99,12060,12063],{"className":12061,"style":12062},[194],"height:0.4451em;",[99,12064],{},[99,12066],{"className":12067},[254,2336],[99,12069,1256],{"className":12070},[173],[67,12072,12073,12074,12143,12144,12213],{},"In CALPHAD method and other physical models, the mole fraction or the composition is the most common state variable for the fraction of the components. And thus, we have a motivation to substitute the amount, i.e., ",[99,12075,12077,12094],{"className":12076},[102],[99,12078,12080],{"className":12079},[106],[108,12081,12082],{"xmlns":110},[112,12083,12084,12092],{},[115,12085,12086],{},[302,12087,12088,12090],{},[126,12089,1278],{},[126,12091,131],{},[149,12093,11572],{"encoding":151},[99,12095,12097],{"className":12096,"ariaHidden":139},[156],[99,12098,12100,12103],{"className":12099},[160],[99,12101],{"className":12102,"style":11582},[164],[99,12104,12106,12109],{"className":12105},[173],[99,12107,1278],{"className":12108},[173,177],[99,12110,12112],{"className":12111},[181],[99,12113,12115,12135],{"className":12114},[185,186],[99,12116,12118,12132],{"className":12117},[190],[99,12119,12121],{"className":12120,"style":366},[194],[99,12122,12123,12126],{"style":369},[99,12124],{"className":12125,"style":203},[202],[99,12127,12129],{"className":12128},[207,208,209,210],[99,12130,131],{"className":12131},[173,177,210],[99,12133,241],{"className":12134},[240],[99,12136,12138],{"className":12137},[190],[99,12139,12141],{"className":12140,"style":388},[194],[99,12142],{}," into fraction, i.e., ",[99,12145,12147,12164],{"className":12146},[102],[99,12148,12150],{"className":12149},[106],[108,12151,12152],{"xmlns":110},[112,12153,12154,12162],{},[115,12155,12156],{},[302,12157,12158,12160],{},[126,12159,306],{},[126,12161,131],{},[149,12163,11674],{"encoding":151},[99,12165,12167],{"className":12166,"ariaHidden":139},[156],[99,12168,12170,12173],{"className":12169},[160],[99,12171],{"className":12172,"style":11582},[164],[99,12174,12176,12179],{"className":12175},[173],[99,12177,306],{"className":12178},[173,177],[99,12180,12182],{"className":12181},[181],[99,12183,12185,12205],{"className":12184},[185,186],[99,12186,12188,12202],{"className":12187},[190],[99,12189,12191],{"className":12190,"style":366},[194],[99,12192,12193,12196],{"style":369},[99,12194],{"className":12195,"style":203},[202],[99,12197,12199],{"className":12198},[207,208,209,210],[99,12200,131],{"className":12201},[173,177,210],[99,12203,241],{"className":12204},[240],[99,12206,12208],{"className":12207},[190],[99,12209,12211],{"className":12210,"style":388},[194],[99,12212],{},", where chain rule of derivatives should be adopted.",[67,12215,12216],{},"As",[67,12218,12219],{},[99,12220,12222,12289],{"className":12221},[102],[99,12223,12225],{"className":12224},[106],[108,12226,12227],{"xmlns":110},[112,12228,12229,12286],{},[115,12230,12231,12237,12239,12241,12243,12246,12248,12254,12256,12262,12264,12266,12268,12270,12272,12284],{},[302,12232,12233,12235],{},[126,12234,1278],{},[126,12236,131],{},[118,12238,313],{},[126,12240,11152],{},[118,12242,11155],{},[126,12244,12245],{},"g",[118,12247,2813],{"stretchy":120},[302,12249,12250,12252],{},[126,12251,306],{},[142,12253,1652],{},[118,12255,140],{"separator":139},[302,12257,12258,12260],{},[126,12259,306],{},[142,12261,10911],{},[118,12263,140],{"separator":139},[126,12265,1256],{"mathvariant":2257},[126,12267,1256],{"mathvariant":2257},[126,12269,1256],{"mathvariant":2257},[118,12271,140],{"separator":139},[302,12273,12274,12276],{},[126,12275,306],{},[115,12277,12278,12280,12282],{},[126,12279,2266],{},[118,12281,2254],{},[142,12283,1652],{},[118,12285,2846],{"stretchy":120},[149,12287,12288],{"encoding":151},"n_i = N \\cdot g(x_1, x_2, ..., x_{m-1})",[99,12290,12292,12347,12365],{"className":12291,"ariaHidden":139},[156],[99,12293,12295,12298,12338,12341,12344],{"className":12294},[160],[99,12296],{"className":12297,"style":11582},[164],[99,12299,12301,12304],{"className":12300},[173],[99,12302,1278],{"className":12303},[173,177],[99,12305,12307],{"className":12306},[181],[99,12308,12310,12330],{"className":12309},[185,186],[99,12311,12313,12327],{"className":12312},[190],[99,12314,12316],{"className":12315,"style":366},[194],[99,12317,12318,12321],{"style":369},[99,12319],{"className":12320,"style":203},[202],[99,12322,12324],{"className":12323},[207,208,209,210],[99,12325,131],{"className":12326},[173,177,210],[99,12328,241],{"className":12329},[240],[99,12331,12333],{"className":12332},[190],[99,12334,12336],{"className":12335,"style":388},[194],[99,12337],{},[99,12339],{"className":12340,"style":398},[397],[99,12342,313],{"className":12343},[402],[99,12345],{"className":12346,"style":398},[397],[99,12348,12350,12353,12356,12359,12362],{"className":12349},[160],[99,12351],{"className":12352,"style":10948},[164],[99,12354,11152],{"className":12355,"style":11235},[173,177],[99,12357],{"className":12358,"style":2590},[397],[99,12360,11155],{"className":12361},[2594],[99,12363],{"className":12364,"style":2590},[397],[99,12366,12368,12371,12375,12378,12418,12421,12424,12464,12467,12470,12473,12476,12479,12528],{"className":12367},[160],[99,12369],{"className":12370,"style":344},[164],[99,12372,12245],{"className":12373,"style":12374},[173,177],"margin-right:0.0359em;",[99,12376,2813],{"className":12377},[169],[99,12379,12381,12384],{"className":12380},[173],[99,12382,306],{"className":12383},[173,177],[99,12385,12387],{"className":12386},[181],[99,12388,12390,12410],{"className":12389},[185,186],[99,12391,12393,12407],{"className":12392},[190],[99,12394,12396],{"className":12395,"style":10991},[194],[99,12397,12398,12401],{"style":369},[99,12399],{"className":12400,"style":203},[202],[99,12402,12404],{"className":12403},[207,208,209,210],[99,12405,1652],{"className":12406},[173,210],[99,12408,241],{"className":12409},[240],[99,12411,12413],{"className":12412},[190],[99,12414,12416],{"className":12415,"style":388},[194],[99,12417],{},[99,12419,140],{"className":12420},[233],[99,12422],{"className":12423,"style":1813},[397],[99,12425,12427,12430],{"className":12426},[173],[99,12428,306],{"className":12429},[173,177],[99,12431,12433],{"className":12432},[181],[99,12434,12436,12456],{"className":12435},[185,186],[99,12437,12439,12453],{"className":12438},[190],[99,12440,12442],{"className":12441,"style":10991},[194],[99,12443,12444,12447],{"style":369},[99,12445],{"className":12446,"style":203},[202],[99,12448,12450],{"className":12449},[207,208,209,210],[99,12451,10911],{"className":12452},[173,210],[99,12454,241],{"className":12455},[240],[99,12457,12459],{"className":12458},[190],[99,12460,12462],{"className":12461,"style":388},[194],[99,12463],{},[99,12465,140],{"className":12466},[233],[99,12468],{"className":12469,"style":1813},[397],[99,12471,11069],{"className":12472},[173],[99,12474,140],{"className":12475},[233],[99,12477],{"className":12478,"style":1813},[397],[99,12480,12482,12485],{"className":12481},[173],[99,12483,306],{"className":12484},[173,177],[99,12486,12488],{"className":12487},[181],[99,12489,12491,12520],{"className":12490},[185,186],[99,12492,12494,12517],{"className":12493},[190],[99,12495,12497],{"className":12496,"style":10991},[194],[99,12498,12499,12502],{"style":369},[99,12500],{"className":12501,"style":203},[202],[99,12503,12505],{"className":12504},[207,208,209,210],[99,12506,12508,12511,12514],{"className":12507},[173,210],[99,12509,2266],{"className":12510},[173,177,210],[99,12512,2254],{"className":12513},[2594,210],[99,12515,1652],{"className":12516},[173,210],[99,12518,241],{"className":12519},[240],[99,12521,12523],{"className":12522},[190],[99,12524,12526],{"className":12525,"style":11123},[194],[99,12527],{},[99,12529,2846],{"className":12530},[254],[67,12532,12533],{},", we can obtain",[67,12535,12536],{},[99,12537,12539,12656],{"className":12538},[102],[99,12540,12542],{"className":12541},[106],[108,12543,12544],{"xmlns":110},[112,12545,12546,12653],{},[115,12547,12548,12554,12556,12562,12580,12582,12584,12609,12631],{},[302,12549,12550,12552],{},[126,12551,128],{},[126,12553,131],{},[118,12555,313],{},[302,12557,12558,12560],{},[126,12559,2263],{},[126,12561,2266],{},[11809,12563,12564,12570],{},[115,12565,12566,12568],{},[126,12567,11815],{"mathvariant":2257},[126,12569,11152],{},[115,12571,12572,12574],{},[126,12573,11815],{"mathvariant":2257},[302,12575,12576,12578],{},[126,12577,1278],{},[126,12579,131],{},[118,12581,3882],{},[126,12583,11152],{},[123,12585,12586,12588,12597],{},[118,12587,1643],{},[115,12589,12590,12593,12595],{},[126,12591,12592],{},"j",[118,12594,313],{},[142,12596,1652],{},[115,12598,12599,12601,12603,12605,12607],{},[126,12600,12592],{},[118,12602,313],{},[126,12604,2266],{},[118,12606,2254],{},[142,12608,1652],{},[11809,12610,12611,12621],{},[115,12612,12613,12615],{},[126,12614,11815],{"mathvariant":2257},[302,12616,12617,12619],{},[126,12618,2263],{},[126,12620,2266],{},[115,12622,12623,12625],{},[126,12624,11815],{"mathvariant":2257},[302,12626,12627,12629],{},[126,12628,306],{},[126,12630,12592],{},[11809,12632,12633,12643],{},[115,12634,12635,12637],{},[126,12636,11815],{"mathvariant":2257},[302,12638,12639,12641],{},[126,12640,306],{},[126,12642,12592],{},[115,12644,12645,12647],{},[126,12646,11815],{"mathvariant":2257},[302,12648,12649,12651],{},[126,12650,1278],{},[126,12652,131],{},[149,12654,12655],{"encoding":151},"\\mu_i = G_m \\frac{\\partial N }{\\partial n_i} + N \\sum_{j=1}^{j=m-1}\\frac{\\partial G_m }{\\partial x_j}\\frac{\\partial x_j }{\\partial n_i}",[99,12657,12659,12714,12883],{"className":12658,"ariaHidden":139},[156],[99,12660,12662,12665,12705,12708,12711],{"className":12661},[160],[99,12663],{"className":12664,"style":11848},[164],[99,12666,12668,12671],{"className":12667},[173],[99,12669,128],{"className":12670},[173,177],[99,12672,12674],{"className":12673},[181],[99,12675,12677,12697],{"className":12676},[185,186],[99,12678,12680,12694],{"className":12679},[190],[99,12681,12683],{"className":12682,"style":366},[194],[99,12684,12685,12688],{"style":369},[99,12686],{"className":12687,"style":203},[202],[99,12689,12691],{"className":12690},[207,208,209,210],[99,12692,131],{"className":12693},[173,177,210],[99,12695,241],{"className":12696},[240],[99,12698,12700],{"className":12699},[190],[99,12701,12703],{"className":12702,"style":388},[194],[99,12704],{},[99,12706],{"className":12707,"style":398},[397],[99,12709,313],{"className":12710},[402],[99,12712],{"className":12713,"style":398},[397],[99,12715,12717,12721,12761,12874,12877,12880],{"className":12716},[160],[99,12718],{"className":12719,"style":12720},[164],"height:1.3252em;vertical-align:-0.4451em;",[99,12722,12724,12727],{"className":12723},[173],[99,12725,2263],{"className":12726},[173,177],[99,12728,12730],{"className":12729},[181],[99,12731,12733,12753],{"className":12732},[185,186],[99,12734,12736,12750],{"className":12735},[190],[99,12737,12739],{"className":12738,"style":11269},[194],[99,12740,12741,12744],{"style":369},[99,12742],{"className":12743,"style":203},[202],[99,12745,12747],{"className":12746},[207,208,209,210],[99,12748,2266],{"className":12749},[173,177,210],[99,12751,241],{"className":12752},[240],[99,12754,12756],{"className":12755},[190],[99,12757,12759],{"className":12758,"style":388},[194],[99,12760],{},[99,12762,12764,12767,12871],{"className":12763},[173],[99,12765],{"className":12766},[169,2336],[99,12768,12770],{"className":12769},[11809],[99,12771,12773,12863],{"className":12772},[185,186],[99,12774,12776,12860],{"className":12775},[190],[99,12777,12780,12834,12842],{"className":12778,"style":12779},[194],"height:0.8801em;",[99,12781,12782,12785],{"style":11926},[99,12783],{"className":12784,"style":4480},[202],[99,12786,12788],{"className":12787},[207,208,209,210],[99,12789,12791,12794],{"className":12790},[173,210],[99,12792,11815],{"className":12793,"style":11939},[173,210],[99,12795,12797,12800],{"className":12796},[173,210],[99,12798,1278],{"className":12799},[173,177,210],[99,12801,12803],{"className":12802},[181],[99,12804,12806,12826],{"className":12805},[185,186],[99,12807,12809,12823],{"className":12808},[190],[99,12810,12812],{"className":12811,"style":11958},[194],[99,12813,12814,12817],{"style":11961},[99,12815],{"className":12816,"style":2513},[202],[99,12818,12820],{"className":12819},[207,2517,2518,210],[99,12821,131],{"className":12822},[173,177,210],[99,12824,241],{"className":12825},[240],[99,12827,12829],{"className":12828},[190],[99,12830,12832],{"className":12831,"style":11980},[194],[99,12833],{},[99,12835,12836,12839],{"style":11985},[99,12837],{"className":12838,"style":4480},[202],[99,12840],{"className":12841,"style":11993},[11992],[99,12843,12845,12848],{"style":12844},"top:-3.394em;",[99,12846],{"className":12847,"style":4480},[202],[99,12849,12851],{"className":12850},[207,208,209,210],[99,12852,12854,12857],{"className":12853},[173,210],[99,12855,11815],{"className":12856,"style":11939},[173,210],[99,12858,11152],{"className":12859,"style":11235},[173,177,210],[99,12861,241],{"className":12862},[240],[99,12864,12866],{"className":12865},[190],[99,12867,12869],{"className":12868,"style":12062},[194],[99,12870],{},[99,12872],{"className":12873},[254,2336],[99,12875],{"className":12876,"style":2590},[397],[99,12878,3882],{"className":12879},[2594],[99,12881],{"className":12882,"style":2590},[397],[99,12884,12886,12890,12893,12896,12978,12981,13131],{"className":12885},[160],[99,12887],{"className":12888,"style":12889},[164],"height:1.5357em;vertical-align:-0.5423em;",[99,12891,11152],{"className":12892,"style":11235},[173,177],[99,12894],{"className":12895,"style":1813},[397],[99,12897,12899,12904],{"className":12898},[1739],[99,12900,1643],{"className":12901,"style":12903},[1739,1784,12902],"small-op","position:relative;top:0em;",[99,12905,12907],{"className":12906},[181],[99,12908,12910,12969],{"className":12909},[185,186],[99,12911,12913,12966],{"className":12912},[190],[99,12914,12917,12939],{"className":12915,"style":12916},[194],"height:0.9646em;",[99,12918,12920,12923],{"style":12919},"top:-2.4003em;margin-left:0em;margin-right:0.05em;",[99,12921],{"className":12922,"style":203},[202],[99,12924,12926],{"className":12925},[207,208,209,210],[99,12927,12929,12933,12936],{"className":12928},[173,210],[99,12930,12592],{"className":12931,"style":12932},[173,177,210],"margin-right:0.0572em;",[99,12934,313],{"className":12935},[402,210],[99,12937,1652],{"className":12938},[173,210],[99,12940,12942,12945],{"style":12941},"top:-3.2029em;margin-right:0.05em;",[99,12943],{"className":12944,"style":203},[202],[99,12946,12948],{"className":12947},[207,208,209,210],[99,12949,12951,12954,12957,12960,12963],{"className":12950},[173,210],[99,12952,12592],{"className":12953,"style":12932},[173,177,210],[99,12955,313],{"className":12956},[402,210],[99,12958,2266],{"className":12959},[173,177,210],[99,12961,2254],{"className":12962},[2594,210],[99,12964,1652],{"className":12965},[173,210],[99,12967,241],{"className":12968},[240],[99,12970,12972],{"className":12971},[190],[99,12973,12976],{"className":12974,"style":12975},[194],"height:0.4358em;",[99,12977],{},[99,12979],{"className":12980,"style":1813},[397],[99,12982,12984,12987,13128],{"className":12983},[173],[99,12985],{"className":12986},[169,2336],[99,12988,12990],{"className":12989},[11809],[99,12991,12993,13119],{"className":12992},[185,186],[99,12994,12996,13116],{"className":12995},[190],[99,12997,12999,13054,13062],{"className":12998,"style":11923},[194],[99,13000,13001,13004],{"style":11926},[99,13002],{"className":13003,"style":4480},[202],[99,13005,13007],{"className":13006},[207,208,209,210],[99,13008,13010,13013],{"className":13009},[173,210],[99,13011,11815],{"className":13012,"style":11939},[173,210],[99,13014,13016,13019],{"className":13015},[173,210],[99,13017,306],{"className":13018},[173,177,210],[99,13020,13022],{"className":13021},[181],[99,13023,13025,13045],{"className":13024},[185,186],[99,13026,13028,13042],{"className":13027},[190],[99,13029,13031],{"className":13030,"style":11958},[194],[99,13032,13033,13036],{"style":11961},[99,13034],{"className":13035,"style":2513},[202],[99,13037,13039],{"className":13038},[207,2517,2518,210],[99,13040,12592],{"className":13041,"style":12932},[173,177,210],[99,13043,241],{"className":13044},[240],[99,13046,13048],{"className":13047},[190],[99,13049,13052],{"className":13050,"style":13051},[194],"height:0.2819em;",[99,13053],{},[99,13055,13056,13059],{"style":11985},[99,13057],{"className":13058,"style":4480},[202],[99,13060],{"className":13061,"style":11993},[11992],[99,13063,13064,13067],{"style":11996},[99,13065],{"className":13066,"style":4480},[202],[99,13068,13070],{"className":13069},[207,208,209,210],[99,13071,13073,13076],{"className":13072},[173,210],[99,13074,11815],{"className":13075,"style":11939},[173,210],[99,13077,13079,13082],{"className":13078},[173,210],[99,13080,2263],{"className":13081},[173,177,210],[99,13083,13085],{"className":13084},[181],[99,13086,13088,13108],{"className":13087},[185,186],[99,13089,13091,13105],{"className":13090},[190],[99,13092,13094],{"className":13093,"style":12030},[194],[99,13095,13096,13099],{"style":11961},[99,13097],{"className":13098,"style":2513},[202],[99,13100,13102],{"className":13101},[207,2517,2518,210],[99,13103,2266],{"className":13104},[173,177,210],[99,13106,241],{"className":13107},[240],[99,13109,13111],{"className":13110},[190],[99,13112,13114],{"className":13113,"style":11980},[194],[99,13115],{},[99,13117,241],{"className":13118},[240],[99,13120,13122],{"className":13121},[190],[99,13123,13126],{"className":13124,"style":13125},[194],"height:0.5423em;",[99,13127],{},[99,13129],{"className":13130},[254,2336],[99,13132,13134,13137,13278],{"className":13133},[173],[99,13135],{"className":13136},[169,2336],[99,13138,13140],{"className":13139},[11809],[99,13141,13143,13270],{"className":13142},[185,186],[99,13144,13146,13267],{"className":13145},[190],[99,13147,13150,13204,13212],{"className":13148,"style":13149},[194],"height:0.9934em;",[99,13151,13152,13155],{"style":11926},[99,13153],{"className":13154,"style":4480},[202],[99,13156,13158],{"className":13157},[207,208,209,210],[99,13159,13161,13164],{"className":13160},[173,210],[99,13162,11815],{"className":13163,"style":11939},[173,210],[99,13165,13167,13170],{"className":13166},[173,210],[99,13168,1278],{"className":13169},[173,177,210],[99,13171,13173],{"className":13172},[181],[99,13174,13176,13196],{"className":13175},[185,186],[99,13177,13179,13193],{"className":13178},[190],[99,13180,13182],{"className":13181,"style":11958},[194],[99,13183,13184,13187],{"style":11961},[99,13185],{"className":13186,"style":2513},[202],[99,13188,13190],{"className":13189},[207,2517,2518,210],[99,13191,131],{"className":13192},[173,177,210],[99,13194,241],{"className":13195},[240],[99,13197,13199],{"className":13198},[190],[99,13200,13202],{"className":13201,"style":11980},[194],[99,13203],{},[99,13205,13206,13209],{"style":11985},[99,13207],{"className":13208,"style":4480},[202],[99,13210],{"className":13211,"style":11993},[11992],[99,13213,13215,13218],{"style":13214},"top:-3.5073em;",[99,13216],{"className":13217,"style":4480},[202],[99,13219,13221],{"className":13220},[207,208,209,210],[99,13222,13224,13227],{"className":13223},[173,210],[99,13225,11815],{"className":13226,"style":11939},[173,210],[99,13228,13230,13233],{"className":13229},[173,210],[99,13231,306],{"className":13232},[173,177,210],[99,13234,13236],{"className":13235},[181],[99,13237,13239,13259],{"className":13238},[185,186],[99,13240,13242,13256],{"className":13241},[190],[99,13243,13245],{"className":13244,"style":11958},[194],[99,13246,13247,13250],{"style":11961},[99,13248],{"className":13249,"style":2513},[202],[99,13251,13253],{"className":13252},[207,2517,2518,210],[99,13254,12592],{"className":13255,"style":12932},[173,177,210],[99,13257,241],{"className":13258},[240],[99,13260,13262],{"className":13261},[190],[99,13263,13265],{"className":13264,"style":13051},[194],[99,13266],{},[99,13268,241],{"className":13269},[240],[99,13271,13273],{"className":13272},[190],[99,13274,13276],{"className":13275,"style":12062},[194],[99,13277],{},[99,13279],{"className":13280},[254,2336],[67,13282,13283],{},"Take the last part from the equation above and we have",[67,13285,13286],{},[99,13287,13289,13352],{"className":13288},[102],[99,13290,13292],{"className":13291},[106],[108,13293,13294],{"xmlns":110},[112,13295,13296,13349],{},[115,13297,13298,13320,13322],{},[11809,13299,13300,13310],{},[115,13301,13302,13304],{},[126,13303,11815],{"mathvariant":2257},[302,13305,13306,13308],{},[126,13307,306],{},[126,13309,12592],{},[115,13311,13312,13314],{},[126,13313,11815],{"mathvariant":2257},[302,13315,13316,13318],{},[126,13317,1278],{},[126,13319,131],{},[118,13321,313],{},[11809,13323,13324,13339],{},[115,13325,13326,13328,13334,13337],{},[126,13327,11815],{"mathvariant":2257},[302,13329,13330,13332],{},[126,13331,1278],{},[126,13333,12592],{},[126,13335,13336],{"mathvariant":2257},"\u002F",[126,13338,11152],{},[115,13340,13341,13343],{},[126,13342,11815],{"mathvariant":2257},[302,13344,13345,13347],{},[126,13346,1278],{},[126,13348,131],{},[149,13350,13351],{"encoding":151},"\\frac{\\partial x_j }{\\partial n_i} = \\frac{\\partial n_j \u002F N }{\\partial n_i}",[99,13353,13355,13519],{"className":13354,"ariaHidden":139},[156],[99,13356,13358,13362,13510,13513,13516],{"className":13357},[160],[99,13359],{"className":13360,"style":13361},[164],"height:1.4385em;vertical-align:-0.4451em;",[99,13363,13365,13368,13507],{"className":13364},[173],[99,13366],{"className":13367},[169,2336],[99,13369,13371],{"className":13370},[11809],[99,13372,13374,13499],{"className":13373},[185,186],[99,13375,13377,13496],{"className":13376},[190],[99,13378,13380,13434,13442],{"className":13379,"style":13149},[194],[99,13381,13382,13385],{"style":11926},[99,13383],{"className":13384,"style":4480},[202],[99,13386,13388],{"className":13387},[207,208,209,210],[99,13389,13391,13394],{"className":13390},[173,210],[99,13392,11815],{"className":13393,"style":11939},[173,210],[99,13395,13397,13400],{"className":13396},[173,210],[99,13398,1278],{"className":13399},[173,177,210],[99,13401,13403],{"className":13402},[181],[99,13404,13406,13426],{"className":13405},[185,186],[99,13407,13409,13423],{"className":13408},[190],[99,13410,13412],{"className":13411,"style":11958},[194],[99,13413,13414,13417],{"style":11961},[99,13415],{"className":13416,"style":2513},[202],[99,13418,13420],{"className":13419},[207,2517,2518,210],[99,13421,131],{"className":13422},[173,177,210],[99,13424,241],{"className":13425},[240],[99,13427,13429],{"className":13428},[190],[99,13430,13432],{"className":13431,"style":11980},[194],[99,13433],{},[99,13435,13436,13439],{"style":11985},[99,13437],{"className":13438,"style":4480},[202],[99,13440],{"className":13441,"style":11993},[11992],[99,13443,13444,13447],{"style":13214},[99,13445],{"className":13446,"style":4480},[202],[99,13448,13450],{"className":13449},[207,208,209,210],[99,13451,13453,13456],{"className":13452},[173,210],[99,13454,11815],{"className":13455,"style":11939},[173,210],[99,13457,13459,13462],{"className":13458},[173,210],[99,13460,306],{"className":13461},[173,177,210],[99,13463,13465],{"className":13464},[181],[99,13466,13468,13488],{"className":13467},[185,186],[99,13469,13471,13485],{"className":13470},[190],[99,13472,13474],{"className":13473,"style":11958},[194],[99,13475,13476,13479],{"style":11961},[99,13477],{"className":13478,"style":2513},[202],[99,13480,13482],{"className":13481},[207,2517,2518,210],[99,13483,12592],{"className":13484,"style":12932},[173,177,210],[99,13486,241],{"className":13487},[240],[99,13489,13491],{"className":13490},[190],[99,13492,13494],{"className":13493,"style":13051},[194],[99,13495],{},[99,13497,241],{"className":13498},[240],[99,13500,13502],{"className":13501},[190],[99,13503,13505],{"className":13504,"style":12062},[194],[99,13506],{},[99,13508],{"className":13509},[254,2336],[99,13511],{"className":13512,"style":398},[397],[99,13514,313],{"className":13515},[402],[99,13517],{"className":13518,"style":398},[397],[99,13520,13522,13526],{"className":13521},[160],[99,13523],{"className":13524,"style":13525},[164],"height:1.4774em;vertical-align:-0.4451em;",[99,13527,13529,13532,13678],{"className":13528},[173],[99,13530],{"className":13531},[169,2336],[99,13533,13535],{"className":13534},[11809],[99,13536,13538,13670],{"className":13537},[185,186],[99,13539,13541,13667],{"className":13540},[190],[99,13542,13545,13599,13607],{"className":13543,"style":13544},[194],"height:1.0323em;",[99,13546,13547,13550],{"style":11926},[99,13548],{"className":13549,"style":4480},[202],[99,13551,13553],{"className":13552},[207,208,209,210],[99,13554,13556,13559],{"className":13555},[173,210],[99,13557,11815],{"className":13558,"style":11939},[173,210],[99,13560,13562,13565],{"className":13561},[173,210],[99,13563,1278],{"className":13564},[173,177,210],[99,13566,13568],{"className":13567},[181],[99,13569,13571,13591],{"className":13570},[185,186],[99,13572,13574,13588],{"className":13573},[190],[99,13575,13577],{"className":13576,"style":11958},[194],[99,13578,13579,13582],{"style":11961},[99,13580],{"className":13581,"style":2513},[202],[99,13583,13585],{"className":13584},[207,2517,2518,210],[99,13586,131],{"className":13587},[173,177,210],[99,13589,241],{"className":13590},[240],[99,13592,13594],{"className":13593},[190],[99,13595,13597],{"className":13596,"style":11980},[194],[99,13598],{},[99,13600,13601,13604],{"style":11985},[99,13602],{"className":13603,"style":4480},[202],[99,13605],{"className":13606,"style":11993},[11992],[99,13608,13609,13612],{"style":13214},[99,13610],{"className":13611,"style":4480},[202],[99,13613,13615],{"className":13614},[207,208,209,210],[99,13616,13618,13621,13661,13664],{"className":13617},[173,210],[99,13619,11815],{"className":13620,"style":11939},[173,210],[99,13622,13624,13627],{"className":13623},[173,210],[99,13625,1278],{"className":13626},[173,177,210],[99,13628,13630],{"className":13629},[181],[99,13631,13633,13653],{"className":13632},[185,186],[99,13634,13636,13650],{"className":13635},[190],[99,13637,13639],{"className":13638,"style":11958},[194],[99,13640,13641,13644],{"style":11961},[99,13642],{"className":13643,"style":2513},[202],[99,13645,13647],{"className":13646},[207,2517,2518,210],[99,13648,12592],{"className":13649,"style":12932},[173,177,210],[99,13651,241],{"className":13652},[240],[99,13654,13656],{"className":13655},[190],[99,13657,13659],{"className":13658,"style":13051},[194],[99,13660],{},[99,13662,13336],{"className":13663},[173,210],[99,13665,11152],{"className":13666,"style":11235},[173,177,210],[99,13668,241],{"className":13669},[240],[99,13671,13673],{"className":13672},[190],[99,13674,13676],{"className":13675,"style":12062},[194],[99,13677],{},[99,13679],{"className":13680},[254,2336],[67,13682,13683,13686,13687,13756,13757,13849],{},[76,13684,13685],{},"Note"," One should keep in mind that we should not substitute ",[99,13688,13690,13707],{"className":13689},[102],[99,13691,13693],{"className":13692},[106],[108,13694,13695],{"xmlns":110},[112,13696,13697,13705],{},[115,13698,13699],{},[302,13700,13701,13703],{},[126,13702,1278],{},[126,13704,131],{},[149,13706,11572],{"encoding":151},[99,13708,13710],{"className":13709,"ariaHidden":139},[156],[99,13711,13713,13716],{"className":13712},[160],[99,13714],{"className":13715,"style":11582},[164],[99,13717,13719,13722],{"className":13718},[173],[99,13720,1278],{"className":13721},[173,177],[99,13723,13725],{"className":13724},[181],[99,13726,13728,13748],{"className":13727},[185,186],[99,13729,13731,13745],{"className":13730},[190],[99,13732,13734],{"className":13733,"style":366},[194],[99,13735,13736,13739],{"style":369},[99,13737],{"className":13738,"style":203},[202],[99,13740,13742],{"className":13741},[207,208,209,210],[99,13743,131],{"className":13744},[173,177,210],[99,13746,241],{"className":13747},[240],[99,13749,13751],{"className":13750},[190],[99,13752,13754],{"className":13753,"style":388},[194],[99,13755],{}," as ",[99,13758,13760,13782],{"className":13759},[102],[99,13761,13763],{"className":13762},[106],[108,13764,13765],{"xmlns":110},[112,13766,13767,13779],{},[115,13768,13769,13771,13773],{},[126,13770,11152],{},[118,13772,11155],{},[302,13774,13775,13777],{},[126,13776,306],{},[126,13778,131],{},[149,13780,13781],{"encoding":151},"N\\cdot x_i",[99,13783,13785,13803],{"className":13784,"ariaHidden":139},[156],[99,13786,13788,13791,13794,13797,13800],{"className":13787},[160],[99,13789],{"className":13790,"style":10948},[164],[99,13792,11152],{"className":13793,"style":11235},[173,177],[99,13795],{"className":13796,"style":2590},[397],[99,13798,11155],{"className":13799},[2594],[99,13801],{"className":13802,"style":2590},[397],[99,13804,13806,13809],{"className":13805},[160],[99,13807],{"className":13808,"style":11582},[164],[99,13810,13812,13815],{"className":13811},[173],[99,13813,306],{"className":13814},[173,177],[99,13816,13818],{"className":13817},[181],[99,13819,13821,13841],{"className":13820},[185,186],[99,13822,13824,13838],{"className":13823},[190],[99,13825,13827],{"className":13826,"style":366},[194],[99,13828,13829,13832],{"style":369},[99,13830],{"className":13831,"style":203},[202],[99,13833,13835],{"className":13834},[207,208,209,210],[99,13836,131],{"className":13837},[173,177,210],[99,13839,241],{"className":13840},[240],[99,13842,13844],{"className":13843},[190],[99,13845,13847],{"className":13846,"style":388},[194],[99,13848],{},", as there is no way to calculate the derivative with respect to fraction number.",[67,13851,13852],{},"Furthermore,",[67,13854,13855],{},[99,13856,13858,13960],{"className":13857},[102],[99,13859,13861],{"className":13860},[106],[108,13862,13863],{"xmlns":110},[112,13864,13865,13957],{},[115,13866,13867,13889,13891,13901,13903,13905,13927,13929,13935,13953,13955],{},[11809,13868,13869,13879],{},[115,13870,13871,13873],{},[126,13872,11815],{"mathvariant":2257},[302,13874,13875,13877],{},[126,13876,306],{},[126,13878,12592],{},[115,13880,13881,13883],{},[126,13882,11815],{"mathvariant":2257},[302,13884,13885,13887],{},[126,13886,1278],{},[126,13888,131],{},[118,13890,313],{},[11809,13892,13893,13895],{},[142,13894,1652],{},[1629,13896,13897,13899],{},[126,13898,11152],{},[142,13900,10911],{},[118,13902,2813],{"stretchy":120},[126,13904,11152],{},[11809,13906,13907,13917],{},[115,13908,13909,13911],{},[126,13910,11815],{"mathvariant":2257},[302,13912,13913,13915],{},[126,13914,1278],{},[126,13916,12592],{},[115,13918,13919,13921],{},[126,13920,11815],{"mathvariant":2257},[302,13922,13923,13925],{},[126,13924,1278],{},[126,13926,131],{},[118,13928,2254],{},[302,13930,13931,13933],{},[126,13932,1278],{},[126,13934,12592],{},[11809,13936,13937,13943],{},[115,13938,13939,13941],{},[126,13940,11815],{"mathvariant":2257},[126,13942,11152],{},[115,13944,13945,13947],{},[126,13946,11815],{"mathvariant":2257},[302,13948,13949,13951],{},[126,13950,1278],{},[126,13952,131],{},[118,13954,2846],{"stretchy":120},[126,13956,1256],{"mathvariant":2257},[149,13958,13959],{"encoding":151},"\\frac{\\partial x_j }{\\partial n_i} = \\frac{1}{N^2} (N\\frac{\\partial n_j}{\\partial n_i} - n_j\\frac{\\partial N}{\\partial n_i}).",[99,13961,13963,14126,14392],{"className":13962,"ariaHidden":139},[156],[99,13964,13966,13969,14117,14120,14123],{"className":13965},[160],[99,13967],{"className":13968,"style":13361},[164],[99,13970,13972,13975,14114],{"className":13971},[173],[99,13973],{"className":13974},[169,2336],[99,13976,13978],{"className":13977},[11809],[99,13979,13981,14106],{"className":13980},[185,186],[99,13982,13984,14103],{"className":13983},[190],[99,13985,13987,14041,14049],{"className":13986,"style":13149},[194],[99,13988,13989,13992],{"style":11926},[99,13990],{"className":13991,"style":4480},[202],[99,13993,13995],{"className":13994},[207,208,209,210],[99,13996,13998,14001],{"className":13997},[173,210],[99,13999,11815],{"className":14000,"style":11939},[173,210],[99,14002,14004,14007],{"className":14003},[173,210],[99,14005,1278],{"className":14006},[173,177,210],[99,14008,14010],{"className":14009},[181],[99,14011,14013,14033],{"className":14012},[185,186],[99,14014,14016,14030],{"className":14015},[190],[99,14017,14019],{"className":14018,"style":11958},[194],[99,14020,14021,14024],{"style":11961},[99,14022],{"className":14023,"style":2513},[202],[99,14025,14027],{"className":14026},[207,2517,2518,210],[99,14028,131],{"className":14029},[173,177,210],[99,14031,241],{"className":14032},[240],[99,14034,14036],{"className":14035},[190],[99,14037,14039],{"className":14038,"style":11980},[194],[99,14040],{},[99,14042,14043,14046],{"style":11985},[99,14044],{"className":14045,"style":4480},[202],[99,14047],{"className":14048,"style":11993},[11992],[99,14050,14051,14054],{"style":13214},[99,14052],{"className":14053,"style":4480},[202],[99,14055,14057],{"className":14056},[207,208,209,210],[99,14058,14060,14063],{"className":14059},[173,210],[99,14061,11815],{"className":14062,"style":11939},[173,210],[99,14064,14066,14069],{"className":14065},[173,210],[99,14067,306],{"className":14068},[173,177,210],[99,14070,14072],{"className":14071},[181],[99,14073,14075,14095],{"className":14074},[185,186],[99,14076,14078,14092],{"className":14077},[190],[99,14079,14081],{"className":14080,"style":11958},[194],[99,14082,14083,14086],{"style":11961},[99,14084],{"className":14085,"style":2513},[202],[99,14087,14089],{"className":14088},[207,2517,2518,210],[99,14090,12592],{"className":14091,"style":12932},[173,177,210],[99,14093,241],{"className":14094},[240],[99,14096,14098],{"className":14097},[190],[99,14099,14101],{"className":14100,"style":13051},[194],[99,14102],{},[99,14104,241],{"className":14105},[240],[99,14107,14109],{"className":14108},[190],[99,14110,14112],{"className":14111,"style":12062},[194],[99,14113],{},[99,14115],{"className":14116},[254,2336],[99,14118],{"className":14119,"style":398},[397],[99,14121,313],{"className":14122},[402],[99,14124],{"className":14125,"style":398},[397],[99,14127,14129,14132,14229,14232,14235,14383,14386,14389],{"className":14128},[160],[99,14130],{"className":14131,"style":13361},[164],[99,14133,14135,14138,14226],{"className":14134},[173],[99,14136],{"className":14137},[169,2336],[99,14139,14141],{"className":14140},[11809],[99,14142,14144,14217],{"className":14143},[185,186],[99,14145,14147,14214],{"className":14146},[190],[99,14148,14151,14192,14200],{"className":14149,"style":14150},[194],"height:0.8451em;",[99,14152,14153,14156],{"style":11926},[99,14154],{"className":14155,"style":4480},[202],[99,14157,14159],{"className":14158},[207,208,209,210],[99,14160,14162],{"className":14161},[173,210],[99,14163,14165,14168],{"className":14164},[173,210],[99,14166,11152],{"className":14167,"style":11235},[173,177,210],[99,14169,14171],{"className":14170},[181],[99,14172,14174],{"className":14173},[185],[99,14175,14177],{"className":14176},[190],[99,14178,14181],{"className":14179,"style":14180},[194],"height:0.7463em;",[99,14182,14183,14186],{"style":2509},[99,14184],{"className":14185,"style":2513},[202],[99,14187,14189],{"className":14188},[207,2517,2518,210],[99,14190,10911],{"className":14191},[173,210],[99,14193,14194,14197],{"style":11985},[99,14195],{"className":14196,"style":4480},[202],[99,14198],{"className":14199,"style":11993},[11992],[99,14201,14202,14205],{"style":12844},[99,14203],{"className":14204,"style":4480},[202],[99,14206,14208],{"className":14207},[207,208,209,210],[99,14209,14211],{"className":14210},[173,210],[99,14212,1652],{"className":14213},[173,210],[99,14215,241],{"className":14216},[240],[99,14218,14220],{"className":14219},[190],[99,14221,14224],{"className":14222,"style":14223},[194],"height:0.345em;",[99,14225],{},[99,14227],{"className":14228},[254,2336],[99,14230,2813],{"className":14231},[169],[99,14233,11152],{"className":14234,"style":11235},[173,177],[99,14236,14238,14241,14380],{"className":14237},[173],[99,14239],{"className":14240},[169,2336],[99,14242,14244],{"className":14243},[11809],[99,14245,14247,14372],{"className":14246},[185,186],[99,14248,14250,14369],{"className":14249},[190],[99,14251,14253,14307,14315],{"className":14252,"style"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this result back into the original equation,",[67,14560,14561],{},[99,14562,14564,14722],{"className":14563},[102],[99,14565,14567],{"className":14566},[106],[108,14568,14569],{"xmlns":110},[112,14570,14571,14719],{},[115,14572,14573,14579,14581,14587,14605,14607,14609,14633,14655,14665,14667,14669,14691,14693,14699,14717],{},[302,14574,14575,14577],{},[126,14576,128],{},[126,14578,131],{},[118,14580,313],{},[302,14582,14583,14585],{},[126,14584,2263],{},[126,14586,2266],{},[11809,14588,14589,14595],{},[115,14590,14591,14593],{},[126,14592,11815],{"mathvariant":2257},[126,14594,11152],{},[115,14596,14597,14599],{},[126,14598,11815],{"mathvariant":2257},[302,14600,14601,14603],{},[126,14602,1278],{},[126,14604,131],{},[118,14606,3882],{},[126,14608,11152],{},[123,14610,14611,14613,14621],{},[118,14612,1643],{},[115,14614,14615,14617,14619],{},[126,14616,12592],{},[118,14618,313],{},[142,14620,1652],{},[115,14622,14623,14625,14627,14629,14631],{},[126,14624,12592],{},[118,14626,313],{},[126,14628,2266],{},[118,14630,2254],{},[142,14632,1652],{},[11809,14634,14635,14645],{},[115,14636,14637,14639],{},[126,14638,11815],{"mathvariant":2257},[302,14640,14641,14643],{},[126,14642,2263],{},[126,14644,2266],{},[115,14646,14647,14649],{},[126,14648,11815],{"mathvariant":2257},[302,14650,14651,14653],{},[126,14652,306],{},[126,14654,12592],{},[11809,14656,14657,14659],{},[142,14658,1652],{},[1629,14660,14661,14663],{},[126,14662,11152],{},[142,14664,10911],{},[118,14666,2813],{"stretchy":120},[126,14668,11152],{},[11809,14670,14671,14681],{},[115,14672,14673,14675],{},[126,14674,11815],{"mathvariant":2257},[302,14676,14677,14679],{},[126,14678,1278],{},[126,14680,12592],{},[115,14682,14683,14685],{},[126,14684,11815],{"mathvariant":2257},[302,14686,14687,14689],{},[126,14688,1278],{},[126,14690,131],{},[118,14692,2254],{},[302,14694,14695,14697],{},[126,14696,1278],{},[126,14698,12592],{},[11809,14700,14701,14707],{},[115,14702,14703,14705],{},[126,14704,11815],{"mathvariant":2257},[126,14706,11152],{},[115,14708,14709,14711],{},[126,14710,11815],{"mathvariant":2257},[302,14712,14713,14715],{},[126,14714,1278],{},[126,14716,131],{},[118,14718,2846],{"stretchy":120},[149,14720,14721],{"encoding":151},"\\mu_i = G_m \\frac{\\partial N }{\\partial n_i} + N \\sum_{j=1}^{j=m-1}\\frac{\\partial G_m }{\\partial x_j}\\frac{1}{N^2} (N\\frac{\\partial n_j}{\\partial n_i} - n_j\\frac{\\partial N}{\\partial n_i})",[99,14723,14725,14780,14946,15441],{"className":14724,"ariaHidden":139},[156],[99,14726,14728,14731,14771,14774,14777],{"className":14727},[160],[99,14729],{"className":14730,"style":11848},[164],[99,14732,14734,14737],{"className":14733},[173],[99,14735,128],{"className":14736},[173,177],[99,14738,14740],{"className":14739},[181],[99,14741,14743,14763],{"className":14742},[185,186],[99,14744,14746,14760],{"className":14745},[190],[99,14747,14749],{"className":14748,"style":366},[194],[99,14750,14751,14754],{"style":369},[99,14752],{"className":14753,"style":203},[202],[99,14755,14757],{"className":14756},[207,208,209,210],[99,14758,131],{"className":14759},[173,177,210],[99,14761,241],{"className":14762},[240],[99,14764,14766],{"className":14765},[190],[99,14767,14769],{"className":14768,"style":388},[194],[99,14770],{},[99,14772],{"className":14773,"style":398},[397],[99,14775,313],{"className":14776},[402],[99,14778],{"className":14779,"style":398},[397],[99,14781,14783,14786,14826,14937,14940,14943],{"className":14782},[160],[99,14784],{"className":14785,"style":12720},[164],[99,14787,14789,14792],{"className":14788},[173],[99,14790,2263],{"className":14791},[173,177],[99,14793,14795],{"className":14794},[181],[99,14796,14798,14818],{"className":14797},[185,186],[99,14799,14801,14815],{"className":14800},[190],[99,14802,14804],{"className":14803,"style":11269},[194],[99,14805,14806,14809],{"style":369},[99,14807],{"className":14808,"style":203},[202],[99,14810,14812],{"className":14811},[207,208,209,210],[99,14813,2266],{"className":14814},[173,177,210],[99,14816,241],{"className":14817},[240],[99,14819,14821],{"className":14820},[190],[99,14822,14824],{"className":14823,"style":388},[194],[99,14825],{},[99,14827,14829,14832,14934],{"className":14828},[173],[99,14830],{"className":14831},[169,2336],[99,14833,14835],{"className":14834},[11809],[99,14836,14838,14926],{"className":14837},[185,186],[99,14839,14841,14923],{"className":14840},[190],[99,14842,14844,14898,14906],{"className":14843,"style":12779},[194],[99,14845,14846,14849],{"style":11926},[99,14847],{"className":14848,"style":4480},[202],[99,14850,14852],{"className":14851},[207,208,209,210],[99,14853,14855,14858],{"className":14854},[173,210],[99,14856,11815],{"className":14857,"style":11939},[173,210],[99,14859,14861,14864],{"className":14860},[173,210],[99,14862,1278],{"className":14863},[173,177,210],[99,14865,14867],{"className":14866},[181],[99,14868,14870,14890],{"className":14869},[185,186],[99,14871,14873,14887],{"className":14872},[190],[99,14874,14876],{"className":14875,"style":11958},[194],[99,14877,14878,14881],{"style":11961},[99,14879],{"className":14880,"style":2513},[202],[99,14882,14884],{"className":14883},[207,2517,2518,210],[99,14885,131],{"className":14886},[173,177,210],[99,14888,241],{"className":14889},[240],[99,14891,14893],{"className":14892},[190],[99,14894,14896],{"className":14895,"style":11980},[194],[99,14897],{},[99,14899,14900,14903],{"style":11985},[99,14901],{"className":14902,"style":4480},[202],[99,14904],{"className":14905,"style":11993},[11992],[99,14907,14908,14911],{"style":12844},[99,14909],{"className":14910,"style":4480},[202],[99,14912,14914],{"className":14913},[207,208,209,210],[99,14915,14917,14920],{"className":14916},[173,210],[99,14918,11815],{"className":14919,"style":11939},[173,210],[99,14921,11152],{"className":14922,"style":11235},[173,177,210],[99,14924,241],{"className":14925},[240],[99,14927,14929],{"className":14928},[190],[99,14930,14932],{"className":14931,"style":12062},[194],[99,14933],{},[99,14935],{"className":14936},[254,2336],[99,14938],{"className":14939,"style":2590},[397],[99,14941,3882],{"className":14942},[2594],[99,14944],{"className":14945,"style":2590},[397],[99,14947,14949,14952,14955,14958,15033,15036,15184,15278,15281,15284,15432,15435,15438],{"className":14948},[160],[99,14950],{"className":14951,"style":12889},[164],[99,14953,11152],{"className":14954,"style":11235},[173,177],[99,14956],{"className":14957,"style":1813},[397],[99,14959,14961,14964],{"className":14960},[1739],[99,14962,1643],{"className":14963,"style":12903},[1739,1784,12902],[99,14965,14967],{"className":14966},[181],[99,14968,14970,15025],{"className":14969},[185,186],[99,14971,14973,15022],{"className":14972},[190],[99,14974,14976,14996],{"className":14975,"style":12916},[194],[99,14977,14978,14981],{"style":12919},[99,14979],{"className":14980,"style":203},[202],[99,14982,14984],{"className":14983},[207,208,209,210],[99,14985,14987,14990,14993],{"className":14986},[173,210],[99,14988,12592],{"className":14989,"style":12932},[173,177,210],[99,14991,313],{"className":14992},[402,210],[99,14994,1652],{"className":14995},[173,210],[99,14997,14998,15001],{"style":12941},[99,14999],{"className":15000,"style":203},[202],[99,15002,15004],{"className":15003},[207,208,209,210],[99,15005,15007,15010,15013,15016,15019],{"className":15006},[173,210],[99,15008,12592],{"className":15009,"style":12932},[173,177,210],[99,15011,313],{"className":15012},[402,210],[99,15014,2266],{"className":15015},[173,177,210],[99,15017,2254],{"className":15018},[2594,210],[99,15020,1652],{"className":15021},[173,210],[99,15023,241],{"className":15024},[240],[99,15026,15028],{"className":15027},[190],[99,15029,15031],{"className":15030,"style":12975},[194],[99,15032],{},[99,15034],{"className":15035,"style":1813},[397],[99,15037,15039,15042,15181],{"className":15038},[173],[99,15040],{"className":15041},[169,2336],[99,15043,15045],{"className":15044},[11809],[99,15046,15048,15173],{"className":15047},[185,186],[99,15049,15051,15170],{"className":15050},[190],[99,15052,15054,15108,15116],{"className":15053,"style":11923},[194],[99,15055,15056,15059],{"style":11926},[99,15057],{"className":15058,"style":4480},[202],[99,15060,15062],{"className":15061},[207,208,209,210],[99,15063,15065,15068],{"className":15064},[173,210],[99,15066,11815],{"className":15067,"style":11939},[173,210],[99,15069,15071,15074],{"className":15070},[173,210],[99,15072,306],{"className":15073},[173,177,210],[99,15075,15077],{"className":15076},[181],[99,15078,15080,15100],{"className":15079},[185,186],[99,15081,15083,15097],{"className":15082},[190],[99,15084,15086],{"className":15085,"style":11958},[194],[99,15087,15088,15091],{"style":11961},[99,15089],{"className":15090,"style":2513},[202],[99,15092,15094],{"className":15093},[207,2517,2518,210],[99,15095,12592],{"className":15096,"style":12932},[173,177,210],[99,15098,241],{"className":15099},[240],[99,15101,15103],{"className":15102},[190],[99,15104,15106],{"className":15105,"style":13051},[194],[99,15107],{},[99,15109,15110,15113],{"style":11985},[99,15111],{"className":15112,"style":4480},[202],[99,15114],{"className":15115,"style":11993},[11992],[99,15117,15118,15121],{"style":11996},[99,15119],{"className":15120,"style":4480},[202],[99,15122,15124],{"className":15123},[207,208,209,210],[99,15125,15127,15130],{"className":15126},[173,210],[99,15128,11815],{"className":15129,"style":11939},[173,210],[99,15131,15133,15136],{"className":15132},[173,210],[99,15134,2263],{"className":15135},[173,177,210],[99,15137,15139],{"className":15138},[181],[99,15140,15142,15162],{"className":15141},[185,186],[99,15143,15145,15159],{"className":15144},[190],[99,15146,15148],{"className":15147,"style":12030},[194],[99,15149,15150,15153],{"style":11961},[99,15151],{"className":15152,"style":2513},[202],[99,15154,15156],{"className":15155},[207,2517,2518,210],[99,15157,2266],{"className":15158},[173,177,210],[99,15160,241],{"className":15161},[240],[99,15163,15165],{"className":15164},[190],[99,15166,15168],{"className":15167,"style":11980},[194],[99,15169],{},[99,15171,241],{"className":15172},[240],[99,15174,15176],{"className":15175},[190],[99,15177,15179],{"className":15178,"style":13125},[194],[99,15180],{},[99,15182],{"className":15183},[254,2336],[99,15185,15187,15190,15275],{"className":15186},[173],[99,15188],{"className":15189},[169,2336],[99,15191,15193],{"className":15192},[11809],[99,15194,15196,15267],{"className":15195},[185,186],[99,15197,15199,15264],{"className":15198},[190],[99,15200,15202,15242,15250],{"className":15201,"style":14150},[194],[99,15203,15204,15207],{"style":11926},[99,15205],{"className":15206,"style":4480},[202],[99,15208,15210],{"className":15209},[207,208,209,210],[99,15211,15213],{"className":15212},[173,210],[99,15214,15216,15219],{"className":15215},[173,210],[99,15217,11152],{"className":15218,"style":11235},[173,177,210],[99,15220,15222],{"className":15221},[181],[99,15223,15225],{"className":15224},[185],[99,15226,15228],{"className":15227},[190],[99,15229,15231],{"className":15230,"style":14180},[194],[99,15232,15233,15236],{"style":2509},[99,15234],{"className":15235,"style":2513},[202],[99,15237,15239],{"className":15238},[207,2517,2518,210],[99,15240,10911],{"className":15241},[173,210],[99,15243,15244,15247],{"style":11985},[99,15245],{"className":15246,"style":4480},[202],[99,15248],{"className":15249,"style":11993},[11992],[99,15251,15252,15255],{"style":12844},[99,15253],{"className":15254,"style":4480},[202],[99,15256,15258],{"className":15257},[207,208,209,210],[99,15259,15261],{"className":15260},[173,210],[99,15262,1652],{"className":15263},[173,210],[99,15265,241],{"className":15266},[240],[99,15268,15270],{"className":15269},[190],[99,15271,15273],{"className":15272,"style":14223},[194],[99,15274],{},[99,15276],{"className":15277},[254,2336],[99,15279,2813],{"className":15280},[169],[99,15282,11152],{"className":15283,"style":11235},[173,177],[99,15285,15287,15290,15429],{"className":15286},[173],[99,15288],{"className":15289},[169,2336],[99,15291,15293],{"className":15292},[11809],[99,15294,15296,15421],{"className":15295},[185,186],[99,15297,15299,15418],{"className":15298},[190],[99,15300,15302,15356,15364],{"className":15301,"style":13149},[194],[99,15303,15304,15307],{"style":11926},[99,15305],{"className":15306,"style":4480},[202],[99,15308,15310],{"className":15309},[207,208,209,210],[99,15311,15313,15316],{"className":15312},[173,210],[99,15314,11815],{"className":15315,"style":11939},[173,210],[99,15317,15319,15322],{"className":15318},[173,210],[99,15320,1278],{"className":15321},[173,177,210],[99,15323,15325],{"className":15324},[181],[99,15326,15328,15348],{"className":15327},[185,186],[99,15329,15331,15345],{"className":15330},[190],[99,15332,15334],{"className":15333,"style":11958},[194],[99,15335,15336,15339],{"style":11961},[99,15337],{"className":15338,"style":2513},[202],[99,15340,15342],{"className":15341},[207,2517,2518,210],[99,15343,131],{"className":15344},[173,177,210],[99,15346,241],{"className":15347},[240],[99,15349,15351],{"className":15350},[190],[99,15352,15354],{"className":15353,"style":11980},[194],[99,15355],{},[99,15357,15358,15361],{"style":11985},[99,15359],{"className":15360,"style":4480},[202],[99,15362],{"className":15363,"style":11993},[11992],[99,15365,15366,15369],{"style":13214},[99,15367],{"className":15368,"style":4480},[202],[99,15370,15372],{"className":15371},[207,208,209,210],[99,15373,15375,15378],{"className":15374},[173,210],[99,15376,11815],{"className":15377,"style":11939},[173,210],[99,15379,15381,15384],{"className":15380},[173,210],[99,15382,1278],{"className":15383},[173,177,210],[99,15385,15387],{"className":15386},[181],[99,15388,15390,15410],{"className":15389},[185,186],[99,15391,15393,15407],{"className":15392},[190],[99,15394,15396],{"className":15395,"style":11958},[194],[99,15397,15398,15401],{"style":11961},[99,15399],{"className":15400,"style":2513},[202],[99,15402,15404],{"className":15403},[207,2517,2518,210],[99,15405,12592],{"className":15406,"style":12932},[173,177,210],[99,15408,241],{"className":15409},[240],[99,15411,15413],{"className":15412},[190],[99,15414,15416],{"className":15415,"style":13051},[194],[99,15417],{},[99,15419,241],{"className":15420},[240],[99,15422,15424],{"className":15423},[190],[99,15425,15427],{"className":15426,"style":12062},[194],[99,15428],{},[99,15430],{"className":15431},[254,2336],[99,15433],{"className":15434,"style":2590},[397],[99,15436,2254],{"className":15437},[2594],[99,15439],{"className":15440,"style":2590},[397],[99,15442,15444,15447,15487,15598],{"className":15443},[160],[99,15445],{"className":15446,"style":12720},[164],[99,15448,15450,15453],{"className":15449},[173],[99,15451,1278],{"className":15452},[173,177],[99,15454,15456],{"className":15455},[181],[99,15457,15459,15479],{"className":15458},[185,186],[99,15460,15462,15476],{"className":15461},[190],[99,15463,15465],{"className":15464,"style":366},[194],[99,15466,15467,15470],{"style":369},[99,15468],{"className":15469,"style":203},[202],[99,15471,15473],{"className":15472},[207,208,209,210],[99,15474,12592],{"className":15475,"style":12932},[173,177,210],[99,15477,241],{"className":15478},[240],[99,15480,15482],{"className":15481},[190],[99,15483,15485],{"className":15484,"style":14436},[194],[99,15486],{},[99,15488,15490,15493,15595],{"className":15489},[173],[99,15491],{"className":15492},[169,2336],[99,15494,15496],{"className":15495},[11809],[99,15497,15499,15587],{"className":15498},[185,186],[99,15500,15502,15584],{"className":15501},[190],[99,15503,15505,15559,15567],{"className":15504,"style":12779},[194],[99,15506,15507,15510],{"style":11926},[99,15508],{"className":15509,"style":4480},[202],[99,15511,15513],{"className":15512},[207,208,209,210],[99,15514,15516,15519],{"className":15515},[173,210],[99,15517,11815],{"className":15518,"style":11939},[173,210],[99,15520,15522,15525],{"className":15521},[173,210],[99,15523,1278],{"className":15524},[173,177,210],[99,15526,15528],{"className":15527},[181],[99,15529,15531,15551],{"className":15530},[185,186],[99,15532,15534,15548],{"className":15533},[190],[99,15535,15537],{"className":15536,"style":11958},[194],[99,15538,15539,15542],{"style":11961},[99,15540],{"className":15541,"style":2513},[202],[99,15543,15545],{"className":15544},[207,2517,2518,210],[99,15546,131],{"className":15547},[173,177,210],[99,15549,241],{"className":15550},[240],[99,15552,15554],{"className":15553},[190],[99,15555,15557],{"className":15556,"style":11980},[194],[99,15558],{},[99,15560,15561,15564],{"style":11985},[99,15562],{"className":15563,"style":4480},[202],[99,15565],{"className":15566,"style":11993},[11992],[99,15568,15569,15572],{"style":12844},[99,15570],{"className":15571,"style":4480},[202],[99,15573,15575],{"className":15574},[207,208,209,210],[99,15576,15578,15581],{"className":15577},[173,210],[99,15579,11815],{"className":15580,"style":11939},[173,210],[99,15582,11152],{"className":15583,"style":11235},[173,177,210],[99,15585,241],{"className":15586},[240],[99,15588,15590],{"className":15589},[190],[99,15591,15593],{"className":15592,"style":12062},[194],[99,15594],{},[99,15596],{"className":15597},[254,2336],[99,15599,2846],{"className":15600},[254],[67,15602,15603],{},"Simplify the equation above,",[67,15605,15606],{},[99,15607,15609,15706],{"className":15608},[102],[99,15610,15612],{"className":15611},[106],[108,15613,15614],{"xmlns":110},[112,15615,15616,15703],{},[115,15617,15618,15624,15626,15632,15634,15658,15680,15682,15693,15695,15701],{},[302,15619,15620,15622],{},[126,15621,128],{},[126,15623,131],{},[118,15625,313],{},[302,15627,15628,15630],{},[126,15629,2263],{},[126,15631,2266],{},[118,15633,3882],{},[123,15635,15636,15638,15646],{},[118,15637,1643],{},[115,15639,15640,15642,15644],{},[126,15641,12592],{},[118,15643,313],{},[142,15645,1652],{},[115,15647,15648,15650,15652,15654,15656],{},[126,15649,12592],{},[118,15651,313],{},[126,15653,2266],{},[118,15655,2254],{},[142,15657,1652],{},[11809,15659,15660,15670],{},[115,15661,15662,15664],{},[126,15663,11815],{"mathvariant":2257},[302,15665,15666,15668],{},[126,15667,2263],{},[126,15669,2266],{},[115,15671,15672,15674],{},[126,15673,11815],{"mathvariant":2257},[302,15675,15676,15678],{},[126,15677,306],{},[126,15679,12592],{},[118,15681,2813],{"stretchy":120},[302,15683,15684,15687],{},[126,15685,15686],{},"δ",[115,15688,15689,15691],{},[126,15690,131],{},[126,15692,12592],{},[118,15694,2254],{},[302,15696,15697,15699],{},[126,15698,306],{},[126,15700,12592],{},[118,15702,2846],{"stretchy":120},[149,15704,15705],{"encoding":151},"\\mu_i = G_m  + \\sum_{j=1}^{j=m-1}\\frac{\\partial G_m }{\\partial x_j} (\\delta_{ij} - x_j)",[99,15707,15709,15764,15819,16110],{"className":15708,"ariaHidden":139},[156],[99,15710,15712,15715,15755,15758,15761],{"className":15711},[160],[99,15713],{"className":15714,"style":11848},[164],[99,15716,15718,15721],{"className":15717},[173],[99,15719,128],{"className":15720},[173,177],[99,15722,15724],{"className":15723},[181],[99,15725,15727,15747],{"className":15726},[185,186],[99,15728,15730,15744],{"className":15729},[190],[99,15731,15733],{"className":15732,"style":366},[194],[99,15734,15735,15738],{"style":369},[99,15736],{"className":15737,"style":203},[202],[99,15739,15741],{"className":15740},[207,208,209,210],[99,15742,131],{"className":15743},[173,177,210],[99,15745,241],{"className":15746},[240],[99,15748,15750],{"className":15749},[190],[99,15751,15753],{"className":15752,"style":388},[194],[99,15754],{},[99,15756],{"className":15757,"style":398},[397],[99,15759,313],{"className":15760},[402],[99,15762],{"className":15763,"style":398},[397],[99,15765,15767,15770,15810,15813,15816],{"className":15766},[160],[99,15768],{"className":15769,"style":11510},[164],[99,15771,15773,15776],{"className":15772},[173],[99,15774,2263],{"className":15775},[173,177],[99,15777,15779],{"className":15778},[181],[99,15780,15782,15802],{"className":15781},[185,186],[99,15783,15785,15799],{"className":15784},[190],[99,15786,15788],{"className":15787,"style":11269},[194],[99,15789,15790,15793],{"style":369},[99,15791],{"className":15792,"style":203},[202],[99,15794,15796],{"className":15795},[207,208,209,210],[99,15797,2266],{"className":15798},[173,177,210],[99,15800,241],{"className":15801},[240],[99,15803,15805],{"className":15804},[190],[99,15806,15808],{"className":15807,"style":388},[194],[99,15809],{},[99,15811],{"className":15812,"style":2590},[397],[99,15814,3882],{"className":15815},[2594],[99,15817],{"className":15818,"style":2590},[397],[99,15820,15822,15826,15901,15904,16052,16055,16101,16104,16107],{"className":15821},[160],[99,15823],{"className":15824,"style":15825},[164],"height:1.5069em;vertical-align:-0.5423em;",[99,15827,15829,15832],{"className":15828},[1739],[99,15830,1643],{"className":15831,"style":12903},[1739,1784,12902],[99,15833,15835],{"className":15834},[181],[99,15836,15838,15893],{"className":15837},[185,186],[99,15839,15841,15890],{"className":15840},[190],[99,15842,15844,15864],{"className":15843,"style":12916},[194],[99,15845,15846,15849],{"style":12919},[99,15847],{"className":15848,"style":203},[202],[99,15850,15852],{"className":15851},[207,208,209,210],[99,15853,15855,15858,15861],{"className":15854},[173,210],[99,15856,12592],{"className":15857,"style":12932},[173,177,210],[99,15859,313],{"className":15860},[402,210],[99,15862,1652],{"className":15863},[173,210],[99,15865,15866,15869],{"style":12941},[99,15867],{"className":15868,"style":203},[202],[99,15870,15872],{"className":15871},[207,208,209,210],[99,15873,15875,15878,15881,15884,15887],{"className":15874},[173,210],[99,15876,12592],{"className":15877,"style":12932},[173,177,210],[99,15879,313],{"className":15880},[402,210],[99,15882,2266],{"className":15883},[173,177,210],[99,15885,2254],{"className":15886},[2594,210],[99,15888,1652],{"className":15889},[173,210],[99,15891,241],{"className":15892},[240],[99,15894,15896],{"className":15895},[190],[99,15897,15899],{"className":15898,"style":12975},[194],[99,15900],{},[99,15902],{"className":15903,"style":1813},[397],[99,15905,15907,15910,16049],{"className":15906},[173],[99,15908],{"className":15909},[169,2336],[99,15911,15913],{"className":15912},[11809],[99,15914,15916,16041],{"className":15915},[185,186],[99,15917,15919,16038],{"className":15918},[190],[99,15920,15922,15976,15984],{"className":15921,"style":11923},[194],[99,15923,15924,15927],{"style":11926},[99,15925],{"className":15926,"style":4480},[202],[99,15928,15930],{"className":15929},[207,208,209,210],[99,15931,15933,15936],{"className":15932},[173,210],[99,15934,11815],{"className":15935,"style":11939},[173,210],[99,15937,15939,15942],{"className":15938},[173,210],[99,15940,306],{"className":15941},[173,177,210],[99,15943,15945],{"className":15944},[181],[99,15946,15948,15968],{"className":15947},[185,186],[99,15949,15951,15965],{"className":15950},[190],[99,15952,15954],{"className":15953,"style":11958},[194],[99,15955,15956,15959],{"style":11961},[99,15957],{"className":15958,"style":2513},[202],[99,15960,15962],{"className":15961},[207,2517,2518,210],[99,15963,12592],{"className":15964,"style":12932},[173,177,210],[99,15966,241],{"className":15967},[240],[99,15969,15971],{"className":15970},[190],[99,15972,15974],{"className":15973,"style":13051},[194],[99,15975],{},[99,15977,15978,15981],{"style":11985},[99,15979],{"className":15980,"style":4480},[202],[99,15982],{"className":15983,"style":11993},[11992],[99,15985,15986,15989],{"style":11996},[99,15987],{"className":15988,"style":4480},[202],[99,15990,15992],{"className":15991},[207,208,209,210],[99,15993,15995,15998],{"className":15994},[173,210],[99,15996,11815],{"className":15997,"style":11939},[173,210],[99,15999,16001,16004],{"className":16000},[173,210],[99,16002,2263],{"className":16003},[173,177,210],[99,16005,16007],{"className":16006},[181],[99,16008,16010,16030],{"className":16009},[185,186],[99,16011,16013,16027],{"className":16012},[190],[99,16014,16016],{"className":16015,"style":12030},[194],[99,16017,16018,16021],{"style":11961},[99,16019],{"className":16020,"style":2513},[202],[99,16022,16024],{"className":16023},[207,2517,2518,210],[99,16025,2266],{"className":16026},[173,177,210],[99,16028,241],{"className":16029},[240],[99,16031,16033],{"className":16032},[190],[99,16034,16036],{"className":16035,"style":11980},[194],[99,16037],{},[99,16039,241],{"className":16040},[240],[99,16042,16044],{"className":16043},[190],[99,16045,16047],{"className":16046,"style":13125},[194],[99,16048],{},[99,16050],{"className":16051},[254,2336],[99,16053,2813],{"className":16054},[169],[99,16056,16058,16062],{"className":16057},[173],[99,16059,15686],{"className":16060,"style":16061},[173,177],"margin-right:0.0379em;",[99,16063,16065],{"className":16064},[181],[99,16066,16068,16093],{"className":16067},[185,186],[99,16069,16071,16090],{"className":16070},[190],[99,16072,16074],{"className":16073,"style":366},[194],[99,16075,16077,16080],{"style":16076},"top:-2.55em;margin-left:-0.0379em;margin-right:0.05em;",[99,16078],{"className":16079,"style":203},[202],[99,16081,16083],{"className":16082},[207,208,209,210],[99,16084,16086],{"className":16085},[173,210],[99,16087,16089],{"className":16088,"style":12932},[173,177,210],"ij",[99,16091,241],{"className":16092},[240],[99,16094,16096],{"className":16095},[190],[99,16097,16099],{"className":16098,"style":14436},[194],[99,16100],{},[99,16102],{"className":16103,"style":2590},[397],[99,16105,2254],{"className":16106},[2594],[99,16108],{"className":16109,"style":2590},[397],[99,16111,16113,16117,16157],{"className":16112},[160],[99,16114],{"className":16115,"style":16116},[164],"height:1.0361em;vertical-align:-0.2861em;",[99,16118,16120,16123],{"className":16119},[173],[99,16121,306],{"className":16122},[173,177],[99,16124,16126],{"className":16125},[181],[99,16127,16129,16149],{"className":16128},[185,186],[99,16130,16132,16146],{"className":16131},[190],[99,16133,16135],{"className":16134,"style":366},[194],[99,16136,16137,16140],{"style":369},[99,16138],{"className":16139,"style":203},[202],[99,16141,16143],{"className":16142},[207,208,209,210],[99,16144,12592],{"className":16145,"style":12932},[173,177,210],[99,16147,241],{"className":16148},[240],[99,16150,16152],{"className":16151},[190],[99,16153,16155],{"className":16154,"style":14436},[194],[99,16156],{},[99,16158,2846],{"className":16159},[254],[1258,16161,16163],{"id":16162},"for-gibbs-energy-with-dependent-composition","For Gibbs energy with dependent composition",[67,16165,10762,16166,10792,16194,10845,16244,10874],{},[99,16167,16169,16182],{"className":16168},[102],[99,16170,16172],{"className":16171},[106],[108,16173,16174],{"xmlns":110},[112,16175,16176,16180],{},[115,16177,16178],{},[142,16179,1652],{},[149,16181,1652],{"encoding":151},[99,16183,16185],{"className":16184,"ariaHidden":139},[156],[99,16186,16188,16191],{"className":16187},[160],[99,16189],{"className":16190,"style":10788},[164],[99,16192,1652],{"className":16193},[173],[99,16195,16197,16214],{"className":16196},[102],[99,16198,16200],{"className":16199},[106],[108,16201,16202],{"xmlns":110},[112,16203,16204,16212],{},[115,16205,16206,16208,16210],{},[126,16207,2266],{},[118,16209,2254],{},[142,16211,1652],{},[149,16213,10813],{"encoding":151},[99,16215,16217,16235],{"className":16216,"ariaHidden":139},[156],[99,16218,16220,16223,16226,16229,16232],{"className":16219},[160],[99,16221],{"className":16222,"style":10823},[164],[99,16224,2266],{"className":16225},[173,177],[99,16227],{"className":16228,"style":2590},[397],[99,16230,2254],{"className":16231},[2594],[99,16233],{"className":16234,"style":2590},[397],[99,16236,16238,16241],{"className":16237},[160],[99,16239],{"className":16240,"style":10788},[164],[99,16242,1652],{"className":16243},[173],[99,16245,16247,16260],{"className":16246},[102],[99,16248,16250],{"className":16249},[106],[108,16251,16252],{"xmlns":110},[112,16253,16254,16258],{},[115,16255,16256],{},[126,16257,2266],{},[149,16259,2266],{"encoding":151},[99,16261,16263],{"className":16262,"ariaHidden":139},[156],[99,16264,16266,16269],{"className":16265},[160],[99,16267],{"className":16268,"style":282},[164],[99,16270,2266],{"className":16271},[173,177],[67,16273,16274],{},[99,16275,16277,16345],{"className":16276},[102],[99,16278,16280],{"className":16279},[106],[108,16281,16282],{"xmlns":110},[112,16283,16284,16342],{},[115,16285,16286,16288,16290,16292,16294,16300,16302,16308,16310,16312,16314,16316,16318,16330,16332,16338,16340],{},[126,16287,2263],{},[118,16289,313],{},[126,16291,1633],{},[118,16293,2813],{"stretchy":120},[302,16295,16296,16298],{},[126,16297,1278],{},[142,16299,1652],{},[118,16301,140],{"separator":139},[302,16303,16304,16306],{},[126,16305,1278],{},[142,16307,10911],{},[118,16309,140],{"separator":139},[126,16311,1256],{"mathvariant":2257},[126,16313,1256],{"mathvariant":2257},[126,16315,1256],{"mathvariant":2257},[118,16317,140],{"separator":139},[302,16319,16320,16322],{},[126,16321,1278],{},[115,16323,16324,16326,16328],{},[126,16325,2266],{},[118,16327,2254],{},[142,16329,1652],{},[118,16331,140],{"separator":139},[302,16333,16334,16336],{},[126,16335,1278],{},[126,16337,2266],{},[118,16339,2846],{"stretchy":120},[118,16341,140],{"separator":139},[149,16343,16344],{"encoding":151},"G = f(n_1, n_2, ..., n_{m-1}, n_m),",[99,16346,16348,16366],{"className":16347,"ariaHidden":139},[156],[99,16349,16351,16354,16357,16360,16363],{"className":16350},[160],[99,16352],{"className":16353,"style":10948},[164],[99,16355,2263],{"className":16356},[173,177],[99,16358],{"className":16359,"style":398},[397],[99,16361,313],{"className":16362},[402],[99,16364],{"className":16365,"style":398},[397],[99,16367,16369,16372,16375,16378,16418,16421,16424,16464,16467,16470,16473,16476,16479,16528,16531,16534,16574,16577],{"className":16368},[160],[99,16370],{"className":16371,"style":344},[164],[99,16373,1633],{"className":16374,"style":1694},[173,177],[99,16376,2813],{"className":16377},[169],[99,16379,16381,16384],{"className":16380},[173],[99,16382,1278],{"className":16383},[173,177],[99,16385,16387],{"className":16386},[181],[99,16388,16390,16410],{"className":16389},[185,186],[99,16391,16393,16407],{"className":16392},[190],[99,16394,16396],{"className":16395,"style":10991},[194],[99,16397,16398,16401],{"style":369},[99,16399],{"className":16400,"style":203},[202],[99,16402,16404],{"className":16403},[207,208,209,210],[99,16405,1652],{"className":16406},[173,210],[99,16408,241],{"className":16409},[240],[99,16411,16413],{"className":16412},[190],[99,16414,16416],{"className":16415,"style":388},[194],[99,16417],{},[99,16419,140],{"className":16420},[233],[99,16422],{"className":16423,"style":1813},[397],[99,16425,16427,16430],{"className":16426},[173],[99,16428,1278],{"className":16429},[173,177],[99,16431,16433],{"className":16432},[181],[99,16434,16436,16456],{"className":16435},[185,186],[99,16437,16439,16453],{"className":16438},[190],[99,16440,16442],{"className":16441,"style":10991},[194],[99,16443,16444,16447],{"style":369},[99,16445],{"className":16446,"style":203},[202],[99,16448,16450],{"className":16449},[207,208,209,210],[99,16451,10911],{"className":16452},[173,210],[99,16454,241],{"className":16455},[240],[99,16457,16459],{"className":16458},[190],[99,16460,16462],{"className":16461,"style":388},[194],[99,16463],{},[99,16465,140],{"className":16466},[233],[99,16468],{"className":16469,"style":1813},[397],[99,16471,11069],{"className":16472},[173],[99,16474,140],{"className":16475},[233],[99,16477],{"className":16478,"style":1813},[397],[99,16480,16482,16485],{"className":16481},[173],[99,16483,1278],{"className":16484},[173,177],[99,16486,16488],{"className":16487},[181],[99,16489,16491,16520],{"className":16490},[185,186],[99,16492,16494,16517],{"className":16493},[190],[99,16495,16497],{"className":16496,"style":10991},[194],[99,16498,16499,16502],{"style":369},[99,16500],{"className":16501,"style":203},[202],[99,16503,16505],{"className":16504},[207,208,209,210],[99,16506,16508,16511,16514],{"className":16507},[173,210],[99,16509,2266],{"className":16510},[173,177,210],[99,16512,2254],{"className":16513},[2594,210],[99,16515,1652],{"className":16516},[173,210],[99,16518,241],{"className":16519},[240],[99,16521,16523],{"className":16522},[190],[99,16524,16526],{"className":16525,"style":11123},[194],[99,16527],{},[99,16529,140],{"className":16530},[233],[99,16532],{"className":16533,"style":1813},[397],[99,16535,16537,16540],{"className":16536},[173],[99,16538,1278],{"className":16539},[173,177],[99,16541,16543],{"className":16542},[181],[99,16544,16546,16566],{"className":16545},[185,186],[99,16547,16549,16563],{"className":16548},[190],[99,16550,16552],{"className":16551,"style":11269},[194],[99,16553,16554,16557],{"style":369},[99,16555],{"className":16556,"style":203},[202],[99,16558,16560],{"className":16559},[207,208,209,210],[99,16561,2266],{"className":16562},[173,177,210],[99,16564,241],{"className":16565},[240],[99,16567,16569],{"className":16568},[190],[99,16570,16572],{"className":16571,"style":388},[194],[99,16573],{},[99,16575,2846],{"className":16576},[254],[99,16578,140],{"className":16579},[233],[67,16581,11131],{},[67,16583,16584],{},[99,16585,16587,16663],{"className":16586},[102],[99,16588,16590],{"className":16589},[106],[108,16591,16592],{"xmlns":110},[112,16593,16594,16660],{},[115,16595,16596,16598,16600,16602,16604,16610,16612,16618,16620,16626,16628,16630,16632,16634,16636,16648,16650,16656,16658],{},[126,16597,2263],{},[118,16599,313],{},[126,16601,11152],{},[118,16603,11155],{},[302,16605,16606,16608],{},[126,16607,2263],{},[126,16609,2266],{},[118,16611,2813],{"stretchy":120},[302,16613,16614,16616],{},[126,16615,306],{},[142,16617,1652],{},[118,16619,140],{"separator":139},[302,16621,16622,16624],{},[126,16623,306],{},[142,16625,10911],{},[118,16627,140],{"separator":139},[126,16629,1256],{"mathvariant":2257},[126,16631,1256],{"mathvariant":2257},[126,16633,1256],{"mathvariant":2257},[118,16635,140],{"separator":139},[302,16637,16638,16640],{},[126,16639,306],{},[115,16641,16642,16644,16646],{},[126,16643,2266],{},[118,16645,2254],{},[142,16647,1652],{},[118,16649,140],{"separator":139},[302,16651,16652,16654],{},[126,16653,306],{},[126,16655,2266],{},[118,16657,2846],{"stretchy":120},[118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= N \\cdot G_m(x_1, x_2, ..., x_{m-1}, 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the spirit of the CALPHAD method and other physical models, the mole fraction or the composition is the most common state variable for the fraction of the components. And thus, we have a motivation to substitute the amount, i.e., ",[99,17585,17587,17604],{"className":17586},[102],[99,17588,17590],{"className":17589},[106],[108,17591,17592],{"xmlns":110},[112,17593,17594,17602],{},[115,17595,17596],{},[302,17597,17598,17600],{},[126,17599,1278],{},[126,17601,131],{},[149,17603,11572],{"encoding":151},[99,17605,17607],{"className":17606,"ariaHidden":139},[156],[99,17608,17610,17613],{"className":17609},[160],[99,17611],{"className":17612,"style":11582},[164],[99,17614,17616,17619],{"className":17615},[173],[99,17617,1278],{"className":17618},[173,177],[99,17620,17622],{"className":17621},[181],[99,17623,17625,17645],{"className":17624},[185,186],[99,17626,17628,17642],{"className":17627},[190],[99,17629,17631],{"className":17630,"style":366},[194],[99,17632,17633,17636],{"style":369},[99,17634],{"className":17635,"style":203},[202],[99,17637,17639],{"className":17638},[207,208,209,210],[99,17640,131],{"className":17641},[173,177,210],[99,17643,241],{"className":17644},[240],[99,17646,17648],{"className":17647},[190],[99,17649,17651],{"className":17650,"style":388},[194],[99,17652],{},[99,17654,17656,17673],{"className":17655},[102],[99,17657,17659],{"className":17658},[106],[108,17660,17661],{"xmlns":110},[112,17662,17663,17671],{},[115,17664,17665],{},[302,17666,17667,17669],{},[126,17668,306],{},[126,17670,131],{},[149,17672,11674],{"encoding":151},[99,17674,17676],{"className":17675,"ariaHidden":139},[156],[99,17677,17679,17682],{"className":17678},[160],[99,17680],{"className":17681,"style":11582},[164],[99,17683,17685,17688],{"className":17684},[173],[99,17686,306],{"className":17687},[173,177],[99,17689,17691],{"className":17690},[181],[99,17692,17694,17714],{"className":17693},[185,186],[99,17695,17697,17711],{"className":17696},[190],[99,17698,17700],{"className":17699,"style":366},[194],[99,17701,17702,17705],{"style":369},[99,17703],{"className":17704,"style":203},[202],[99,17706,17708],{"className":17707},[207,208,209,210],[99,17709,131],{"className":17710},[173,177,210],[99,17712,241],{"className":17713},[240],[99,17715,17717],{"className":17716},[190],[99,17718,17720],{"className":17719,"style":388},[194],[99,17721],{},[67,17723,12216],{},[67,17725,17726],{},[99,17727,17729,17803],{"className":17728},[102],[99,17730,17732],{"className":17731},[106],[108,17733,17734],{"xmlns":110},[112,17735,17736,17800],{},[115,17737,17738,17744,17746,17748,17750,17752,17754,17760,17762,17768,17770,17772,17774,17776,17778,17790,17792,17798],{},[302,17739,17740,17742],{},[126,17741,1278],{},[126,17743,131],{},[118,17745,313],{},[126,17747,11152],{},[118,17749,11155],{},[126,17751,12245],{},[118,17753,2813],{"stretchy":120},[302,17755,17756,17758],{},[126,17757,306],{},[142,17759,1652],{},[118,17761,140],{"separator":139},[302,17763,17764,17766],{},[126,17765,306],{},[142,17767,10911],{},[118,17769,140],{"separator":139},[126,17771,1256],{"mathvariant":2257},[126,17773,1256],{"mathvariant":2257},[126,17775,1256],{"mathvariant":2257},[118,17777,140],{"separator":139},[302,17779,17780,17782],{},[126,17781,306],{},[115,17783,17784,17786,17788],{},[126,17785,2266],{},[118,17787,2254],{},[142,17789,1652],{},[118,17791,140],{"separator":139},[302,17793,17794,17796],{},[126,17795,306],{},[126,17797,2266],{},[118,17799,2846],{"stretchy":120},[149,17801,17802],{"encoding":151},"n_i = N \\cdot g(x_1, x_2, ..., x_{m-1}, x_m)",[99,17804,17806,17861,17879],{"className":17805,"ariaHidden":139},[156],[99,17807,17809,17812,17852,17855,17858],{"className":17808},[160],[99,17810],{"className":17811,"style":11582},[164],[99,17813,17815,17818],{"className":17814},[173],[99,17816,1278],{"className":17817},[173,177],[99,17819,17821],{"className":17820},[181],[99,17822,17824,17844],{"className":17823},[185,186],[99,17825,17827,17841],{"className":17826},[190],[99,17828,17830],{"className":17829,"style":366},[194],[99,17831,17832,17835],{"style":369},[99,17833],{"className":17834,"style":203},[202],[99,17836,17838],{"className":17837},[207,208,209,210],[99,17839,131],{"className":17840},[173,177,210],[99,17842,241],{"className":17843},[240],[99,17845,17847],{"className":17846},[190],[99,17848,17850],{"className":17849,"style":388},[194],[99,17851],{},[99,17853],{"className":17854,"style":398},[397],[99,17856,313],{"className":17857},[402],[99,17859],{"className":17860,"style":398},[397],[99,17862,17864,17867,17870,17873,17876],{"className":17863},[160],[99,17865],{"className":17866,"style":10948},[164],[99,17868,11152],{"className":17869,"style":11235},[173,177],[99,17871],{"className":17872,"style":2590},[397],[99,17874,11155],{"className":17875},[2594],[99,17877],{"className":17878,"style":2590},[397],[99,17880,17882,17885,17888,17891,17931,17934,17937,17977,17980,17983,17986,17989,17992,18041,18044,18047,18087],{"className":17881},[160],[99,17883],{"className":17884,"style":344},[164],[99,17886,12245],{"className":17887,"style":12374},[173,177],[99,17889,2813],{"className":17890},[169],[99,17892,17894,17897],{"className":17893},[173],[99,17895,306],{"className":17896},[173,177],[99,17898,17900],{"className":17899},[181],[99,17901,17903,17923],{"className":17902},[185,186],[99,17904,17906,17920],{"className":17905},[190],[99,17907,17909],{"className":17908,"style":10991},[194],[99,17910,17911,17914],{"style":369},[99,17912],{"className":17913,"style":203},[202],[99,17915,17917],{"className":17916},[207,208,209,210],[99,17918,1652],{"className":17919},[173,210],[99,17921,241],{"className":17922},[240],[99,17924,17926],{"className":17925},[190],[99,17927,17929],{"className":17928,"style":388},[194],[99,17930],{},[99,17932,140],{"className":17933},[233],[99,17935],{"className":17936,"style":1813},[397],[99,17938,17940,17943],{"className":17939},[173],[99,17941,306],{"className":17942},[173,177],[99,17944,17946],{"className":17945},[181],[99,17947,17949,17969],{"className":17948},[185,186],[99,17950,17952,17966],{"className":17951},[190],[99,17953,17955],{"className":17954,"style":10991},[194],[99,17956,17957,17960],{"style":369},[99,17958],{"className":17959,"style":203},[202],[99,17961,17963],{"className":17962},[207,208,209,210],[99,17964,10911],{"className":17965},[173,210],[99,17967,241],{"className":17968},[240],[99,17970,17972],{"className":17971},[190],[99,17973,17975],{"className":17974,"style":388},[194],[99,17976],{},[99,17978,140],{"className":17979},[233],[99,17981],{"className":17982,"style":1813},[397],[99,17984,11069],{"className":17985},[173],[99,17987,140],{"className":17988},[233],[99,17990],{"className":17991,"style":1813},[397],[99,17993,17995,17998],{"className":17994},[173],[99,17996,306],{"className":17997},[173,177],[99,17999,18001],{"className":18000},[181],[99,18002,18004,18033],{"className":18003},[185,186],[99,18005,18007,18030],{"className":18006},[190],[99,18008,18010],{"className":18009,"style":10991},[194],[99,18011,18012,18015],{"style":369},[99,18013],{"className":18014,"style":203},[202],[99,18016,18018],{"className":18017},[207,208,209,210],[99,18019,18021,18024,18027],{"className":18020},[173,210],[99,18022,2266],{"className":18023},[173,177,210],[99,18025,2254],{"className":18026},[2594,210],[99,18028,1652],{"className":18029},[173,210],[99,18031,241],{"className":18032},[240],[99,18034,18036],{"className":18035},[190],[99,18037,18039],{"className":18038,"style":11123},[194],[99,18040],{},[99,18042,140],{"className":18043},[233],[99,18045],{"className":18046,"style":1813},[397],[99,18048,18050,18053],{"className":18049},[173],[99,18051,306],{"className":18052},[173,177],[99,18054,18056],{"className":18055},[181],[99,18057,18059,18079],{"className":18058},[185,186],[99,18060,18062,18076],{"className":18061},[190],[99,18063,18065],{"className":18064,"style":11269},[194],[99,18066,18067,18070],{"style":369},[99,18068],{"className":18069,"style":203},[202],[99,18071,18073],{"className":18072},[207,208,209,210],[99,18074,2266],{"className":18075},[173,177,210],[99,18077,241],{"className":18078},[240],[99,18080,18082],{"className":18081},[190],[99,18083,18085],{"className":18084,"style":388},[194],[99,18086],{},[99,18088,2846],{"className":18089},[254],[67,18091,18092],{},"with the previous constraint, and we can obtain",[67,18094,18095],{},[99,18096,18098,18210],{"className":18097},[102],[99,18099,18101],{"className":18100},[106],[108,18102,18103],{"xmlns":110},[112,18104,18105,18207],{},[115,18106,18107,18113,18115,18121,18139,18141,18143,18163,18185],{},[302,18108,18109,18111],{},[126,18110,128],{},[126,18112,131],{},[118,18114,313],{},[302,18116,18117,18119],{},[126,18118,2263],{},[126,18120,2266],{},[11809,18122,18123,18129],{},[115,18124,18125,18127],{},[126,18126,11815],{"mathvariant":2257},[126,18128,11152],{},[115,18130,18131,18133],{},[126,18132,11815],{"mathvariant":2257},[302,18134,18135,18137],{},[126,18136,1278],{},[126,18138,131],{},[118,18140,3882],{},[126,18142,11152],{},[123,18144,18145,18147,18155],{},[118,18146,1643],{},[115,18148,18149,18151,18153],{},[126,18150,12592],{},[118,18152,313],{},[142,18154,1652],{},[115,18156,18157,18159,18161],{},[126,18158,12592],{},[118,18160,313],{},[126,18162,2266],{},[11809,18164,18165,18175],{},[115,18166,18167,18169],{},[126,18168,11815],{"mathvariant":2257},[302,18170,18171,18173],{},[126,18172,2263],{},[126,18174,2266],{},[115,18176,18177,18179],{},[126,18178,11815],{"mathvariant":2257},[302,18180,18181,18183],{},[126,18182,306],{},[126,18184,12592],{},[11809,18186,18187,18197],{},[115,18188,18189,18191],{},[126,18190,11815],{"mathvariant":2257},[302,18192,18193,18195],{},[126,18194,306],{},[126,18196,12592],{},[115,18198,18199,18201],{},[126,18200,11815],{"mathvariant":2257},[302,18202,18203,18205],{},[126,18204,1278],{},[126,18206,131],{},[149,18208,18209],{"encoding":151},"\\mu_i = G_m \\frac{\\partial N }{\\partial n_i} + N \\sum_{j=1}^{j=m}\\frac{\\partial G_m }{\\partial x_j}\\frac{\\partial x_j }{\\partial n_i}",[99,18211,18213,18268,18434],{"className":18212,"ariaHidden":139},[156],[99,18214,18216,18219,18259,18262,18265],{"className":18215},[160],[99,18217],{"className":18218,"style":11848},[164],[99,18220,18222,18225],{"className":18221},[173],[99,18223,128],{"className":18224},[173,177],[99,18226,18228],{"className":18227},[181],[99,18229,18231,18251],{"className":18230},[185,186],[99,18232,18234,18248],{"className":18233},[190],[99,18235,18237],{"className":18236,"style":366},[194],[99,18238,18239,18242],{"style":369},[99,18240],{"className":18241,"style":203},[202],[99,18243,18245],{"className":18244},[207,208,209,210],[99,18246,131],{"className":18247},[173,177,210],[99,18249,241],{"className":18250},[240],[99,18252,18254],{"className":18253},[190],[99,18255,18257],{"className":18256,"style":388},[194],[99,18258],{},[99,18260],{"className":18261,"style":398},[397],[99,18263,313],{"className":18264},[402],[99,18266],{"className":18267,"style":398},[397],[99,18269,18271,18274,18314,18425,18428,18431],{"className":18270},[160],[99,18272],{"className":18273,"style":12720},[164],[99,18275,18277,18280],{"className":18276},[173],[99,18278,2263],{"className":18279},[173,177],[99,18281,18283],{"className":18282},[181],[99,18284,18286,18306],{"className":18285},[185,186],[99,18287,18289,18303],{"className":18288},[190],[99,18290,18292],{"className":18291,"style":11269},[194],[99,18293,18294,18297],{"style":369},[99,18295],{"className":18296,"style":203},[202],[99,18298,18300],{"className":18299},[207,208,209,210],[99,18301,2266],{"className":18302},[173,177,210],[99,18304,241],{"className":18305},[240],[99,18307,18309],{"className":18308},[190],[99,18310,18312],{"className":18311,"style":388},[194],[99,18313],{},[99,18315,18317,18320,18422],{"className":18316},[173],[99,18318],{"className":18319},[169,2336],[99,18321,18323],{"className":18322},[11809],[99,18324,18326,18414],{"className":18325},[185,186],[99,18327,18329,18411],{"className":18328},[190],[99,18330,18332,18386,18394],{"className":18331,"style":12779},[194],[99,18333,18334,18337],{"style":11926},[99,18335],{"className":18336,"style":4480},[202],[99,18338,18340],{"className":18339},[207,208,209,210],[99,18341,18343,18346],{"className":18342},[173,210],[99,18344,11815],{"className":18345,"style":11939},[173,210],[99,18347,18349,18352],{"className":18348},[173,210],[99,18350,1278],{"className":18351},[173,177,210],[99,18353,18355],{"className":18354},[181],[99,18356,18358,18378],{"className":18357},[185,186],[99,18359,18361,18375],{"className":18360},[190],[99,18362,18364],{"className":18363,"style":11958},[194],[99,18365,18366,18369],{"style":11961},[99,18367],{"className":18368,"style":2513},[202],[99,18370,18372],{"className":18371},[207,2517,2518,210],[99,18373,131],{"className":18374},[173,177,210],[99,18376,241],{"className":18377},[240],[99,18379,18381],{"className":18380},[190],[99,18382,18384],{"className":18383,"style":11980},[194],[99,18385],{},[99,18387,18388,18391],{"style":11985},[99,18389],{"className":18390,"style":4480},[202],[99,18392],{"className":18393,"style":11993},[11992],[99,18395,18396,18399],{"style":12844},[99,18397],{"className":18398,"style":4480},[202],[99,18400,18402],{"className":18401},[207,208,209,210],[99,18403,18405,18408],{"className":18404},[173,210],[99,18406,11815],{"className":18407,"style":11939},[173,210],[99,18409,11152],{"className":18410,"style":11235},[173,177,210],[99,18412,241],{"className":18413},[240],[99,18415,18417],{"className":18416},[190],[99,18418,18420],{"className":18419,"style":12062},[194],[99,18421],{},[99,18423],{"className":18424},[254,2336],[99,18426],{"className":18427,"style":2590},[397],[99,18429,3882],{"className":18430},[2594],[99,18432],{"className":18433,"style":2590},[397],[99,18435,18437,18440,18443,18446,18515,18518,18666],{"className":18436},[160],[99,18438],{"className":18439,"style":12889},[164],[99,18441,11152],{"className":18442,"style":11235},[173,177],[99,18444],{"className":18445,"style":1813},[397],[99,18447,18449,18452],{"className":18448},[1739],[99,18450,1643],{"className":18451,"style":12903},[1739,1784,12902],[99,18453,18455],{"className":18454},[181],[99,18456,18458,18507],{"className":18457},[185,186],[99,18459,18461,18504],{"className":18460},[190],[99,18462,18464,18484],{"className":18463,"style":12916},[194],[99,18465,18466,18469],{"style":12919},[99,18467],{"className":18468,"style":203},[202],[99,18470,18472],{"className":18471},[207,208,209,210],[99,18473,18475,18478,18481],{"className":18474},[173,210],[99,18476,12592],{"className":18477,"style":12932},[173,177,210],[99,18479,313],{"className":18480},[402,210],[99,18482,1652],{"className":18483},[173,210],[99,18485,18486,18489],{"style":12941},[99,18487],{"className":18488,"style":203},[202],[99,18490,18492],{"className":18491},[207,208,209,210],[99,18493,18495,18498,18501],{"className":18494},[173,210],[99,18496,12592],{"className":18497,"style":12932},[173,177,210],[99,18499,313],{"className":18500},[402,210],[99,18502,2266],{"className":18503},[173,177,210],[99,18505,241],{"className":18506},[240],[99,18508,18510],{"className":18509},[190],[99,18511,18513],{"className":18512,"style":12975},[194],[99,18514],{},[99,18516],{"className":18517,"style":1813},[397],[99,18519,18521,18524,18663],{"className":18520},[173],[99,18522],{"className":18523},[169,2336],[99,18525,18527],{"className":18526},[11809],[99,18528,18530,18655],{"className":18529},[185,186],[99,18531,18533,18652],{"className":18532},[190],[99,18534,18536,18590,18598],{"className":18535,"style":11923},[194],[99,18537,18538,18541],{"style":11926},[99,18539],{"className":18540,"style":4480},[202],[99,18542,18544],{"className":18543},[207,208,209,210],[99,18545,18547,18550],{"className":18546},[173,210],[99,18548,11815],{"className":18549,"style":11939},[173,210],[99,18551,18553,18556],{"className":18552},[173,210],[99,18554,306],{"className":18555},[173,177,210],[99,18557,18559],{"className":18558},[181],[99,18560,18562,18582],{"className":18561},[185,186],[99,18563,18565,18579],{"className":18564},[190],[99,18566,18568],{"className":18567,"style":11958},[194],[99,18569,18570,18573],{"style":11961},[99,18571],{"className":18572,"style":2513},[202],[99,18574,18576],{"className":18575},[207,2517,2518,210],[99,18577,12592],{"className":18578,"style":12932},[173,177,210],[99,18580,241],{"className":18581},[240],[99,18583,18585],{"className":18584},[190],[99,18586,18588],{"className":18587,"style":13051},[194],[99,18589],{},[99,18591,18592,18595],{"style":11985},[99,18593],{"className":18594,"style":4480},[202],[99,18596],{"className":18597,"style":11993},[11992],[99,18599,18600,18603],{"style":11996},[99,18601],{"className":18602,"style":4480},[202],[99,18604,18606],{"className":18605},[207,208,209,210],[99,18607,18609,18612],{"className":18608},[173,210],[99,18610,11815],{"className":18611,"style":11939},[173,210],[99,18613,18615,18618],{"className":18614},[173,210],[99,18616,2263],{"className":18617},[173,177,210],[99,18619,18621],{"className":18620},[181],[99,18622,18624,18644],{"className":18623},[185,186],[99,18625,18627,18641],{"className":18626},[190],[99,18628,18630],{"className":18629,"style":12030},[194],[99,18631,18632,18635],{"style":11961},[99,18633],{"className":18634,"style":2513},[202],[99,18636,18638],{"className":18637},[207,2517,2518,210],[99,18639,2266],{"className":18640},[173,177,210],[99,18642,241],{"className":18643},[240],[99,18645,18647],{"className":18646},[190],[99,18648,18650],{"className":18649,"style":11980},[194],[99,18651],{},[99,18653,241],{"className":18654},[240],[99,18656,18658],{"className":18657},[190],[99,18659,18661],{"className":18660,"style":13125},[194],[99,18662],{},[99,18664],{"className":18665},[254,2336],[99,18667,18669,18672,18811],{"className":18668},[173],[99,18670],{"className":18671},[169,2336],[99,18673,18675],{"className":18674},[11809],[99,18676,18678,18803],{"className":18677},[185,186],[99,18679,18681,18800],{"className":18680},[190],[99,18682,18684,18738,18746],{"className":18683,"style":13149},[194],[99,18685,18686,18689],{"style":11926},[99,18687],{"className":18688,"style":4480},[202],[99,18690,18692],{"className":18691},[207,208,209,210],[99,18693,18695,18698],{"className":18694},[173,210],[99,18696,11815],{"className":18697,"style":11939},[173,210],[99,18699,18701,18704],{"className":18700},[173,210],[99,18702,1278],{"className":18703},[173,177,210],[99,18705,18707],{"className":18706},[181],[99,18708,18710,18730],{"className":18709},[185,186],[99,18711,18713,18727],{"className":18712},[190],[99,18714,18716],{"className":18715,"style":11958},[194],[99,18717,18718,18721],{"style":11961},[99,18719],{"className":18720,"style":2513},[202],[99,18722,18724],{"className":18723},[207,2517,2518,210],[99,18725,131],{"className":18726},[173,177,210],[99,18728,241],{"className":18729},[240],[99,18731,18733],{"className":18732},[190],[99,18734,18736],{"className":18735,"style":11980},[194],[99,18737],{},[99,18739,18740,18743],{"style":11985},[99,18741],{"className":18742,"style":4480},[202],[99,18744],{"className":18745,"style":11993},[11992],[99,18747,18748,18751],{"style":13214},[99,18749],{"className":18750,"style":4480},[202],[99,18752,18754],{"className":18753},[207,208,209,210],[99,18755,18757,18760],{"className":18756},[173,210],[99,18758,11815],{"className":18759,"style":11939},[173,210],[99,18761,18763,18766],{"className":18762},[173,210],[99,18764,306],{"className":18765},[173,177,210],[99,18767,18769],{"className":18768},[181],[99,18770,18772,18792],{"className":18771},[185,186],[99,18773,18775,18789],{"className":18774},[190],[99,18776,18778],{"className":18777,"style":11958},[194],[99,18779,18780,18783],{"style":11961},[99,18781],{"className":18782,"style":2513},[202],[99,18784,18786],{"className":18785},[207,2517,2518,210],[99,18787,12592],{"className":18788,"style":12932},[173,177,210],[99,18790,241],{"className":18791},[240],[99,18793,18795],{"className":18794},[190],[99,18796,18798],{"className":18797,"style":13051},[194],[99,18799],{},[99,18801,241],{"className":18802},[240],[99,18804,18806],{"className":18805},[190],[99,18807,18809],{"className":18808,"style":12062},[194],[99,18810],{},[99,18812],{"className":18813},[254,2336],[67,18815,18816,18818,18819,10792,18869,1256],{},[76,18817,13685],{}," It is worthy of noticing that the superscript of the summation has been changed from 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between the chemical potential and the diffusion potential",[67,22838,22839],{},"Diffusion potential is one of the most important variables in phase-field modeling. Mathematically, it should be defined as the partial derivative of the mole Gibbs energy.",[67,22841,22842,22844],{},[76,22843,13685],{}," partial derivative of the mole Gibbs energy and the partial quantity of the Gibbs energy are two completely different things.",[67,22846,22847],{},"Considering that the mole Gibbs energy is described with those independent composition variables,",[67,22849,22850],{},[99,22851,22853,22919],{"className":22852},[102],[99,22854,22856],{"className":22855},[106],[108,22857,22858],{"xmlns":110},[112,22859,22860,22916],{},[115,22861,22862,22868,22870,22876,22878,22884,22886,22892,22894,22896,22898,22900,22902,22914],{},[302,22863,22864,22866],{},[126,22865,2263],{},[126,22867,2266],{},[118,22869,313],{},[302,22871,22872,22874],{},[126,22873,2263],{},[126,22875,2266],{},[118,22877,2813],{"stretchy":120},[302,22879,22880,22882],{},[126,22881,306],{},[142,22883,1652],{},[118,22885,140],{"separator":139},[302,22887,22888,22890],{},[126,22889,306],{},[142,22891,10911],{},[118,22893,140],{"separator":139},[126,22895,1256],{"mathvariant":2257},[126,22897,1256],{"mathvariant":2257},[126,22899,1256],{"mathvariant":2257},[118,22901,140],{"separator":139},[302,22903,22904,22906],{},[126,22905,306],{},[115,22907,22908,22910,22912],{},[126,22909,2266],{},[118,22911,2254],{},[142,22913,1652],{},[118,22915,2846],{"stretchy":120},[149,22917,22918],{"encoding":151},"G_m = G_m(x_1, x_2, ..., x_{m-1})",[99,22920,22922,22977],{"className":22921,"ariaHidden":139},[156],[99,22923,22925,22928,22968,22971,22974],{"className":22924},[160],[99,22926],{"className":22927,"style":11510},[164],[99,22929,22931,22934],{"className":22930},[173],[99,22932,2263],{"className":22933},[173,177],[99,22935,22937],{"className":22936},[181],[99,22938,22940,22960],{"className":22939},[185,186],[99,22941,22943,22957],{"className":22942},[190],[99,22944,22946],{"className":22945,"style":11269},[194],[99,22947,22948,22951],{"style":369},[99,22949],{"className":22950,"style":203},[202],[99,22952,22954],{"className":22953},[207,208,209,210],[99,22955,2266],{"className":22956},[173,177,210],[99,22958,241],{"className":22959},[240],[99,22961,22963],{"className":22962},[190],[99,22964,22966],{"className":22965,"style":388},[194],[99,22967],{},[99,22969],{"className":22970,"style":398},[397],[99,22972,313],{"className":22973},[402],[99,22975],{"className":22976,"style":398},[397],[99,22978,22980,22983,23023,23026,23066,23069,23072,23112,23115,23118,23121,23124,23127,23176],{"className":22979},[160],[99,22981],{"className":22982,"style":344},[164],[99,22984,22986,22989],{"className":22985},[173],[99,22987,2263],{"className":22988},[173,177],[99,22990,22992],{"className":22991},[181],[99,22993,22995,23015],{"className":22994},[185,186],[99,22996,22998,23012],{"className":22997},[190],[99,22999,23001],{"className":23000,"style":11269},[194],[99,23002,23003,23006],{"style":369},[99,23004],{"className":23005,"style":203},[202],[99,23007,23009],{"className":23008},[207,208,209,210],[99,23010,2266],{"className":23011},[173,177,210],[99,23013,241],{"className":23014},[240],[99,23016,23018],{"className":23017},[190],[99,23019,23021],{"className":23020,"style":388},[194],[99,23022],{},[99,23024,2813],{"className":23025},[169],[99,23027,23029,23032],{"className":23028},[173],[99,23030,306],{"className":23031},[173,177],[99,23033,23035],{"className":23034},[181],[99,23036,23038,23058],{"className":23037},[185,186],[99,23039,23041,23055],{"className":23040},[190],[99,23042,23044],{"className":23043,"style":10991},[194],[99,23045,23046,23049],{"style":369},[99,23047],{"className":23048,"style":203},[202],[99,23050,23052],{"className":23051},[207,208,209,210],[99,23053,1652],{"className":23054},[173,210],[99,23056,241],{"className":23057},[240],[99,23059,23061],{"className":23060},[190],[99,23062,23064],{"className":23063,"style":388},[194],[99,23065],{},[99,23067,140],{"className":23068},[233],[99,23070],{"className":23071,"style":1813},[397],[99,23073,23075,23078],{"className":23074},[173],[99,23076,306],{"className":23077},[173,177],[99,23079,23081],{"className":23080},[181],[99,23082,23084,23104],{"className":23083},[185,186],[99,23085,23087,23101],{"className":23086},[190],[99,23088,23090],{"className":23089,"style":10991},[194],[99,23091,23092,23095],{"style":369},[99,23093],{"className":23094,"style":203},[202],[99,23096,23098],{"className":23097},[207,208,209,210],[99,23099,10911],{"className":23100},[173,210],[99,23102,241],{"className":23103},[240],[99,23105,23107],{"className":23106},[190],[99,23108,23110],{"className":23109,"style":388},[194],[99,23111],{},[99,23113,140],{"className":23114},[233],[99,23116],{"className":23117,"style":1813},[397],[99,23119,11069],{"className":23120},[173],[99,23122,140],{"className":23123},[233],[99,23125],{"className":23126,"style":1813},[397],[99,23128,23130,23133],{"className":23129},[173],[99,23131,306],{"className":23132},[173,177],[99,23134,23136],{"className":23135},[181],[99,23137,23139,23168],{"className":23138},[185,186],[99,23140,23142,23165],{"className":23141},[190],[99,23143,23145],{"className":23144,"style":10991},[194],[99,23146,23147,23150],{"style":369},[99,23148],{"className":23149,"style":203},[202],[99,23151,23153],{"className":23152},[207,208,209,210],[99,23154,23156,23159,23162],{"className":23155},[173,210],[99,23157,2266],{"className":23158},[173,177,210],[99,23160,2254],{"className":23161},[2594,210],[99,23163,1652],{"className":23164},[173,210],[99,23166,241],{"className":23167},[240],[99,23169,23171],{"className":23170},[190],[99,23172,23174],{"className":23173,"style":11123},[194],[99,23175],{},[99,23177,2846],{"className":23178},[254],[67,23180,23181,23182,23210,23211,23239],{},"the diffusion potential of the ",[99,23183,23185,23198],{"className":23184},[102],[99,23186,23188],{"className":23187},[106],[108,23189,23190],{"xmlns":110},[112,23191,23192,23196],{},[115,23193,23194],{},[126,23195,131],{},[149,23197,131],{"encoding":151},[99,23199,23201],{"className":23200,"ariaHidden":139},[156],[99,23202,23204,23207],{"className":23203},[160],[99,23205],{"className":23206,"style":11649},[164],[99,23208,131],{"className":23209},[173,177],"-th component with respect to ",[99,23212,23214,23227],{"className":23213},[102],[99,23215,23217],{"className":23216},[106],[108,23218,23219],{"xmlns":110},[112,23220,23221,23225],{},[115,23222,23223],{},[126,23224,2266],{},[149,23226,2266],{"encoding":151},[99,23228,23230],{"className":23229,"ariaHidden":139},[156],[99,23231,23233,23236],{"className":23232},[160],[99,23234],{"className":23235,"style":282},[164],[99,23237,2266],{"className":23238},[173,177],"-th component is",[67,23241,23242],{},[99,23243,23245,23291],{"className":23244},[102],[99,23246,23248],{"className":23247},[106],[108,23249,23250],{"xmlns":110},[112,23251,23252,23288],{},[115,23253,23254,23264,23266],{},[302,23255,23256,23262],{},[3934,23257,23258,23260],{"accent":139},[126,23259,128],{},[118,23261,3940],{},[126,23263,131],{},[118,23265,313],{},[11809,23267,23268,23278],{},[115,23269,23270,23272],{},[126,23271,11815],{"mathvariant":2257},[302,23273,23274,23276],{},[126,23275,2263],{},[126,23277,2266],{},[115,23279,23280,23282],{},[126,23281,11815],{"mathvariant":2257},[302,23283,23284,23286],{},[126,23285,306],{},[126,23287,131],{},[149,23289,23290],{"encoding":151},"\\tilde \\mu_i = \\frac{\\partial G_m}{\\partial x_i}",[99,23292,23294,23389],{"className":23293,"ariaHidden":139},[156],[99,23295,23297,23301,23380,23383,23386],{"className":23296},[160],[99,23298],{"className":23299,"style":23300},[164],"height:0.8623em;vertical-align:-0.1944em;",[99,23302,23304,23346],{"className":23303},[173],[99,23305,23307],{"className":23306},[173,4463],[99,23308,23310,23338],{"className":23309},[185,186],[99,23311,23313,23335],{"className":23312},[190],[99,23314,23316,23324],{"className":23315,"style":4473},[194],[99,23317,23318,23321],{"style":4476},[99,23319],{"className":23320,"style":4480},[202],[99,23322,128],{"className":23323},[173,177],[99,23325,23326,23329],{"style":4486},[99,23327],{"className":23328,"style":4480},[202],[99,23330,23332],{"className":23331,"style":4494},[4493],[99,23333,3940],{"className":23334},[173],[99,23336,241],{"className":23337},[240],[99,23339,23341],{"className":23340},[190],[99,23342,23344],{"className":23343,"style":4507},[194],[99,23345],{},[99,23347,23349],{"className":23348},[181],[99,23350,23352,23372],{"className":23351},[185,186],[99,23353,23355,23369],{"className":23354},[190],[99,23356,23358],{"className":23357,"style":366},[194],[99,23359,23360,23363],{"style":369},[99,23361],{"className":23362,"style":203},[202],[99,23364,23366],{"className":23365},[207,208,209,210],[99,23367,131],{"className":23368},[173,177,210],[99,23370,241],{"className":23371},[240],[99,23373,23375],{"className":23374},[190],[99,23376,23378],{"className":23377,"style":388},[194],[99,23379],{},[99,23381],{"className":23382,"style":398},[397],[99,23384,313],{"className":23385},[402],[99,23387],{"className":23388,"style":398},[397],[99,23390,23392,23395],{"className":23391},[160],[99,23393],{"className":23394,"style":11904},[164],[99,23396,23398,23401,23540],{"className":23397},[173],[99,23399],{"className":23400},[169,2336],[99,23402,23404],{"className":23403},[11809],[99,23405,23407,23532],{"className":23406},[185,186],[99,23408,23410,23529],{"className":23409},[190],[99,23411,23413,23467,23475],{"className":23412,"style":11923},[194],[99,23414,23415,23418],{"style":11926},[99,23416],{"className":23417,"style":4480},[202],[99,23419,23421],{"className":23420},[207,208,209,210],[99,23422,23424,23427],{"className":23423},[173,210],[99,23425,11815],{"className":23426,"style":11939},[173,210],[99,23428,23430,23433],{"className":23429},[173,210],[99,23431,306],{"className":23432},[173,177,210],[99,23434,23436],{"className":23435},[181],[99,23437,23439,23459],{"className":23438},[185,186],[99,23440,23442,23456],{"className":23441},[190],[99,23443,23445],{"className":23444,"style":11958},[194],[99,23446,23447,23450],{"style":11961},[99,23448],{"className":23449,"style":2513},[202],[99,23451,23453],{"className":23452},[207,2517,2518,210],[99,23454,131],{"className":23455},[173,177,210],[99,23457,241],{"className":23458},[240],[99,23460,23462],{"className":23461},[190],[99,23463,23465],{"className":23464,"style":11980},[194],[99,23466],{},[99,23468,23469,23472],{"style":11985},[99,23470],{"className":23471,"style":4480},[202],[99,23473],{"className":23474,"style":11993},[11992],[99,23476,23477,23480],{"style":11996},[99,23478],{"className":23479,"style":4480},[202],[99,23481,23483],{"className":23482},[207,208,209,210],[99,23484,23486,23489],{"className":23485},[173,210],[99,23487,11815],{"className":23488,"style":11939},[173,210],[99,23490,23492,23495],{"className":23491},[173,210],[99,23493,2263],{"className":23494},[173,177,210],[99,23496,23498],{"className":23497},[181],[99,23499,23501,23521],{"className":23500},[185,186],[99,23502,23504,23518],{"className":23503},[190],[99,23505,23507],{"className":23506,"style":12030},[194],[99,23508,23509,23512],{"style":11961},[99,23510],{"className":23511,"style":2513},[202],[99,23513,23515],{"className":23514},[207,2517,2518,210],[99,23516,2266],{"className":23517},[173,177,210],[99,23519,241],{"className":23520},[240],[99,23522,23524],{"className":23523},[190],[99,23525,23527],{"className":23526,"style":11980},[194],[99,23528],{},[99,23530,241],{"className":23531},[240],[99,23533,23535],{"className":23534},[190],[99,23536,23538],{"className":23537,"style":12062},[194],[99,23539],{},[99,23541],{"className":23542},[254,2336],[67,23544,23545,23547],{},[76,23546,13685],{}," I am writing this to tell that, diffusion potential, is state variable of the solute, which means that a solvent component always exists in this context.",[67,23549,23550],{},"The equation above is really convenient when you have a description of the mole Gibbs energy related to compositions of the solute components. However, CALPHAD technique has adopted the second strategy to demonstrate the relationship between the mole Gibbs energy and composition, which is",[67,23552,23553],{},[99,23554,23556,23632],{"className":23555},[102],[99,23557,23559],{"className":23558},[106],[108,23560,23561],{"xmlns":110},[112,23562,23563,23629],{},[115,23564,23565,23571,23573,23579,23581,23587,23589,23595,23597,23599,23601,23603,23605,23617,23619,23625,23627],{},[302,23566,23567,23569],{},[126,23568,2263],{},[126,23570,2266],{},[118,23572,313],{},[302,23574,23575,23577],{},[126,23576,2263],{},[126,23578,2266],{},[118,23580,2813],{"stretchy":120},[302,23582,23583,23585],{},[126,23584,306],{},[142,23586,1652],{},[118,23588,140],{"separator":139},[302,23590,23591,23593],{},[126,23592,306],{},[142,23594,10911],{},[118,23596,140],{"separator":139},[126,23598,1256],{"mathvariant":2257},[126,23600,1256],{"mathvariant":2257},[126,23602,1256],{"mathvariant":2257},[118,23604,140],{"separator":139},[302,23606,23607,23609],{},[126,23608,306],{},[115,23610,23611,23613,23615],{},[126,23612,2266],{},[118,23614,2254],{},[142,23616,1652],{},[118,23618,140],{"separator":139},[302,23620,23621,23623],{},[126,23622,306],{},[126,23624,2266],{},[118,23626,2846],{"stretchy":120},[118,23628,140],{"separator":139},[149,23630,23631],{"encoding":151},"G_m = G_m(x_1, x_2, ..., x_{m-1}, x_m),",[99,23633,23635,23690],{"className":23634,"ariaHidden":139},[156],[99,23636,23638,23641,23681,23684,23687],{"className":23637},[160],[99,23639],{"className":23640,"style":11510},[164],[99,23642,23644,23647],{"className":23643},[173],[99,23645,2263],{"className":23646},[173,177],[99,23648,23650],{"className":23649},[181],[99,23651,23653,23673],{"className":23652},[185,186],[99,23654,23656,23670],{"className":23655},[190],[99,23657,23659],{"className":23658,"style":11269},[194],[99,23660,23661,23664],{"style":369},[99,23662],{"className":23663,"style":203},[202],[99,23665,23667],{"className":23666},[207,208,209,210],[99,23668,2266],{"className":23669},[173,177,210],[99,23671,241],{"className":23672},[240],[99,23674,23676],{"className":23675},[190],[99,23677,23679],{"className":23678,"style":388},[194],[99,23680],{},[99,23682],{"className":23683,"style":398},[397],[99,23685,313],{"className":23686},[402],[99,23688],{"className":23689,"style":398},[397],[99,23691,23693,23696,23736,23739,23779,23782,23785,23825,23828,23831,23834,23837,23840,23889,23892,23895,23935,23938],{"className":23692},[160],[99,23694],{"className":23695,"style":344},[164],[99,23697,23699,23702],{"className":23698},[173],[99,23700,2263],{"className":23701},[173,177],[99,23703,23705],{"className":23704},[181],[99,23706,23708,23728],{"className":23707},[185,186],[99,23709,23711,23725],{"className":23710},[190],[99,23712,23714],{"className":23713,"style":11269},[194],[99,23715,23716,23719],{"style":369},[99,23717],{"className":23718,"style":203},[202],[99,23720,23722],{"className":23721},[207,208,209,210],[99,23723,2266],{"className":23724},[173,177,210],[99,23726,241],{"className":23727},[240],[99,23729,23731],{"className":23730},[190],[99,23732,23734],{"className":23733,"style":388},[194],[99,23735],{},[99,23737,2813],{"className":23738},[169],[99,23740,23742,23745],{"className":23741},[173],[99,23743,306],{"className":23744},[173,177],[99,23746,23748],{"className":23747},[181],[99,23749,23751,23771],{"className":23750},[185,186],[99,23752,23754,23768],{"className":23753},[190],[99,23755,23757],{"className":23756,"style":10991},[194],[99,23758,23759,23762],{"style":369},[99,23760],{"className":23761,"style":203},[202],[99,23763,23765],{"className":23764},[207,208,209,210],[99,23766,1652],{"className":23767},[173,210],[99,23769,241],{"className":23770},[240],[99,23772,23774],{"className":23773},[190],[99,23775,23777],{"className":23776,"style":388},[194],[99,23778],{},[99,23780,140],{"className":23781},[233],[99,23783],{"className":23784,"style":1813},[397],[99,23786,23788,23791],{"className":23787},[173],[99,23789,306],{"className":23790},[173,177],[99,23792,23794],{"className":23793},[181],[99,23795,23797,23817],{"className":23796},[185,186],[99,23798,23800,23814],{"className":23799},[190],[99,23801,23803],{"className":23802,"style":10991},[194],[99,23804,23805,23808],{"style":369},[99,23806],{"className":23807,"style":203},[202],[99,23809,23811],{"className":23810},[207,208,209,210],[99,23812,10911],{"className":23813},[173,210],[99,23815,241],{"className":23816},[240],[99,23818,23820],{"className":23819},[190],[99,23821,23823],{"className":23822,"style":388},[194],[99,23824],{},[99,23826,140],{"className":23827},[233],[99,23829],{"className":23830,"style":1813},[397],[99,23832,11069],{"className":23833},[173],[99,23835,140],{"className":23836},[233],[99,23838],{"className":23839,"style":1813},[397],[99,23841,23843,23846],{"className":23842},[173],[99,23844,306],{"className":23845},[173,177],[99,23847,23849],{"className":23848},[181],[99,23850,23852,23881],{"className":23851},[185,186],[99,23853,23855,23878],{"className":23854},[190],[99,23856,23858],{"className":23857,"style":10991},[194],[99,23859,23860,23863],{"style":369},[99,23861],{"className":23862,"style":203},[202],[99,23864,23866],{"className":23865},[207,208,209,210],[99,23867,23869,23872,23875],{"className":23868},[173,210],[99,23870,2266],{"className":23871},[173,177,210],[99,23873,2254],{"className":23874},[2594,210],[99,23876,1652],{"className":23877},[173,210],[99,23879,241],{"className":23880},[240],[99,23882,23884],{"className":23883},[190],[99,23885,23887],{"className":23886,"style":11123},[194],[99,23888],{},[99,23890,140],{"className":23891},[233],[99,23893],{"className":23894,"style":1813},[397],[99,23896,23898,23901],{"className":23897},[173],[99,23899,306],{"className":23900},[173,177],[99,23902,23904],{"className":23903},[181],[99,23905,23907,23927],{"className":23906},[185,186],[99,23908,23910,23924],{"className":23909},[190],[99,23911,23913],{"className":23912,"style":11269},[194],[99,23914,23915,23918],{"style":369},[99,23916],{"className":23917,"style":203},[202],[99,23919,23921],{"className":23920},[207,208,209,210],[99,23922,2266],{"className":23923},[173,177,210],[99,23925,241],{"className":23926},[240],[99,23928,23930],{"className":23929},[190],[99,23931,23933],{"className":23932,"style":388},[194],[99,23934],{},[99,23936,2846],{"className":23937},[254],[99,23939,140],{"className":23940},[233],[67,23942,16955],{},[67,23944,23945],{},[99,23946,23948,24007],{"className":23947},[102],[99,23949,23951],{"className":23950},[106],[108,23952,23953],{"xmlns":110},[112,23954,23955,24005],{},[115,23956,23957,23963,23965,23971,23973,23975,23977,23979,23981,23993,23995,24001,24003],{},[302,23958,23959,23961],{},[126,23960,306],{},[142,23962,1652],{},[118,23964,3882],{},[302,23966,23967,23969],{},[126,23968,306],{},[142,23970,10911],{},[118,23972,3882],{},[126,23974,1256],{"mathvariant":2257},[126,23976,1256],{"mathvariant":2257},[126,23978,1256],{"mathvariant":2257},[118,23980,3882],{},[302,23982,23983,23985],{},[126,23984,306],{},[115,23986,23987,23989,23991],{},[126,23988,2266],{},[118,23990,2254],{},[142,23992,1652],{},[118,23994,3882],{},[302,23996,23997,23999],{},[126,23998,306],{},[126,24000,2266],{},[118,24002,313],{},[142,24004,17018],{},[149,24006,17021],{"encoding":151},[99,24008,24010,24065,24120,24138,24202,24257],{"className":24009,"ariaHidden":139},[156],[99,24011,24013,24016,24056,24059,24062],{"className":24012},[160],[99,24014],{"className":24015,"style":17031},[164],[99,24017,24019,24022],{"className":24018},[173],[99,24020,306],{"className":24021},[173,177],[99,24023,24025],{"className":24024},[181],[99,24026,24028,24048],{"className":24027},[185,186],[99,24029,24031,24045],{"className":24030},[190],[99,24032,24034],{"className":24033,"style":10991},[194],[99,24035,24036,24039],{"style":369},[99,24037],{"className":24038,"style":203},[202],[99,24040,24042],{"className":24041},[207,208,209,210],[99,24043,1652],{"className":24044},[173,210],[99,24046,241],{"className":24047},[240],[99,24049,24051],{"className":24050},[190],[99,24052,24054],{"className":24053,"style":388},[194],[99,24055],{},[99,24057],{"className":24058,"style":2590},[397],[99,24060,3882],{"className":24061},[2594],[99,24063],{"className":24064,"style":2590},[397],[99,24066,24068,24071,24111,24114,24117],{"className":24067},[160],[99,24069],{"className":24070,"style":17031},[164],[99,24072,24074,24077],{"className":24073},[173],[99,24075,306],{"className":24076},[173,177],[99,24078,24080],{"className":24079},[181],[99,24081,24083,24103],{"className":24082},[185,186],[99,24084,24086,24100],{"className":24085},[190],[99,24087,24089],{"className":24088,"style":10991},[194],[99,24090,24091,24094],{"style":369},[99,24092],{"className":24093,"style":203},[202],[99,24095,24097],{"className":24096},[207,208,209,210],[99,24098,10911],{"className":24099},[173,210],[99,24101,241],{"className":24102},[240],[99,24104,24106],{"className":24105},[190],[99,24107,24109],{"className":24108,"style":388},[194],[99,24110],{},[99,24112],{"className":24113,"style":2590},[397],[99,24115,3882],{"className":24116},[2594],[99,24118],{"className":24119,"style":2590},[397],[99,24121,24123,24126,24129,24132,24135],{"className":24122},[160],[99,24124],{"className":24125,"style":10823},[164],[99,24127,11069],{"className":24128},[173],[99,24130],{"className":24131,"style":2590},[397],[99,24133,3882],{"className":24134},[2594],[99,24136],{"className":24137,"style":2590},[397],[99,24139,24141,24144,24193,24196,24199],{"className":24140},[160],[99,24142],{"className":24143,"style":17160},[164],[99,24145,24147,24150],{"className":24146},[173],[99,24148,306],{"className":24149},[173,177],[99,24151,24153],{"className":24152},[181],[99,24154,24156,24185],{"className":24155},[185,186],[99,24157,24159,24182],{"className":24158},[190],[99,24160,24162],{"className":24161,"style":10991},[194],[99,24163,24164,24167],{"style":369},[99,24165],{"className":24166,"style":203},[202],[99,24168,24170],{"className":24169},[207,208,209,210],[99,24171,24173,24176,24179],{"className":24172},[173,210],[99,24174,2266],{"className":24175},[173,177,210],[99,24177,2254],{"className":24178},[2594,210],[99,24180,1652],{"className":24181},[173,210],[99,24183,241],{"className":24184},[240],[99,24186,24188],{"className":24187},[190],[99,24189,24191],{"className":24190,"style":11123},[194],[99,24192],{},[99,24194],{"className":24195,"style":2590},[397],[99,24197,3882],{"className":24198},[2594],[99,24200],{"className":24201,"style":2590},[397],[99,24203,24205,24208,24248,24251,24254],{"className":24204},[160],[99,24206],{"className":24207,"style":11582},[164],[99,24209,24211,24214],{"className":24210},[173],[99,24212,306],{"className":24213},[173,177],[99,24215,24217],{"className":24216},[181],[99,24218,24220,24240],{"className":24219},[185,186],[99,24221,24223,24237],{"className":24222},[190],[99,24224,24226],{"className":24225,"style":11269},[194],[99,24227,24228,24231],{"style":369},[99,24229],{"className":24230,"style":203},[202],[99,24232,24234],{"className":24233},[207,208,209,210],[99,24235,2266],{"className":24236},[173,177,210],[99,24238,241],{"className":24239},[240],[99,24241,24243],{"className":24242},[190],[99,24244,24246],{"className":24245,"style":388},[194],[99,24247],{},[99,24249],{"className":24250,"style":398},[397],[99,24252,313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there is no straight-forward way to compute the derivative of such a formula of the Gibbs energy, as a constraint has been imposed on the function.",[67,24270,24271],{},"Fortunately, we have another definition of the mole Gibbs energy,",[67,24273,24274],{},[99,24275,24277,24371],{"className":24276},[102],[99,24278,24280],{"className":24279},[106],[108,24281,24282],{"xmlns":110},[112,24283,24284,24368],{},[115,24285,24286,24292,24294,24300,24306,24308,24314,24320,24322,24324,24326,24328,24330,24342,24354,24356,24362],{},[302,24287,24288,24290],{},[126,24289,2263],{},[126,24291,2266],{},[118,24293,313],{},[302,24295,24296,24298],{},[126,24297,306],{},[142,24299,1652],{},[302,24301,24302,24304],{},[126,24303,128],{},[142,24305,1652],{},[118,24307,3882],{},[302,24309,24310,24312],{},[126,24311,306],{},[142,24313,10911],{},[302,24315,24316,24318],{},[126,24317,128],{},[142,24319,10911],{},[118,24321,3882],{},[126,24323,1256],{"mathvariant":2257},[126,24325,1256],{"mathvariant":2257},[126,24327,1256],{"mathvariant":2257},[118,24329,3882],{},[302,24331,24332,24334],{},[126,24333,306],{},[115,24335,24336,24338,24340],{},[126,24337,2266],{},[118,24339,2254],{},[142,24341,1652],{},[302,24343,24344,24346],{},[126,24345,128],{},[115,24347,24348,24350,24352],{},[126,24349,2266],{},[118,24351,2254],{},[142,24353,1652],{},[118,24355,3882],{},[302,24357,24358,24360],{},[126,24359,306],{},[126,24361,2266],{},[302,24363,24364,24366],{},[126,24365,128],{},[126,24367,2266],{},[149,24369,24370],{"encoding":151},"G_m = x_1 \\mu_1 + x_2 \\mu_2 + ... + x_{m-1} \\mu_{m-1} + x_{m} \\mu_{m}",[99,24372,24374,24429,24525,24620,24638,24751],{"className":24373,"ariaHidden":139},[156],[99,24375,24377,24380,24420,24423,24426],{"className":24376},[160],[99,24378],{"className":24379,"style":11510},[164],[99,24381,24383,24386],{"className":24382},[173],[99,24384,2263],{"className":24385},[173,177],[99,24387,24389],{"className":24388},[181],[99,24390,24392,24412],{"className":24391},[185,186],[99,24393,24395,24409],{"className":24394},[190],[99,24396,24398],{"className":24397,"style":11269},[194],[99,24399,24400,24403],{"style":369},[99,24401],{"className":24402,"style":203},[202],[99,24404,24406],{"className":24405},[207,208,209,210],[99,24407,2266],{"className":24408},[173,177,210],[99,24410,241],{"className":24411},[240],[99,24413,24415],{"className":24414},[190],[99,24416,24418],{"className":24417,"style":388},[194],[99,24419],{},[99,24421],{"className":24422,"style":398},[397],[99,24424,313],{"className":24425},[402],[99,24427],{"className":24428,"style":398},[397],[99,24430,24432,24436,24476,24516,24519,24522],{"className":24431},[160],[99,24433],{"className":24434,"style":24435},[164],"height:0.7778em;vertical-align:-0.1944em;",[99,24437,24439,24442],{"className":24438},[173],[99,24440,306],{"className":24441},[173,177],[99,24443,24445],{"className":24444},[181],[99,24446,24448,24468],{"className":24447},[185,186],[99,24449,24451,24465],{"className":24450},[190],[99,24452,24454],{"className":24453,"style":10991},[194],[99,24455,24456,24459],{"style":369},[99,24457],{"className":24458,"style":203},[202],[99,24460,24462],{"className":24461},[207,208,209,210],[99,24463,1652],{"className":24464},[173,210],[99,24466,241],{"className":24467},[240],[99,24469,24471],{"className":24470},[190],[99,24472,24474],{"className":24473,"style":388},[194],[99,24475],{},[99,24477,24479,24482],{"className":24478},[173],[99,24480,128],{"className":24481},[173,177],[99,24483,24485],{"className":24484},[181],[99,24486,24488,24508],{"className":24487},[185,186],[99,24489,24491,24505],{"className":24490},[190],[99,24492,24494],{"className":24493,"style":10991},[194],[99,24495,24496,24499],{"style":369},[99,24497],{"className":24498,"style":203},[202],[99,24500,24502],{"className":24501},[207,208,209,210],[99,24503,1652],{"className":24504},[173,210],[99,24506,241],{"className":24507},[240],[99,24509,24511],{"className":24510},[190],[99,24512,24514],{"className":24513,"style":388},[194],[99,24515],{},[99,24517],{"className":24518,"style":2590},[397],[99,24520,3882],{"className":24521},[2594],[99,24523],{"className":24524,"style":2590},[397],[99,24526,24528,24531,24571,24611,24614,24617],{"className":24527},[160],[99,24529],{"className":24530,"style":24435},[164],[99,24532,24534,24537],{"className":24533},[173],[99,24535,306],{"className":24536},[173,177],[99,24538,24540],{"className":24539},[181],[99,24541,24543,24563],{"className":24542},[185,186],[99,24544,24546,24560],{"className":24545},[190],[99,24547,24549],{"className":24548,"style":10991},[194],[99,24550,24551,24554],{"style":369},[99,24552],{"className":24553,"style":203},[202],[99,24555,24557],{"className":24556},[207,208,209,210],[99,24558,10911],{"className":24559},[173,210],[99,24561,241],{"className":24562},[240],[99,24564,24566],{"className":24565},[190],[99,24567,24569],{"className":24568,"style":388},[194],[99,24570],{},[99,24572,24574,24577],{"className":24573},[173],[99,24575,128],{"className":24576},[173,177],[99,24578,24580],{"className":24579},[181],[99,24581,24583,24603],{"className":24582},[185,186],[99,24584,24586,24600],{"className":24585},[190],[99,24587,24589],{"className":24588,"style":10991},[194],[99,24590,24591,24594],{"style":369},[99,24592],{"className":24593,"style":203},[202],[99,24595,24597],{"className":24596},[207,208,209,210],[99,24598,10911],{"className":24599},[173,210],[99,24601,241],{"className":24602},[240],[99,24604,24606],{"className":24605},[190],[99,24607,24609],{"className":24608,"style":388},[194],[99,24610],{},[99,24612],{"className":24613,"style":2590},[397],[99,24615,3882],{"className":24616},[2594],[99,24618],{"className":24619,"style":2590},[397],[99,24621,24623,24626,24629,24632,24635],{"className":24622},[160],[99,24624],{"className":24625,"style":10823},[164],[99,24627,11069],{"className":24628},[173],[99,24630],{"className":24631,"style":2590},[397],[99,24633,3882],{"className":24634},[2594],[99,24636],{"className":24637,"style":2590},[397],[99,24639,24641,24644,24693,24742,24745,24748],{"className":24640},[160],[99,24642],{"className":24643,"style":17160},[164],[99,24645,24647,24650],{"className":24646},[173],[99,24648,306],{"className":24649},[173,177],[99,24651,24653],{"className":24652},[181],[99,24654,24656,24685],{"className":24655},[185,186],[99,24657,24659,24682],{"className":24658},[190],[99,24660,24662],{"className":24661,"style":10991},[194],[99,24663,24664,24667],{"style":369},[99,24665],{"className":24666,"style":203},[202],[99,24668,24670],{"className":24669},[207,208,209,210],[99,24671,24673,24676,24679],{"className":24672},[173,210],[99,24674,2266],{"className":24675},[173,177,210],[99,24677,2254],{"className":24678},[2594,210],[99,24680,1652],{"className":24681},[173,210],[99,24683,241],{"className":24684},[240],[99,24686,24688],{"className":24687},[190],[99,24689,24691],{"className":24690,"style":11123},[194],[99,24692],{},[99,24694,24696,24699],{"className":24695},[173],[99,24697,128],{"className":24698},[173,177],[99,24700,24702],{"className":24701},[181],[99,24703,24705,24734],{"className":24704},[185,186],[99,24706,24708,24731],{"className":24707},[190],[99,24709,24711],{"className":24710,"style":10991},[194],[99,24712,24713,24716],{"style":369},[99,24714],{"className":24715,"style":203},[202],[99,24717,24719],{"className":24718},[207,208,209,210],[99,24720,24722,24725,24728],{"className":24721},[173,210],[99,24723,2266],{"className":24724},[173,177,210],[99,24726,2254],{"className":24727},[2594,210],[99,24729,1652],{"className":24730},[173,210],[99,24732,241],{"className":24733},[240],[99,24735,24737],{"className":24736},[190],[99,24738,24740],{"className":24739,"style":11123},[194],[99,24741],{},[99,24743],{"className":24744,"style":2590},[397],[99,24746,3882],{"className":24747},[2594],[99,24749],{"className":24750,"style":2590},[397],[99,24752,24754,24757,24800],{"className":24753},[160],[99,24755],{"className":24756,"style":11848},[164],[99,24758,24760,24763],{"className":24759},[173],[99,24761,306],{"className":24762},[173,177],[99,24764,24766],{"className":24765},[181],[99,24767,24769,24792],{"className":24768},[185,186],[99,24770,24772,24789],{"className":24771},[190],[99,24773,24775],{"className":24774,"style":11269},[194],[99,24776,24777,24780],{"style":369},[99,24778],{"className":24779,"style":203},[202],[99,24781,24783],{"className":24782},[207,208,209,210],[99,24784,24786],{"className":24785},[173,210],[99,24787,2266],{"className":24788},[173,177,210],[99,24790,241],{"className":24791},[240],[99,24793,24795],{"className":24794},[190],[99,24796,24798],{"className":24797,"style":388},[194],[99,24799],{},[99,24801,24803,24806],{"className":24802},[173],[99,24804,128],{"className":24805},[173,177],[99,24807,24809],{"className":24808},[181],[99,24810,24812,24835],{"className":24811},[185,186],[99,24813,24815,24832],{"className":24814},[190],[99,24816,24818],{"className":24817,"style":11269},[194],[99,24819,24820,24823],{"style":369},[99,24821],{"className":24822,"style":203},[202],[99,24824,24826],{"className":24825},[207,208,209,210],[99,24827,24829],{"className":24828},[173,210],[99,24830,2266],{"className":24831},[173,177,210],[99,24833,241],{"className":24834},[240],[99,24836,24838],{"className":24837},[190],[99,24839,24841],{"className":24840,"style":388},[194],[99,24842],{},[67,24844,24845],{},"Apply the rule of total derivative to the equation above",[67,24847,24848],{},[99,24849,24851,24944],{"className":24850},[102],[99,24852,24854],{"className":24853},[106],[108,24855,24856],{"xmlns":110},[112,24857,24858,24941],{},[115,24859,24860,24863,24869,24871,24891,24893,24899,24905,24907,24927,24933,24935],{},[510,24861,24862],{},"d",[302,24864,24865,24867],{},[126,24866,2263],{},[126,24868,2266],{},[118,24870,313],{},[123,24872,24873,24875,24883],{},[118,24874,1643],{},[115,24876,24877,24879,24881],{},[126,24878,12592],{},[118,24880,313],{},[142,24882,1652],{},[115,24884,24885,24887,24889],{},[126,24886,12592],{},[118,24888,313],{},[126,24890,2266],{},[510,24892,24862],{},[302,24894,24895,24897],{},[126,24896,306],{},[126,24898,12592],{},[302,24900,24901,24903],{},[126,24902,128],{},[126,24904,12592],{},[118,24906,3882],{},[123,24908,24909,24911,24919],{},[118,24910,1643],{},[115,24912,24913,24915,24917],{},[126,24914,12592],{},[118,24916,313],{},[142,24918,1652],{},[115,24920,24921,24923,24925],{},[126,24922,12592],{},[118,24924,313],{},[126,24926,2266],{},[302,24928,24929,24931],{},[126,24930,306],{},[126,24932,12592],{},[510,24934,24862],{},[302,24936,24937,24939],{},[126,24938,128],{},[126,24940,12592],{},[149,24942,24943],{"encoding":151},"\\textrm{d}G_m = \\sum_{j=1}^{j=m} \\textrm{d}x_j \\mu_j + \\sum_{j=1}^{j=m} x_j \\textrm{d} \\mu_j",[99,24945,24947,25009,25183],{"className":24946,"ariaHidden":139},[156],[99,24948,24950,24954,24960,25000,25003,25006],{"className":24949},[160],[99,24951],{"className":24952,"style":24953},[164],"height:0.8444em;vertical-align:-0.15em;",[99,24955,24957],{"className":24956},[173,582],[99,24958,24862],{"className":24959},[173,586],[99,24961,24963,24966],{"className":24962},[173],[99,24964,2263],{"className":24965},[173,177],[99,24967,24969],{"className":24968},[181],[99,24970,24972,24992],{"className":24971},[185,186],[99,24973,24975,24989],{"className":24974},[190],[99,24976,24978],{"className":24977,"style":11269},[194],[99,24979,24980,24983],{"style":369},[99,24981],{"className":24982,"style":203},[202],[99,24984,24986],{"className":24985},[207,208,209,210],[99,24987,2266],{"className":24988},[173,177,210],[99,24990,241],{"className":24991},[240],[99,24993,24995],{"className":24994},[190],[99,24996,24998],{"className":24997,"style":388},[194],[99,24999],{},[99,25001],{"className":25002,"style":398},[397],[99,25004,313],{"className":25005},[402],[99,25007],{"className":25008,"style":398},[397],[99,25010,25012,25016,25085,25088,25094,25134,25174,25177,25180],{"className":25011},[160],[99,25013],{"className":25014,"style":25015},[164],"height:1.4004em;vertical-align:-0.4358em;",[99,25017,25019,25022],{"className":25018},[1739],[99,25020,1643],{"className":25021,"style":12903},[1739,1784,12902],[99,25023,25025],{"className":25024},[181],[99,25026,25028,25077],{"className":25027},[185,186],[99,25029,25031,25074],{"className":25030},[190],[99,25032,25034,25054],{"className":25033,"style":12916},[194],[99,25035,25036,25039],{"style":12919},[99,25037],{"className":25038,"style":203},[202],[99,25040,25042],{"className":25041},[207,208,209,210],[99,25043,25045,25048,25051],{"className":25044},[173,210],[99,25046,12592],{"className":25047,"style":12932},[173,177,210],[99,25049,313],{"className":25050},[402,210],[99,25052,1652],{"className":25053},[173,210],[99,25055,25056,25059],{"style":12941},[99,25057],{"className":25058,"style":203},[202],[99,25060,25062],{"className":25061},[207,208,209,210],[99,25063,25065,25068,25071],{"className":25064},[173,210],[99,25066,12592],{"className":25067,"style":12932},[173,177,210],[99,25069,313],{"className":25070},[402,210],[99,25072,2266],{"className":25073},[173,177,210],[99,25075,241],{"className":25076},[240],[99,25078,25080],{"className":25079},[190],[99,25081,25083],{"className":25082,"style":12975},[194],[99,25084],{},[99,25086],{"className":25087,"style":1813},[397],[99,25089,25091],{"className":25090},[173,582],[99,25092,24862],{"className":25093},[173,586],[99,25095,25097,25100],{"className":25096},[173],[99,25098,306],{"className":25099},[173,177],[99,25101,25103],{"className":25102},[181],[99,25104,25106,25126],{"className":25105},[185,186],[99,25107,25109,25123],{"className":25108},[190],[99,25110,25112],{"className":25111,"style":366},[194],[99,25113,25114,25117],{"style":369},[99,25115],{"className":25116,"style":203},[202],[99,25118,25120],{"className":25119},[207,208,209,210],[99,25121,12592],{"className":25122,"style":12932},[173,177,210],[99,25124,241],{"className":25125},[240],[99,25127,25129],{"className":25128},[190],[99,25130,25132],{"className":25131,"style":14436},[194],[99,25133],{},[99,25135,25137,25140],{"className":25136},[173],[99,25138,128],{"className":25139},[173,177],[99,25141,25143],{"className":25142},[181],[99,25144,25146,25166],{"className":25145},[185,186],[99,25147,25149,25163],{"className":25148},[190],[99,25150,25152],{"className":25151,"style":366},[194],[99,25153,25154,25157],{"style":369},[99,25155],{"className":25156,"style":203},[202],[99,25158,25160],{"className":25159},[207,208,209,210],[99,25161,12592],{"className":25162,"style":12932},[173,177,210],[99,25164,241],{"className":25165},[240],[99,25167,25169],{"className":25168},[190],[99,25170,25172],{"className":25171,"style":14436},[194],[99,25173],{},[99,25175],{"className":25176,"style":2590},[397],[99,25178,3882],{"className":25179},[2594],[99,25181],{"className":25182,"style":2590},[397],[99,25184,25186,25189,25258,25261,25301,25307],{"className":25185},[160],[99,25187],{"className":25188,"style":25015},[164],[99,25190,25192,25195],{"className":25191},[1739],[99,25193,1643],{"className":25194,"style":12903},[1739,1784,12902],[99,25196,25198],{"className":25197},[181],[99,25199,25201,25250],{"className":25200},[185,186],[99,25202,25204,25247],{"className":25203},[190],[99,25205,25207,25227],{"className":25206,"style":12916},[194],[99,25208,25209,25212],{"style":12919},[99,25210],{"className":25211,"style":203},[202],[99,25213,25215],{"className":25214},[207,208,209,210],[99,25216,25218,25221,25224],{"className":25217},[173,210],[99,25219,12592],{"className":25220,"style":12932},[173,177,210],[99,25222,313],{"className":25223},[402,210],[99,25225,1652],{"className":25226},[173,210],[99,25228,25229,25232],{"style":12941},[99,25230],{"className":25231,"style":203},[202],[99,25233,25235],{"className":25234},[207,208,209,210],[99,25236,25238,25241,25244],{"className":25237},[173,210],[99,25239,12592],{"className":25240,"style":12932},[173,177,210],[99,25242,313],{"className":25243},[402,210],[99,25245,2266],{"className":25246},[173,177,210],[99,25248,241],{"className":25249},[240],[99,25251,25253],{"className":25252},[190],[99,25254,25256],{"className":25255,"style":12975},[194],[99,25257],{},[99,25259],{"className":25260,"style":1813},[397],[99,25262,25264,25267],{"className":25263},[173],[99,25265,306],{"className":25266},[173,177],[99,25268,25270],{"className":25269},[181],[99,25271,25273,25293],{"className":25272},[185,186],[99,25274,25276,25290],{"className":25275},[190],[99,25277,25279],{"className":25278,"style":366},[194],[99,25280,25281,25284],{"style":369},[99,25282],{"className":25283,"style":203},[202],[99,25285,25287],{"className":25286},[207,208,209,210],[99,25288,12592],{"className":25289,"style":12932},[173,177,210],[99,25291,241],{"className":25292},[240],[99,25294,25296],{"className":25295},[190],[99,25297,25299],{"className":25298,"style":14436},[194],[99,25300],{},[99,25302,25304],{"className":25303},[173,582],[99,25305,24862],{"className":25306},[173,586],[99,25308,25310,25313],{"className":25309},[173],[99,25311,128],{"className":25312},[173,177],[99,25314,25316],{"className":25315},[181],[99,25317,25319,25339],{"className":25318},[185,186],[99,25320,25322,25336],{"className":25321},[190],[99,25323,25325],{"className":25324,"style":366},[194],[99,25326,25327,25330],{"style":369},[99,25328],{"className":25329,"style":203},[202],[99,25331,25333],{"className":25332},[207,208,209,210],[99,25334,12592],{"className":25335,"style":12932},[173,177,210],[99,25337,241],{"className":25338},[240],[99,25340,25342],{"className":25341},[190],[99,25343,25345],{"className":25344,"style":14436},[194],[99,25346],{},[67,25348,25349],{},"According to Gibbs-Duhem equation, we have",[67,25351,25352],{},[99,25353,25355,25405],{"className":25354},[102],[99,25356,25358],{"className":25357},[106],[108,25359,25360],{"xmlns":110},[112,25361,25362,25402],{},[115,25363,25364,25384,25390,25392,25398,25400],{},[123,25365,25366,25368,25376],{},[118,25367,1643],{},[115,25369,25370,25372,25374],{},[126,25371,12592],{},[118,25373,313],{},[142,25375,1652],{},[115,25377,25378,25380,25382],{},[126,25379,12592],{},[118,25381,313],{},[126,25383,2266],{},[302,25385,25386,25388],{},[126,25387,306],{},[126,25389,12592],{},[510,25391,24862],{},[302,25393,25394,25396],{},[126,25395,128],{},[126,25397,12592],{},[118,25399,313],{},[142,25401,144],{},[149,25403,25404],{"encoding":151},"\\sum_{j=1}^{j=m} x_j \\textrm{d} \\mu_j = 0",[99,25406,25408,25581],{"className":25407,"ariaHidden":139},[156],[99,25409,25411,25414,25483,25486,25526,25532,25572,25575,25578],{"className":25410},[160],[99,25412],{"className":25413,"style":25015},[164],[99,25415,25417,25420],{"className":25416},[1739],[99,25418,1643],{"className":25419,"style":12903},[1739,1784,12902],[99,25421,25423],{"className":25422},[181],[99,25424,25426,25475],{"className":25425},[185,186],[99,25427,25429,25472],{"className":25428},[190],[99,25430,25432,25452],{"className":25431,"style":12916},[194],[99,25433,25434,25437],{"style":12919},[99,25435],{"className":25436,"style":203},[202],[99,25438,25440],{"className":25439},[207,208,209,210],[99,25441,25443,25446,25449],{"className":25442},[173,210],[99,25444,12592],{"className":25445,"style":12932},[173,177,210],[99,25447,313],{"className":25448},[402,210],[99,25450,1652],{"className":25451},[173,210],[99,25453,25454,25457],{"style":12941},[99,25455],{"className":25456,"style":203},[202],[99,25458,25460],{"className":25459},[207,208,209,210],[99,25461,25463,25466,25469],{"className":25462},[173,210],[99,25464,12592],{"className":25465,"style":12932},[173,177,210],[99,25467,313],{"className":25468},[402,210],[99,25470,2266],{"className":25471},[173,177,210],[99,25473,241],{"className":25474},[240],[99,25476,25478],{"className":25477},[190],[99,25479,25481],{"className":25480,"style":12975},[194],[99,25482],{},[99,25484],{"className":25485,"style":1813},[397],[99,25487,25489,25492],{"className":25488},[173],[99,25490,306],{"className":25491},[173,177],[99,25493,25495],{"className":25494},[181],[99,25496,25498,25518],{"className":25497},[185,186],[99,25499,25501,25515],{"className":25500},[190],[99,25502,25504],{"className":25503,"style":366},[194],[99,25505,25506,25509],{"style":369},[99,25507],{"className":25508,"style":203},[202],[99,25510,25512],{"className":25511},[207,208,209,210],[99,25513,12592],{"className":25514,"style":12932},[173,177,210],[99,25516,241],{"className":25517},[240],[99,25519,25521],{"className":25520},[190],[99,25522,25524],{"className":25523,"style":14436},[194],[99,25525],{},[99,25527,25529],{"className":25528},[173,582],[99,25530,24862],{"className":25531},[173,586],[99,25533,25535,25538],{"className":25534},[173],[99,25536,128],{"className":25537},[173,177],[99,25539,25541],{"className":25540},[181],[99,25542,25544,25564],{"className":25543},[185,186],[99,25545,25547,25561],{"className":25546},[190],[99,25548,25550],{"className":25549,"style":366},[194],[99,25551,25552,25555],{"style":369},[99,25553],{"className":25554,"style":203},[202],[99,25556,25558],{"className":25557},[207,208,209,210],[99,25559,12592],{"className":25560,"style":12932},[173,177,210],[99,25562,241],{"className":25563},[240],[99,25565,25567],{"className":25566},[190],[99,25568,25570],{"className":25569,"style":14436},[194],[99,25571],{},[99,25573],{"className":25574,"style":398},[397],[99,25576,313],{"className":25577},[402],[99,25579],{"className":25580,"style":398},[397],[99,25582,25584,25587],{"className":25583},[160],[99,25585],{"className":25586,"style":10788},[164],[99,25588,144],{"className":25589},[173],[67,25591,25592],{},"and thus",[67,25594,25595],{},[99,25596,25598,25654],{"className":25597},[102],[99,25599,25601],{"className":25600},[106],[108,25602,25603],{"xmlns":110},[112,25604,25605,25651],{},[115,25606,25607,25609,25615,25617,25637,25639,25645],{},[510,25608,24862],{},[302,25610,25611,25613],{},[126,25612,2263],{},[126,25614,2266],{},[118,25616,313],{},[123,25618,25619,25621,25629],{},[118,25620,1643],{},[115,25622,25623,25625,25627],{},[126,25624,12592],{},[118,25626,313],{},[142,25628,1652],{},[115,25630,25631,25633,25635],{},[126,25632,12592],{},[118,25634,313],{},[126,25636,2266],{},[510,25638,24862],{},[302,25640,25641,25643],{},[126,25642,306],{},[126,25644,12592],{},[302,25646,25647,25649],{},[126,25648,128],{},[126,25650,12592],{},[149,25652,25653],{"encoding":151},"\\textrm{d}G_m = \\sum_{j=1}^{j=m} \\textrm{d}x_j 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= 1 - \\sum_{j=1}^{j=m-1} x_j",[99,26527,26529,26584,26603],{"className":26528,"ariaHidden":139},[156],[99,26530,26532,26535,26575,26578,26581],{"className":26531},[160],[99,26533],{"className":26534,"style":11582},[164],[99,26536,26538,26541],{"className":26537},[173],[99,26539,306],{"className":26540},[173,177],[99,26542,26544],{"className":26543},[181],[99,26545,26547,26567],{"className":26546},[185,186],[99,26548,26550,26564],{"className":26549},[190],[99,26551,26553],{"className":26552,"style":11269},[194],[99,26554,26555,26558],{"style":369},[99,26556],{"className":26557,"style":203},[202],[99,26559,26561],{"className":26560},[207,208,209,210],[99,26562,2266],{"className":26563},[173,177,210],[99,26565,241],{"className":26566},[240],[99,26568,26570],{"className":26569},[190],[99,26571,26573],{"className":26572,"style":388},[194],[99,26574],{},[99,26576],{"className":26577,"style":398},[397],[99,26579,313],{"className":26580},[402],[99,26582],{"className":26583,"style":398},[397],[99,26585,26587,26591,26594,26597,26600],{"className":26586},[160],[99,26588],{"className":26589,"style":26590},[164],"height:0.7278em;vertical-align:-0.0833em;",[99,26592,1652],{"className":26593},[173],[99,26595],{"className":26596,"style":2590},[397],[99,26598,2254],{"className":26599},[2594],[99,26601],{"className":26602,"style":2590},[397],[99,26604,26606,26609,26684,26687],{"className":26605},[160],[99,26607],{"className":26608,"style":25015},[164],[99,26610,26612,26615],{"className":26611},[1739],[99,26613,1643],{"className":26614,"style":12903},[1739,1784,12902],[99,26616,26618],{"className":26617},[181],[99,26619,26621,26676],{"className":26620},[185,186],[99,26622,26624,26673],{"className":26623},[190],[99,26625,26627,26647],{"className":26626,"style":12916},[194],[99,26628,26629,26632],{"style":12919},[99,26630],{"className":26631,"style":203},[202],[99,26633,26635],{"className":26634},[207,208,209,210],[99,26636,26638,26641,26644],{"className":26637},[173,210],[99,26639,12592],{"className":26640,"style":12932},[173,177,210],[99,26642,313],{"className":26643},[402,210],[99,26645,1652],{"className":26646},[173,210],[99,26648,26649,26652],{"style":12941},[99,26650],{"className":26651,"style":203},[202],[99,26653,26655],{"className":26654},[207,208,209,210],[99,26656,26658,26661,26664,26667,26670],{"className":26657},[173,210],[99,26659,12592],{"className":26660,"style":12932},[173,177,210],[99,26662,313],{"className":26663},[402,210],[99,26665,2266],{"className":26666},[173,177,210],[99,26668,2254],{"className":26669},[2594,210],[99,26671,1652],{"className":26672},[173,210],[99,26674,241],{"className":26675},[240],[99,26677,26679],{"className":26678},[190],[99,26680,26682],{"className":26681,"style":12975},[194],[99,26683],{},[99,26685],{"className":26686,"style":1813},[397],[99,26688,26690,26693],{"className":26689},[173],[99,26691,306],{"className":26692},[173,177],[99,26694,26696],{"className":26695},[181],[99,26697,26699,26719],{"className":26698},[185,186],[99,26700,26702,26716],{"className":26701},[190],[99,26703,26705],{"className":26704,"style":366},[194],[99,26706,26707,26710],{"style":369},[99,26708],{"className":26709,"style":203},[202],[99,26711,26713],{"className":26712},[207,208,209,210],[99,26714,12592],{"className":26715,"style":12932},[173,177,210],[99,26717,241],{"className":26718},[240],[99,26720,26722],{"className":26721},[190],[99,26723,26725],{"className":26724,"style":14436},[194],[99,26726],{},[67,26728,26729],{},"Consequently, all the composition variables in the equation above become independent, and we know",[67,26731,26732],{},[99,26733,26735,26785],{"className":26734},[102],[99,26736,26738],{"className":26737},[106],[108,26739,26740],{"xmlns":110},[112,26741,26742,26782],{},[115,26743,26744,26766,26768,26774,26776],{},[11809,26745,26746,26756],{},[115,26747,26748,26750],{},[126,26749,11815],{"mathvariant":2257},[302,26751,26752,26754],{},[126,26753,2263],{},[126,26755,2266],{},[115,26757,26758,26760],{},[126,26759,11815],{"mathvariant":2257},[302,26761,26762,26764],{},[126,26763,306],{},[126,26765,131],{},[118,26767,313],{},[302,26769,26770,26772],{},[126,26771,128],{},[126,26773,131],{},[118,26775,2254],{},[302,26777,26778,26780],{},[126,26779,128],{},[126,26781,2266],{},[149,26783,26784],{"encoding":151},"\\frac{\\partial G_m}{\\partial x_i} = \\mu_i - \\mu_{m}",[99,26786,26788,26951,27006],{"className":26787,"ariaHidden":139},[156],[99,26789,26791,26794,26942,26945,26948],{"className":26790},[160],[99,26792],{"className":26793,"style":11904},[164],[99,26795,26797,26800,26939],{"className":26796},[173],[99,26798],{"className":26799},[169,2336],[99,26801,26803],{"className":26802},[11809],[99,26804,26806,26931],{"className":26805},[185,186],[99,26807,26809,26928],{"className":26808},[190],[99,26810,26812,26866,26874],{"className":26811,"style":11923},[194],[99,26813,26814,26817],{"style":11926},[99,26815],{"className":26816,"style":4480},[202],[99,26818,26820],{"className":26819},[207,208,209,210],[99,26821,26823,26826],{"className":26822},[173,210],[99,26824,11815],{"className":26825,"style":11939},[173,210],[99,26827,26829,26832],{"className":26828},[173,210],[99,26830,306],{"className":26831},[173,177,210],[99,26833,26835],{"className":26834},[181],[99,26836,26838,26858],{"className":26837},[185,186],[99,26839,26841,26855],{"className":26840},[190],[99,26842,26844],{"className":26843,"style":11958},[194],[99,26845,26846,26849],{"style":11961},[99,26847],{"className":26848,"style":2513},[202],[99,26850,26852],{"className":26851},[207,2517,2518,210],[99,26853,131],{"className":26854},[173,177,210],[99,26856,241],{"className":26857},[240],[99,26859,26861],{"className":26860},[190],[99,26862,26864],{"className":26863,"style":11980},[194],[99,26865],{},[99,26867,26868,26871],{"style":11985},[99,26869],{"className":26870,"style":4480},[202],[99,26872],{"className":26873,"style":11993},[11992],[99,26875,26876,26879],{"style":11996},[99,26877],{"className":26878,"style":4480},[202],[99,26880,26882],{"className":26881},[207,208,209,210],[99,26883,26885,26888],{"className":26884},[173,210],[99,26886,11815],{"className":26887,"style":11939},[173,210],[99,26889,26891,26894],{"className":26890},[173,210],[99,26892,2263],{"className":26893},[173,177,210],[99,26895,26897],{"className":26896},[181],[99,26898,26900,26920],{"className":26899},[185,186],[99,26901,26903,26917],{"className":26902},[190],[99,26904,26906],{"className":26905,"style":12030},[194],[99,26907,26908,26911],{"style":11961},[99,26909],{"className":26910,"style":2513},[202],[99,26912,26914],{"className":26913},[207,2517,2518,210],[99,26915,2266],{"className":26916},[173,177,210],[99,26918,241],{"className":26919},[240],[99,26921,26923],{"className":26922},[190],[99,26924,26926],{"className":26925,"style":11980},[194],[99,26927],{},[99,26929,241],{"className":26930},[240],[99,26932,26934],{"className":26933},[190],[99,26935,26937],{"className":26936,"style":12062},[194],[99,26938],{},[99,26940],{"className":26941},[254,2336],[99,26943],{"className":26944,"style":398},[397],[99,26946,313],{"className":26947},[402],[99,26949],{"className":26950,"style":398},[397],[99,26952,26954,26957,26997,27000,27003],{"className":26953},[160],[99,26955],{"className":26956,"style":24435},[164],[99,26958,26960,26963],{"className":26959},[173],[99,26961,128],{"className":26962},[173,177],[99,26964,26966],{"className":26965},[181],[99,26967,26969,26989],{"className":26968},[185,186],[99,26970,26972,26986],{"className":26971},[190],[99,26973,26975],{"className":26974,"style":366},[194],[99,26976,26977,26980],{"style":369},[99,26978],{"className":26979,"style":203},[202],[99,26981,26983],{"className":26982},[207,208,209,210],[99,26984,131],{"className":26985},[173,177,210],[99,26987,241],{"className":26988},[240],[99,26990,26992],{"className":26991},[190],[99,26993,26995],{"className":26994,"style":388},[194],[99,26996],{},[99,26998],{"className":26999,"style":2590},[397],[99,27001,2254],{"className":27002},[2594],[99,27004],{"className":27005,"style":2590},[397],[99,27007,27009,27012],{"className":27008},[160],[99,27010],{"className":27011,"style":11848},[164],[99,27013,27015,27018],{"className":27014},[173],[99,27016,128],{"className":27017},[173,177],[99,27019,27021],{"className":27020},[181],[99,27022,27024,27047],{"className":27023},[185,186],[99,27025,27027,27044],{"className":27026},[190],[99,27028,27030],{"className":27029,"style":11269},[194],[99,27031,27032,27035],{"style":369},[99,27033],{"className":27034,"style":203},[202],[99,27036,27038],{"className":27037},[207,208,209,210],[99,27039,27041],{"className":27040},[173,210],[99,27042,2266],{"className":27043},[173,177,210],[99,27045,241],{"className":27046},[240],[99,27048,27050],{"className":27049},[190],[99,27051,27053],{"className":27052,"style":388},[194],[99,27054],{},[67,27056,27057],{},"according to the properties of the total derivative.",[1258,27059,27061],{"id":27060},"计算理想固溶体的吉布斯自由能化学势和扩散势","计算理想固溶体的吉布斯自由能、化学势和扩散势",[10562,27063,27066],{"className":27064,"code":27065,"language":582},[10707],"void func_compenstate_multicomponent(const double *x, double *f, int cnum)\n{\n    double T = x[cnum-1]; \u002F\u002F the last element is temperature\n    double vars[cnum];\n    double v = 0;\n    for (int i = 0; i \u003C cnum-1; i++)\n    {\n        vars[i] = x[i] \u003C 1.0e-6 ? 1.0e-6 : (x[i] > 1.0 - 1.0e-6 ? 1.0 - 1.0e-6 : x[i]);\n        v += vars[i];\n    }\n    vars[cnum-1] = 1.0 - v;\n\n    double gm = 0;\n    for (int ci=0; ci\u003Ccnum; ci++)\n    {\n        gm += vars[ci] * log(vars[ci]);\n    }\n    gm = 8.31451 * T * gm;\n    f[0] = gm;\n\n    double partial_gm[cnum];\n    for (int ci=0; ci\u003Ccnum; ci++)\n    {\n        partial_gm[ci] = 8.31451 * T * (log(vars[ci]) + 1);\n    }\n\n    double sum_partial_gm = 0;\n    for (int ci=0; ci\u003Ccnum; ci++)\n    {\n        sum_partial_gm += partial_gm[ci] * vars[ci];\n    }\n\n    double mus[cnum];\n    for (int ci=0; ci\u003Ccnum; ci++)\n    {\n        mus[ci] = gm + partial_gm[ci] - sum_partial_gm;\n    }\n\n    for (int ci=0; ci\u003Ccnum-1; ci++)\n    {\n        f[ci+1] = mus[ci] - mus[cnum-1];\n    }\n}\n\nvoid func_compenstate_quaternary(const double *x, double *f)\n{\n    func_compenstate_multicomponent(x, f, 4);\n}\n",[10569,27067,27065],{"__ignoreMap":10567},{"title":10567,"searchDepth":10580,"depth":10580,"links":27069},[27070],{"id":10746,"depth":10580,"text":10747,"children":27071},[27072,27073,27074,27075,27076],{"id":10758,"depth":10586,"text":10759},{"id":16162,"depth":10586,"text":16163},{"id":21733,"depth":10586,"text":21734},{"id":22835,"depth":10586,"text":22836},{"id":27060,"depth":10586,"text":27061},"2026-09-05","从偏摩尔量的定义出发，推导独立成分与约束成分变量下化学势的两种公式，并阐明化学势与相场模拟中扩散势的关系。","\u002Fblog\u002Fchemical-potential.svg",{},{"title":10,"description":27078},"iT6owxaYKsgqZJ6_RKSJtr8_KDhaWfw-k1CPG9t7rlk",{"id":27084,"title":34,"author":27085,"body":27087,"date":28921,"description":28922,"extension":10734,"image":28923,"meta":28924,"minRead":10657,"navigation":53,"path":35,"seo":28925,"stem":36,"__hash__":28926},"blog\u002Fblog\u002Ftauri-rust-tech-stack-and-build.md",{"name":60,"avatar":27086},{"src":62,"alt":60},{"type":64,"value":27088,"toc":28884},[27089,27098,27101,27105,27111,27122,27125,27127,27131,27135,27138,27158,27162,27168,27172,27210,27214,27301,27303,27307,27329,27333,27341,27373,27376,27406,27410,27419,27422,27444,27446,27472,27476,27479,27484,27495,27498,27527,27538,27542,27558,27561,27564,27595,27598,27600,27604,27608,27629,27632,27646,27650,27668,27670,27696,27701,27705,27721,27723,27751,27757,27812,27826,27829,27835,27838,27844,27848,27975,27977,27981,27985,27990,28004,28008,28078,28082,28085,28138,28140,28144,28150,28152,28156,28160,28181,28185,28190,28197,28217,28261,28265,28279,28283,28298,28313,28317,28328,28333,28394,28399,28412,28417,28420,28598,28604,28609,28675,28680,28730,28732,28736,28739,28822,28825,28838,28840,28844,28881],[71,27090,27091],{},[67,27092,27093,27094,27097],{},"本文以 ",[10569,27095,27096],{},"csv_editor_app"," 为例，说明基于 Tauri 2 + Rust + React + Vite + TypeScript 的桌面应用开发环境、编译流程与技术栈。",[27099,27100],"hr",{},[86,27102,27104],{"id":27103},"_0-参考项目","0. 参考项目",[67,27106,27107,27108,27110],{},"本文配套的示例项目 ",[10569,27109,27096],{}," 可以从以下地址下载：",[21736,27112,27113],{},[21739,27114,27115],{},[27116,27117,27121],"a",{"href":27118,"rel":27119},"https:\u002F\u002Fppm-sources.oss-cn-hongkong.aliyuncs.com\u002Fzj\u002Fcsv_editor_app-main.zip",[27120],"nofollow","csv_editor_app-main.zip",[67,27123,27124],{},"下载后解压，即可按照下文步骤进行编译和运行。",[27099,27126],{},[86,27128,27130],{"id":27129},"_1-tauri-rust-框架介绍","1. Tauri + Rust 框架介绍",[1258,27132,27134],{"id":27133},"_11-什么是-tauri","1.1 什么是 Tauri",[67,27136,27137],{},"Tauri 是一个使用 Web 前端技术构建跨平台桌面应用（以及移动端应用）的框架。它的核心思路是：",[21736,27139,27140,27146,27152],{},[21739,27141,27142,27145],{},[76,27143,27144],{},"前端","：使用 React \u002F Vue \u002F Svelte \u002F 原生 JS 等 Web 技术开发界面。",[21739,27147,27148,27151],{},[76,27149,27150],{},"后端\u002F原生层","：使用 Rust 编写，负责与操作系统交互（窗口、文件、对话框、通知等）。",[21739,27153,27154,27157],{},[76,27155,27156],{},"运行时","：操作系统自带的 WebView 渲染前端，Rust 进程提供原生能力，二者通过 Tauri 的 IPC 机制通信。",[1258,27159,27161],{"id":27160},"_12-架构模式","1.2 架构模式",[10562,27163,27166],{"className":27164,"code":27165,"language":582,"meta":10567},[10707],"┌─────────────────────────────────────────┐\n│  前端 UI 层（React + TypeScript）          │\n│  运行在系统 WebView 中                   │\n└────────────┬────────────────────────────┘\n             │ IPC（进程间通信）\n┌────────────▼────────────────────────────┐\n│  Rust 后端层（Tauri Runtime）             │\n│  窗口管理、文件读写、系统对话框等         │\n└─────────────────────────────────────────┘\n",[10569,27167,27165],{"__ignoreMap":10567},[1258,27169,27171],{"id":27170},"_13-tauri-rust-的主要优势","1.3 Tauri + Rust 的主要优势",[21736,27173,27174,27180,27186,27192,27198,27204],{},[21739,27175,27176,27179],{},[76,27177,27178],{},"体积小","：相比 Electron，Tauri 应用不需要打包 Chromium，安装包通常只有几 MB 到十几 MB。",[21739,27181,27182,27185],{},[76,27183,27184],{},"启动快、内存占用低","：运行时复用系统 WebView，没有冗余的浏览器内核。",[21739,27187,27188,27191],{},[76,27189,27190],{},"安全性高","：Rust 的内存安全特性 + Tauri 的权限系统（capabilities），默认最小权限原则。",[21739,27193,27194,27197],{},[76,27195,27196],{},"原生性能","：文件 IO、CPU 密集型计算等操作在 Rust 侧执行，性能接近原生应用。",[21739,27199,27200,27203],{},[76,27201,27202],{},"跨平台","：一份代码可构建 Windows、macOS、Linux 桌面应用；Tauri 2 还支持 iOS \u002F Android 移动端构建。",[21739,27205,27206,27209],{},[76,27207,27208],{},"复用 Web 生态","：前端可以复用 npm 生态中的 UI 库、工具链、组件库等。",[1258,27211,27213],{"id":27212},"_14-tauri-与-electron-的对比","1.4 Tauri 与 Electron 的对比",[27215,27216,27217,27233],"table",{},[27218,27219,27220],"thead",{},[27221,27222,27223,27227,27230],"tr",{},[27224,27225,27226],"th",{},"特性",[27224,27228,27229],{},"Tauri",[27224,27231,27232],{},"Electron",[27234,27235,27236,27247,27258,27269,27280,27291],"tbody",{},[27221,27237,27238,27241,27244],{},[27239,27240,27156],"td",{},[27239,27242,27243],{},"系统 WebView",[27239,27245,27246],{},"内置 Chromium + Node.js",[27221,27248,27249,27252,27255],{},[27239,27250,27251],{},"包体积",[27239,27253,27254],{},"通常 \u003C 5 MB",[27239,27256,27257],{},"通常 > 100 MB",[27221,27259,27260,27263,27266],{},[27239,27261,27262],{},"内存占用",[27239,27264,27265],{},"较低",[27239,27267,27268],{},"较高",[27221,27270,27271,27274,27277],{},[27239,27272,27273],{},"后端语言",[27239,27275,27276],{},"Rust",[27239,27278,27279],{},"Node.js",[27221,27281,27282,27285,27288],{},[27239,27283,27284],{},"安全模型",[27239,27286,27287],{},"基于 capabilities，IPC 受限",[27239,27289,27290],{},"需额外加固",[27221,27292,27293,27296,27299],{},[27239,27294,27295],{},"前端技术",[27239,27297,27298],{},"任意 Web 框架",[27239,27300,27298],{},[27099,27302],{},[86,27304,27306],{"id":27305},"_2-基础开发环境安装","2. 基础开发环境安装",[67,27308,27309,27310,27313,27314,27316,27317,27320,27321,27324,27325,27328],{},"本项目默认使用 ",[76,27311,27312],{},"bun"," 作为包管理器，请优先使用 bun 执行所有前端依赖安装与脚本命令。若不使用 bun，需自行将下述命令中的 ",[10569,27315,27312],{}," 替换为对应的包管理器，并同步修改 ",[10569,27318,27319],{},"src-tauri\u002Ftauri.conf.json"," 中的 ",[10569,27322,27323],{},"beforeDevCommand"," 和 ",[10569,27326,27327],{},"beforeBuildCommand","。",[1258,27330,27332],{"id":27331},"_21-nodejs-bun","2.1 Node.js \u002F bun",[67,27334,27335,27336,27340],{},"Tauri 前端使用 npm 生态。项目脚本默认通过 bun 调用，因此需要先安装 ",[27116,27337,27312],{"href":27338,"rel":27339},"https:\u002F\u002Fbun.sh\u002F",[27120],"。同时需要安装 Node.js（建议 LTS v22 或更高）以兼容前端工具链。",[21736,27342,27343,27358],{},[21739,27344,27345,27346,27349,27350,27353,27354,27357],{},"建议安装 ",[76,27347,27348],{},"LTS 版本","（当前项目依赖 ",[10569,27351,27352],{},"@types\u002Fnode: ^24.12.0","，建议 Node.js ",[10569,27355,27356],{},"v22"," 或更高）。",[21739,27359,27360,27361,27366,27367,27372],{},"使用 ",[27116,27362,27365],{"href":27363,"rel":27364},"https:\u002F\u002Fnodejs.org\u002F",[27120],"nodejs.org"," 官网安装包，或通过 ",[27116,27368,27371],{"href":27369,"rel":27370},"https:\u002F\u002Fgithub.com\u002Fcoreybutler\u002Fnvm-windows",[27120],"nvm-windows"," 管理多版本。",[67,27374,27375],{},"安装后验证：",[10562,27377,27381],{"className":27378,"code":27379,"language":27380,"meta":10567,"style":10567},"language-bash shiki shiki-themes material-theme-lighter material-theme material-theme-palenight","node -v   # 例如 v22.x.x\nbun -v    # 例如 1.x.x\n","bash",[10569,27382,27383,27397],{"__ignoreMap":10567},[99,27384,27385,27389,27393],{"class":10573,"line":10574},[99,27386,27388],{"class":27387},"sBMFI","node",[99,27390,27392],{"class":27391},"sfazB"," -v",[99,27394,27396],{"class":27395},"sHwdD","   # 例如 v22.x.x\n",[99,27398,27399,27401,27403],{"class":10573,"line":10580},[99,27400,27312],{"class":27387},[99,27402,27392],{"class":27391},[99,27404,27405],{"class":27395},"    # 例如 1.x.x\n",[1258,27407,27409],{"id":27408},"_22-rust-与-cargo","2.2 Rust 与 Cargo",[67,27411,27412,27413,27418],{},"Tauri 后端使用 Rust，通过 ",[27116,27414,27417],{"href":27415,"rel":27416},"https:\u002F\u002Frustup.rs\u002F",[27120],"rustup"," 安装最新稳定版。",[67,27420,27421],{},"Windows 安装步骤：",[27423,27424,27425,27431,27438,27441],"ol",{},[21739,27426,27427,27428],{},"访问 ",[27116,27429,27415],{"href":27415,"rel":27430},[27120],[21739,27432,27433,27434,27437],{},"下载 ",[10569,27435,27436],{},"rustup-init.exe"," 并运行。",[21739,27439,27440],{},"按提示选择默认安装（选项 1 - Proceed with default install）。",[21739,27442,27443],{},"安装完成后可能需要重新打开终端，或按提示执行环境变量刷新命令。",[67,27445,27375],{},[10562,27447,27449],{"className":27378,"code":27448,"language":27380,"meta":10567,"style":10567},"rustc --version   # 例如 rustc 1.x.x\ncargo --version   # 例如 cargo 1.x.x\n",[10569,27450,27451,27462],{"__ignoreMap":10567},[99,27452,27453,27456,27459],{"class":10573,"line":10574},[99,27454,27455],{"class":27387},"rustc",[99,27457,27458],{"class":27391}," --version",[99,27460,27461],{"class":27395},"   # 例如 rustc 1.x.x\n",[99,27463,27464,27467,27469],{"class":10573,"line":10580},[99,27465,27466],{"class":27387},"cargo",[99,27468,27458],{"class":27391},[99,27470,27471],{"class":27395},"   # 例如 cargo 1.x.x\n",[1258,27473,27475],{"id":27474},"_23-windows-下的-tauri-系统依赖","2.3 Windows 下的 Tauri 系统依赖",[67,27477,27478],{},"Windows 平台编译 Tauri 需要以下额外工具：",[27480,27481,27483],"h4",{"id":27482},"_1microsoft-visual-c-build-tools","（1）Microsoft Visual C++ Build Tools",[67,27485,27486,27487,27490,27491,27494],{},"Tauri 2 在 Windows 上编译 Rust 代码需要 MSVC 编译器。推荐安装 ",[76,27488,27489],{},"Visual Studio Build Tools"," 的 ",[76,27492,27493],{},"使用 C++ 的桌面开发"," 工作负载。",[67,27496,27497],{},"通过 winget 安装示例：",[10562,27499,27501],{"className":27378,"code":27500,"language":27380,"meta":10567,"style":10567},"winget install Microsoft.VisualStudio.2022.BuildTools --override \"--wait --add Microsoft.VisualStudio.Workload.VCTools --includeRecommended\"\n",[10569,27502,27503],{"__ignoreMap":10567},[99,27504,27505,27508,27511,27514,27517,27521,27524],{"class":10573,"line":10574},[99,27506,27507],{"class":27387},"winget",[99,27509,27510],{"class":27391}," install",[99,27512,27513],{"class":27391}," Microsoft.VisualStudio.2022.BuildTools",[99,27515,27516],{"class":27391}," --override",[99,27518,27520],{"class":27519},"sMK4o"," \"",[99,27522,27523],{"class":27391},"--wait --add Microsoft.VisualStudio.Workload.VCTools --includeRecommended",[99,27525,27526],{"class":27519},"\"\n",[67,27528,27529,27530,27535,27536,27328],{},"或者从 ",[27116,27531,27534],{"href":27532,"rel":27533},"https:\u002F\u002Fvisualstudio.microsoft.com\u002Fvisual-cpp-build-tools\u002F",[27120],"Visual Studio 下载页面"," 手动下载 Build Tools 并勾选 ",[76,27537,27493],{},[27480,27539,27541],{"id":27540},"_2webview2-runtime","（2）WebView2 Runtime",[21736,27543,27544,27547,27550],{},[21739,27545,27546],{},"Windows 10\u002F11 通常已内置 WebView2 运行时。",[21739,27548,27549],{},"开发构建需要 WebView2 SDK，Tauri 工具链通常会自动处理。",[21739,27551,27552,27553,27328],{},"如出现异常，可手动安装 ",[27116,27554,27557],{"href":27555,"rel":27556},"https:\u002F\u002Fdeveloper.microsoft.com\u002Fen-us\u002Fmicrosoft-edge\u002Fwebview2\u002F",[27120],"WebView2 Runtime",[27480,27559,27560],{"id":27560},"环境验证",[67,27562,27563],{},"完成上述安装后，在 PowerShell 或 Git Bash 中执行：",[10562,27565,27567],{"className":27378,"code":27566,"language":27380,"meta":10567,"style":10567},"rustc --version\ncargo --version\nnode -v\nbun -v\n",[10569,27568,27569,27576,27582,27589],{"__ignoreMap":10567},[99,27570,27571,27573],{"class":10573,"line":10574},[99,27572,27455],{"class":27387},[99,27574,27575],{"class":27391}," --version\n",[99,27577,27578,27580],{"class":10573,"line":10580},[99,27579,27466],{"class":27387},[99,27581,27575],{"class":27391},[99,27583,27584,27586],{"class":10573,"line":10586},[99,27585,27388],{"class":27387},[99,27587,27588],{"class":27391}," -v\n",[99,27590,27591,27593],{"class":10573,"line":10592},[99,27592,27312],{"class":27387},[99,27594,27588],{"class":27391},[67,27596,27597],{},"全部正常输出版本号即表示 Windows 开发环境准备就绪。",[27099,27599],{},[86,27601,27603],{"id":27602},"_3-项目快速编译","3. 项目快速编译",[1258,27605,27607],{"id":27606},"_31-进入项目目录并安装依赖","3.1 进入项目目录并安装依赖",[10562,27609,27611],{"className":27378,"code":27610,"language":27380,"meta":10567,"style":10567},"cd apps\u002Fcsv_editor_app\nbun install\n",[10569,27612,27613,27622],{"__ignoreMap":10567},[99,27614,27615,27619],{"class":10573,"line":10574},[99,27616,27618],{"class":27617},"s2Zo4","cd",[99,27620,27621],{"class":27391}," apps\u002Fcsv_editor_app\n",[99,27623,27624,27626],{"class":10573,"line":10580},[99,27625,27312],{"class":27387},[99,27627,27628],{"class":27391}," install\n",[67,27630,27631],{},"执行后：",[21736,27633,27634,27640],{},[21739,27635,27636,27637,27328],{},"前端依赖下载到 ",[10569,27638,27639],{},"node_modules\u002F",[21739,27641,27642,27645],{},[10569,27643,27644],{},"src-tauri\u002FCargo.toml"," 中的 Rust 依赖会通过 Cargo 自动下载。",[1258,27647,27649],{"id":27648},"_32-开发模式编译运行","3.2 开发模式编译运行",[10562,27651,27653],{"className":27378,"code":27652,"language":27380,"meta":10567,"style":10567},"bun run tauri dev\n",[10569,27654,27655],{"__ignoreMap":10567},[99,27656,27657,27659,27662,27665],{"class":10573,"line":10574},[99,27658,27312],{"class":27387},[99,27660,27661],{"class":27391}," run",[99,27663,27664],{"class":27391}," tauri",[99,27666,27667],{"class":27391}," dev\n",[67,27669,27631],{},[21736,27671,27672,27683,27686],{},[21739,27673,27674,27675,27678,27679,27682],{},"Vite 启动前端开发服务器，固定端口 ",[10569,27676,27677],{},"1424","（见 ",[10569,27680,27681],{},"vite.config.ts","）。",[21739,27684,27685],{},"Cargo 编译 Rust 后端，生成调试版本可执行文件。",[21739,27687,27688,27689,27692,27693,27328],{},"自动打开应用窗口，标题为 ",[10569,27690,27691],{},"CSV Editor","，默认尺寸 ",[10569,27694,27695],{},"1200x800",[71,27697,27698],{},[67,27699,27700],{},"首次编译 Rust 会下载并编译大量依赖，耗时较长，后续会利用增量编译加速。",[1258,27702,27704],{"id":27703},"_33-生产模式编译打包","3.3 生产模式编译打包",[10562,27706,27708],{"className":27378,"code":27707,"language":27380,"meta":10567,"style":10567},"bun run tauri build\n",[10569,27709,27710],{"__ignoreMap":10567},[99,27711,27712,27714,27716,27718],{"class":10573,"line":10574},[99,27713,27312],{"class":27387},[99,27715,27661],{"class":27391},[99,27717,27664],{"class":27391},[99,27719,27720],{"class":27391}," build\n",[67,27722,27631],{},[21736,27724,27725,27735,27738],{},[21739,27726,27727,27728,27731,27732,27328],{},"前端执行 ",[10569,27729,27730],{},"tsc -b && vite build","，输出到 ",[10569,27733,27734],{},"dist\u002F",[21739,27736,27737],{},"Rust 以 release 模式编译。",[21739,27739,27740,27741,27744,27745,27748,27749,27682],{},"默认不打包安装程序（",[10569,27742,27743],{},"tauri.conf.json"," 中 ",[10569,27746,27747],{},"bundle.active"," 为 ",[10569,27750,120],{},[67,27752,27753,27754,27756],{},"本项目 ",[10569,27755,27743],{}," 当前打包配置如下：",[10562,27758,27762],{"className":27759,"code":27760,"language":27761,"meta":10567,"style":10567},"language-json shiki shiki-themes material-theme-lighter material-theme material-theme-palenight","{\n  \"bundle\": {\n    \"active\": false\n  }\n}\n","json",[10569,27763,27764,27769,27787,27802,27807],{"__ignoreMap":10567},[99,27765,27766],{"class":10573,"line":10574},[99,27767,27768],{"class":27519},"{\n",[99,27770,27771,27774,27778,27781,27784],{"class":10573,"line":10580},[99,27772,27773],{"class":27519},"  \"",[99,27775,27777],{"class":27776},"spNyl","bundle",[99,27779,27780],{"class":27519},"\"",[99,27782,27783],{"class":27519},":",[99,27785,27786],{"class":27519}," {\n",[99,27788,27789,27792,27795,27797,27799],{"class":10573,"line":10586},[99,27790,27791],{"class":27519},"    \"",[99,27793,27794],{"class":27387},"active",[99,27796,27780],{"class":27519},[99,27798,27783],{"class":27519},[99,27800,27801],{"class":27519}," false\n",[99,27803,27804],{"class":10573,"line":10592},[99,27805,27806],{"class":27519},"  }\n",[99,27808,27809],{"class":10573,"line":10598},[99,27810,27811],{"class":27519},"}\n",[67,27813,27814,27815,27817,27818,27821,27822,27825],{},"如需生成安装包，可将其改为 ",[10569,27816,139],{}," 并配置 ",[10569,27819,27820],{},"targets","（如 ",[10569,27823,27824],{},"nsis","）。注意首次打包安装程序可能需要从网络下载 NSIS 工具。",[67,27827,27828],{},"产物默认位于：",[10562,27830,27833],{"className":27831,"code":27832,"language":582,"meta":10567},[10707],"csv_editor_app\u002Fsrc-tauri\u002Ftarget\u002Frelease\u002F\n",[10569,27834,27832],{"__ignoreMap":10567},[67,27836,27837],{},"直接可执行文件为：",[10562,27839,27842],{"className":27840,"code":27841,"language":582,"meta":10567},[10707],"src-tauri\u002Ftarget\u002Frelease\u002Fcsv-editor-app.exe\n",[10569,27843,27841],{"__ignoreMap":10567},[1258,27845,27847],{"id":27846},"_34-常用脚本速查","3.4 常用脚本速查",[10562,27849,27851],{"className":27378,"code":27850,"language":27380,"meta":10567,"style":10567},"bun run dev          # 仅启动 Vite 前端开发服务器（不启动 Tauri 窗口）\nbun run build        # 仅构建前端静态资源到 dist\u002F\nbun run preview      # 预览生产构建后的前端\nbun run tauri dev    # 启动 Tauri 开发模式（Vite + Rust + 窗口）\nbun run tauri build  # 完整构建 Tauri 桌面应用安装包\nbun run test         # 运行 Vitest 单元测试\nbun run test:run     # 单次运行 Vitest 测试\nbun run lint         # 运行 ESLint 检查\nbun run format       # 使用 Prettier 格式化代码\nbun run typecheck    # 运行 TypeScript 类型检查\n",[10569,27852,27853,27865,27877,27889,27902,27915,27927,27939,27951,27963],{"__ignoreMap":10567},[99,27854,27855,27857,27859,27862],{"class":10573,"line":10574},[99,27856,27312],{"class":27387},[99,27858,27661],{"class":27391},[99,27860,27861],{"class":27391}," dev",[99,27863,27864],{"class":27395},"          # 仅启动 Vite 前端开发服务器（不启动 Tauri 窗口）\n",[99,27866,27867,27869,27871,27874],{"class":10573,"line":10580},[99,27868,27312],{"class":27387},[99,27870,27661],{"class":27391},[99,27872,27873],{"class":27391}," build",[99,27875,27876],{"class":27395},"        # 仅构建前端静态资源到 dist\u002F\n",[99,27878,27879,27881,27883,27886],{"class":10573,"line":10586},[99,27880,27312],{"class":27387},[99,27882,27661],{"class":27391},[99,27884,27885],{"class":27391}," preview",[99,27887,27888],{"class":27395},"      # 预览生产构建后的前端\n",[99,27890,27891,27893,27895,27897,27899],{"class":10573,"line":10592},[99,27892,27312],{"class":27387},[99,27894,27661],{"class":27391},[99,27896,27664],{"class":27391},[99,27898,27861],{"class":27391},[99,27900,27901],{"class":27395},"    # 启动 Tauri 开发模式（Vite + Rust + 窗口）\n",[99,27903,27904,27906,27908,27910,27912],{"class":10573,"line":10598},[99,27905,27312],{"class":27387},[99,27907,27661],{"class":27391},[99,27909,27664],{"class":27391},[99,27911,27873],{"class":27391},[99,27913,27914],{"class":27395},"  # 完整构建 Tauri 桌面应用安装包\n",[99,27916,27917,27919,27921,27924],{"class":10573,"line":10604},[99,27918,27312],{"class":27387},[99,27920,27661],{"class":27391},[99,27922,27923],{"class":27391}," test",[99,27925,27926],{"class":27395},"         # 运行 Vitest 单元测试\n",[99,27928,27929,27931,27933,27936],{"class":10573,"line":10610},[99,27930,27312],{"class":27387},[99,27932,27661],{"class":27391},[99,27934,27935],{"class":27391}," test:run",[99,27937,27938],{"class":27395},"     # 单次运行 Vitest 测试\n",[99,27940,27941,27943,27945,27948],{"class":10573,"line":10616},[99,27942,27312],{"class":27387},[99,27944,27661],{"class":27391},[99,27946,27947],{"class":27391}," lint",[99,27949,27950],{"class":27395},"         # 运行 ESLint 检查\n",[99,27952,27953,27955,27957,27960],{"class":10573,"line":10622},[99,27954,27312],{"class":27387},[99,27956,27661],{"class":27391},[99,27958,27959],{"class":27391}," format",[99,27961,27962],{"class":27395},"       # 使用 Prettier 格式化代码\n",[99,27964,27965,27967,27969,27972],{"class":10573,"line":10627},[99,27966,27312],{"class":27387},[99,27968,27661],{"class":27391},[99,27970,27971],{"class":27391}," typecheck",[99,27973,27974],{"class":27395},"    # 运行 TypeScript 类型检查\n",[27099,27976],{},[86,27978,27980],{"id":27979},"_4-csv_editor_app-功能与技术栈","4. csv_editor_app 功能与技术栈",[1258,27982,27984],{"id":27983},"_41-项目功能","4.1 项目功能",[67,27986,27987,27989],{},[10569,27988,27096],{}," 是一个基于 Tauri 2 的桌面端 CSV 查看与编辑工具，核心功能包括：",[21736,27991,27992,27995,27998,28001],{},[21739,27993,27994],{},"通过系统对话框打开本地 CSV 文件。",[21739,27996,27997],{},"以表格形式展示 CSV 内容并支持编辑。",[21739,27999,28000],{},"将修改后的内容保存为 CSV 文件。",[21739,28002,28003],{},"提供简洁的工具栏与状态管理。",[1258,28005,28007],{"id":28006},"_42-主要技术栈","4.2 主要技术栈",[27215,28009,28010,28020],{},[27218,28011,28012],{},[27221,28013,28014,28017],{},[27224,28015,28016],{},"层级",[27224,28018,28019],{},"技术",[27234,28021,28022,28030,28038,28046,28054,28062,28070],{},[27221,28023,28024,28027],{},[27239,28025,28026],{},"前端 UI",[27239,28028,28029],{},"React 19 + TypeScript",[27221,28031,28032,28035],{},[27239,28033,28034],{},"构建工具",[27239,28036,28037],{},"Vite 7",[27221,28039,28040,28043],{},[27239,28041,28042],{},"样式",[27239,28044,28045],{},"Tailwind CSS 4 + shadcn\u002Fui",[27221,28047,28048,28051],{},[27239,28049,28050],{},"状态管理",[27239,28052,28053],{},"Zustand 5",[27221,28055,28056,28059],{},[27239,28057,28058],{},"测试",[27239,28060,28061],{},"Vitest",[27221,28063,28064,28067],{},[27239,28065,28066],{},"后端\u002F原生能力",[27239,28068,28069],{},"Rust + Tauri 2",[27221,28071,28072,28075],{},[27239,28073,28074],{},"代码规范",[27239,28076,28077],{},"ESLint 9 + Prettier 3",[1258,28079,28081],{"id":28080},"_43-进一步探索","4.3 进一步探索",[67,28083,28084],{},"以下文件值得自行阅读：",[21736,28086,28087,28093,28098,28103,28108,28114,28120,28126,28132],{},[21739,28088,28089,28092],{},[10569,28090,28091],{},"package.json","：Node 依赖与脚本。",[21739,28094,28095,28097],{},[10569,28096,27681],{},"：Vite 开发服务器与路径别名配置。",[21739,28099,28100,28102],{},[10569,28101,27644],{},"：Rust 依赖与 release 优化配置。",[21739,28104,28105,28107],{},[10569,28106,27319],{},"：应用名称、窗口、打包目标等核心配置。",[21739,28109,28110,28113],{},[10569,28111,28112],{},"src-tauri\u002Fcapabilities\u002Fdefault.json","：前端可调用的原生能力权限声明。",[21739,28115,28116,28119],{},[10569,28117,28118],{},"src-tauri\u002Fsrc\u002Flib.rs","：Rust 入口，插件初始化与窗口事件处理。",[21739,28121,28122,28125],{},[10569,28123,28124],{},"src\u002Fcomponents\u002FCsvTable.tsx","：CSV 表格组件。",[21739,28127,28128,28131],{},[10569,28129,28130],{},"src\u002Flib\u002Fcsv.ts","：CSV 解析逻辑。",[21739,28133,28134,28137],{},[10569,28135,28136],{},"src\u002Fstore\u002FcsvStore.ts","：Zustand 状态管理。",[27099,28139],{},[86,28141,28143],{"id":28142},"_5-项目目录结构","5. 项目目录结构",[10562,28145,28148],{"className":28146,"code":28147,"language":582,"meta":10567},[10707],"csv_editor_app\u002F\n├── src\u002F                          # 前端源代码\n│   ├── App.tsx                   # 应用根组件\n│   ├── components\u002F\n│   │   ├── CsvTable.tsx          # CSV 表格展示\u002F编辑组件\n│   │   ├── Toolbar.tsx           # 工具栏组件\n│   │   └── ui\u002F                   # shadcn\u002Fui 组件库\n│   ├── lib\u002F\n│   │   ├── csv.ts                # CSV 解析逻辑\n│   │   ├── csv.test.ts           # CSV 解析单元测试\n│   │   └── file.ts               # 文件操作辅助函数\n│   ├── store\u002F\n│   │   └── csvStore.ts           # Zustand 状态管理\n│   └── main.tsx                  # 前端入口\n├── src-tauri\u002F                    # Rust 后端与 Tauri 配置\n│   ├── src\u002F\n│   │   └── lib.rs                # Rust 入口与插件初始化\n│   ├── Cargo.toml                # Rust 依赖与构建配置\n│   ├── tauri.conf.json           # Tauri 应用配置\n│   ├── capabilities\u002F\n│   │   └── default.json          # 前端可调用原生 API 的权限声明\n│   └── icons\u002F                    # 应用图标\n├── public\u002F                       # 静态资源\n├── dist\u002F                         # 前端生产构建输出\n├── docs\u002F                         # 项目文档\n├── package.json                  # Node 依赖与脚本\n├── vite.config.ts                # Vite 配置\n└── tsconfig*.json                # TypeScript 配置\n",[10569,28149,28147],{"__ignoreMap":10567},[27099,28151],{},[86,28153,28155],{"id":28154},"_6-常见问题","6. 常见问题",[1258,28157,28159],{"id":28158},"_61-rust-编译缓慢","6.1 Rust 编译缓慢",[21736,28161,28162,28165,28171],{},[21739,28163,28164],{},"首次编译会下载并编译大量依赖，建议使用 SSD 并保持网络畅通。",[21739,28166,28167,28168,28170],{},"后续开发中，",[10569,28169,27466],{}," 会利用增量编译显著提速。",[21739,28172,27753,28173,28176,28177,28180],{},[10569,28174,28175],{},"Cargo.toml"," 已开启 ",[10569,28178,28179],{},"profile.dev.incremental = true","，提升开发编译速度。",[1258,28182,28184],{"id":28183},"_62-windows-上提示缺少-msvc","6.2 Windows 上提示缺少 MSVC",[67,28186,28187,28188,27494],{},"安装 Visual Studio Build Tools 的 ",[76,28189,27493],{},[1258,28191,28193,28194,28196],{"id":28192},"_63-bun-命令找不到","6.3 ",[10569,28195,27312],{}," 命令找不到",[67,28198,28199,28201,28202,28205,28206,28209,28210,28212,28213,28216],{},[10569,28200,27743],{}," 当前写的是 ",[10569,28203,28204],{},"bun run dev"," \u002F ",[10569,28207,28208],{},"bun run build","。如果本机没有安装 ",[10569,28211,27312],{},"，只有 ",[10569,28214,28215],{},"npm","，请将这两项改为：",[10562,28218,28220],{"className":27759,"code":28219,"language":27761,"meta":10567,"style":10567},"\"beforeDevCommand\": \"npm run dev\",\n\"beforeBuildCommand\": \"npm run build\"\n",[10569,28221,28222,28244],{"__ignoreMap":10567},[99,28223,28224,28226,28228,28230,28234,28236,28239,28241],{"class":10573,"line":10574},[99,28225,27780],{"class":27519},[99,28227,27323],{"class":27391},[99,28229,27780],{"class":27519},[99,28231,28233],{"class":28232},"sTEyZ",": ",[99,28235,27780],{"class":27519},[99,28237,28238],{"class":27391},"npm run dev",[99,28240,27780],{"class":27519},[99,28242,28243],{"class":28232},",\n",[99,28245,28246,28248,28250,28252,28254,28256,28259],{"class":10573,"line":10580},[99,28247,27780],{"class":27519},[99,28249,27327],{"class":27391},[99,28251,27780],{"class":27519},[99,28253,28233],{"class":28232},[99,28255,27780],{"class":27519},[99,28257,28258],{"class":27391},"npm run build",[99,28260,27526],{"class":27519},[1258,28262,28264],{"id":28263},"_64-前端调用-rust-函数失败","6.4 前端调用 Rust 函数失败",[67,28266,28267,28268,28270,28271,28274,28275,28278],{},"检查 ",[10569,28269,28112],{}," 中的权限配置，确保相关能力（如 ",[10569,28272,28273],{},"fs:read","、",[10569,28276,28277],{},"dialog:open"," 等）已声明并分配给对应窗口。",[1258,28280,28282],{"id":28281},"_65-打包时报-nsis-缺失-无法生成安装包","6.5 打包时报 NSIS 缺失 \u002F 无法生成安装包",[67,28284,28285,28286,28289,28290,28293,28294,28297],{},"现象：",[10569,28287,28288],{},"bun run tauri build"," 在 Windows 上提示 NSIS 缺失或下载失败（",[10569,28291,28292],{},"%TEMP%"," 里可能残留一个下载了却没解压的 ",[10569,28295,28296],{},"nsis-3.x.zip","）。原因是本机连不上 GitHub，Tauri 的自动下载中断。",[67,28299,28300,28301,28308,28309,28312],{},"注意 Tauri 在 Windows 上",[76,28302,28303,28304,28307],{},"不用系统已安装的 NSIS、也不读 ",[10569,28305,28306],{},"NSIS_PATH"," 环境变量","，只认自己的缓存目录 ",[10569,28310,28311],{},"%LOCALAPPDATA%\\tauri\\NSIS\\","，所以\"装一个 NSIS 然后设环境变量\"是无效的。完整的离线修复步骤（基于公司 OSS，已验证可用）见下文「NSIS 工具链（Windows 打包依赖）」一节；该缓存全局共享，配好后本机所有 Tauri 项目均可直接打包。",[1258,28314,28316],{"id":28315},"_66-nsis-工具链windows-打包依赖","6.6 NSIS 工具链（Windows 打包依赖）",[67,28318,28319,28320,28323,28324,28327],{},"Tauri 在 Windows 上生成 ",[10569,28321,28322],{},".exe"," 安装程序依赖 ",[76,28325,28326],{},"NSIS","。它的获取机制与直觉不同，理解机制才能在自动下载失败时正确处理。",[67,28329,28330],{},[76,28331,28332],{},"工作机制（关键，决定了解决思路）：",[21736,28334,28335,28346,28376],{},[21739,28336,28337,28338,28343,28344,27328],{},"Tauri ",[76,28339,28340,28341,28307],{},"不使用系统已安装的 NSIS，也不读 ",[10569,28342,28306],{},"（该变量仅 macOS \u002F Linux 生效）。Windows 下它只认自己缓存目录里的 NSIS：",[10569,28345,28311],{},[21739,28347,28348,28349,28352,28353],{},"首次打包时，Tauri 会从 ",[76,28350,28351],{},"GitHub"," 自动下载两份文件到该缓存：\n",[27423,28354,28355,28365],{},[21739,28356,28357,28358,28360,28361,28364],{},"NSIS 本体（",[10569,28359,28296],{},"，来自 ",[10569,28362,28363],{},"tauri-apps\u002Fbinary-releases","）；",[21739,28366,28367,28368,28371,28372,28375],{},"Tauri 专属插件 ",[10569,28369,28370],{},"nsis_tauri_utils.dll","（来自 ",[10569,28373,28374],{},"tauri-apps\u002Fnsis-tauri-utils","，当前 v0.5.3）。",[21739,28377,28378,28379,28382,28383,28386,28387,28389,28390,28393],{},"每次打包前，Tauri 会校验缓存中 13 个必需文件（",[10569,28380,28381],{},"NSIS_REQUIRED_FILES","）是否齐全——",[76,28384,28385],{},"缺任意一个就会整体删除并重新下载","。其中只有 ",[10569,28388,28370],{}," 会被哈希校验（SHA1 ",[10569,28391,28392],{},"75197fee3c6a814fe035788d1c34ead39349b860","），NSIS 本体文件只检查是否存在。",[67,28395,28396],{},[76,28397,28398],{},"常见故障现象（国内网络环境）：",[67,28400,28401,28402,28404,28405,28407,28408,28411],{},"打包时报 NSIS 缺失 \u002F 下载失败，且 ",[10569,28403,28292],{}," 下残留一个下载了却没解压的 ",[10569,28406,28296],{},"。根因是本机",[76,28409,28410],{},"无法稳定访问 GitHub","（自动下载源头），导致下载或解压中断；杀毒软件误删缓存目录也会引发同样现象。",[67,28413,28414],{},[76,28415,28416],{},"离线安装（推荐，已验证可用）：",[67,28418,28419],{},"公司已将所需文件发布到内网可达的 OSS，可完全不依赖 GitHub 完成配置。在 Git Bash 中执行：",[10562,28421,28423],{"className":27378,"code":28422,"language":27380,"meta":10567,"style":10567},"CACHE=\"$LOCALAPPDATA\u002Ftauri\"\n\n# 1) 安装 NSIS 3.12（运行安装包，默认装到 C:\\Program Files (x86)\\NSIS）\n#    下载：https:\u002F\u002Fppm-sources.oss-cn-hongkong.aliyuncs.com\u002Fzj\u002F3rd\u002Fnsis-3.12-setup.exe\n\n# 2) 把安装好的 NSIS 整体复制进 Tauri 缓存目录，命名为 NSIS\nmkdir -p \"$CACHE\"\nrm -rf \"$CACHE\u002FNSIS\"\ncp -r \"\u002Fc\u002FProgram Files (x86)\u002FNSIS\" \"$CACHE\u002FNSIS\"\n\n# 3) 下载 Tauri 专属插件到指定位置\nmkdir -p \"$CACHE\u002FNSIS\u002FPlugins\u002Fx86-unicode\u002Fadditional\"\ncurl -L \"https:\u002F\u002Fppm-sources.oss-cn-hongkong.aliyuncs.com\u002Fzj\u002F3rd\u002Fnsis_tauri_utils.dll\" \\\n  -o \"$CACHE\u002FNSIS\u002FPlugins\u002Fx86-unicode\u002Fadditional\u002Fnsis_tauri_utils.dll\"\n\n# 4) 校验插件完整性（应输出 75197fee3c6a814fe035788d1c34ead39349b860）\nsha1sum \"$CACHE\u002FNSIS\u002FPlugins\u002Fx86-unicode\u002Fadditional\u002Fnsis_tauri_utils.dll\"\n",[10569,28424,28425,28442,28446,28451,28456,28460,28465,28480,28497,28520,28524,28529,28544,28562,28576,28580,28585],{"__ignoreMap":10567},[99,28426,28427,28430,28432,28434,28437,28440],{"class":10573,"line":10574},[99,28428,28429],{"class":28232},"CACHE",[99,28431,313],{"class":27519},[99,28433,27780],{"class":27519},[99,28435,28436],{"class":28232},"$LOCALAPPDATA",[99,28438,28439],{"class":27391},"\u002Ftauri",[99,28441,27526],{"class":27519},[99,28443,28444],{"class":10573,"line":10580},[99,28445,10613],{"emptyLinePlaceholder":53},[99,28447,28448],{"class":10573,"line":10586},[99,28449,28450],{"class":27395},"# 1) 安装 NSIS 3.12（运行安装包，默认装到 C:\\Program Files (x86)\\NSIS）\n",[99,28452,28453],{"class":10573,"line":10592},[99,28454,28455],{"class":27395},"#    下载：https:\u002F\u002Fppm-sources.oss-cn-hongkong.aliyuncs.com\u002Fzj\u002F3rd\u002Fnsis-3.12-setup.exe\n",[99,28457,28458],{"class":10573,"line":10598},[99,28459,10613],{"emptyLinePlaceholder":53},[99,28461,28462],{"class":10573,"line":10604},[99,28463,28464],{"class":27395},"# 2) 把安装好的 NSIS 整体复制进 Tauri 缓存目录，命名为 NSIS\n",[99,28466,28467,28470,28473,28475,28478],{"class":10573,"line":10610},[99,28468,28469],{"class":27387},"mkdir",[99,28471,28472],{"class":27391}," -p",[99,28474,27520],{"class":27519},[99,28476,28477],{"class":28232},"$CACHE",[99,28479,27526],{"class":27519},[99,28481,28482,28485,28488,28490,28492,28495],{"class":10573,"line":10616},[99,28483,28484],{"class":27387},"rm",[99,28486,28487],{"class":27391}," -rf",[99,28489,27520],{"class":27519},[99,28491,28477],{"class":28232},[99,28493,28494],{"class":27391},"\u002FNSIS",[99,28496,27526],{"class":27519},[99,28498,28499,28502,28505,28507,28510,28512,28514,28516,28518],{"class":10573,"line":10622},[99,28500,28501],{"class":27387},"cp",[99,28503,28504],{"class":27391}," -r",[99,28506,27520],{"class":27519},[99,28508,28509],{"class":27391},"\u002Fc\u002FProgram Files (x86)\u002FNSIS",[99,28511,27780],{"class":27519},[99,28513,27520],{"class":27519},[99,28515,28477],{"class":28232},[99,28517,28494],{"class":27391},[99,28519,27526],{"class":27519},[99,28521,28522],{"class":10573,"line":10627},[99,28523,10613],{"emptyLinePlaceholder":53},[99,28525,28526],{"class":10573,"line":10633},[99,28527,28528],{"class":27395},"# 3) 下载 Tauri 专属插件到指定位置\n",[99,28530,28531,28533,28535,28537,28539,28542],{"class":10573,"line":10639},[99,28532,28469],{"class":27387},[99,28534,28472],{"class":27391},[99,28536,27520],{"class":27519},[99,28538,28477],{"class":28232},[99,28540,28541],{"class":27391},"\u002FNSIS\u002FPlugins\u002Fx86-unicode\u002Fadditional",[99,28543,27526],{"class":27519},[99,28545,28546,28549,28552,28554,28557,28559],{"class":10573,"line":10645},[99,28547,28548],{"class":27387},"curl",[99,28550,28551],{"class":27391}," -L",[99,28553,27520],{"class":27519},[99,28555,28556],{"class":27391},"https:\u002F\u002Fppm-sources.oss-cn-hongkong.aliyuncs.com\u002Fzj\u002F3rd\u002Fnsis_tauri_utils.dll",[99,28558,27780],{"class":27519},[99,28560,28561],{"class":28232}," \\\n",[99,28563,28564,28567,28569,28571,28574],{"class":10573,"line":10651},[99,28565,28566],{"class":27391},"  -o",[99,28568,27520],{"class":27519},[99,28570,28477],{"class":28232},[99,28572,28573],{"class":27391},"\u002FNSIS\u002FPlugins\u002Fx86-unicode\u002Fadditional\u002Fnsis_tauri_utils.dll",[99,28575,27526],{"class":27519},[99,28577,28578],{"class":10573,"line":10657},[99,28579,10613],{"emptyLinePlaceholder":53},[99,28581,28582],{"class":10573,"line":10663},[99,28583,28584],{"class":27395},"# 4) 校验插件完整性（应输出 75197fee3c6a814fe035788d1c34ead39349b860）\n",[99,28586,28587,28590,28592,28594,28596],{"class":10573,"line":10669},[99,28588,28589],{"class":27387},"sha1sum",[99,28591,27520],{"class":27519},[99,28593,28477],{"class":28232},[99,28595,28573],{"class":27391},[99,28597,27526],{"class":27519},[67,28599,28600,28601,28603],{},"完成后回到项目执行 ",[10569,28602,28288],{},"，Tauri 会跳过下载直接打包。",[67,28605,28606],{},[76,28607,28608],{},"注意事项：",[21736,28610,28611,28621,28630,28644],{},[21739,28612,28613,28616,28617,28620],{},[76,28614,28615],{},"版本差异不影响打包","：OSS 提供的是 NSIS 3.12，而 Tauri 默认下载 3.11。由于 Tauri 每次只校验插件 dll 的哈希、本体文件只查存在性，用 3.12 本体 + 正确插件即可正常打包（已在 ",[10569,28618,28619],{},"@tauri-apps\u002Fcli"," 2.11.x 实测通过）。",[21739,28622,28623,28626,28627,28629],{},[76,28624,28625],{},"缓存全局共享","：配好一次后，本机所有 Tauri 项目共用 ",[10569,28628,28311],{},"，无需对每个项目重复操作——新项目遇到同样问题，先检查该目录是否完整即可。",[21739,28631,28632,28635,28636,28639,28640,28643],{},[76,28633,28634],{},"持久性","：只要该缓存目录不被清理即可长期使用。建议在杀毒软件中把 ",[10569,28637,28638],{},"%LOCALAPPDATA%\\tauri\\"," 加入白名单，避免 ",[10569,28641,28642],{},"makensis.exe"," 被误删后再次触发 GitHub 下载。",[21739,28645,28646,28649,28650,28652,28653,28655,28656,28205,28659,28662,28663,28666,28667,28670,28671,28674],{},[76,28647,28648],{},"Tauri 升级后插件版本漂移怎么办","：OSS 上的 ",[10569,28651,28370],{}," 是 v0.5.3，与当前 ",[10569,28654,28619],{}," 2.x 匹配。若升级 Tauri 后构建报插件哈希不匹配（日志出现 ",[10569,28657,28658],{},"mis-hashed files",[10569,28660,28661],{},"Redownloading","），说明 OSS 版本已过时——",[76,28664,28665],{},"直接自行下载即可，无需更新本文档的 SHA1","：构建日志里会给出新的下载地址（形如 ",[10569,28668,28669],{},"nsis_tauri_utils-vX.Y.Z","），用浏览器从 GitHub 取回该 dll，替换缓存目录下 ",[10569,28672,28673],{},"NSIS\\Plugins\\x86-unicode\\additional\\nsis_tauri_utils.dll"," 即可。NSIS 本体不受影响，无需重装。",[67,28676,28677],{},[76,28678,28679],{},"相关下载地址汇总：",[27215,28681,28682,28695],{},[27218,28683,28684],{},[27221,28685,28686,28689,28692],{},[27224,28687,28688],{},"文件",[27224,28690,28691],{},"OSS（内网推荐）",[27224,28693,28694],{},"GitHub 官方源（需国际网络）",[27234,28696,28697,28714],{},[27221,28698,28699,28702,28708],{},[27239,28700,28701],{},"NSIS 安装包",[27239,28703,28704],{},[27116,28705,28706],{"href":28706,"rel":28707},"https:\u002F\u002Fppm-sources.oss-cn-hongkong.aliyuncs.com\u002Fzj\u002F3rd\u002Fnsis-3.12-setup.exe",[27120],[27239,28709,28710],{},[27116,28711,28712],{"href":28712,"rel":28713},"https:\u002F\u002Fnsis.sourceforge.io\u002FDownload",[27120],[27221,28715,28716,28719,28724],{},[27239,28717,28718],{},"Tauri 插件",[27239,28720,28721],{},[27116,28722,28556],{"href":28556,"rel":28723},[27120],[27239,28725,28726],{},[27116,28727,28728],{"href":28728,"rel":28729},"https:\u002F\u002Fgithub.com\u002Ftauri-apps\u002Fnsis-tauri-utils\u002Freleases\u002Ftag\u002Fnsis_tauri_utils-v0.5.3",[27120],[27099,28731],{},[86,28733,28735],{"id":28734},"_7-其他linux-系统依赖简要说明","7. 其他：Linux 系统依赖（简要说明）",[67,28737,28738],{},"Linux 平台主要需要 GTK 和 WebKitGTK 开发库。以 Ubuntu\u002FDebian 为例：",[10562,28740,28742],{"className":27378,"code":28741,"language":27380,"meta":10567,"style":10567},"sudo apt update\nsudo apt install libwebkit2gtk-4.1-dev \\\n  build-essential \\\n  curl \\\n  wget \\\n  file \\\n  libxdo3 \\\n  libssl-dev \\\n  libayatana-appindicator3-dev \\\n  librsvg2-dev\n",[10569,28743,28744,28755,28768,28775,28782,28789,28796,28803,28810,28817],{"__ignoreMap":10567},[99,28745,28746,28749,28752],{"class":10573,"line":10574},[99,28747,28748],{"class":27387},"sudo",[99,28750,28751],{"class":27391}," apt",[99,28753,28754],{"class":27391}," update\n",[99,28756,28757,28759,28761,28763,28766],{"class":10573,"line":10580},[99,28758,28748],{"class":27387},[99,28760,28751],{"class":27391},[99,28762,27510],{"class":27391},[99,28764,28765],{"class":27391}," libwebkit2gtk-4.1-dev",[99,28767,28561],{"class":28232},[99,28769,28770,28773],{"class":10573,"line":10586},[99,28771,28772],{"class":27391},"  build-essential",[99,28774,28561],{"class":28232},[99,28776,28777,28780],{"class":10573,"line":10592},[99,28778,28779],{"class":27391},"  curl",[99,28781,28561],{"class":28232},[99,28783,28784,28787],{"class":10573,"line":10598},[99,28785,28786],{"class":27391},"  wget",[99,28788,28561],{"class":28232},[99,28790,28791,28794],{"class":10573,"line":10604},[99,28792,28793],{"class":27391},"  file",[99,28795,28561],{"class":28232},[99,28797,28798,28801],{"class":10573,"line":10610},[99,28799,28800],{"class":27391},"  libxdo3",[99,28802,28561],{"class":28232},[99,28804,28805,28808],{"class":10573,"line":10616},[99,28806,28807],{"class":27391},"  libssl-dev",[99,28809,28561],{"class":28232},[99,28811,28812,28815],{"class":10573,"line":10622},[99,28813,28814],{"class":27391},"  libayatana-appindicator3-dev",[99,28816,28561],{"class":28232},[99,28818,28819],{"class":10573,"line":10627},[99,28820,28821],{"class":27391},"  librsvg2-dev\n",[67,28823,28824],{},"macOS 环境需要安装 Xcode Command Line Tools：",[10562,28826,28828],{"className":27378,"code":28827,"language":27380,"meta":10567,"style":10567},"xcode-select --install\n",[10569,28829,28830],{"__ignoreMap":10567},[99,28831,28832,28835],{"class":10573,"line":10574},[99,28833,28834],{"class":27387},"xcode-select",[99,28836,28837],{"class":27391}," --install\n",[27099,28839],{},[86,28841,28843],{"id":28842},"_8-参考资源","8. 参考资源",[21736,28845,28846,28853,28860,28867,28874],{},[21739,28847,28848],{},[27116,28849,28852],{"href":28850,"rel":28851},"https:\u002F\u002Ftauri.app\u002F",[27120],"Tauri 官方文档",[21739,28854,28855],{},[27116,28856,28859],{"href":28857,"rel":28858},"https:\u002F\u002Ftauri.app\u002Fstart\u002Fprerequisites\u002F",[27120],"Tauri 前置条件",[21739,28861,28862],{},[27116,28863,28866],{"href":28864,"rel":28865},"https:\u002F\u002Fwww.rust-lang.org\u002Flearn",[27120],"Rust 官方文档",[21739,28868,28869],{},[27116,28870,28873],{"href":28871,"rel":28872},"https:\u002F\u002Fvitejs.dev\u002F",[27120],"Vite 官方文档",[21739,28875,28876],{},[27116,28877,28880],{"href":28878,"rel":28879},"https:\u002F\u002Freact.dev\u002F",[27120],"React 官方文档",[10721,28882,28883],{},"html pre.shiki code .sBMFI, html code.shiki .sBMFI{--shiki-light:#E2931D;--shiki-default:#FFCB6B;--shiki-dark:#FFCB6B}html pre.shiki code .sfazB, html code.shiki .sfazB{--shiki-light:#91B859;--shiki-default:#C3E88D;--shiki-dark:#C3E88D}html pre.shiki code .sHwdD, html code.shiki .sHwdD{--shiki-light:#90A4AE;--shiki-light-font-style:italic;--shiki-default:#546E7A;--shiki-default-font-style:italic;--shiki-dark:#676E95;--shiki-dark-font-style:italic}html .light .shiki span {color: var(--shiki-light);background: var(--shiki-light-bg);font-style: var(--shiki-light-font-style);font-weight: var(--shiki-light-font-weight);text-decoration: var(--shiki-light-text-decoration);}html.light .shiki span {color: var(--shiki-light);background: var(--shiki-light-bg);font-style: var(--shiki-light-font-style);font-weight: var(--shiki-light-font-weight);text-decoration: var(--shiki-light-text-decoration);}html .default .shiki span {color: var(--shiki-default);background: var(--shiki-default-bg);font-style: var(--shiki-default-font-style);font-weight: var(--shiki-default-font-weight);text-decoration: var(--shiki-default-text-decoration);}html .shiki span {color: var(--shiki-default);background: var(--shiki-default-bg);font-style: var(--shiki-default-font-style);font-weight: var(--shiki-default-font-weight);text-decoration: var(--shiki-default-text-decoration);}html .dark .shiki span {color: var(--shiki-dark);background: var(--shiki-dark-bg);font-style: var(--shiki-dark-font-style);font-weight: var(--shiki-dark-font-weight);text-decoration: var(--shiki-dark-text-decoration);}html.dark .shiki span {color: var(--shiki-dark);background: var(--shiki-dark-bg);font-style: var(--shiki-dark-font-style);font-weight: var(--shiki-dark-font-weight);text-decoration: var(--shiki-dark-text-decoration);}html pre.shiki code .sMK4o, html code.shiki .sMK4o{--shiki-light:#39ADB5;--shiki-default:#89DDFF;--shiki-dark:#89DDFF}html pre.shiki code .s2Zo4, html code.shiki .s2Zo4{--shiki-light:#6182B8;--shiki-default:#82AAFF;--shiki-dark:#82AAFF}html pre.shiki code .sTEyZ, html code.shiki .sTEyZ{--shiki-light:#90A4AE;--shiki-default:#EEFFFF;--shiki-dark:#BABED8}html pre.shiki code .spNyl, html code.shiki .spNyl{--shiki-light:#9C3EDA;--shiki-default:#C792EA;--shiki-dark:#C792EA}",{"title":10567,"searchDepth":10580,"depth":10580,"links":28885},[28886,28887,28893,28898,28904,28909,28910,28919,28920],{"id":27103,"depth":10580,"text":27104},{"id":27129,"depth":10580,"text":27130,"children":28888},[28889,28890,28891,28892],{"id":27133,"depth":10586,"text":27134},{"id":27160,"depth":10586,"text":27161},{"id":27170,"depth":10586,"text":27171},{"id":27212,"depth":10586,"text":27213},{"id":27305,"depth":10580,"text":27306,"children":28894},[28895,28896,28897],{"id":27331,"depth":10586,"text":27332},{"id":27408,"depth":10586,"text":27409},{"id":27474,"depth":10586,"text":27475},{"id":27602,"depth":10580,"text":27603,"children":28899},[28900,28901,28902,28903],{"id":27606,"depth":10586,"text":27607},{"id":27648,"depth":10586,"text":27649},{"id":27703,"depth":10586,"text":27704},{"id":27846,"depth":10586,"text":27847},{"id":27979,"depth":10580,"text":27980,"children":28905},[28906,28907,28908],{"id":27983,"depth":10586,"text":27984},{"id":28006,"depth":10586,"text":28007},{"id":28080,"depth":10586,"text":28081},{"id":28142,"depth":10580,"text":28143},{"id":28154,"depth":10580,"text":28155,"children":28911},[28912,28913,28914,28916,28917,28918],{"id":28158,"depth":10586,"text":28159},{"id":28183,"depth":10586,"text":28184},{"id":28192,"depth":10586,"text":28915},"6.3 bun 命令找不到",{"id":28263,"depth":10586,"text":28264},{"id":28281,"depth":10586,"text":28282},{"id":28315,"depth":10586,"text":28316},{"id":28734,"depth":10580,"text":28735},{"id":28842,"depth":10580,"text":28843},"2026-08-12","以 csv_editor_app 为例，说明基于 Tauri 2 + Rust + React + Vite + TypeScript 的桌面应用开发环境、编译流程与技术栈。","https:\u002F\u002Fppm-sources.oss-cn-hongkong.aliyuncs.com\u002Fzj\u002Ftauri.jpeg",{},{"title":34,"description":28922},"ivLqMA2vBSfDb0Wk3FIzJqjKvH9MmLFuwEWbU7o3z8I",{"id":28928,"title":22,"author":28929,"body":28931,"date":29750,"description":29751,"extension":10734,"image":29752,"meta":29753,"minRead":10598,"navigation":53,"path":23,"seo":29754,"stem":24,"__hash__":29755},"blog\u002Fblog\u002Fpython-environment-setup-guide.md",{"name":60,"avatar":28930},{"src":62,"alt":60},{"type":64,"value":28932,"toc":29733},[28933,28936,28939,28942,28946,28949,28970,28973,29005,29009,29016,29041,29044,29050,29072,29075,29078,29167,29170,29200,29203,29206,29217,29221,29224,29227,29257,29260,29294,29297,29300,29325,29391,29394,29418,29421,29522,29525,29628,29631,29663,29666,29670,29673,29678,29700,29705,29730],[67,28934,28935],{},"Python 环境管理是每个 Python 开发者的必备技能。本文将首先介绍如何配置国内镜像源来解决网络问题，然后详细介绍如何使用 Conda 管理虚拟环境。",[86,28937,28938],{"id":28938},"配置国内镜像源",[67,28940,28941],{},"由于网络原因，从官方源下载包可能会很慢或遇到 SSL 错误。使用国内镜像源可以有效解决这些问题。",[1258,28943,28945],{"id":28944},"pip-镜像源","pip 镜像源",[67,28947,28948],{},"临时使用清华镜像源安装包：",[10562,28950,28952],{"className":27378,"code":28951,"language":27380,"meta":10567,"style":10567},"pip install -i https:\u002F\u002Fmirrors.tuna.tsinghua.edu.cn\u002Fpypi\u002Fweb\u002Fsimple some-package\n",[10569,28953,28954],{"__ignoreMap":10567},[99,28955,28956,28959,28961,28964,28967],{"class":10573,"line":10574},[99,28957,28958],{"class":27387},"pip",[99,28960,27510],{"class":27391},[99,28962,28963],{"class":27391}," -i",[99,28965,28966],{"class":27391}," https:\u002F\u002Fmirrors.tuna.tsinghua.edu.cn\u002Fpypi\u002Fweb\u002Fsimple",[99,28968,28969],{"class":27391}," some-package\n",[67,28971,28972],{},"使用镜像源并添加信任主机（解决 SSL 错误）：",[10562,28974,28976],{"className":27378,"code":28975,"language":27380,"meta":10567,"style":10567},"pip install -U \"mineru[all]\" -i https:\u002F\u002Fpypi.tuna.tsinghua.edu.cn\u002Fsimple --trusted-host pypi.tuna.tsinghua.edu.cn\n",[10569,28977,28978],{"__ignoreMap":10567},[99,28979,28980,28982,28984,28987,28989,28992,28994,28996,28999,29002],{"class":10573,"line":10574},[99,28981,28958],{"class":27387},[99,28983,27510],{"class":27391},[99,28985,28986],{"class":27391}," -U",[99,28988,27520],{"class":27519},[99,28990,28991],{"class":27391},"mineru[all]",[99,28993,27780],{"class":27519},[99,28995,28963],{"class":27391},[99,28997,28998],{"class":27391}," https:\u002F\u002Fpypi.tuna.tsinghua.edu.cn\u002Fsimple",[99,29000,29001],{"class":27391}," --trusted-host",[99,29003,29004],{"class":27391}," pypi.tuna.tsinghua.edu.cn\n",[1258,29006,29008],{"id":29007},"conda-镜像源配置","Conda 镜像源配置",[67,29010,29011,29012,29015],{},"Conda 镜像源通过修改用户目录下的 ",[10569,29013,29014],{},".condarc"," 文件来配置。不同系统下的文件位置如下：",[21736,29017,29018,29026,29033],{},[21739,29019,29020,28233,29023],{},[76,29021,29022],{},"Linux",[10569,29024,29025],{},"${HOME}\u002F.condarc",[21739,29027,29028,28233,29031],{},[76,29029,29030],{},"macOS",[10569,29032,29025],{},[21739,29034,29035,28233,29038],{},[76,29036,29037],{},"Windows",[10569,29039,29040],{},"C:\\Users\\\u003CYourUserName>\\.condarc",[27480,29042,29043],{"id":29043},"创建配置文件",[67,29045,29046,29047,29049],{},"Windows 用户无法直接创建名为 ",[10569,29048,29014],{}," 的文件，可先执行以下命令生成：",[10562,29051,29053],{"className":27378,"code":29052,"language":27380,"meta":10567,"style":10567},"conda config --set show_channel_urls yes\n",[10569,29054,29055],{"__ignoreMap":10567},[99,29056,29057,29060,29063,29066,29069],{"class":10573,"line":10574},[99,29058,29059],{"class":27387},"conda",[99,29061,29062],{"class":27391}," config",[99,29064,29065],{"class":27391}," --set",[99,29067,29068],{"class":27391}," show_channel_urls",[99,29070,29071],{"class":27391}," yes\n",[27480,29073,29074],{"id":29074},"配置内容",[67,29076,29077],{},"以下是推荐的清华镜像源配置：",[10562,29079,29083],{"className":29080,"code":29081,"language":29082,"meta":10567,"style":10567},"language-yaml shiki shiki-themes material-theme-lighter material-theme material-theme-palenight","channels:\n  - defaults\nshow_channel_urls: true\ndefault_channels:\n  - https:\u002F\u002Fmirrors.tuna.tsinghua.edu.cn\u002Fanaconda\u002Fpkgs\u002Fmain\n  - https:\u002F\u002Fmirrors.tuna.tsinghua.edu.cn\u002Fanaconda\u002Fpkgs\u002Fr\n  - https:\u002F\u002Fmirrors.tuna.tsinghua.edu.cn\u002Fanaconda\u002Fpkgs\u002Fmsys2\ncustom_channels:\n  conda-forge: https:\u002F\u002Fmirrors.tuna.tsinghua.edu.cn\u002Fanaconda\u002Fcloud\n  pytorch: https:\u002F\u002Fmirrors.tuna.tsinghua.edu.cn\u002Fanaconda\u002Fcloud\n","yaml",[10569,29084,29085,29094,29102,29113,29120,29127,29134,29141,29148,29158],{"__ignoreMap":10567},[99,29086,29087,29091],{"class":10573,"line":10574},[99,29088,29090],{"class":29089},"swJcz","channels",[99,29092,29093],{"class":27519},":\n",[99,29095,29096,29099],{"class":10573,"line":10580},[99,29097,29098],{"class":27519},"  -",[99,29100,29101],{"class":27391}," defaults\n",[99,29103,29104,29107,29109],{"class":10573,"line":10586},[99,29105,29106],{"class":29089},"show_channel_urls",[99,29108,27783],{"class":27519},[99,29110,29112],{"class":29111},"sfNiH"," true\n",[99,29114,29115,29118],{"class":10573,"line":10592},[99,29116,29117],{"class":29089},"default_channels",[99,29119,29093],{"class":27519},[99,29121,29122,29124],{"class":10573,"line":10598},[99,29123,29098],{"class":27519},[99,29125,29126],{"class":27391}," https:\u002F\u002Fmirrors.tuna.tsinghua.edu.cn\u002Fanaconda\u002Fpkgs\u002Fmain\n",[99,29128,29129,29131],{"class":10573,"line":10604},[99,29130,29098],{"class":27519},[99,29132,29133],{"class":27391}," https:\u002F\u002Fmirrors.tuna.tsinghua.edu.cn\u002Fanaconda\u002Fpkgs\u002Fr\n",[99,29135,29136,29138],{"class":10573,"line":10610},[99,29137,29098],{"class":27519},[99,29139,29140],{"class":27391}," https:\u002F\u002Fmirrors.tuna.tsinghua.edu.cn\u002Fanaconda\u002Fpkgs\u002Fmsys2\n",[99,29142,29143,29146],{"class":10573,"line":10616},[99,29144,29145],{"class":29089},"custom_channels",[99,29147,29093],{"class":27519},[99,29149,29150,29153,29155],{"class":10573,"line":10622},[99,29151,29152],{"class":29089},"  conda-forge",[99,29154,27783],{"class":27519},[99,29156,29157],{"class":27391}," https:\u002F\u002Fmirrors.tuna.tsinghua.edu.cn\u002Fanaconda\u002Fcloud\n",[99,29159,29160,29163,29165],{"class":10573,"line":10627},[99,29161,29162],{"class":29089},"  pytorch",[99,29164,27783],{"class":27519},[99,29166,29157],{"class":27391},[27480,29168,29169],{"id":29169},"注意事项",[27423,29171,29172,29188,29194],{},[21739,29173,29174,29177,29178,28274,29181,28274,29184,29187],{},[76,29175,29176],{},"同步延迟","：由于更新过快，部分镜像站不同步 ",[10569,29179,29180],{},"pytorch-nightly",[10569,29182,29183],{},"pytorch-nightly-cpu",[10569,29185,29186],{},"ignite-nightly"," 这三个包",[21739,29189,29190,29193],{},[76,29191,29192],{},"平台兼容性","：切换镜像源时，请检查镜像源是否支持你的平台（如 linux-64）",[21739,29195,29196,29199],{},[76,29197,29198],{},"第三方源","：各镜像站的第三方源（conda-forge、msys2、pytorch 等）并不完全相同",[86,29201,29202],{"id":29202},"为什么需要虚拟环境",[67,29204,29205],{},"在实际开发中，不同的项目往往需要不同版本的 Python 和依赖包。虚拟环境能够：",[21736,29207,29208,29211,29214],{},[21739,29209,29210],{},"隔离项目依赖，避免版本冲突",[21739,29212,29213],{},"保持系统 Python 环境的整洁",[21739,29215,29216],{},"方便项目迁移和部署",[86,29218,29220],{"id":29219},"conda-环境管理基础","Conda 环境管理基础",[1258,29222,29223],{"id":29223},"创建环境",[67,29225,29226],{},"创建一个新的 Conda 环境并指定 Python 版本：",[10562,29228,29230],{"className":27378,"code":29229,"language":27380,"meta":10567,"style":10567},"# 创建环境并指定 Python 版本（最新）\nconda create -n myenv python=3.11\n",[10569,29231,29232,29237],{"__ignoreMap":10567},[99,29233,29234],{"class":10573,"line":10574},[99,29235,29236],{"class":27395},"# 创建环境并指定 Python 版本（最新）\n",[99,29238,29239,29241,29244,29247,29250,29253],{"class":10573,"line":10580},[99,29240,29059],{"class":27387},[99,29242,29243],{"class":27391}," create",[99,29245,29246],{"class":27391}," -n",[99,29248,29249],{"class":27391}," myenv",[99,29251,29252],{"class":27391}," python=",[99,29254,29256],{"class":29255},"sbssI","3.11\n",[67,29258,29259],{},"创建环境并同时安装所需的包：",[10562,29261,29263],{"className":27378,"code":29262,"language":27380,"meta":10567,"style":10567},"# 创建环境、指定 Python 版本并安装包\nconda create -n myenv python=3.10 numpy scipy jupyter\n",[10569,29264,29265,29270],{"__ignoreMap":10567},[99,29266,29267],{"class":10573,"line":10574},[99,29268,29269],{"class":27395},"# 创建环境、指定 Python 版本并安装包\n",[99,29271,29272,29274,29276,29278,29280,29282,29285,29288,29291],{"class":10573,"line":10580},[99,29273,29059],{"class":27387},[99,29275,29243],{"class":27391},[99,29277,29246],{"class":27391},[99,29279,29249],{"class":27391},[99,29281,29252],{"class":27391},[99,29283,29284],{"class":29255},"3.10",[99,29286,29287],{"class":27391}," numpy",[99,29289,29290],{"class":27391}," scipy",[99,29292,29293],{"class":27391}," jupyter\n",[1258,29295,29296],{"id":29296},"使用配置文件",[67,29298,29299],{},"对于复杂的项目，推荐使用 YAML 配置文件来管理环境：",[10562,29301,29303],{"className":27378,"code":29302,"language":27380,"meta":10567,"style":10567},"# 先创建配置文件，然后创建环境\nconda env create -f environment.yml\n",[10569,29304,29305,29310],{"__ignoreMap":10567},[99,29306,29307],{"class":10573,"line":10574},[99,29308,29309],{"class":27395},"# 先创建配置文件，然后创建环境\n",[99,29311,29312,29314,29317,29319,29322],{"class":10573,"line":10580},[99,29313,29059],{"class":27387},[99,29315,29316],{"class":27391}," env",[99,29318,29243],{"class":27391},[99,29320,29321],{"class":27391}," -f",[99,29323,29324],{"class":27391}," environment.yml\n",[10562,29326,29328],{"className":29080,"code":29327,"language":29082,"meta":10567,"style":10567},"# environment.yml 示例\nname: myenv\nchannels:\n  - defaults\ndependencies:\n  - python=3.11\n  - numpy\n  - scipy\n  - jupyter\n",[10569,29329,29330,29335,29345,29351,29357,29364,29371,29378,29385],{"__ignoreMap":10567},[99,29331,29332],{"class":10573,"line":10574},[99,29333,29334],{"class":27395},"# environment.yml 示例\n",[99,29336,29337,29340,29342],{"class":10573,"line":10580},[99,29338,29339],{"class":29089},"name",[99,29341,27783],{"class":27519},[99,29343,29344],{"class":27391}," myenv\n",[99,29346,29347,29349],{"class":10573,"line":10586},[99,29348,29090],{"class":29089},[99,29350,29093],{"class":27519},[99,29352,29353,29355],{"class":10573,"line":10592},[99,29354,29098],{"class":27519},[99,29356,29101],{"class":27391},[99,29358,29359,29362],{"class":10573,"line":10598},[99,29360,29361],{"class":29089},"dependencies",[99,29363,29093],{"class":27519},[99,29365,29366,29368],{"class":10573,"line":10604},[99,29367,29098],{"class":27519},[99,29369,29370],{"class":27391}," python=3.11\n",[99,29372,29373,29375],{"class":10573,"line":10610},[99,29374,29098],{"class":27519},[99,29376,29377],{"class":27391}," numpy\n",[99,29379,29380,29382],{"class":10573,"line":10616},[99,29381,29098],{"class":27519},[99,29383,29384],{"class":27391}," scipy\n",[99,29386,29387,29389],{"class":10573,"line":10622},[99,29388,29098],{"class":27519},[99,29390,29293],{"class":27391},[67,29392,29393],{},"导出当前环境配置，方便与他人共享或在其他机器上重建：",[10562,29395,29397],{"className":27378,"code":29396,"language":27380,"meta":10567,"style":10567},"# 从现有环境导出配置\nconda env export > environment.yml\n",[10569,29398,29399,29404],{"__ignoreMap":10567},[99,29400,29401],{"class":10573,"line":10574},[99,29402,29403],{"class":27395},"# 从现有环境导出配置\n",[99,29405,29406,29408,29410,29413,29416],{"class":10573,"line":10580},[99,29407,29059],{"class":27387},[99,29409,29316],{"class":27391},[99,29411,29412],{"class":27391}," export",[99,29414,29415],{"class":27519}," >",[99,29417,29324],{"class":27391},[1258,29419,29420],{"id":29420},"环境操作",[10562,29422,29424],{"className":27378,"code":29423,"language":27380,"meta":10567,"style":10567},"# 克隆指定环境\nconda create -n newenv --clone oldenv\n\n# 激活环境\nconda activate myenv\n\n# 退出环境\nconda deactivate\n\n# 查看所有环境\nconda env list\n\n# 删除环境\nconda env remove -n myenv\n",[10569,29425,29426,29431,29448,29452,29457,29466,29470,29475,29482,29486,29491,29500,29504,29509],{"__ignoreMap":10567},[99,29427,29428],{"class":10573,"line":10574},[99,29429,29430],{"class":27395},"# 克隆指定环境\n",[99,29432,29433,29435,29437,29439,29442,29445],{"class":10573,"line":10580},[99,29434,29059],{"class":27387},[99,29436,29243],{"class":27391},[99,29438,29246],{"class":27391},[99,29440,29441],{"class":27391}," newenv",[99,29443,29444],{"class":27391}," --clone",[99,29446,29447],{"class":27391}," oldenv\n",[99,29449,29450],{"class":10573,"line":10586},[99,29451,10613],{"emptyLinePlaceholder":53},[99,29453,29454],{"class":10573,"line":10592},[99,29455,29456],{"class":27395},"# 激活环境\n",[99,29458,29459,29461,29464],{"class":10573,"line":10598},[99,29460,29059],{"class":27387},[99,29462,29463],{"class":27391}," activate",[99,29465,29344],{"class":27391},[99,29467,29468],{"class":10573,"line":10604},[99,29469,10613],{"emptyLinePlaceholder":53},[99,29471,29472],{"class":10573,"line":10610},[99,29473,29474],{"class":27395},"# 退出环境\n",[99,29476,29477,29479],{"class":10573,"line":10616},[99,29478,29059],{"class":27387},[99,29480,29481],{"class":27391}," deactivate\n",[99,29483,29484],{"class":10573,"line":10622},[99,29485,10613],{"emptyLinePlaceholder":53},[99,29487,29488],{"class":10573,"line":10627},[99,29489,29490],{"class":27395},"# 查看所有环境\n",[99,29492,29493,29495,29497],{"class":10573,"line":10633},[99,29494,29059],{"class":27387},[99,29496,29316],{"class":27391},[99,29498,29499],{"class":27391}," list\n",[99,29501,29502],{"class":10573,"line":10639},[99,29503,10613],{"emptyLinePlaceholder":53},[99,29505,29506],{"class":10573,"line":10645},[99,29507,29508],{"class":27395},"# 删除环境\n",[99,29510,29511,29513,29515,29518,29520],{"class":10573,"line":10651},[99,29512,29059],{"class":27387},[99,29514,29316],{"class":27391},[99,29516,29517],{"class":27391}," remove",[99,29519,29246],{"class":27391},[99,29521,29344],{"class":27391},[86,29523,29524],{"id":29524},"常用命令速查表",[27215,29526,29527,29537],{},[27218,29528,29529],{},[27221,29530,29531,29534],{},[27224,29532,29533],{},"操作",[27224,29535,29536],{},"命令",[27234,29538,29539,29548,29558,29568,29578,29588,29598,29608,29618],{},[27221,29540,29541,29543],{},[27239,29542,29223],{},[27239,29544,29545],{},[10569,29546,29547],{},"conda create -n envname python=3.11",[27221,29549,29550,29553],{},[27239,29551,29552],{},"激活环境",[27239,29554,29555],{},[10569,29556,29557],{},"conda activate envname",[27221,29559,29560,29563],{},[27239,29561,29562],{},"退出环境",[27239,29564,29565],{},[10569,29566,29567],{},"conda deactivate",[27221,29569,29570,29573],{},[27239,29571,29572],{},"查看环境列表",[27239,29574,29575],{},[10569,29576,29577],{},"conda env list",[27221,29579,29580,29583],{},[27239,29581,29582],{},"安装包",[27239,29584,29585],{},[10569,29586,29587],{},"conda install package_name",[27221,29589,29590,29593],{},[27239,29591,29592],{},"安装 pip 包",[27239,29594,29595],{},[10569,29596,29597],{},"pip install package_name",[27221,29599,29600,29603],{},[27239,29601,29602],{},"导出环境",[27239,29604,29605],{},[10569,29606,29607],{},"conda env export > environment.yml",[27221,29609,29610,29613],{},[27239,29611,29612],{},"从文件创建",[27239,29614,29615],{},[10569,29616,29617],{},"conda env create -f environment.yml",[27221,29619,29620,29623],{},[27239,29621,29622],{},"删除环境",[27239,29624,29625],{},[10569,29626,29627],{},"conda env remove -n envname",[86,29629,29630],{"id":29630},"最佳实践",[27423,29632,29633,29639,29645,29651,29657],{},[21739,29634,29635,29638],{},[76,29636,29637],{},"为每个项目创建独立环境","：避免依赖冲突",[21739,29640,29641,29644],{},[76,29642,29643],{},"使用 requirements.txt 或 environment.yml","：记录项目依赖",[21739,29646,29647,29650],{},[76,29648,29649],{},"定期更新包","：保持环境安全和稳定",[21739,29652,29653,29656],{},[76,29654,29655],{},"使用版本号锁定","：确保可重现性",[21739,29658,29659,29662],{},[76,29660,29661],{},"测试环境配置","：在新机器上验证环境可正常重建",[86,29664,29665],{"id":29665},"常见问题",[1258,29667,29669],{"id":29668},"ssl-错误","SSL 错误",[67,29671,29672],{},"SSL 错误通常是网络连接问题导致的，解决方法：",[67,29674,29675],{},[76,29676,29677],{},"方法 1：使用国内镜像源并添加信任主机",[10562,29679,29681],{"className":27378,"code":29680,"language":27380,"meta":10567,"style":10567},"pip install package_name -i https:\u002F\u002Fpypi.tuna.tsinghua.edu.cn\u002Fsimple --trusted-host pypi.tuna.tsinghua.edu.cn\n",[10569,29682,29683],{"__ignoreMap":10567},[99,29684,29685,29687,29689,29692,29694,29696,29698],{"class":10573,"line":10574},[99,29686,28958],{"class":27387},[99,29688,27510],{"class":27391},[99,29690,29691],{"class":27391}," package_name",[99,29693,28963],{"class":27391},[99,29695,28998],{"class":27391},[99,29697,29001],{"class":27391},[99,29699,29004],{"class":27391},[67,29701,29702],{},[76,29703,29704],{},"方法 2：升级 pip 并使用镜像源",[10562,29706,29708],{"className":27378,"code":29707,"language":27380,"meta":10567,"style":10567},"pip install --upgrade pip -i https:\u002F\u002Fpypi.tuna.tsinghua.edu.cn\u002Fsimple --trusted-host pypi.tuna.tsinghua.edu.cn\n",[10569,29709,29710],{"__ignoreMap":10567},[99,29711,29712,29714,29716,29719,29722,29724,29726,29728],{"class":10573,"line":10574},[99,29713,28958],{"class":27387},[99,29715,27510],{"class":27391},[99,29717,29718],{"class":27391}," --upgrade",[99,29720,29721],{"class":27391}," pip",[99,29723,28963],{"class":27391},[99,29725,28998],{"class":27391},[99,29727,29001],{"class":27391},[99,29729,29004],{"class":27391},[10721,29731,29732],{},"html pre.shiki code .sBMFI, html code.shiki .sBMFI{--shiki-light:#E2931D;--shiki-default:#FFCB6B;--shiki-dark:#FFCB6B}html pre.shiki code .sfazB, html code.shiki .sfazB{--shiki-light:#91B859;--shiki-default:#C3E88D;--shiki-dark:#C3E88D}html .light .shiki span {color: var(--shiki-light);background: var(--shiki-light-bg);font-style: var(--shiki-light-font-style);font-weight: var(--shiki-light-font-weight);text-decoration: var(--shiki-light-text-decoration);}html.light .shiki span {color: var(--shiki-light);background: var(--shiki-light-bg);font-style: var(--shiki-light-font-style);font-weight: var(--shiki-light-font-weight);text-decoration: var(--shiki-light-text-decoration);}html .default .shiki span {color: var(--shiki-default);background: var(--shiki-default-bg);font-style: var(--shiki-default-font-style);font-weight: var(--shiki-default-font-weight);text-decoration: var(--shiki-default-text-decoration);}html .shiki span {color: var(--shiki-default);background: var(--shiki-default-bg);font-style: var(--shiki-default-font-style);font-weight: var(--shiki-default-font-weight);text-decoration: var(--shiki-default-text-decoration);}html .dark .shiki span {color: var(--shiki-dark);background: var(--shiki-dark-bg);font-style: var(--shiki-dark-font-style);font-weight: var(--shiki-dark-font-weight);text-decoration: var(--shiki-dark-text-decoration);}html.dark .shiki span {color: var(--shiki-dark);background: var(--shiki-dark-bg);font-style: var(--shiki-dark-font-style);font-weight: var(--shiki-dark-font-weight);text-decoration: var(--shiki-dark-text-decoration);}html pre.shiki code .sMK4o, html code.shiki .sMK4o{--shiki-light:#39ADB5;--shiki-default:#89DDFF;--shiki-dark:#89DDFF}html pre.shiki code .sHwdD, html code.shiki .sHwdD{--shiki-light:#90A4AE;--shiki-light-font-style:italic;--shiki-default:#546E7A;--shiki-default-font-style:italic;--shiki-dark:#676E95;--shiki-dark-font-style:italic}html pre.shiki code .sbssI, html code.shiki .sbssI{--shiki-light:#F76D47;--shiki-default:#F78C6C;--shiki-dark:#F78C6C}html pre.shiki code .swJcz, html code.shiki .swJcz{--shiki-light:#E53935;--shiki-default:#F07178;--shiki-dark:#F07178}html pre.shiki code .sfNiH, html code.shiki .sfNiH{--shiki-light:#FF5370;--shiki-default:#FF9CAC;--shiki-dark:#FF9CAC}",{"title":10567,"searchDepth":10580,"depth":10580,"links":29734},[29735,29739,29740,29745,29746,29747],{"id":28938,"depth":10580,"text":28938,"children":29736},[29737,29738],{"id":28944,"depth":10586,"text":28945},{"id":29007,"depth":10586,"text":29008},{"id":29202,"depth":10580,"text":29202},{"id":29219,"depth":10580,"text":29220,"children":29741},[29742,29743,29744],{"id":29223,"depth":10586,"text":29223},{"id":29296,"depth":10586,"text":29296},{"id":29420,"depth":10586,"text":29420},{"id":29524,"depth":10580,"text":29524},{"id":29630,"depth":10580,"text":29630},{"id":29665,"depth":10580,"text":29665,"children":29748},[29749],{"id":29668,"depth":10586,"text":29669},"2026-01-11","从零开始掌握 Python 环境管理，包括 Conda 环境创建、配置文件使用、镜像源配置等实用技巧。","https:\u002F\u002Fppm-sources.oss-cn-hongkong.aliyuncs.com\u002Fzj\u002F3rd\u002Fpython.png",{},{"title":22,"description":29751},"qNfNyttHNGdmWNoXQh-Va6JFWHOa6zSTB0_UJbw59jo",{"id":29757,"title":26,"author":29758,"body":29760,"date":30019,"description":30020,"extension":10734,"image":30021,"meta":30022,"minRead":10586,"navigation":53,"path":27,"seo":30023,"stem":28,"__hash__":30024},"blog\u002Fblog\u002Frust-compilation-and-configuration.md",{"name":60,"avatar":29759},{"src":62,"alt":60},{"type":64,"value":29761,"toc":30010},[29762,29765,29769,29772,29806,29809,29820,29824,29833,29836,29843,29860,29867,29871,29874,29904,29907,29921,29925,29936,29973,29976,29987,29990,29993,30007],[67,29763,29764],{},"Rust作为一门系统级编程语言，在编译和配置方面有其独特之处。本文将介绍几个常用的Rust编译配置场景。",[86,29766,29768],{"id":29767},"编译-musl-目标","编译 musl 目标",[67,29770,29771],{},"在某些场景下，需要编译生成静态链接的可执行文件。使用musl可以创建不依赖系统动态链接库的二进制文件：",[10562,29773,29775],{"className":27378,"code":29774,"language":27380,"meta":10567,"style":10567},"podman run -v .\u002F:\u002Fvolume --rm -t clux\u002Fmuslrust:stable cargo build --release\n",[10569,29776,29777],{"__ignoreMap":10567},[99,29778,29779,29782,29784,29786,29789,29792,29795,29798,29801,29803],{"class":10573,"line":10574},[99,29780,29781],{"class":27387},"podman",[99,29783,27661],{"class":27391},[99,29785,27392],{"class":27391},[99,29787,29788],{"class":27391}," .\u002F:\u002Fvolume",[99,29790,29791],{"class":27391}," --rm",[99,29793,29794],{"class":27391}," -t",[99,29796,29797],{"class":27391}," clux\u002Fmuslrust:stable",[99,29799,29800],{"class":27391}," cargo",[99,29802,27873],{"class":27391},[99,29804,29805],{"class":27391}," --release\n",[67,29807,29808],{},"这条命令的作用：",[21736,29810,29811,29814,29817],{},[21739,29812,29813],{},"使用muslrust容器进行交叉编译",[21739,29815,29816],{},"将当前目录挂载到容器的\u002Fvolume路径",[21739,29818,29819],{},"编译为release版本，生成静态链接的可执行文件",[1258,29821,29823],{"id":29822},"podman-安装","Podman 安装",[67,29825,29826,29827,29832],{},"在Windows系统上安装Podman可以参考",[27116,29828,29831],{"href":29829,"rel":29830},"https:\u002F\u002Fgithub.com\u002Fcontainers\u002Fpodman\u002Fblob\u002Fmain\u002Fdocs\u002Ftutorials\u002Fpodman-for-windows.md",[27120],"官方文档","。Podman提供了无守护程序的容器化解决方案，适合在Windows环境下进行交叉编译。",[86,29834,29835],{"id":29835},"运行示例代码",[67,29837,29838,29839,29842],{},"对于项目中的示例代码，可以使用",[10569,29840,29841],{},"--example","标志直接运行：",[10562,29844,29846],{"className":27378,"code":29845,"language":27380,"meta":10567,"style":10567},"cargo run --example example_1\n",[10569,29847,29848],{"__ignoreMap":10567},[99,29849,29850,29852,29854,29857],{"class":10573,"line":10574},[99,29851,27466],{"class":27387},[99,29853,27661],{"class":27391},[99,29855,29856],{"class":27391}," --example",[99,29858,29859],{"class":27391}," example_1\n",[67,29861,29862,29863,29866],{},"这将编译并运行",[10569,29864,29865],{},"examples\u002Fexample_1.rs","文件，无需手动处理示例的编译配置。",[86,29868,29870],{"id":29869},"设置-rustup-镜像","设置 Rustup 镜像",[67,29872,29873],{},"在国内环境下，使用官方源可能会比较慢。可以通过设置环境变量临时替换镜像源：",[10562,29875,29877],{"className":27378,"code":29876,"language":27380,"meta":10567,"style":10567},"export RUSTUP_UPDATE_ROOT=https:\u002F\u002Fmirrors.aliyun.com\u002Frustup\u002Frustup\nexport RUSTUP_DIST_SERVER=https:\u002F\u002Fmirrors.aliyun.com\u002Frustup\n",[10569,29878,29879,29892],{"__ignoreMap":10567},[99,29880,29881,29884,29887,29889],{"class":10573,"line":10574},[99,29882,29883],{"class":27776},"export",[99,29885,29886],{"class":28232}," RUSTUP_UPDATE_ROOT",[99,29888,313],{"class":27519},[99,29890,29891],{"class":28232},"https:\u002F\u002Fmirrors.aliyun.com\u002Frustup\u002Frustup\n",[99,29893,29894,29896,29899,29901],{"class":10573,"line":10580},[99,29895,29883],{"class":27776},[99,29897,29898],{"class":28232}," RUSTUP_DIST_SERVER",[99,29900,313],{"class":27519},[99,29902,29903],{"class":28232},"https:\u002F\u002Fmirrors.aliyun.com\u002Frustup\n",[67,29905,29906],{},"这两个环境变量分别控制：",[21736,29908,29909,29915],{},[21739,29910,29911,29914],{},[10569,29912,29913],{},"RUSTUP_UPDATE_ROOT","：rustup更新服务器地址",[21739,29916,29917,29920],{},[10569,29918,29919],{},"RUSTUP_DIST_SERVER","：Rust分发服务器地址",[86,29922,29924],{"id":29923},"配置-cratesio-镜像","配置 crates.io 镜像",[67,29926,29927,29928,29931,29932,29935],{},"为了加速Cargo的依赖包下载，需要配置crates.io的镜像源。在",[10569,29929,29930],{},"~\u002F.cargo\u002Fconfig","文件（Windows系统为",[10569,29933,29934],{},"%USERPROFILE%\\.cargo\\config","）中添加：",[10562,29937,29941],{"className":29938,"code":29939,"language":29940,"meta":10567,"style":10567},"language-toml shiki shiki-themes material-theme-lighter material-theme material-theme-palenight","[registry]\nindex = \"https:\u002F\u002Fgithub.com\u002Frust-lang\u002Fcrates.io-index\"\n[source.crates-io]\nreplace-with = 'aliyun'\n[source.aliyun]\nregistry = \"sparse+https:\u002F\u002Fmirrors.aliyun.com\u002Fcrates.io-index\u002F\"\n","toml",[10569,29942,29943,29948,29953,29958,29963,29968],{"__ignoreMap":10567},[99,29944,29945],{"class":10573,"line":10574},[99,29946,29947],{},"[registry]\n",[99,29949,29950],{"class":10573,"line":10580},[99,29951,29952],{},"index = \"https:\u002F\u002Fgithub.com\u002Frust-lang\u002Fcrates.io-index\"\n",[99,29954,29955],{"class":10573,"line":10586},[99,29956,29957],{},"[source.crates-io]\n",[99,29959,29960],{"class":10573,"line":10592},[99,29961,29962],{},"replace-with = 'aliyun'\n",[99,29964,29965],{"class":10573,"line":10598},[99,29966,29967],{},"[source.aliyun]\n",[99,29969,29970],{"class":10573,"line":10604},[99,29971,29972],{},"registry = \"sparse+https:\u002F\u002Fmirrors.aliyun.com\u002Fcrates.io-index\u002F\"\n",[67,29974,29975],{},"配置说明：",[21736,29977,29978,29981,29984],{},[21739,29979,29980],{},"设置crates.io索引仓库地址",[21739,29982,29983],{},"将默认源替换为阿里云镜像",[21739,29985,29986],{},"使用稀疏协议提高索引加载性能",[86,29988,29989],{"id":29989},"总结",[67,29991,29992],{},"通过以上配置，可以显著提升Rust在国内环境下的开发体验：",[27423,29994,29995,29998,30001,30004],{},[21739,29996,29997],{},"使用musl编译生成静态链接二进制文件",[21739,29999,30000],{},"便捷运行项目示例",[21739,30002,30003],{},"配置Rustup镜像源加速工具链更新",[21739,30005,30006],{},"设置crates.io镜像加速依赖下载",[10721,30008,30009],{},"html pre.shiki code .sBMFI, html code.shiki .sBMFI{--shiki-light:#E2931D;--shiki-default:#FFCB6B;--shiki-dark:#FFCB6B}html pre.shiki code .sfazB, html code.shiki .sfazB{--shiki-light:#91B859;--shiki-default:#C3E88D;--shiki-dark:#C3E88D}html .light .shiki span {color: var(--shiki-light);background: var(--shiki-light-bg);font-style: var(--shiki-light-font-style);font-weight: var(--shiki-light-font-weight);text-decoration: var(--shiki-light-text-decoration);}html.light .shiki span {color: var(--shiki-light);background: var(--shiki-light-bg);font-style: var(--shiki-light-font-style);font-weight: var(--shiki-light-font-weight);text-decoration: var(--shiki-light-text-decoration);}html .default .shiki span {color: var(--shiki-default);background: var(--shiki-default-bg);font-style: var(--shiki-default-font-style);font-weight: var(--shiki-default-font-weight);text-decoration: var(--shiki-default-text-decoration);}html .shiki span {color: var(--shiki-default);background: var(--shiki-default-bg);font-style: var(--shiki-default-font-style);font-weight: var(--shiki-default-font-weight);text-decoration: var(--shiki-default-text-decoration);}html .dark .shiki span {color: var(--shiki-dark);background: var(--shiki-dark-bg);font-style: var(--shiki-dark-font-style);font-weight: var(--shiki-dark-font-weight);text-decoration: var(--shiki-dark-text-decoration);}html.dark .shiki span {color: var(--shiki-dark);background: var(--shiki-dark-bg);font-style: var(--shiki-dark-font-style);font-weight: var(--shiki-dark-font-weight);text-decoration: var(--shiki-dark-text-decoration);}html pre.shiki code .spNyl, html code.shiki .spNyl{--shiki-light:#9C3EDA;--shiki-default:#C792EA;--shiki-dark:#C792EA}html pre.shiki code .sTEyZ, html code.shiki .sTEyZ{--shiki-light:#90A4AE;--shiki-default:#EEFFFF;--shiki-dark:#BABED8}html pre.shiki code .sMK4o, html code.shiki .sMK4o{--shiki-light:#39ADB5;--shiki-default:#89DDFF;--shiki-dark:#89DDFF}",{"title":10567,"searchDepth":10580,"depth":10580,"links":30011},[30012,30015,30016,30017,30018],{"id":29767,"depth":10580,"text":29768,"children":30013},[30014],{"id":29822,"depth":10586,"text":29823},{"id":29835,"depth":10580,"text":29835},{"id":29869,"depth":10580,"text":29870},{"id":29923,"depth":10580,"text":29924},{"id":29989,"depth":10580,"text":29989},"2026-01-09","介绍Rust的编译配置、镜像源设置和常见编译场景，包括musl编译、示例运行和镜像加速配置。","https:\u002F\u002Fppm-sources.oss-cn-hongkong.aliyuncs.com\u002Fzj\u002Frust-.crab.jpg",{},{"title":26,"description":30020},"IzCnyyGieRsjsu2FJY52qtchCTJGvuZyvpnBtq7Oui0",{"id":30026,"title":42,"author":30027,"body":30030,"date":30629,"description":30630,"extension":10734,"image":30021,"meta":30631,"minRead":10616,"navigation":53,"path":43,"seo":30632,"stem":44,"__hash__":30633},"blog\u002Fblog\u002Fwhy-rust-priority.md",{"name":60,"avatar":30028},{"src":62,"alt":30029},"Emma Thompson",{"type":64,"value":30031,"toc":30602},[30032,30035,30039,30042,30045,30049,30053,30056,30059,30063,30066,30072,30098,30104,30110,30114,30117,30146,30149,30153,30157,30160,30186,30207,30211,30218,30225,30279,30283,30298,30302,30308,30311,30315,30318,30351,30354,30358,30362,30430,30434,30442,30480,30484,30487,30491,30504,30508,30511,30515,30526,30530,30533,30536,30540,30543,30577,30586,30590,30593,30596,30599],[67,30033,30034],{},"In today's fragmented technology landscape, developers often face a daunting challenge: how to build applications that run seamlessly across different platforms without maintaining separate codebases for each one. Enter Rust—a systems programming language that has revolutionized cross-platform development with its powerful compilation capabilities and \"code once, build anywhere\" philosophy.",[86,30036,30038],{"id":30037},"the-cross-platform-promise","The Cross-Platform Promise",[67,30040,30041],{},"The traditional approach to cross-platform development often involves trade-offs. You might use web technologies with frameworks like Electron (paying a size and performance penalty), maintain separate codebases in different languages, or rely on virtual machines and runtimes that add overhead.",[67,30043,30044],{},"Rust takes a different approach. Through its sophisticated compiler toolchain and support for diverse target architectures, Rust enables you to write your code once and compile it to run natively on virtually any platform—all without sacrificing performance, safety, or developer experience.",[86,30046,30048],{"id":30047},"how-rust-makes-it-possible","How Rust Makes It Possible",[1258,30050,30052],{"id":30051},"llvm-backend-architecture","LLVM Backend Architecture",[67,30054,30055],{},"At the heart of Rust's cross-platform capabilities is its use of LLVM (Low-Level Virtual Machine) as its compiler backend. LLVM provides a powerful infrastructure for building compilers, supporting multiple CPU architectures and optimization strategies. When you write Rust code, the front-end parses and type-checks your code, then LLVM handles the platform-specific code generation and optimization.",[67,30057,30058],{},"This architecture means that adding support for a new platform often \"just works\" once LLVM supports it—the Rust team doesn't need to rebuild the entire compilation pipeline for each target.",[1258,30060,30062],{"id":30061},"tiered-platform-support","Tiered Platform Support",[67,30064,30065],{},"Rust organizes platforms into three tiers, each representing different levels of support and guaranteed stability:",[67,30067,30068,30071],{},[76,30069,30070],{},"Tier 1 platforms"," are guaranteed to work with the latest stable Rust release. These platforms have full testing infrastructure, and the Rust team commits to maintaining them. Examples include:",[21736,30073,30074,30080,30086,30092],{},[21739,30075,30076,30079],{},[10569,30077,30078],{},"x86_64-unknown-linux-gnu"," (64-bit Linux)",[21739,30081,30082,30085],{},[10569,30083,30084],{},"x86_64-pc-windows-msvc"," (64-bit Windows)",[21739,30087,30088,30091],{},[10569,30089,30090],{},"x86_64-apple-darwin"," (64-bit macOS)",[21739,30093,30094,30097],{},[10569,30095,30096],{},"aarch64-apple-darwin"," (Apple Silicon)",[67,30099,30100,30103],{},[76,30101,30102],{},"Tier 2 platforms"," are guaranteed to build but may not have full test coverage. This includes many Linux architectures and Windows variants.",[67,30105,30106,30109],{},[76,30107,30108],{},"Tier 3 platforms"," are those where Rust might work but aren't officially guaranteed. This is where experimental support for new architectures often lives.",[1258,30111,30113],{"id":30112},"cross-compilation-made-simple","Cross-Compilation Made Simple",[67,30115,30116],{},"Rust makes cross-compilation straightforward through its target system. To compile for a different architecture, you simply add the target and specify it when building:",[10562,30118,30120],{"className":27378,"code":30119,"language":27380,"meta":10567,"style":10567},"rustup target add x86_64-unknown-linux-musl\ncargo build --target x86_64-unknown-linux-musl\n",[10569,30121,30122,30135],{"__ignoreMap":10567},[99,30123,30124,30126,30129,30132],{"class":10573,"line":10574},[99,30125,27417],{"class":27387},[99,30127,30128],{"class":27391}," target",[99,30130,30131],{"class":27391}," add",[99,30133,30134],{"class":27391}," x86_64-unknown-linux-musl\n",[99,30136,30137,30139,30141,30144],{"class":10573,"line":10580},[99,30138,27466],{"class":27387},[99,30140,27873],{"class":27391},[99,30142,30143],{"class":27391}," --target",[99,30145,30134],{"class":27391},[67,30147,30148],{},"This simplicity extends to continuous integration pipelines, where you can build for multiple platforms in parallel without complex toolchain setup.",[86,30150,30152],{"id":30151},"real-world-cross-platform-scenarios","Real-World Cross-Platform Scenarios",[1258,30154,30156],{"id":30155},"webassembly-running-rust-in-the-browser","WebAssembly: Running Rust in the Browser",[67,30158,30159],{},"One of Rust's most exciting cross-platform capabilities is its excellent WebAssembly (Wasm) support. You can compile Rust code to Wasm and run it in browsers at near-native speed, opening up possibilities for performance-critical web applications.",[10562,30161,30163],{"className":27378,"code":30162,"language":27380,"meta":10567,"style":10567},"cargo install wasm-pack\nwasm-pack build --target web\n",[10569,30164,30165,30174],{"__ignoreMap":10567},[99,30166,30167,30169,30171],{"class":10573,"line":10574},[99,30168,27466],{"class":27387},[99,30170,27510],{"class":27391},[99,30172,30173],{"class":27391}," wasm-pack\n",[99,30175,30176,30179,30181,30183],{"class":10573,"line":10580},[99,30177,30178],{"class":27387},"wasm-pack",[99,30180,27873],{"class":27391},[99,30182,30143],{"class":27391},[99,30184,30185],{"class":27391}," web\n",[67,30187,30188,30189,30194,30195,30200,30201,30206],{},"Projects like ",[27116,30190,30193],{"href":30191,"rel":30192},"https:\u002F\u002Fyew.rs\u002F",[27120],"Yew",", ",[27116,30196,30199],{"href":30197,"rel":30198},"https:\u002F\u002Fleptos.dev\u002F",[27120],"Leptos",", and ",[27116,30202,30205],{"href":30203,"rel":30204},"https:\u002F\u002Fsycamore-rs.netlify.app\u002F",[27120],"Sycamore"," enable full-stack web development with Rust, sharing code between client and server.",[1258,30208,30210],{"id":30209},"embedded-systems-from-microcontrollers-to-iot","Embedded Systems: From Microcontrollers to IoT",[67,30212,30213,30214,30217],{},"Rust's zero-cost abstractions and minimal runtime make it ideal for embedded systems. Using the ",[10569,30215,30216],{},"embedded-hal"," (Hardware Abstraction Layer) ecosystem, you can write drivers that work across countless microcontroller families.",[67,30219,30220,30221,30224],{},"The ",[10569,30222,30223],{},"#[no_std]"," attribute allows Rust to run without the standard library, making it suitable for bare-metal systems:",[10562,30226,30230],{"className":30227,"code":30228,"language":30229,"meta":10567,"style":10567},"language-rust shiki shiki-themes material-theme-lighter material-theme material-theme-palenight","#![no_std]\n#![no_main]\n\nuse panic_halt as _;\n\n#[entry]\nfn main() -> ! {\n    \u002F\u002F Your embedded code here\n    loop {}\n}\n","rust",[10569,30231,30232,30237,30242,30246,30251,30255,30260,30265,30270,30275],{"__ignoreMap":10567},[99,30233,30234],{"class":10573,"line":10574},[99,30235,30236],{},"#![no_std]\n",[99,30238,30239],{"class":10573,"line":10580},[99,30240,30241],{},"#![no_main]\n",[99,30243,30244],{"class":10573,"line":10586},[99,30245,10613],{"emptyLinePlaceholder":53},[99,30247,30248],{"class":10573,"line":10592},[99,30249,30250],{},"use panic_halt as _;\n",[99,30252,30253],{"class":10573,"line":10598},[99,30254,10613],{"emptyLinePlaceholder":53},[99,30256,30257],{"class":10573,"line":10604},[99,30258,30259],{},"#[entry]\n",[99,30261,30262],{"class":10573,"line":10610},[99,30263,30264],{},"fn main() -> ! {\n",[99,30266,30267],{"class":10573,"line":10616},[99,30268,30269],{},"    \u002F\u002F Your embedded code here\n",[99,30271,30272],{"class":10573,"line":10622},[99,30273,30274],{},"    loop {}\n",[99,30276,30277],{"class":10573,"line":10627},[99,30278,27811],{},[1258,30280,30282],{"id":30281},"mobile-development-ios-and-android","Mobile Development: iOS and Android",[67,30284,30285,30286,30291,30292,30297],{},"While Rust doesn't have a mobile UI framework in its standard library, tools like ",[27116,30287,30290],{"href":30288,"rel":30289},"https:\u002F\u002Fkotlinlang.org\u002F",[27120],"Kotlin"," (Android) and ",[27116,30293,30296],{"href":30294,"rel":30295},"https:\u002F\u002Fwww.swift.org\u002F",[27120],"Swift"," (iOS) provide Foreign Function Interfaces (FFI) that make it easy to call Rust code. This pattern allows you to write performance-critical or shared business logic in Rust while using platform-native UI frameworks.",[1258,30299,30301],{"id":30300},"desktop-applications-with-tauri-and-wry","Desktop Applications with Tauri and Wry",[67,30303,30188,30304,30307],{},[27116,30305,27229],{"href":28850,"rel":30306},[27120]," demonstrate Rust's cross-platform prowess for desktop applications. Tauri lets you build desktop apps using a web frontend while Rust handles the backend, resulting in dramatically smaller bundle sizes compared to Electron.",[67,30309,30310],{},"A typical Tauri app might be 3-5 MB, whereas an equivalent Electron app could easily exceed 100 MB—all because Rust compiles to native code rather than bundling an entire Chromium browser.",[86,30312,30314],{"id":30313},"the-power-of-cargo-universal-dependency-management","The Power of Cargo: Universal Dependency Management",[67,30316,30317],{},"Cargo, Rust's package manager and build system, plays a crucial role in the \"code once\" philosophy. Cargo handles:",[21736,30319,30320,30326,30336,30342],{},[21739,30321,30322,30325],{},[76,30323,30324],{},"Cross-platform dependency resolution",": Libraries declare their supported platforms, and Cargo handles the rest",[21739,30327,30328,30331,30332,30335],{},[76,30329,30330],{},"Conditional compilation",": Use ",[10569,30333,30334],{},"#[cfg(target_os = \"windows\")]"," to include platform-specific code",[21739,30337,30338,30341],{},[76,30339,30340],{},"Automatic feature flags",": Enable or disable functionality based on target platform",[21739,30343,30344,28233,30347,30350],{},[76,30345,30346],{},"Build scripts",[10569,30348,30349],{},"build.rs"," files can run platform-specific build logic",[67,30352,30353],{},"This means you can write a library that abstracts platform differences internally while exposing a consistent API to users.",[86,30355,30357],{"id":30356},"practical-examples","Practical Examples",[1258,30359,30361],{"id":30360},"platform-specific-code","Platform-Specific Code",[10562,30363,30365],{"className":30227,"code":30364,"language":30229,"meta":10567,"style":10567},"#[cfg(target_os = \"windows\")]\nfn get_system_info() -> String {\n    format!(\"Windows {}\", windows_version())\n}\n\n#[cfg(target_os = \"linux\")]\nfn get_system_info() -> String {\n    fs::read_to_string(\"\u002Fetc\u002Fos-release\").unwrap()\n}\n\n#[cfg(target_os = \"macos\")]\nfn get_system_info() -> String {\n    \"macOS\".to_string()\n}\n",[10569,30366,30367,30372,30377,30382,30386,30390,30395,30399,30404,30408,30412,30417,30421,30426],{"__ignoreMap":10567},[99,30368,30369],{"class":10573,"line":10574},[99,30370,30371],{},"#[cfg(target_os = \"windows\")]\n",[99,30373,30374],{"class":10573,"line":10580},[99,30375,30376],{},"fn get_system_info() -> String {\n",[99,30378,30379],{"class":10573,"line":10586},[99,30380,30381],{},"    format!(\"Windows {}\", windows_version())\n",[99,30383,30384],{"class":10573,"line":10592},[99,30385,27811],{},[99,30387,30388],{"class":10573,"line":10598},[99,30389,10613],{"emptyLinePlaceholder":53},[99,30391,30392],{"class":10573,"line":10604},[99,30393,30394],{},"#[cfg(target_os = \"linux\")]\n",[99,30396,30397],{"class":10573,"line":10610},[99,30398,30376],{},[99,30400,30401],{"class":10573,"line":10616},[99,30402,30403],{},"    fs::read_to_string(\"\u002Fetc\u002Fos-release\").unwrap()\n",[99,30405,30406],{"class":10573,"line":10622},[99,30407,27811],{},[99,30409,30410],{"class":10573,"line":10627},[99,30411,10613],{"emptyLinePlaceholder":53},[99,30413,30414],{"class":10573,"line":10633},[99,30415,30416],{},"#[cfg(target_os = \"macos\")]\n",[99,30418,30419],{"class":10573,"line":10639},[99,30420,30376],{},[99,30422,30423],{"class":10573,"line":10645},[99,30424,30425],{},"    \"macOS\".to_string()\n",[99,30427,30428],{"class":10573,"line":10651},[99,30429,27811],{},[1258,30431,30433],{"id":30432},"cross-platform-networking-with-tokio","Cross-Platform Networking with Tokio",[67,30435,30220,30436,30441],{},[27116,30437,30440],{"href":30438,"rel":30439},"https:\u002F\u002Ftokio.rs\u002F",[27120],"Tokio"," runtime provides asynchronous networking that works across platforms:",[10562,30443,30445],{"className":30227,"code":30444,"language":30229,"meta":10567,"style":10567},"use tokio::net::TcpListener;\n\n#[tokio::main]\nasync fn main() -> Result\u003C(), Box\u003Cdyn std::error::Error>> {\n    let listener = TcpListener::bind(\"0.0.0.0:8080\").await?;\n    \u002F\u002F Same code works on Linux, Windows, and macOS\n}\n",[10569,30446,30447,30452,30456,30461,30466,30471,30476],{"__ignoreMap":10567},[99,30448,30449],{"class":10573,"line":10574},[99,30450,30451],{},"use tokio::net::TcpListener;\n",[99,30453,30454],{"class":10573,"line":10580},[99,30455,10613],{"emptyLinePlaceholder":53},[99,30457,30458],{"class":10573,"line":10586},[99,30459,30460],{},"#[tokio::main]\n",[99,30462,30463],{"class":10573,"line":10592},[99,30464,30465],{},"async fn main() -> Result\u003C(), Box\u003Cdyn std::error::Error>> {\n",[99,30467,30468],{"class":10573,"line":10598},[99,30469,30470],{},"    let listener = TcpListener::bind(\"0.0.0.0:8080\").await?;\n",[99,30472,30473],{"class":10573,"line":10604},[99,30474,30475],{},"    \u002F\u002F Same code works on Linux, Windows, and macOS\n",[99,30477,30478],{"class":10573,"line":10610},[99,30479,27811],{},[86,30481,30483],{"id":30482},"challenges-and-considerations","Challenges and Considerations",[67,30485,30486],{},"While Rust makes cross-platform development remarkably smooth, it's not without challenges:",[1258,30488,30490],{"id":30489},"platform-specific-apis","Platform-Specific APIs",[67,30492,30493,30494,30194,30497,30200,30500,30503],{},"Some functionality inherently differs across platforms. File paths, permissions, threading behavior, and system calls may vary. Crates like ",[10569,30495,30496],{},"dirs",[10569,30498,30499],{},"sys-info",[10569,30501,30502],{},"whoami"," help abstract these differences.",[1258,30505,30507],{"id":30506},"testing-burden","Testing Burden",[67,30509,30510],{},"Cross-platform code needs testing on all target platforms. Continuous integration with multiple test runners is essential. Services like GitHub Actions make this manageable with matrix builds.",[1258,30512,30514],{"id":30513},"binary-size-considerations","Binary Size Considerations",[67,30516,30517,30518,30521,30522,30525],{},"While Rust produces optimized binaries, static linking (common for portability) can increase size. Techniques like using ",[10569,30519,30520],{},"musl-gc"," for Linux or enabling link-time optimization (",[10569,30523,30524],{},"lto = true"," in Cargo.toml) help reduce footprint.",[86,30527,30529],{"id":30528},"the-ecosystem-effect","The Ecosystem Effect",[67,30531,30532],{},"Rust's cross-platform capabilities have catalyzed an ecosystem of portable libraries. When you publish a crate, you're implicitly contributing to a codebase that can run everywhere. Network protocols, serialization formats, data structures, algorithms—these all work identically across platforms.",[67,30534,30535],{},"This ecosystem effect creates a virtuous cycle: developers build portable libraries because the toolchain makes it easy, which makes Rust more attractive for cross-platform projects, which drives more portable library development.",[86,30537,30539],{"id":30538},"getting-started","Getting Started",[67,30541,30542],{},"Ready to build cross-platform Rust applications? Here's how to start:",[27423,30544,30545,30553,30561,30569],{},[21739,30546,30547,28233,30550],{},[76,30548,30549],{},"Install Rust",[10569,30551,30552],{},"curl --proto '=https' --tlsv1.2 -sSf https:\u002F\u002Fsh.rustup.rs | sh",[21739,30554,30555,28233,30558],{},[76,30556,30557],{},"List available targets",[10569,30559,30560],{},"rustup target list",[21739,30562,30563,28233,30566],{},[76,30564,30565],{},"Add a cross-compilation target",[10569,30567,30568],{},"rustup target add aarch64-apple-ios",[21739,30570,30571,28233,30574],{},[76,30572,30573],{},"Build for your target",[10569,30575,30576],{},"cargo build --target aarch64-apple-ios",[67,30578,30579,30580,30585],{},"For more advanced cross-compilation scenarios, check out ",[27116,30581,30584],{"href":30582,"rel":30583},"https:\u002F\u002Fgithub.com\u002Fcross-rs\u002Fcross",[27120],"cross",", a tool that simplifies cross-compilation using Docker containers.",[86,30587,30589],{"id":30588},"conclusion","Conclusion",[67,30591,30592],{},"Rust's \"code once, build anywhere\" capability isn't just a nice-to-have—it's a fundamental shift in how we think about cross-platform development. By combining the safety of a high-level language with the performance of low-level code and the portability of a sophisticated compiler toolchain, Rust enables developers to build software that truly runs everywhere without compromise.",[67,30594,30595],{},"Whether you're building web applications with WebAssembly, embedded systems on microcontrollers, mobile apps with native UIs, or desktop applications with Tauri, Rust provides a unified foundation that adapts to your needs.",[67,30597,30598],{},"The future of software development is cross-platform, and Rust is leading the way.",[10721,30600,30601],{},"html pre.shiki code .sBMFI, html code.shiki .sBMFI{--shiki-light:#E2931D;--shiki-default:#FFCB6B;--shiki-dark:#FFCB6B}html pre.shiki code .sfazB, html code.shiki .sfazB{--shiki-light:#91B859;--shiki-default:#C3E88D;--shiki-dark:#C3E88D}html .light .shiki span {color: var(--shiki-light);background: var(--shiki-light-bg);font-style: var(--shiki-light-font-style);font-weight: var(--shiki-light-font-weight);text-decoration: var(--shiki-light-text-decoration);}html.light .shiki span {color: var(--shiki-light);background: var(--shiki-light-bg);font-style: var(--shiki-light-font-style);font-weight: var(--shiki-light-font-weight);text-decoration: var(--shiki-light-text-decoration);}html .default .shiki span {color: var(--shiki-default);background: var(--shiki-default-bg);font-style: var(--shiki-default-font-style);font-weight: var(--shiki-default-font-weight);text-decoration: var(--shiki-default-text-decoration);}html .shiki span {color: var(--shiki-default);background: var(--shiki-default-bg);font-style: var(--shiki-default-font-style);font-weight: var(--shiki-default-font-weight);text-decoration: var(--shiki-default-text-decoration);}html .dark .shiki span {color: var(--shiki-dark);background: var(--shiki-dark-bg);font-style: var(--shiki-dark-font-style);font-weight: var(--shiki-dark-font-weight);text-decoration: var(--shiki-dark-text-decoration);}html.dark .shiki span {color: var(--shiki-dark);background: var(--shiki-dark-bg);font-style: var(--shiki-dark-font-style);font-weight: var(--shiki-dark-font-weight);text-decoration: var(--shiki-dark-text-decoration);}",{"title":10567,"searchDepth":10580,"depth":10580,"links":30603},[30604,30605,30610,30616,30617,30621,30626,30627,30628],{"id":30037,"depth":10580,"text":30038},{"id":30047,"depth":10580,"text":30048,"children":30606},[30607,30608,30609],{"id":30051,"depth":10586,"text":30052},{"id":30061,"depth":10586,"text":30062},{"id":30112,"depth":10586,"text":30113},{"id":30151,"depth":10580,"text":30152,"children":30611},[30612,30613,30614,30615],{"id":30155,"depth":10586,"text":30156},{"id":30209,"depth":10586,"text":30210},{"id":30281,"depth":10586,"text":30282},{"id":30300,"depth":10586,"text":30301},{"id":30313,"depth":10580,"text":30314},{"id":30356,"depth":10580,"text":30357,"children":30618},[30619,30620],{"id":30360,"depth":10586,"text":30361},{"id":30432,"depth":10586,"text":30433},{"id":30482,"depth":10580,"text":30483,"children":30622},[30623,30624,30625],{"id":30489,"depth":10586,"text":30490},{"id":30506,"depth":10586,"text":30507},{"id":30513,"depth":10586,"text":30514},{"id":30528,"depth":10580,"text":30529},{"id":30538,"depth":10580,"text":30539},{"id":30588,"depth":10580,"text":30589},"2025-12-28","Explore how Rust's powerful cross-platform compilation capabilities enable developers to build once and deploy everywhere—from embedded systems to webAssembly.",{},{"title":42,"description":30630},"ffeHvdY73BN95vATCxpqcJyzYOl4BdwKqcFFRIy39AE",{"id":30635,"title":30,"author":30636,"body":30638,"date":31285,"description":31286,"extension":10734,"image":31287,"meta":31288,"minRead":10598,"navigation":53,"path":31,"seo":31289,"stem":32,"__hash__":31290},"blog\u002Fblog\u002Fssh-key-authentication-setup.md",{"name":60,"avatar":30637},{"src":62,"alt":60},{"type":64,"value":30639,"toc":31269},[30640,30643,30647,30653,30657,30661,30664,30689,30694,30711,30715,30718,30731,30736,30750,30755,30784,30788,30791,30803,30806,30810,30815,30835,30840,30863,30867,30870,30929,30933,31022,31026,31031,31093,31098,31124,31129,31150,31154,31158,31165,31225,31228,31247,31249,31252,31266],[67,30641,30642],{},"SSH key authentication provides a secure and convenient way to access remote servers without entering passwords each time. This guide will walk you through the quick setup process.",[86,30644,30646],{"id":30645},"objective","Objective",[67,30648,30649,30650],{},"Configure SSH key authentication to enable passwordless login to remote server ",[10569,30651,30652],{},"user@203.0.113.42",[86,30654,30656],{"id":30655},"quick-configuration-steps","Quick Configuration Steps",[1258,30658,30660],{"id":30659},"_1-generate-key-pair","1. Generate Key Pair",[67,30662,30663],{},"Generate a new SSH key pair using ED25519 algorithm (recommended) or RSA:",[10562,30665,30667],{"className":27378,"code":30666,"language":27380,"meta":10567,"style":10567},"ssh-keygen -t ed25519 -C \"your_email@example.com\"\n",[10569,30668,30669],{"__ignoreMap":10567},[99,30670,30671,30674,30676,30679,30682,30684,30687],{"class":10573,"line":10574},[99,30672,30673],{"class":27387},"ssh-keygen",[99,30675,29794],{"class":27391},[99,30677,30678],{"class":27391}," ed25519",[99,30680,30681],{"class":27391}," -C",[99,30683,27520],{"class":27519},[99,30685,30686],{"class":27391},"your_email@example.com",[99,30688,27526],{"class":27519},[67,30690,30691],{},[76,30692,30693],{},"Options:",[21736,30695,30696,30702,30705],{},[21739,30697,30698,30699],{},"Use default path: ",[10569,30700,30701],{},"~\u002F.ssh\u002Fid_ed25519",[21739,30703,30704],{},"Passphrase is optional (leave empty for complete passwordless login)",[21739,30706,30707,30708],{},"For RSA keys: ",[10569,30709,30710],{},"ssh-keygen -t rsa -b 4096 -C \"your_email@example.com\"",[1258,30712,30714],{"id":30713},"_2-upload-public-key-to-remote-server","2. Upload Public Key to Remote Server",[67,30716,30717],{},"Copy your public key to the remote server:",[10562,30719,30721],{"className":27378,"code":30720,"language":27380,"meta":10567,"style":10567},"ssh-copy-id user@203.0.113.42\n",[10569,30722,30723],{"__ignoreMap":10567},[99,30724,30725,30728],{"class":10573,"line":10574},[99,30726,30727],{"class":27387},"ssh-copy-id",[99,30729,30730],{"class":27391}," user@203.0.113.42\n",[67,30732,30733],{},[76,30734,30735],{},"What happens:",[21736,30737,30738,30741,30747],{},[21739,30739,30740],{},"Enter password once for the initial connection",[21739,30742,30743,30744],{},"Automatically configures ",[10569,30745,30746],{},"~\u002F.ssh\u002Fauthorized_keys",[21739,30748,30749],{},"Sets correct permissions (700 for .ssh directory, 600 for authorized_keys)",[67,30751,30752],{},[76,30753,30754],{},"Alternative method (if ssh-copy-id is not available):",[10562,30756,30758],{"className":27378,"code":30757,"language":27380,"meta":10567,"style":10567},"cat ~\u002F.ssh\u002Fid_ed25519.pub | ssh user@203.0.113.42 \"mkdir -p ~\u002F.ssh && chmod 700 ~\u002F.ssh && cat >> ~\u002F.ssh\u002Fauthorized_keys && chmod 600 ~\u002F.ssh\u002Fauthorized_keys\"\n",[10569,30759,30760],{"__ignoreMap":10567},[99,30761,30762,30765,30768,30771,30774,30777,30779,30782],{"class":10573,"line":10574},[99,30763,30764],{"class":27387},"cat",[99,30766,30767],{"class":27391}," ~\u002F.ssh\u002Fid_ed25519.pub",[99,30769,30770],{"class":27519}," |",[99,30772,30773],{"class":27387}," ssh",[99,30775,30776],{"class":27391}," user@203.0.113.42",[99,30778,27520],{"class":27519},[99,30780,30781],{"class":27391},"mkdir -p ~\u002F.ssh && chmod 700 ~\u002F.ssh && cat >> ~\u002F.ssh\u002Fauthorized_keys && chmod 600 ~\u002F.ssh\u002Fauthorized_keys",[99,30783,27526],{"class":27519},[1258,30785,30787],{"id":30786},"_3-verify-passwordless-login","3. Verify Passwordless Login",[67,30789,30790],{},"Test the configuration:",[10562,30792,30794],{"className":27378,"code":30793,"language":27380,"meta":10567,"style":10567},"ssh user@203.0.113.42\n",[10569,30795,30796],{"__ignoreMap":10567},[99,30797,30798,30801],{"class":10573,"line":10574},[99,30799,30800],{"class":27387},"ssh",[99,30802,30730],{"class":27391},[67,30804,30805],{},"You should now be logged in without entering a password!",[86,30807,30809],{"id":30808},"understanding-ssh-keys","Understanding SSH Keys",[67,30811,30812],{},[76,30813,30814],{},"Private Key:",[21736,30816,30817,30822,30825,30832],{},[21739,30818,30819,30820],{},"Location: ",[10569,30821,30701],{},[21739,30823,30824],{},"Purpose: Authentication credential, must be kept secret",[21739,30826,30827,30828,30831],{},"Permissions: Should be ",[10569,30829,30830],{},"600"," (read\u002Fwrite for owner only)",[21739,30833,30834],{},"NEVER share this file",[67,30836,30837],{},[76,30838,30839],{},"Public Key:",[21736,30841,30842,30847,30850,30857],{},[21739,30843,30819,30844],{},[10569,30845,30846],{},"~\u002F.ssh\u002Fid_ed25519.pub",[21739,30848,30849],{},"Purpose: Can be freely shared and placed on servers",[21739,30851,30852,30853,30856],{},"Permissions: Can be ",[10569,30854,30855],{},"644"," (readable by others)",[21739,30858,30859,30860,30862],{},"Added to ",[10569,30861,30746],{}," on remote server",[86,30864,30866],{"id":30865},"usage-in-deployment-scripts","Usage in Deployment Scripts",[67,30868,30869],{},"After configuration, your deployment scripts can run without password prompts:",[10562,30871,30873],{"className":27378,"code":30872,"language":27380,"meta":10567,"style":10567},"#!\u002Fbin\u002Fbash\n# scripts\u002Fdeploy.sh\n\n# Now you can execute commands without password prompts\nssh user@203.0.113.42 \"cd \u002Fvar\u002Fwww\u002Fapp && git pull && npm install && npm run build\"\n\n# Or copy files without password\nscp -r .\u002Fdist user@203.0.113.42:\u002Fvar\u002Fwww\u002Fapp\u002F\n",[10569,30874,30875,30880,30885,30889,30894,30907,30911,30916],{"__ignoreMap":10567},[99,30876,30877],{"class":10573,"line":10574},[99,30878,30879],{"class":27395},"#!\u002Fbin\u002Fbash\n",[99,30881,30882],{"class":10573,"line":10580},[99,30883,30884],{"class":27395},"# scripts\u002Fdeploy.sh\n",[99,30886,30887],{"class":10573,"line":10586},[99,30888,10613],{"emptyLinePlaceholder":53},[99,30890,30891],{"class":10573,"line":10592},[99,30892,30893],{"class":27395},"# Now you can execute commands without password prompts\n",[99,30895,30896,30898,30900,30902,30905],{"class":10573,"line":10598},[99,30897,30800],{"class":27387},[99,30899,30776],{"class":27391},[99,30901,27520],{"class":27519},[99,30903,30904],{"class":27391},"cd \u002Fvar\u002Fwww\u002Fapp && git pull && npm install && npm run build",[99,30906,27526],{"class":27519},[99,30908,30909],{"class":10573,"line":10604},[99,30910,10613],{"emptyLinePlaceholder":53},[99,30912,30913],{"class":10573,"line":10610},[99,30914,30915],{"class":27395},"# Or copy files without password\n",[99,30917,30918,30921,30923,30926],{"class":10573,"line":10616},[99,30919,30920],{"class":27387},"scp",[99,30922,28504],{"class":27391},[99,30924,30925],{"class":27391}," .\u002Fdist",[99,30927,30928],{"class":27391}," user@203.0.113.42:\u002Fvar\u002Fwww\u002Fapp\u002F\n",[86,30930,30932],{"id":30931},"security-best-practices","Security Best Practices",[27423,30934,30935,30941,30950,30956,30980,30986],{},[21739,30936,30937,30940],{},[76,30938,30939],{},"Use a passphrase"," for your private key (optional but recommended)",[21739,30942,30943,30946,30947,2846],{},[76,30944,30945],{},"Never share your private key"," (",[10569,30948,30949],{},"id_ed25519",[21739,30951,30952,30955],{},[76,30953,30954],{},"Use different keys"," for different services",[21739,30957,30958,30961,30962],{},[76,30959,30960],{},"Disable password authentication"," on the server after setting up keys:\n",[10562,30963,30965],{"className":27378,"code":30964,"language":27380,"meta":10567,"style":10567},"# Edit \u002Fetc\u002Fssh\u002Fsshd_config\nPasswordAuthentication no\n",[10569,30966,30967,30972],{"__ignoreMap":10567},[99,30968,30969],{"class":10573,"line":10574},[99,30970,30971],{"class":27395},"# Edit \u002Fetc\u002Fssh\u002Fsshd_config\n",[99,30973,30974,30977],{"class":10573,"line":10580},[99,30975,30976],{"class":27387},"PasswordAuthentication",[99,30978,30979],{"class":27391}," no\n",[21739,30981,30982,30985],{},[76,30983,30984],{},"Regularly rotate keys"," for critical systems",[21739,30987,30988,30991,30992],{},[76,30989,30990],{},"Use SSH agent"," to manage keys:\n",[10562,30993,30995],{"className":27378,"code":30994,"language":27380,"meta":10567,"style":10567},"eval \"$(ssh-agent -s)\"\nssh-add ~\u002F.ssh\u002Fid_ed25519\n",[10569,30996,30997,31014],{"__ignoreMap":10567},[99,30998,30999,31002,31005,31008,31011],{"class":10573,"line":10574},[99,31000,31001],{"class":27617},"eval",[99,31003,31004],{"class":27519}," \"$(",[99,31006,31007],{"class":27387},"ssh-agent",[99,31009,31010],{"class":27391}," -s",[99,31012,31013],{"class":27519},")\"\n",[99,31015,31016,31019],{"class":10573,"line":10580},[99,31017,31018],{"class":27387},"ssh-add",[99,31020,31021],{"class":27391}," ~\u002F.ssh\u002Fid_ed25519\n",[86,31023,31025],{"id":31024},"troubleshooting","Troubleshooting",[67,31027,31028],{},[76,31029,31030],{},"Permission denied error:",[10562,31032,31034],{"className":27378,"code":31033,"language":27380,"meta":10567,"style":10567},"# Fix permissions on local machine\nchmod 700 ~\u002F.ssh\nchmod 600 ~\u002F.ssh\u002Fid_ed25519\nchmod 644 ~\u002F.ssh\u002Fid_ed25519.pub\n\n# Fix permissions on remote server\nssh user@203.0.113.42 \"chmod 700 ~\u002F.ssh && chmod 600 ~\u002F.ssh\u002Fauthorized_keys\"\n",[10569,31035,31036,31041,31052,31061,31071,31075,31080],{"__ignoreMap":10567},[99,31037,31038],{"class":10573,"line":10574},[99,31039,31040],{"class":27395},"# Fix permissions on local machine\n",[99,31042,31043,31046,31049],{"class":10573,"line":10580},[99,31044,31045],{"class":27387},"chmod",[99,31047,31048],{"class":29255}," 700",[99,31050,31051],{"class":27391}," ~\u002F.ssh\n",[99,31053,31054,31056,31059],{"class":10573,"line":10586},[99,31055,31045],{"class":27387},[99,31057,31058],{"class":29255}," 600",[99,31060,31021],{"class":27391},[99,31062,31063,31065,31068],{"class":10573,"line":10592},[99,31064,31045],{"class":27387},[99,31066,31067],{"class":29255}," 644",[99,31069,31070],{"class":27391}," ~\u002F.ssh\u002Fid_ed25519.pub\n",[99,31072,31073],{"class":10573,"line":10598},[99,31074,10613],{"emptyLinePlaceholder":53},[99,31076,31077],{"class":10573,"line":10604},[99,31078,31079],{"class":27395},"# Fix permissions on remote server\n",[99,31081,31082,31084,31086,31088,31091],{"class":10573,"line":10610},[99,31083,30800],{"class":27387},[99,31085,30776],{"class":27391},[99,31087,27520],{"class":27519},[99,31089,31090],{"class":27391},"chmod 700 ~\u002F.ssh && chmod 600 ~\u002F.ssh\u002Fauthorized_keys",[99,31092,27526],{"class":27519},[67,31094,31095],{},[76,31096,31097],{},"Still asks for password:",[21736,31099,31100,31105,31111,31118],{},[21739,31101,31102,31103,30862],{},"Verify public key is in ",[10569,31104,30746],{},[21739,31106,31107,31108],{},"Check SSH server configuration: ",[10569,31109,31110],{},"\u002Fetc\u002Fssh\u002Fsshd_config",[21739,31112,31113,31114,31117],{},"Ensure ",[10569,31115,31116],{},"PubkeyAuthentication yes"," is set",[21739,31119,31120,31121],{},"Restart SSH service: ",[10569,31122,31123],{},"sudo systemctl restart sshd",[67,31125,31126],{},[76,31127,31128],{},"Multiple keys:",[10562,31130,31132],{"className":27378,"code":31131,"language":27380,"meta":10567,"style":10567},"# Specify which key to use\nssh -i ~\u002F.ssh\u002Fspecific_key user@203.0.113.42\n",[10569,31133,31134,31139],{"__ignoreMap":10567},[99,31135,31136],{"class":10573,"line":10574},[99,31137,31138],{"class":27395},"# Specify which key to use\n",[99,31140,31141,31143,31145,31148],{"class":10573,"line":10580},[99,31142,30800],{"class":27387},[99,31144,28963],{"class":27391},[99,31146,31147],{"class":27391}," ~\u002F.ssh\u002Fspecific_key",[99,31149,30730],{"class":27391},[86,31151,31153],{"id":31152},"advanced-configuration","Advanced Configuration",[1258,31155,31157],{"id":31156},"ssh-config-file","SSH Config File",[67,31159,31160,31161,31164],{},"Create ",[10569,31162,31163],{},"~\u002F.ssh\u002Fconfig"," for easier connections:",[10562,31166,31169],{"className":31167,"code":31168,"language":30800,"meta":10567,"style":10567},"language-ssh shiki shiki-themes material-theme-lighter material-theme material-theme-palenight","Host myserver\n    HostName 203.0.113.42\n    User user\n    IdentityFile ~\u002F.ssh\u002Fid_ed25519\n    Port 22\n\nHost production\n    HostName 198.51.100.17\n    User deploy\n    IdentityFile ~\u002F.ssh\u002Fwork_key\n    Port 2222\n",[10569,31170,31171,31176,31181,31186,31191,31196,31200,31205,31210,31215,31220],{"__ignoreMap":10567},[99,31172,31173],{"class":10573,"line":10574},[99,31174,31175],{},"Host myserver\n",[99,31177,31178],{"class":10573,"line":10580},[99,31179,31180],{},"    HostName 203.0.113.42\n",[99,31182,31183],{"class":10573,"line":10586},[99,31184,31185],{},"    User user\n",[99,31187,31188],{"class":10573,"line":10592},[99,31189,31190],{},"    IdentityFile ~\u002F.ssh\u002Fid_ed25519\n",[99,31192,31193],{"class":10573,"line":10598},[99,31194,31195],{},"    Port 22\n",[99,31197,31198],{"class":10573,"line":10604},[99,31199,10613],{"emptyLinePlaceholder":53},[99,31201,31202],{"class":10573,"line":10610},[99,31203,31204],{},"Host production\n",[99,31206,31207],{"class":10573,"line":10616},[99,31208,31209],{},"    HostName 198.51.100.17\n",[99,31211,31212],{"class":10573,"line":10622},[99,31213,31214],{},"    User deploy\n",[99,31216,31217],{"class":10573,"line":10627},[99,31218,31219],{},"    IdentityFile ~\u002F.ssh\u002Fwork_key\n",[99,31221,31222],{"class":10573,"line":10633},[99,31223,31224],{},"    Port 2222\n",[67,31226,31227],{},"Now you can connect with:",[10562,31229,31231],{"className":27378,"code":31230,"language":27380,"meta":10567,"style":10567},"ssh myserver\nssh production\n",[10569,31232,31233,31240],{"__ignoreMap":10567},[99,31234,31235,31237],{"class":10573,"line":10574},[99,31236,30800],{"class":27387},[99,31238,31239],{"class":27391}," myserver\n",[99,31241,31242,31244],{"class":10573,"line":10580},[99,31243,30800],{"class":27387},[99,31245,31246],{"class":27391}," production\n",[86,31248,30589],{"id":30588},[67,31250,31251],{},"SSH key authentication provides:",[21736,31253,31254,31257,31260,31263],{},[21739,31255,31256],{},"✅ Enhanced security (cryptographic authentication)",[21739,31258,31259],{},"✅ Convenience (no password typing)",[21739,31261,31262],{},"✅ Automation support (scripts, CI\u002FCD)",[21739,31264,31265],{},"✅ Single sign-on experience (with SSH agent)",[10721,31267,31268],{},"html pre.shiki code .sBMFI, html code.shiki .sBMFI{--shiki-light:#E2931D;--shiki-default:#FFCB6B;--shiki-dark:#FFCB6B}html pre.shiki code .sfazB, html code.shiki .sfazB{--shiki-light:#91B859;--shiki-default:#C3E88D;--shiki-dark:#C3E88D}html pre.shiki code .sMK4o, html code.shiki .sMK4o{--shiki-light:#39ADB5;--shiki-default:#89DDFF;--shiki-dark:#89DDFF}html .light .shiki span {color: var(--shiki-light);background: var(--shiki-light-bg);font-style: var(--shiki-light-font-style);font-weight: var(--shiki-light-font-weight);text-decoration: var(--shiki-light-text-decoration);}html.light .shiki span {color: var(--shiki-light);background: var(--shiki-light-bg);font-style: var(--shiki-light-font-style);font-weight: var(--shiki-light-font-weight);text-decoration: var(--shiki-light-text-decoration);}html .default .shiki span {color: var(--shiki-default);background: var(--shiki-default-bg);font-style: var(--shiki-default-font-style);font-weight: var(--shiki-default-font-weight);text-decoration: var(--shiki-default-text-decoration);}html .shiki span {color: var(--shiki-default);background: var(--shiki-default-bg);font-style: var(--shiki-default-font-style);font-weight: var(--shiki-default-font-weight);text-decoration: var(--shiki-default-text-decoration);}html .dark .shiki span {color: var(--shiki-dark);background: var(--shiki-dark-bg);font-style: var(--shiki-dark-font-style);font-weight: var(--shiki-dark-font-weight);text-decoration: var(--shiki-dark-text-decoration);}html.dark .shiki span {color: var(--shiki-dark);background: var(--shiki-dark-bg);font-style: var(--shiki-dark-font-style);font-weight: var(--shiki-dark-font-weight);text-decoration: var(--shiki-dark-text-decoration);}html pre.shiki code .sHwdD, html code.shiki .sHwdD{--shiki-light:#90A4AE;--shiki-light-font-style:italic;--shiki-default:#546E7A;--shiki-default-font-style:italic;--shiki-dark:#676E95;--shiki-dark-font-style:italic}html pre.shiki code .s2Zo4, html code.shiki .s2Zo4{--shiki-light:#6182B8;--shiki-default:#82AAFF;--shiki-dark:#82AAFF}html pre.shiki code .sbssI, html code.shiki .sbssI{--shiki-light:#F76D47;--shiki-default:#F78C6C;--shiki-dark:#F78C6C}",{"title":10567,"searchDepth":10580,"depth":10580,"links":31270},[31271,31272,31277,31278,31279,31280,31281,31284],{"id":30645,"depth":10580,"text":30646},{"id":30655,"depth":10580,"text":30656,"children":31273},[31274,31275,31276],{"id":30659,"depth":10586,"text":30660},{"id":30713,"depth":10586,"text":30714},{"id":30786,"depth":10586,"text":30787},{"id":30808,"depth":10580,"text":30809},{"id":30865,"depth":10580,"text":30866},{"id":30931,"depth":10580,"text":30932},{"id":31024,"depth":10580,"text":31025},{"id":31152,"depth":10580,"text":31153,"children":31282},[31283],{"id":31156,"depth":10586,"text":31157},{"id":30588,"depth":10580,"text":30589},"2025-01-04","Learn how to configure SSH key authentication for passwordless remote server login with quick and easy steps.","https:\u002F\u002Fppm-sources.oss-cn-hongkong.aliyuncs.com\u002Fzj\u002F3rd\u002Fssh.png",{},{"title":30,"description":31286},"n__8R9u4Qho7yxoHUzRVvPoWZ25jgJBCJogk820QI6A",{"id":31292,"title":38,"author":31293,"body":31295,"date":34812,"description":34813,"extension":10734,"image":30021,"meta":34814,"minRead":10639,"navigation":53,"path":39,"seo":34815,"stem":40,"__hash__":34816},"blog\u002Fblog\u002Futoipa-integration-with-axum.md",{"name":60,"avatar":31294},{"src":62,"alt":60},{"type":64,"value":31296,"toc":34753},[31297,31300,31304,31307,31339,31343,31347,31352,31439,31444,31468,31472,31475,31481,31485,31488,31494,31498,31502,31509,31554,31558,31565,31752,31758,31798,31802,31807,31821,31826,31840,31845,31861,31865,31869,32016,32020,32108,32112,32208,32212,32308,32312,32391,32395,32399,32470,32474,32562,32566,32625,32629,32692,32695,32755,32759,32763,33168,33172,33176,33351,33355,33419,33423,33426,33446,33450,33454,33559,33563,33634,33638,33729,33733,33932,33936,33959,33963,33967,33972,33998,34003,34060,34064,34068,34088,34092,34127,34131,34136,34160,34164,34190,34197,34202,34208,34217,34225,34283,34287,34344,34347,34351,34355,34385,34389,34423,34427,34466,34470,34510,34514,34591,34595,34649,34651,34654,34715,34718,34722,34751],[67,31298,31299],{},"Building RESTful APIs in Rust with Axum is fantastic, but comprehensive API documentation is equally important. That's where utoipa comes in - a powerful OpenAPI documentation generator that integrates seamlessly with Axum and Swagger UI. Let's dive into how to set up a complete documentation system with multiple authentication methods.",[86,31301,31303],{"id":31302},"why-utoipa","Why Utoipa?",[67,31305,31306],{},"utoipa provides compile-time OpenAPI documentation generation using Rust macros:",[21736,31308,31309,31315,31321,31327,31333],{},[21739,31310,31311,31314],{},[76,31312,31313],{},"Type Safety",": Leverages Rust's type system for accurate API docs",[21739,31316,31317,31320],{},[76,31318,31319],{},"No Code Duplication",": Documentation lives alongside your code",[21739,31322,31323,31326],{},[76,31324,31325],{},"Multiple Auth Methods",": Support for JWT, API Keys, Cookies",[21739,31328,31329,31332],{},[76,31330,31331],{},"Swagger UI Integration",": Beautiful, interactive API documentation",[21739,31334,31335,31338],{},[76,31336,31337],{},"OpenAPI 3.0 Compatible",": Standard-compliant specification",[86,31340,31342],{"id":31341},"project-setup","Project Setup",[1258,31344,31346],{"id":31345},"dependency-configuration","Dependency Configuration",[67,31348,31349,31350,27783],{},"Start by adding the necessary dependencies to your ",[10569,31351,28175],{},[10562,31353,31355],{"className":29938,"code":31354,"language":29940,"meta":10567,"style":10567},"[dependencies]\n# Core dependencies\naxum = \"0.7\"\ntokio = { version = \"1\", features = [\"full\"] }\nsea-orm = \"0.12\"\n\n# OpenAPI documentation\nutoipa = { version = \"4\", features = [\"uuid\", \"chrono\"] }\nutoipa-swagger-ui = { version = \"6\", features = [\"axum\"] }\n\n# Serialization\nserde = { version = \"1.0\", features = [\"derive\"] }\nserde_json = \"1.0\"\n\n# Time and UUID\nchrono = { version = \"0.4\", features = [\"serde\"] }\nuuid = { version = \"1\", features = [\"v4\", \"serde\"] }\n",[10569,31356,31357,31362,31367,31372,31377,31382,31386,31391,31396,31401,31405,31410,31415,31420,31424,31429,31434],{"__ignoreMap":10567},[99,31358,31359],{"class":10573,"line":10574},[99,31360,31361],{},"[dependencies]\n",[99,31363,31364],{"class":10573,"line":10580},[99,31365,31366],{},"# Core dependencies\n",[99,31368,31369],{"class":10573,"line":10586},[99,31370,31371],{},"axum = \"0.7\"\n",[99,31373,31374],{"class":10573,"line":10592},[99,31375,31376],{},"tokio = { version = \"1\", features = [\"full\"] }\n",[99,31378,31379],{"class":10573,"line":10598},[99,31380,31381],{},"sea-orm = \"0.12\"\n",[99,31383,31384],{"class":10573,"line":10604},[99,31385,10613],{"emptyLinePlaceholder":53},[99,31387,31388],{"class":10573,"line":10610},[99,31389,31390],{},"# OpenAPI documentation\n",[99,31392,31393],{"class":10573,"line":10616},[99,31394,31395],{},"utoipa = { version = \"4\", features = [\"uuid\", \"chrono\"] }\n",[99,31397,31398],{"class":10573,"line":10622},[99,31399,31400],{},"utoipa-swagger-ui = { version = \"6\", features = [\"axum\"] }\n",[99,31402,31403],{"class":10573,"line":10627},[99,31404,10613],{"emptyLinePlaceholder":53},[99,31406,31407],{"class":10573,"line":10633},[99,31408,31409],{},"# Serialization\n",[99,31411,31412],{"class":10573,"line":10639},[99,31413,31414],{},"serde = { version = \"1.0\", features = [\"derive\"] }\n",[99,31416,31417],{"class":10573,"line":10645},[99,31418,31419],{},"serde_json = \"1.0\"\n",[99,31421,31422],{"class":10573,"line":10651},[99,31423,10613],{"emptyLinePlaceholder":53},[99,31425,31426],{"class":10573,"line":10657},[99,31427,31428],{},"# Time and UUID\n",[99,31430,31431],{"class":10573,"line":10663},[99,31432,31433],{},"chrono = { version = \"0.4\", features = [\"serde\"] }\n",[99,31435,31436],{"class":10573,"line":10669},[99,31437,31438],{},"uuid = { version = \"1\", features = [\"v4\", \"serde\"] }\n",[67,31440,31441,27783],{},[76,31442,31443],{},"Important Notes",[21736,31445,31446,31449,31459],{},[21739,31447,31448],{},"Use utoipa version 4.x (avoid 5.x for better stability)",[21739,31450,31451,31452,926,31455,31458],{},"Enable ",[10569,31453,31454],{},"uuid",[10569,31456,31457],{},"chrono"," features for proper type support",[21739,31460,31113,31461,31464,31465],{},[10569,31462,31463],{},"utoipa-swagger-ui"," version is compatible with ",[10569,31466,31467],{},"utoipa",[1258,31469,31471],{"id":31470},"project-structure","Project Structure",[67,31473,31474],{},"Organize your documentation code for clarity:",[10562,31476,31479],{"className":31477,"code":31478,"language":582},[10707],"src\u002F\n├── docs\u002F\n│   ├── mod.rs              # Documentation module entry\n│   ├── security.rs         # Security schemes (Modify trait)\n│   ├── openapi.rs          # OpenAPI helpers\n│   └── schemas.rs          # Data model definitions\n├── handler.rs              # API handlers\n├── main.rs                 # App entry + ApiDoc definition\n└── route.rs                # Route definitions\n",[10569,31480,31478],{"__ignoreMap":10567},[86,31482,31484],{"id":31483},"understanding-utoipas-architecture","Understanding Utoipa's Architecture",[67,31486,31487],{},"utoipa generates OpenAPI documentation through three key components:",[10562,31489,31492],{"className":31490,"code":31491,"language":582},[10707],"┌─────────────────────────────────────────────────┐\n│  utoipa::path (marks handler functions)         │\n│  ↓                                              │\n│  Collects API info (path, method, params, resp) │\n│                                                 │\n├─────────────────────────────────────────────────┤\n│  ToSchema (marks data structures)               │\n│  ↓                                              │\n│  Generates Schema definitions (request\u002Fresponse)│\n│                                                 │\n├─────────────────────────────────────────────────┤\n│  OpenApi (aggregates configuration)             │\n│  ↓                                              │\n│  Generates complete OpenAPI JSON document       │\n│                                                 │\n├─────────────────────────────────────────────────┤\n│  SwaggerUi (serves documentation interface)     │\n│  ↓                                              │\n│  Provides visual API docs and testing UI        │\n└─────────────────────────────────────────────────┘\n",[10569,31493,31491],{"__ignoreMap":10567},[86,31495,31497],{"id":31496},"security-configuration-the-modify-trait","Security Configuration: The Modify Trait",[1258,31499,31501],{"id":31500},"the-challenge","The Challenge",[67,31503,31504,31505,31508],{},"utoipa 4.x doesn't support defining security schemes directly in the ",[10569,31506,31507],{},"#[openapi]"," macro:",[10562,31510,31512],{"className":30227,"code":31511,"language":30229,"meta":10567,"style":10567},"\u002F\u002F ❌ This doesn't work in utoipa 4.x!\n#[derive(OpenApi)]\n#[openapi(\n    security_schemes(\n        (\"bearerAuth\" = ...)\n    )\n)]\nstruct ApiDoc;\n",[10569,31513,31514,31519,31524,31529,31534,31539,31544,31549],{"__ignoreMap":10567},[99,31515,31516],{"class":10573,"line":10574},[99,31517,31518],{},"\u002F\u002F ❌ This doesn't work in utoipa 4.x!\n",[99,31520,31521],{"class":10573,"line":10580},[99,31522,31523],{},"#[derive(OpenApi)]\n",[99,31525,31526],{"class":10573,"line":10586},[99,31527,31528],{},"#[openapi(\n",[99,31530,31531],{"class":10573,"line":10592},[99,31532,31533],{},"    security_schemes(\n",[99,31535,31536],{"class":10573,"line":10598},[99,31537,31538],{},"        (\"bearerAuth\" = ...)\n",[99,31540,31541],{"class":10573,"line":10604},[99,31542,31543],{},"    )\n",[99,31545,31546],{"class":10573,"line":10610},[99,31547,31548],{},")]\n",[99,31550,31551],{"class":10573,"line":10616},[99,31552,31553],{},"struct ApiDoc;\n",[1258,31555,31557],{"id":31556},"the-solution-modify-trait","The Solution: Modify Trait",[67,31559,31560,31561,31564],{},"Create a custom type that implements the ",[10569,31562,31563],{},"Modify"," trait:",[10562,31566,31568],{"className":30227,"code":31567,"language":30229,"meta":10567,"style":10567},"\u002F\u002F src\u002Fdocs\u002Fsecurity.rs\nuse utoipa::{Modify, OpenApi};\nuse utoipa::openapi::security::{SecurityScheme, HttpAuthScheme, Http, ApiKey, ApiKeyValue};\n\n\u002F\u002F\u002F JWT and API Key security configuration\npub struct JwtSecurityAddon;\n\nimpl Modify for JwtSecurityAddon {\n    fn modify(&self, openapi: &mut utoipa::openapi::OpenApi) {\n        if let Some(components) = openapi.components.as_mut() {\n            \u002F\u002F 1. JWT Bearer Token authentication\n            components.add_security_scheme(\n                \"bearerAuth\",\n                SecurityScheme::Http(\n                    Http::new(HttpAuthScheme::Bearer)\n                ),\n            );\n\n            \u002F\u002F 2. Cookie authentication\n            components.add_security_scheme(\n                \"cookieAuth\",\n                SecurityScheme::ApiKey(\n                    ApiKey::Cookie(ApiKeyValue::new(\"token\"))\n                ),\n            );\n\n            \u002F\u002F 3. API Key authentication (Header-based)\n            components.add_security_scheme(\n                \"apiKeyAuth\",\n                SecurityScheme::ApiKey(\n                    ApiKey::Header(ApiKeyValue::new(\"X-API-Key\"))\n                ),\n            );\n        }\n    }\n}\n",[10569,31569,31570,31575,31580,31585,31589,31594,31599,31603,31608,31613,31618,31623,31628,31633,31638,31643,31648,31653,31657,31662,31666,31671,31676,31682,31687,31692,31697,31703,31708,31714,31719,31725,31730,31735,31741,31747],{"__ignoreMap":10567},[99,31571,31572],{"class":10573,"line":10574},[99,31573,31574],{},"\u002F\u002F src\u002Fdocs\u002Fsecurity.rs\n",[99,31576,31577],{"class":10573,"line":10580},[99,31578,31579],{},"use utoipa::{Modify, OpenApi};\n",[99,31581,31582],{"class":10573,"line":10586},[99,31583,31584],{},"use utoipa::openapi::security::{SecurityScheme, HttpAuthScheme, Http, ApiKey, ApiKeyValue};\n",[99,31586,31587],{"class":10573,"line":10592},[99,31588,10613],{"emptyLinePlaceholder":53},[99,31590,31591],{"class":10573,"line":10598},[99,31592,31593],{},"\u002F\u002F\u002F JWT and API Key security configuration\n",[99,31595,31596],{"class":10573,"line":10604},[99,31597,31598],{},"pub struct JwtSecurityAddon;\n",[99,31600,31601],{"class":10573,"line":10610},[99,31602,10613],{"emptyLinePlaceholder":53},[99,31604,31605],{"class":10573,"line":10616},[99,31606,31607],{},"impl Modify for JwtSecurityAddon {\n",[99,31609,31610],{"class":10573,"line":10622},[99,31611,31612],{},"    fn modify(&self, openapi: &mut utoipa::openapi::OpenApi) {\n",[99,31614,31615],{"class":10573,"line":10627},[99,31616,31617],{},"        if let Some(components) = openapi.components.as_mut() {\n",[99,31619,31620],{"class":10573,"line":10633},[99,31621,31622],{},"            \u002F\u002F 1. JWT Bearer Token authentication\n",[99,31624,31625],{"class":10573,"line":10639},[99,31626,31627],{},"            components.add_security_scheme(\n",[99,31629,31630],{"class":10573,"line":10645},[99,31631,31632],{},"                \"bearerAuth\",\n",[99,31634,31635],{"class":10573,"line":10651},[99,31636,31637],{},"                SecurityScheme::Http(\n",[99,31639,31640],{"class":10573,"line":10657},[99,31641,31642],{},"                    Http::new(HttpAuthScheme::Bearer)\n",[99,31644,31645],{"class":10573,"line":10663},[99,31646,31647],{},"                ),\n",[99,31649,31650],{"class":10573,"line":10669},[99,31651,31652],{},"            );\n",[99,31654,31655],{"class":10573,"line":10674},[99,31656,10613],{"emptyLinePlaceholder":53},[99,31658,31659],{"class":10573,"line":10680},[99,31660,31661],{},"            \u002F\u002F 2. Cookie authentication\n",[99,31663,31664],{"class":10573,"line":10686},[99,31665,31627],{},[99,31667,31668],{"class":10573,"line":10691},[99,31669,31670],{},"                \"cookieAuth\",\n",[99,31672,31673],{"class":10573,"line":10697},[99,31674,31675],{},"                SecurityScheme::ApiKey(\n",[99,31677,31679],{"class":10573,"line":31678},23,[99,31680,31681],{},"                    ApiKey::Cookie(ApiKeyValue::new(\"token\"))\n",[99,31683,31685],{"class":10573,"line":31684},24,[99,31686,31647],{},[99,31688,31690],{"class":10573,"line":31689},25,[99,31691,31652],{},[99,31693,31695],{"class":10573,"line":31694},26,[99,31696,10613],{"emptyLinePlaceholder":53},[99,31698,31700],{"class":10573,"line":31699},27,[99,31701,31702],{},"            \u002F\u002F 3. API Key authentication (Header-based)\n",[99,31704,31706],{"class":10573,"line":31705},28,[99,31707,31627],{},[99,31709,31711],{"class":10573,"line":31710},29,[99,31712,31713],{},"                \"apiKeyAuth\",\n",[99,31715,31717],{"class":10573,"line":31716},30,[99,31718,31675],{},[99,31720,31722],{"class":10573,"line":31721},31,[99,31723,31724],{},"                    ApiKey::Header(ApiKeyValue::new(\"X-API-Key\"))\n",[99,31726,31728],{"class":10573,"line":31727},32,[99,31729,31647],{},[99,31731,31733],{"class":10573,"line":31732},33,[99,31734,31652],{},[99,31736,31738],{"class":10573,"line":31737},34,[99,31739,31740],{},"        }\n",[99,31742,31744],{"class":10573,"line":31743},35,[99,31745,31746],{},"    }\n",[99,31748,31750],{"class":10573,"line":31749},36,[99,31751,27811],{},[67,31753,31754,31755,27783],{},"Then use it in your ",[10569,31756,31757],{},"ApiDoc",[10562,31759,31761],{"className":30227,"code":31760,"language":30229,"meta":10567,"style":10567},"\u002F\u002F src\u002Fmain.rs\nuse acrospire_auth::docs::JwtSecurityAddon;\n\n#[derive(OpenApi)]\n#[openapi(\n    modifiers(&JwtSecurityAddon)  \u002F\u002F ← Key! Use modifiers to add security schemes\n)]\nstruct ApiDoc;\n",[10569,31762,31763,31768,31773,31777,31781,31785,31790,31794],{"__ignoreMap":10567},[99,31764,31765],{"class":10573,"line":10574},[99,31766,31767],{},"\u002F\u002F src\u002Fmain.rs\n",[99,31769,31770],{"class":10573,"line":10580},[99,31771,31772],{},"use acrospire_auth::docs::JwtSecurityAddon;\n",[99,31774,31775],{"class":10573,"line":10586},[99,31776,10613],{"emptyLinePlaceholder":53},[99,31778,31779],{"class":10573,"line":10592},[99,31780,31523],{},[99,31782,31783],{"class":10573,"line":10598},[99,31784,31528],{},[99,31786,31787],{"class":10573,"line":10604},[99,31788,31789],{},"    modifiers(&JwtSecurityAddon)  \u002F\u002F ← Key! Use modifiers to add security schemes\n",[99,31791,31792],{"class":10573,"line":10610},[99,31793,31548],{},[99,31795,31796],{"class":10573,"line":10616},[99,31797,31553],{},[1258,31799,31801],{"id":31800},"authentication-methods-explained","Authentication Methods Explained",[67,31803,31804],{},[76,31805,31806],{},"1. Bearer Token (JWT)",[21736,31808,31809,31812,31815,31818],{},[21739,31810,31811],{},"Type: HTTP Authentication",[21739,31813,31814],{},"Scheme: Bearer",[21739,31816,31817],{},"Usage: JWT Token authentication",[21739,31819,31820],{},"Client: Enter JWT Token directly in Swagger UI (no \"Bearer \" prefix needed)",[67,31822,31823],{},[76,31824,31825],{},"2. Cookie Authentication",[21736,31827,31828,31831,31834,31837],{},[21739,31829,31830],{},"Type: API Key",[21739,31832,31833],{},"Location: Cookie",[21739,31835,31836],{},"Name: token",[21739,31838,31839],{},"Usage: Cookie-based authentication, browser auto-carries cookie",[67,31841,31842],{},[76,31843,31844],{},"3. API Key (Header)",[21736,31846,31847,31849,31852,31855],{},[21739,31848,31830],{},[21739,31850,31851],{},"Location: Header",[21739,31853,31854],{},"Name: X-API-Key",[21739,31856,31857,31858,2846],{},"Usage: API Key authentication (e.g., ",[10569,31859,31860],{},"ak_live_xxxxxx",[86,31862,31864],{"id":31863},"defining-api-paths","Defining API Paths",[1258,31866,31868],{"id":31867},"basic-syntax","Basic Syntax",[10562,31870,31872],{"className":30227,"code":31871,"language":30229,"meta":10567,"style":10567},"use utoipa::path;\n\n#[utoipa::path(\n    \u002F\u002F HTTP method and path\n    post,\n    path = \"\u002Fapi\u002Fauth\u002Flogin\",\n\n    \u002F\u002F Grouping tag\n    tag = \"Authentication\",\n\n    \u002F\u002F Request body\n    request_body = LoginRequest,\n\n    \u002F\u002F Authentication requirements\n    security(\n        (\"bearerAuth\" = []),\n        (\"cookieAuth\" = [])\n    ),\n\n    \u002F\u002F Response definitions\n    responses(\n        (status = 200, description = \"Login successful\", body = LoginResponse),\n        (status = 401, description = \"Authentication failed\", body = ErrorResponse)\n    )\n)]\npub async fn login_handler(\n    Json(payload): Json\u003CLoginRequest>,\n) -> Result\u003CJson\u003CLoginResponse>, StatusCode> {\n    \u002F\u002F Handler implementation\n}\n",[10569,31873,31874,31879,31883,31888,31893,31898,31903,31907,31912,31917,31921,31926,31931,31935,31940,31945,31950,31955,31960,31964,31969,31974,31979,31984,31988,31992,31997,32002,32007,32012],{"__ignoreMap":10567},[99,31875,31876],{"class":10573,"line":10574},[99,31877,31878],{},"use utoipa::path;\n",[99,31880,31881],{"class":10573,"line":10580},[99,31882,10613],{"emptyLinePlaceholder":53},[99,31884,31885],{"class":10573,"line":10586},[99,31886,31887],{},"#[utoipa::path(\n",[99,31889,31890],{"class":10573,"line":10592},[99,31891,31892],{},"    \u002F\u002F HTTP method and path\n",[99,31894,31895],{"class":10573,"line":10598},[99,31896,31897],{},"    post,\n",[99,31899,31900],{"class":10573,"line":10604},[99,31901,31902],{},"    path = \"\u002Fapi\u002Fauth\u002Flogin\",\n",[99,31904,31905],{"class":10573,"line":10610},[99,31906,10613],{"emptyLinePlaceholder":53},[99,31908,31909],{"class":10573,"line":10616},[99,31910,31911],{},"    \u002F\u002F Grouping tag\n",[99,31913,31914],{"class":10573,"line":10622},[99,31915,31916],{},"    tag = \"Authentication\",\n",[99,31918,31919],{"class":10573,"line":10627},[99,31920,10613],{"emptyLinePlaceholder":53},[99,31922,31923],{"class":10573,"line":10633},[99,31924,31925],{},"    \u002F\u002F Request body\n",[99,31927,31928],{"class":10573,"line":10639},[99,31929,31930],{},"    request_body = LoginRequest,\n",[99,31932,31933],{"class":10573,"line":10645},[99,31934,10613],{"emptyLinePlaceholder":53},[99,31936,31937],{"class":10573,"line":10651},[99,31938,31939],{},"    \u002F\u002F Authentication requirements\n",[99,31941,31942],{"class":10573,"line":10657},[99,31943,31944],{},"    security(\n",[99,31946,31947],{"class":10573,"line":10663},[99,31948,31949],{},"        (\"bearerAuth\" = []),\n",[99,31951,31952],{"class":10573,"line":10669},[99,31953,31954],{},"        (\"cookieAuth\" = [])\n",[99,31956,31957],{"class":10573,"line":10674},[99,31958,31959],{},"    ),\n",[99,31961,31962],{"class":10573,"line":10680},[99,31963,10613],{"emptyLinePlaceholder":53},[99,31965,31966],{"class":10573,"line":10686},[99,31967,31968],{},"    \u002F\u002F Response definitions\n",[99,31970,31971],{"class":10573,"line":10691},[99,31972,31973],{},"    responses(\n",[99,31975,31976],{"class":10573,"line":10697},[99,31977,31978],{},"        (status = 200, description = \"Login successful\", body = LoginResponse),\n",[99,31980,31981],{"class":10573,"line":31678},[99,31982,31983],{},"        (status = 401, description = \"Authentication failed\", body = ErrorResponse)\n",[99,31985,31986],{"class":10573,"line":31684},[99,31987,31543],{},[99,31989,31990],{"class":10573,"line":31689},[99,31991,31548],{},[99,31993,31994],{"class":10573,"line":31694},[99,31995,31996],{},"pub async fn login_handler(\n",[99,31998,31999],{"class":10573,"line":31699},[99,32000,32001],{},"    Json(payload): Json\u003CLoginRequest>,\n",[99,32003,32004],{"class":10573,"line":31705},[99,32005,32006],{},") -> Result\u003CJson\u003CLoginResponse>, StatusCode> {\n",[99,32008,32009],{"class":10573,"line":31710},[99,32010,32011],{},"    \u002F\u002F Handler implementation\n",[99,32013,32014],{"class":10573,"line":31716},[99,32015,27811],{},[1258,32017,32019],{"id":32018},"public-endpoint-no-authentication","Public Endpoint (No Authentication)",[10562,32021,32023],{"className":30227,"code":32022,"language":30229,"meta":10567,"style":10567},"\u002F\u002F\u002F User registration\n#[utoipa::path(\n    post,\n    path = \"\u002Fapi\u002Fauth\u002Fregister\",\n    tag = \"Authentication\",\n    request_body = RegisterUserSchema,\n    responses(\n        (status = 201, description = \"Registration successful\", body = UserResponse),\n        (status = 409, description = \"Email already exists\", body = ErrorResponse),\n        (status = 500, description = \"Server error\", body = ErrorResponse)\n    )\n)]\npub async fn register_user_handler(\n    State(data): State\u003CAppState>,\n    Json(body): Json\u003CRegisterUserSchema>,\n) -> Result\u003Cimpl IntoResponse, (StatusCode, Json\u003Cserde_json::Value>)> {\n    \u002F\u002F Implementation...\n}\n",[10569,32024,32025,32030,32034,32038,32043,32047,32052,32056,32061,32066,32071,32075,32079,32084,32089,32094,32099,32104],{"__ignoreMap":10567},[99,32026,32027],{"class":10573,"line":10574},[99,32028,32029],{},"\u002F\u002F\u002F User registration\n",[99,32031,32032],{"class":10573,"line":10580},[99,32033,31887],{},[99,32035,32036],{"class":10573,"line":10586},[99,32037,31897],{},[99,32039,32040],{"class":10573,"line":10592},[99,32041,32042],{},"    path = \"\u002Fapi\u002Fauth\u002Fregister\",\n",[99,32044,32045],{"class":10573,"line":10598},[99,32046,31916],{},[99,32048,32049],{"class":10573,"line":10604},[99,32050,32051],{},"    request_body = RegisterUserSchema,\n",[99,32053,32054],{"class":10573,"line":10610},[99,32055,31973],{},[99,32057,32058],{"class":10573,"line":10616},[99,32059,32060],{},"        (status = 201, description = \"Registration successful\", body = UserResponse),\n",[99,32062,32063],{"class":10573,"line":10622},[99,32064,32065],{},"        (status = 409, description = \"Email already exists\", body = ErrorResponse),\n",[99,32067,32068],{"class":10573,"line":10627},[99,32069,32070],{},"        (status = 500, description = \"Server error\", body = ErrorResponse)\n",[99,32072,32073],{"class":10573,"line":10633},[99,32074,31543],{},[99,32076,32077],{"class":10573,"line":10639},[99,32078,31548],{},[99,32080,32081],{"class":10573,"line":10645},[99,32082,32083],{},"pub async fn register_user_handler(\n",[99,32085,32086],{"class":10573,"line":10651},[99,32087,32088],{},"    State(data): State\u003CAppState>,\n",[99,32090,32091],{"class":10573,"line":10657},[99,32092,32093],{},"    Json(body): Json\u003CRegisterUserSchema>,\n",[99,32095,32096],{"class":10573,"line":10663},[99,32097,32098],{},") -> Result\u003Cimpl IntoResponse, (StatusCode, Json\u003Cserde_json::Value>)> {\n",[99,32100,32101],{"class":10573,"line":10669},[99,32102,32103],{},"    \u002F\u002F Implementation...\n",[99,32105,32106],{"class":10573,"line":10674},[99,32107,27811],{},[1258,32109,32111],{"id":32110},"protected-endpoint-requires-authentication","Protected Endpoint (Requires Authentication)",[10562,32113,32115],{"className":30227,"code":32114,"language":30229,"meta":10567,"style":10567},"\u002F\u002F\u002F Get current user information\n\u002F\u002F\u002F Requires JWT Bearer Token or Cookie authentication\n#[utoipa::path(\n    get,\n    path = \"\u002Fapi\u002Fusers\u002Fme\",\n    tag = \"Users\",\n    security(\n        (\"bearerAuth\" = []),   \u002F\u002F Method 1: JWT Token\n        (\"cookieAuth\" = [])     \u002F\u002F Method 2: Cookie\n    ),\n    responses(\n        (status = 200, description = \"Success\", body = UserResponse),\n        (status = 401, description = \"Unauthorized\", body = ErrorResponse)\n    )\n)]\npub async fn get_me_handler(\n    Extension(user): Extension\u003CUserModel>,\n) -> Result\u003Cimpl IntoResponse, (StatusCode, Json\u003Cserde_json::Value>)> {\n    \u002F\u002F Implementation...\n}\n",[10569,32116,32117,32122,32127,32131,32136,32141,32146,32150,32155,32160,32164,32168,32173,32178,32182,32186,32191,32196,32200,32204],{"__ignoreMap":10567},[99,32118,32119],{"class":10573,"line":10574},[99,32120,32121],{},"\u002F\u002F\u002F Get current user information\n",[99,32123,32124],{"class":10573,"line":10580},[99,32125,32126],{},"\u002F\u002F\u002F Requires JWT Bearer Token or Cookie authentication\n",[99,32128,32129],{"class":10573,"line":10586},[99,32130,31887],{},[99,32132,32133],{"class":10573,"line":10592},[99,32134,32135],{},"    get,\n",[99,32137,32138],{"class":10573,"line":10598},[99,32139,32140],{},"    path = \"\u002Fapi\u002Fusers\u002Fme\",\n",[99,32142,32143],{"class":10573,"line":10604},[99,32144,32145],{},"    tag = \"Users\",\n",[99,32147,32148],{"class":10573,"line":10610},[99,32149,31944],{},[99,32151,32152],{"class":10573,"line":10616},[99,32153,32154],{},"        (\"bearerAuth\" = []),   \u002F\u002F Method 1: JWT Token\n",[99,32156,32157],{"class":10573,"line":10622},[99,32158,32159],{},"        (\"cookieAuth\" = [])     \u002F\u002F Method 2: Cookie\n",[99,32161,32162],{"class":10573,"line":10627},[99,32163,31959],{},[99,32165,32166],{"class":10573,"line":10633},[99,32167,31973],{},[99,32169,32170],{"class":10573,"line":10639},[99,32171,32172],{},"        (status = 200, description = \"Success\", body = UserResponse),\n",[99,32174,32175],{"class":10573,"line":10645},[99,32176,32177],{},"        (status = 401, description = \"Unauthorized\", body = ErrorResponse)\n",[99,32179,32180],{"class":10573,"line":10651},[99,32181,31543],{},[99,32183,32184],{"class":10573,"line":10657},[99,32185,31548],{},[99,32187,32188],{"class":10573,"line":10663},[99,32189,32190],{},"pub async fn get_me_handler(\n",[99,32192,32193],{"class":10573,"line":10669},[99,32194,32195],{},"    Extension(user): Extension\u003CUserModel>,\n",[99,32197,32198],{"class":10573,"line":10674},[99,32199,32098],{},[99,32201,32202],{"class":10573,"line":10680},[99,32203,32103],{},[99,32205,32206],{"class":10573,"line":10686},[99,32207,27811],{},[1258,32209,32211],{"id":32210},"path-parameters","Path Parameters",[10562,32213,32215],{"className":30227,"code":32214,"language":30229,"meta":10567,"style":10567},"#[utoipa::path(\n    delete,\n    path = \"\u002Fapi\u002Fkeys\u002F{key_id}\",\n    tag = \"API Keys\",\n    params(\n        (\"key_id\" = String, Path, description = \"ID of the API Key\")\n    ),\n    security(\n        (\"bearerAuth\" = [])\n    ),\n    responses(\n        (status = 200, description = \"Deletion successful\"),\n        (status = 404, description = \"Key not found\")\n    )\n)]\npub async fn delete_api_key_handler(\n    Path(key_id): Path\u003CString>,\n) -> impl IntoResponse {\n    \u002F\u002F Implementation...\n}\n",[10569,32216,32217,32221,32226,32231,32236,32241,32246,32250,32254,32259,32263,32267,32272,32277,32281,32285,32290,32295,32300,32304],{"__ignoreMap":10567},[99,32218,32219],{"class":10573,"line":10574},[99,32220,31887],{},[99,32222,32223],{"class":10573,"line":10580},[99,32224,32225],{},"    delete,\n",[99,32227,32228],{"class":10573,"line":10586},[99,32229,32230],{},"    path = \"\u002Fapi\u002Fkeys\u002F{key_id}\",\n",[99,32232,32233],{"class":10573,"line":10592},[99,32234,32235],{},"    tag = \"API Keys\",\n",[99,32237,32238],{"class":10573,"line":10598},[99,32239,32240],{},"    params(\n",[99,32242,32243],{"class":10573,"line":10604},[99,32244,32245],{},"        (\"key_id\" = String, Path, description = \"ID of the API Key\")\n",[99,32247,32248],{"class":10573,"line":10610},[99,32249,31959],{},[99,32251,32252],{"class":10573,"line":10616},[99,32253,31944],{},[99,32255,32256],{"class":10573,"line":10622},[99,32257,32258],{},"        (\"bearerAuth\" = [])\n",[99,32260,32261],{"class":10573,"line":10627},[99,32262,31959],{},[99,32264,32265],{"class":10573,"line":10633},[99,32266,31973],{},[99,32268,32269],{"class":10573,"line":10639},[99,32270,32271],{},"        (status = 200, description = \"Deletion successful\"),\n",[99,32273,32274],{"class":10573,"line":10645},[99,32275,32276],{},"        (status = 404, description = \"Key not found\")\n",[99,32278,32279],{"class":10573,"line":10651},[99,32280,31543],{},[99,32282,32283],{"class":10573,"line":10657},[99,32284,31548],{},[99,32286,32287],{"class":10573,"line":10663},[99,32288,32289],{},"pub async fn delete_api_key_handler(\n",[99,32291,32292],{"class":10573,"line":10669},[99,32293,32294],{},"    Path(key_id): Path\u003CString>,\n",[99,32296,32297],{"class":10573,"line":10674},[99,32298,32299],{},") -> impl IntoResponse {\n",[99,32301,32302],{"class":10573,"line":10680},[99,32303,32103],{},[99,32305,32306],{"class":10573,"line":10686},[99,32307,27811],{},[1258,32309,32311],{"id":32310},"query-parameters","Query Parameters",[10562,32313,32315],{"className":30227,"code":32314,"language":30229,"meta":10567,"style":10567},"#[utoipa::path(\n    get,\n    path = \"\u002Fapi\u002Fusers\",\n    tag = \"Users\",\n    params(\n        (\"page\" = Option\u003Ci32>, Query, description = \"Page number\"),\n        (\"limit\" = Option\u003Ci32>, Query, description = \"Items per page\")\n    ),\n    responses(\n        (status = 200, description = \"Success\")\n    )\n)]\npub async fn list_users(\n    Query(params): Query\u003CListParams>,\n) -> impl IntoResponse {\n    \u002F\u002F Implementation...\n}\n",[10569,32316,32317,32321,32325,32330,32334,32338,32343,32348,32352,32356,32361,32365,32369,32374,32379,32383,32387],{"__ignoreMap":10567},[99,32318,32319],{"class":10573,"line":10574},[99,32320,31887],{},[99,32322,32323],{"class":10573,"line":10580},[99,32324,32135],{},[99,32326,32327],{"class":10573,"line":10586},[99,32328,32329],{},"    path = \"\u002Fapi\u002Fusers\",\n",[99,32331,32332],{"class":10573,"line":10592},[99,32333,32145],{},[99,32335,32336],{"class":10573,"line":10598},[99,32337,32240],{},[99,32339,32340],{"class":10573,"line":10604},[99,32341,32342],{},"        (\"page\" = Option\u003Ci32>, Query, description = \"Page number\"),\n",[99,32344,32345],{"class":10573,"line":10610},[99,32346,32347],{},"        (\"limit\" = Option\u003Ci32>, Query, description = \"Items per page\")\n",[99,32349,32350],{"class":10573,"line":10616},[99,32351,31959],{},[99,32353,32354],{"class":10573,"line":10622},[99,32355,31973],{},[99,32357,32358],{"class":10573,"line":10627},[99,32359,32360],{},"        (status = 200, description = \"Success\")\n",[99,32362,32363],{"class":10573,"line":10633},[99,32364,31543],{},[99,32366,32367],{"class":10573,"line":10639},[99,32368,31548],{},[99,32370,32371],{"class":10573,"line":10645},[99,32372,32373],{},"pub async fn list_users(\n",[99,32375,32376],{"class":10573,"line":10651},[99,32377,32378],{},"    Query(params): Query\u003CListParams>,\n",[99,32380,32381],{"class":10573,"line":10657},[99,32382,32299],{},[99,32384,32385],{"class":10573,"line":10663},[99,32386,32103],{},[99,32388,32389],{"class":10573,"line":10669},[99,32390,27811],{},[86,32392,32394],{"id":32393},"defining-data-models","Defining Data Models",[1258,32396,32398],{"id":32397},"basic-usage","Basic Usage",[10562,32400,32402],{"className":30227,"code":32401,"language":30229,"meta":10567,"style":10567},"use serde::{Deserialize, Serialize};\nuse utoipa::ToSchema;\n\n#[derive(Debug, Serialize, Deserialize, ToSchema)]\npub struct UserResponse {\n    #[schema(example = \"123e4567-e89b-12d3-a456-426614174000\")]\n    pub id: String,\n\n    #[schema(example = \"john@example.com\")]\n    pub email: String,\n\n    #[schema(example = \"John Doe\")]\n    pub name: String,\n}\n",[10569,32403,32404,32409,32414,32418,32423,32428,32433,32438,32442,32447,32452,32456,32461,32466],{"__ignoreMap":10567},[99,32405,32406],{"class":10573,"line":10574},[99,32407,32408],{},"use serde::{Deserialize, Serialize};\n",[99,32410,32411],{"class":10573,"line":10580},[99,32412,32413],{},"use utoipa::ToSchema;\n",[99,32415,32416],{"class":10573,"line":10586},[99,32417,10613],{"emptyLinePlaceholder":53},[99,32419,32420],{"class":10573,"line":10592},[99,32421,32422],{},"#[derive(Debug, Serialize, Deserialize, ToSchema)]\n",[99,32424,32425],{"class":10573,"line":10598},[99,32426,32427],{},"pub struct UserResponse {\n",[99,32429,32430],{"class":10573,"line":10604},[99,32431,32432],{},"    #[schema(example = \"123e4567-e89b-12d3-a456-426614174000\")]\n",[99,32434,32435],{"class":10573,"line":10610},[99,32436,32437],{},"    pub id: String,\n",[99,32439,32440],{"class":10573,"line":10616},[99,32441,10613],{"emptyLinePlaceholder":53},[99,32443,32444],{"class":10573,"line":10622},[99,32445,32446],{},"    #[schema(example = \"john@example.com\")]\n",[99,32448,32449],{"class":10573,"line":10627},[99,32450,32451],{},"    pub email: String,\n",[99,32453,32454],{"class":10573,"line":10633},[99,32455,10613],{"emptyLinePlaceholder":53},[99,32457,32458],{"class":10573,"line":10639},[99,32459,32460],{},"    #[schema(example = \"John Doe\")]\n",[99,32462,32463],{"class":10573,"line":10645},[99,32464,32465],{},"    pub name: String,\n",[99,32467,32468],{"class":10573,"line":10651},[99,32469,27811],{},[1258,32471,32473],{"id":32472},"advanced-field-level-annotations","Advanced Field-Level Annotations",[10562,32475,32477],{"className":30227,"code":32476,"language":30229,"meta":10567,"style":10567},"#[derive(Debug, Serialize, Deserialize, ToSchema)]\npub struct RegisterUserSchema {\n    \u002F\u002F\u002F Email address (must be unique)\n    #[schema(example = \"user@example.com\", max_length = 100)]\n    pub email: String,\n\n    \u002F\u002F\u002F Password (minimum 8 characters)\n    #[schema(example = \"password123\", min_length = 8)]\n    pub password: String,\n\n    \u002F\u002F\u002F User's full name\n    #[schema(example = \"张三\")]\n    pub name: String,\n\n    \u002F\u002F\u002F Whether user is an admin\n    #[schema(example = false)]\n    pub is_admin: bool,\n}\n",[10569,32478,32479,32483,32488,32493,32498,32502,32506,32511,32516,32521,32525,32530,32535,32539,32543,32548,32553,32558],{"__ignoreMap":10567},[99,32480,32481],{"class":10573,"line":10574},[99,32482,32422],{},[99,32484,32485],{"class":10573,"line":10580},[99,32486,32487],{},"pub struct RegisterUserSchema {\n",[99,32489,32490],{"class":10573,"line":10586},[99,32491,32492],{},"    \u002F\u002F\u002F Email address (must be unique)\n",[99,32494,32495],{"class":10573,"line":10592},[99,32496,32497],{},"    #[schema(example = \"user@example.com\", max_length = 100)]\n",[99,32499,32500],{"class":10573,"line":10598},[99,32501,32451],{},[99,32503,32504],{"class":10573,"line":10604},[99,32505,10613],{"emptyLinePlaceholder":53},[99,32507,32508],{"class":10573,"line":10610},[99,32509,32510],{},"    \u002F\u002F\u002F Password (minimum 8 characters)\n",[99,32512,32513],{"class":10573,"line":10616},[99,32514,32515],{},"    #[schema(example = \"password123\", min_length = 8)]\n",[99,32517,32518],{"class":10573,"line":10622},[99,32519,32520],{},"    pub password: String,\n",[99,32522,32523],{"class":10573,"line":10627},[99,32524,10613],{"emptyLinePlaceholder":53},[99,32526,32527],{"class":10573,"line":10633},[99,32528,32529],{},"    \u002F\u002F\u002F User's full name\n",[99,32531,32532],{"class":10573,"line":10639},[99,32533,32534],{},"    #[schema(example = \"张三\")]\n",[99,32536,32537],{"class":10573,"line":10645},[99,32538,32465],{},[99,32540,32541],{"class":10573,"line":10651},[99,32542,10613],{"emptyLinePlaceholder":53},[99,32544,32545],{"class":10573,"line":10657},[99,32546,32547],{},"    \u002F\u002F\u002F Whether user is an admin\n",[99,32549,32550],{"class":10573,"line":10663},[99,32551,32552],{},"    #[schema(example = false)]\n",[99,32554,32555],{"class":10573,"line":10669},[99,32556,32557],{},"    pub is_admin: bool,\n",[99,32559,32560],{"class":10573,"line":10674},[99,32561,27811],{},[1258,32563,32565],{"id":32564},"nested-structures","Nested Structures",[10562,32567,32569],{"className":30227,"code":32568,"language":30229,"meta":10567,"style":10567},"#[derive(Debug, Serialize, Deserialize, ToSchema)]\npub struct LoginResponse {\n    pub data: LoginData,\n}\n\n#[derive(Debug, Serialize, Deserialize, ToSchema)]\npub struct LoginData {\n    #[schema(example = \"eyJhbGciOiJIUzI1NiIsInR5cCI6IkpXVCJ9...\")]\n    pub token: String,\n\n    pub user: FilteredUser,\n}\n",[10569,32570,32571,32575,32580,32585,32589,32593,32597,32602,32607,32612,32616,32621],{"__ignoreMap":10567},[99,32572,32573],{"class":10573,"line":10574},[99,32574,32422],{},[99,32576,32577],{"class":10573,"line":10580},[99,32578,32579],{},"pub struct LoginResponse {\n",[99,32581,32582],{"class":10573,"line":10586},[99,32583,32584],{},"    pub data: LoginData,\n",[99,32586,32587],{"class":10573,"line":10592},[99,32588,27811],{},[99,32590,32591],{"class":10573,"line":10598},[99,32592,10613],{"emptyLinePlaceholder":53},[99,32594,32595],{"class":10573,"line":10604},[99,32596,32422],{},[99,32598,32599],{"class":10573,"line":10610},[99,32600,32601],{},"pub struct LoginData {\n",[99,32603,32604],{"class":10573,"line":10616},[99,32605,32606],{},"    #[schema(example = \"eyJhbGciOiJIUzI1NiIsInR5cCI6IkpXVCJ9...\")]\n",[99,32608,32609],{"class":10573,"line":10622},[99,32610,32611],{},"    pub token: String,\n",[99,32613,32614],{"class":10573,"line":10627},[99,32615,10613],{"emptyLinePlaceholder":53},[99,32617,32618],{"class":10573,"line":10633},[99,32619,32620],{},"    pub user: FilteredUser,\n",[99,32622,32623],{"class":10573,"line":10639},[99,32624,27811],{},[1258,32626,32628],{"id":32627},"datetime-handling-important","DateTime Handling (Important!)",[10562,32630,32632],{"className":30227,"code":32631,"language":30229,"meta":10567,"style":10567},"use chrono::{DateTime, Utc};\n\n#[derive(Debug, Serialize, Deserialize, ToSchema)]\npub struct UserResponse {\n    pub id: String,\n\n    \u002F\u002F ❌ This might not work in utoipa 4.x\n    \u002F\u002F pub created_at: DateTime\u003CUtc>,\n\n    \u002F\u002F ✅ Correct: Use value_type override\n    #[schema(value_type = String, format = \"date-time\")]\n    pub created_at: DateTime\u003CUtc>,\n}\n",[10569,32633,32634,32639,32643,32647,32651,32655,32659,32664,32669,32673,32678,32683,32688],{"__ignoreMap":10567},[99,32635,32636],{"class":10573,"line":10574},[99,32637,32638],{},"use chrono::{DateTime, Utc};\n",[99,32640,32641],{"class":10573,"line":10580},[99,32642,10613],{"emptyLinePlaceholder":53},[99,32644,32645],{"class":10573,"line":10586},[99,32646,32422],{},[99,32648,32649],{"class":10573,"line":10592},[99,32650,32427],{},[99,32652,32653],{"class":10573,"line":10598},[99,32654,32437],{},[99,32656,32657],{"class":10573,"line":10604},[99,32658,10613],{"emptyLinePlaceholder":53},[99,32660,32661],{"class":10573,"line":10610},[99,32662,32663],{},"    \u002F\u002F ❌ This might not work in utoipa 4.x\n",[99,32665,32666],{"class":10573,"line":10616},[99,32667,32668],{},"    \u002F\u002F pub created_at: DateTime\u003CUtc>,\n",[99,32670,32671],{"class":10573,"line":10622},[99,32672,10613],{"emptyLinePlaceholder":53},[99,32674,32675],{"class":10573,"line":10627},[99,32676,32677],{},"    \u002F\u002F ✅ Correct: Use value_type override\n",[99,32679,32680],{"class":10573,"line":10633},[99,32681,32682],{},"    #[schema(value_type = String, format = \"date-time\")]\n",[99,32684,32685],{"class":10573,"line":10639},[99,32686,32687],{},"    pub created_at: DateTime\u003CUtc>,\n",[99,32689,32690],{"class":10573,"line":10645},[99,32691,27811],{},[67,32693,32694],{},"Or use custom formatting:",[10562,32696,32698],{"className":30227,"code":32697,"language":30229,"meta":10567,"style":10567},"#[derive(Debug, Serialize, Deserialize, ToSchema)]\npub struct ApiKeyInfo {\n    pub id: String,\n    pub name: String,\n\n    \u002F\u002F\u002F Creation time (ISO 8601 format)\n    #[schema(\n        value_type = String,\n        example = \"2024-01-15T10:30:00Z\"\n    )]\n    pub created_at: DateTimeWithTimeZone,\n}\n",[10569,32699,32700,32704,32709,32713,32717,32721,32726,32731,32736,32741,32746,32751],{"__ignoreMap":10567},[99,32701,32702],{"class":10573,"line":10574},[99,32703,32422],{},[99,32705,32706],{"class":10573,"line":10580},[99,32707,32708],{},"pub struct ApiKeyInfo {\n",[99,32710,32711],{"class":10573,"line":10586},[99,32712,32437],{},[99,32714,32715],{"class":10573,"line":10592},[99,32716,32465],{},[99,32718,32719],{"class":10573,"line":10598},[99,32720,10613],{"emptyLinePlaceholder":53},[99,32722,32723],{"class":10573,"line":10604},[99,32724,32725],{},"    \u002F\u002F\u002F Creation time (ISO 8601 format)\n",[99,32727,32728],{"class":10573,"line":10610},[99,32729,32730],{},"    #[schema(\n",[99,32732,32733],{"class":10573,"line":10616},[99,32734,32735],{},"        value_type = String,\n",[99,32737,32738],{"class":10573,"line":10622},[99,32739,32740],{},"        example = \"2024-01-15T10:30:00Z\"\n",[99,32742,32743],{"class":10573,"line":10627},[99,32744,32745],{},"    )]\n",[99,32747,32748],{"class":10573,"line":10633},[99,32749,32750],{},"    pub created_at: DateTimeWithTimeZone,\n",[99,32752,32753],{"class":10573,"line":10639},[99,32754,27811],{},[86,32756,32758],{"id":32757},"generating-openapi-documentation","Generating OpenAPI Documentation",[1258,32760,32762],{"id":32761},"complete-apidoc-definition","Complete ApiDoc Definition",[10562,32764,32766],{"className":30227,"code":32765,"language":30229,"meta":10567,"style":10567},"use acrospire_auth::{\n    docs::JwtSecurityAddon,\n    docs::schemas::*,\n    handler::*,\n};\nuse utoipa::OpenApi;\n\n#[derive(OpenApi)]\n#[openapi(\n    \u002F\u002F 1. Register all API paths\n    paths(\n        health_checker_handler,\n        register_user_handler,\n        login_user_handler,\n        logout_handler,\n        get_me_handler,\n        refresh_token_handler,\n        create_api_key_handler,\n        list_api_keys_handler,\n        validate_api_key_handler,\n        delete_api_key_handler,\n        protected_data_handler\n    ),\n\n    \u002F\u002F 2. Register all data models\n    components(\n        schemas(\n            HealthCheckResponse,\n            RegisterUserSchema,\n            LoginUserSchema,\n            UserResponse,\n            FilteredUser,\n            LoginResponse,\n            LoginData,\n            LogoutResponse,\n            RefreshTokenRequest,\n            TokenPairResponse,\n            TokenPairData,\n            CreateApiKeySchema,\n            CreateApiKeyResponse,\n            CreateApiKeyData,\n            ApiKeyListResponse,\n            ApiKeyListData,\n            ApiKeyInfo,\n            ValidateApiKeySchema,\n            ValidateApiKeyResponse,\n            ValidateApiKeyData,\n            DeleteApiKeyResponse,\n            ErrorResponse,\n        )\n    ),\n\n    \u002F\u002F 3. Define tag groups\n    tags(\n        (name = \"System\", description = \"System health check and similar endpoints\"),\n        (name = \"Authentication\", description = \"User registration, login, logout endpoints\"),\n        (name = \"Users\", description = \"User information management endpoints\"),\n        (name = \"API Keys\", description = \"API Key management endpoints\"),\n        (name = \"Protected\", description = \"Protected endpoints requiring API Key authentication\")\n    ),\n\n    \u002F\u002F 4. API basic information\n    info(\n        title = \"API Key Store Auth API\",\n        version = \"1.0.0\",\n        description = \"Authentication service API documentation based on JWT and API Key\"\n    ),\n\n    \u002F\u002F 5. Add security schemes (critical!)\n    modifiers(&JwtSecurityAddon)\n)]\nstruct ApiDoc;\n\n\u002F\u002F Generate OpenAPI documentation\nlet openapi = ApiDoc::openapi();\n",[10569,32767,32768,32773,32778,32783,32788,32793,32798,32802,32806,32810,32815,32820,32825,32830,32835,32840,32845,32850,32855,32860,32865,32870,32875,32879,32883,32888,32893,32898,32903,32908,32913,32918,32923,32928,32933,32938,32943,32949,32955,32961,32967,32973,32979,32985,32991,32997,33003,33009,33015,33021,33027,33032,33037,33043,33049,33055,33061,33067,33073,33079,33084,33089,33095,33101,33107,33113,33119,33124,33129,33135,33141,33146,33151,33156,33162],{"__ignoreMap":10567},[99,32769,32770],{"class":10573,"line":10574},[99,32771,32772],{},"use acrospire_auth::{\n",[99,32774,32775],{"class":10573,"line":10580},[99,32776,32777],{},"    docs::JwtSecurityAddon,\n",[99,32779,32780],{"class":10573,"line":10586},[99,32781,32782],{},"    docs::schemas::*,\n",[99,32784,32785],{"class":10573,"line":10592},[99,32786,32787],{},"    handler::*,\n",[99,32789,32790],{"class":10573,"line":10598},[99,32791,32792],{},"};\n",[99,32794,32795],{"class":10573,"line":10604},[99,32796,32797],{},"use utoipa::OpenApi;\n",[99,32799,32800],{"class":10573,"line":10610},[99,32801,10613],{"emptyLinePlaceholder":53},[99,32803,32804],{"class":10573,"line":10616},[99,32805,31523],{},[99,32807,32808],{"class":10573,"line":10622},[99,32809,31528],{},[99,32811,32812],{"class":10573,"line":10627},[99,32813,32814],{},"    \u002F\u002F 1. Register all API paths\n",[99,32816,32817],{"class":10573,"line":10633},[99,32818,32819],{},"    paths(\n",[99,32821,32822],{"class":10573,"line":10639},[99,32823,32824],{},"        health_checker_handler,\n",[99,32826,32827],{"class":10573,"line":10645},[99,32828,32829],{},"        register_user_handler,\n",[99,32831,32832],{"class":10573,"line":10651},[99,32833,32834],{},"        login_user_handler,\n",[99,32836,32837],{"class":10573,"line":10657},[99,32838,32839],{},"        logout_handler,\n",[99,32841,32842],{"class":10573,"line":10663},[99,32843,32844],{},"        get_me_handler,\n",[99,32846,32847],{"class":10573,"line":10669},[99,32848,32849],{},"        refresh_token_handler,\n",[99,32851,32852],{"class":10573,"line":10674},[99,32853,32854],{},"        create_api_key_handler,\n",[99,32856,32857],{"class":10573,"line":10680},[99,32858,32859],{},"        list_api_keys_handler,\n",[99,32861,32862],{"class":10573,"line":10686},[99,32863,32864],{},"        validate_api_key_handler,\n",[99,32866,32867],{"class":10573,"line":10691},[99,32868,32869],{},"        delete_api_key_handler,\n",[99,32871,32872],{"class":10573,"line":10697},[99,32873,32874],{},"        protected_data_handler\n",[99,32876,32877],{"class":10573,"line":31678},[99,32878,31959],{},[99,32880,32881],{"class":10573,"line":31684},[99,32882,10613],{"emptyLinePlaceholder":53},[99,32884,32885],{"class":10573,"line":31689},[99,32886,32887],{},"    \u002F\u002F 2. Register all data models\n",[99,32889,32890],{"class":10573,"line":31694},[99,32891,32892],{},"    components(\n",[99,32894,32895],{"class":10573,"line":31699},[99,32896,32897],{},"        schemas(\n",[99,32899,32900],{"class":10573,"line":31705},[99,32901,32902],{},"            HealthCheckResponse,\n",[99,32904,32905],{"class":10573,"line":31710},[99,32906,32907],{},"            RegisterUserSchema,\n",[99,32909,32910],{"class":10573,"line":31716},[99,32911,32912],{},"            LoginUserSchema,\n",[99,32914,32915],{"class":10573,"line":31721},[99,32916,32917],{},"            UserResponse,\n",[99,32919,32920],{"class":10573,"line":31727},[99,32921,32922],{},"            FilteredUser,\n",[99,32924,32925],{"class":10573,"line":31732},[99,32926,32927],{},"            LoginResponse,\n",[99,32929,32930],{"class":10573,"line":31737},[99,32931,32932],{},"            LoginData,\n",[99,32934,32935],{"class":10573,"line":31743},[99,32936,32937],{},"            LogoutResponse,\n",[99,32939,32940],{"class":10573,"line":31749},[99,32941,32942],{},"            RefreshTokenRequest,\n",[99,32944,32946],{"class":10573,"line":32945},37,[99,32947,32948],{},"            TokenPairResponse,\n",[99,32950,32952],{"class":10573,"line":32951},38,[99,32953,32954],{},"            TokenPairData,\n",[99,32956,32958],{"class":10573,"line":32957},39,[99,32959,32960],{},"            CreateApiKeySchema,\n",[99,32962,32964],{"class":10573,"line":32963},40,[99,32965,32966],{},"            CreateApiKeyResponse,\n",[99,32968,32970],{"class":10573,"line":32969},41,[99,32971,32972],{},"            CreateApiKeyData,\n",[99,32974,32976],{"class":10573,"line":32975},42,[99,32977,32978],{},"            ApiKeyListResponse,\n",[99,32980,32982],{"class":10573,"line":32981},43,[99,32983,32984],{},"            ApiKeyListData,\n",[99,32986,32988],{"class":10573,"line":32987},44,[99,32989,32990],{},"            ApiKeyInfo,\n",[99,32992,32994],{"class":10573,"line":32993},45,[99,32995,32996],{},"            ValidateApiKeySchema,\n",[99,32998,33000],{"class":10573,"line":32999},46,[99,33001,33002],{},"            ValidateApiKeyResponse,\n",[99,33004,33006],{"class":10573,"line":33005},47,[99,33007,33008],{},"            ValidateApiKeyData,\n",[99,33010,33012],{"class":10573,"line":33011},48,[99,33013,33014],{},"            DeleteApiKeyResponse,\n",[99,33016,33018],{"class":10573,"line":33017},49,[99,33019,33020],{},"            ErrorResponse,\n",[99,33022,33024],{"class":10573,"line":33023},50,[99,33025,33026],{},"        )\n",[99,33028,33030],{"class":10573,"line":33029},51,[99,33031,31959],{},[99,33033,33035],{"class":10573,"line":33034},52,[99,33036,10613],{"emptyLinePlaceholder":53},[99,33038,33040],{"class":10573,"line":33039},53,[99,33041,33042],{},"    \u002F\u002F 3. Define tag groups\n",[99,33044,33046],{"class":10573,"line":33045},54,[99,33047,33048],{},"    tags(\n",[99,33050,33052],{"class":10573,"line":33051},55,[99,33053,33054],{},"        (name = \"System\", description = \"System health check and similar endpoints\"),\n",[99,33056,33058],{"class":10573,"line":33057},56,[99,33059,33060],{},"        (name = \"Authentication\", description = \"User registration, login, logout endpoints\"),\n",[99,33062,33064],{"class":10573,"line":33063},57,[99,33065,33066],{},"        (name = \"Users\", description = \"User information management endpoints\"),\n",[99,33068,33070],{"class":10573,"line":33069},58,[99,33071,33072],{},"        (name = \"API Keys\", description = \"API Key management endpoints\"),\n",[99,33074,33076],{"class":10573,"line":33075},59,[99,33077,33078],{},"        (name = \"Protected\", description = \"Protected endpoints requiring API Key authentication\")\n",[99,33080,33082],{"class":10573,"line":33081},60,[99,33083,31959],{},[99,33085,33087],{"class":10573,"line":33086},61,[99,33088,10613],{"emptyLinePlaceholder":53},[99,33090,33092],{"class":10573,"line":33091},62,[99,33093,33094],{},"    \u002F\u002F 4. API basic information\n",[99,33096,33098],{"class":10573,"line":33097},63,[99,33099,33100],{},"    info(\n",[99,33102,33104],{"class":10573,"line":33103},64,[99,33105,33106],{},"        title = \"API Key Store Auth API\",\n",[99,33108,33110],{"class":10573,"line":33109},65,[99,33111,33112],{},"        version = \"1.0.0\",\n",[99,33114,33116],{"class":10573,"line":33115},66,[99,33117,33118],{},"        description = \"Authentication service API documentation based on JWT and API Key\"\n",[99,33120,33122],{"class":10573,"line":33121},67,[99,33123,31959],{},[99,33125,33127],{"class":10573,"line":33126},68,[99,33128,10613],{"emptyLinePlaceholder":53},[99,33130,33132],{"class":10573,"line":33131},69,[99,33133,33134],{},"    \u002F\u002F 5. Add security schemes (critical!)\n",[99,33136,33138],{"class":10573,"line":33137},70,[99,33139,33140],{},"    modifiers(&JwtSecurityAddon)\n",[99,33142,33144],{"class":10573,"line":33143},71,[99,33145,31548],{},[99,33147,33149],{"class":10573,"line":33148},72,[99,33150,31553],{},[99,33152,33154],{"class":10573,"line":33153},73,[99,33155,10613],{"emptyLinePlaceholder":53},[99,33157,33159],{"class":10573,"line":33158},74,[99,33160,33161],{},"\u002F\u002F Generate OpenAPI documentation\n",[99,33163,33165],{"class":10573,"line":33164},75,[99,33166,33167],{},"let openapi = ApiDoc::openapi();\n",[86,33169,33171],{"id":33170},"integrating-swagger-ui","Integrating Swagger UI",[1258,33173,33175],{"id":33174},"method-integration-in-mainrs-recommended","Method: Integration in main.rs (Recommended)",[10562,33177,33179],{"className":30227,"code":33178,"language":30229,"meta":10567,"style":10567},"use utoipa_swagger_ui::SwaggerUi;\n\n#[tokio::main]\nasync fn main() -> Result\u003C(), Box\u003Cdyn std::error::Error>> {\n    let app_state = AppState::new().await?;\n\n    \u002F\u002F Generate OpenAPI documentation\n    #[derive(OpenApi)]\n    #[openapi(\n        paths(...),\n        components(schemas(...)),\n        modifiers(&JwtSecurityAddon)\n    )]\n    struct ApiDoc;\n\n    let openapi = ApiDoc::openapi();\n\n    \u002F\u002F Create router\n    let app = create_router()\n        .merge(\n            SwaggerUi::new(\"\u002Fswagger-ui\")\n                .url(\"\u002Fapi-docs\u002Fopenapi.json\", openapi)\n                .config(\n                    utoipa_swagger_ui::Config::default()\n                        .try_it_out_enabled(true)      \u002F\u002F Enable \"Try it out\"\n                        .deep_linking(true)           \u002F\u002F Enable deep linking\n                        .display_request_duration(true) \u002F\u002F Show request duration\n                )\n        );\n\n    \u002F\u002F Start server\n    let listener = tokio::net::TcpListener::bind(\"0.0.0.0:3081\").await?;\n    axum::serve(listener, app).await?;\n\n    Ok(())\n}\n",[10569,33180,33181,33186,33190,33194,33198,33203,33207,33212,33217,33222,33227,33232,33237,33241,33246,33250,33255,33259,33264,33269,33274,33279,33284,33289,33294,33299,33304,33309,33314,33319,33323,33328,33333,33338,33342,33347],{"__ignoreMap":10567},[99,33182,33183],{"class":10573,"line":10574},[99,33184,33185],{},"use utoipa_swagger_ui::SwaggerUi;\n",[99,33187,33188],{"class":10573,"line":10580},[99,33189,10613],{"emptyLinePlaceholder":53},[99,33191,33192],{"class":10573,"line":10586},[99,33193,30460],{},[99,33195,33196],{"class":10573,"line":10592},[99,33197,30465],{},[99,33199,33200],{"class":10573,"line":10598},[99,33201,33202],{},"    let app_state = AppState::new().await?;\n",[99,33204,33205],{"class":10573,"line":10604},[99,33206,10613],{"emptyLinePlaceholder":53},[99,33208,33209],{"class":10573,"line":10610},[99,33210,33211],{},"    \u002F\u002F Generate OpenAPI documentation\n",[99,33213,33214],{"class":10573,"line":10616},[99,33215,33216],{},"    #[derive(OpenApi)]\n",[99,33218,33219],{"class":10573,"line":10622},[99,33220,33221],{},"    #[openapi(\n",[99,33223,33224],{"class":10573,"line":10627},[99,33225,33226],{},"        paths(...),\n",[99,33228,33229],{"class":10573,"line":10633},[99,33230,33231],{},"        components(schemas(...)),\n",[99,33233,33234],{"class":10573,"line":10639},[99,33235,33236],{},"        modifiers(&JwtSecurityAddon)\n",[99,33238,33239],{"class":10573,"line":10645},[99,33240,32745],{},[99,33242,33243],{"class":10573,"line":10651},[99,33244,33245],{},"    struct ApiDoc;\n",[99,33247,33248],{"class":10573,"line":10657},[99,33249,10613],{"emptyLinePlaceholder":53},[99,33251,33252],{"class":10573,"line":10663},[99,33253,33254],{},"    let openapi = ApiDoc::openapi();\n",[99,33256,33257],{"class":10573,"line":10669},[99,33258,10613],{"emptyLinePlaceholder":53},[99,33260,33261],{"class":10573,"line":10674},[99,33262,33263],{},"    \u002F\u002F Create router\n",[99,33265,33266],{"class":10573,"line":10680},[99,33267,33268],{},"    let app = create_router()\n",[99,33270,33271],{"class":10573,"line":10686},[99,33272,33273],{},"        .merge(\n",[99,33275,33276],{"class":10573,"line":10691},[99,33277,33278],{},"            SwaggerUi::new(\"\u002Fswagger-ui\")\n",[99,33280,33281],{"class":10573,"line":10697},[99,33282,33283],{},"                .url(\"\u002Fapi-docs\u002Fopenapi.json\", openapi)\n",[99,33285,33286],{"class":10573,"line":31678},[99,33287,33288],{},"                .config(\n",[99,33290,33291],{"class":10573,"line":31684},[99,33292,33293],{},"                    utoipa_swagger_ui::Config::default()\n",[99,33295,33296],{"class":10573,"line":31689},[99,33297,33298],{},"                        .try_it_out_enabled(true)      \u002F\u002F Enable \"Try it out\"\n",[99,33300,33301],{"class":10573,"line":31694},[99,33302,33303],{},"                        .deep_linking(true)           \u002F\u002F Enable deep linking\n",[99,33305,33306],{"class":10573,"line":31699},[99,33307,33308],{},"                        .display_request_duration(true) \u002F\u002F Show request duration\n",[99,33310,33311],{"class":10573,"line":31705},[99,33312,33313],{},"                )\n",[99,33315,33316],{"class":10573,"line":31710},[99,33317,33318],{},"        );\n",[99,33320,33321],{"class":10573,"line":31716},[99,33322,10613],{"emptyLinePlaceholder":53},[99,33324,33325],{"class":10573,"line":31721},[99,33326,33327],{},"    \u002F\u002F Start server\n",[99,33329,33330],{"class":10573,"line":31727},[99,33331,33332],{},"    let listener = tokio::net::TcpListener::bind(\"0.0.0.0:3081\").await?;\n",[99,33334,33335],{"class":10573,"line":31732},[99,33336,33337],{},"    axum::serve(listener, app).await?;\n",[99,33339,33340],{"class":10573,"line":31737},[99,33341,10613],{"emptyLinePlaceholder":53},[99,33343,33344],{"class":10573,"line":31743},[99,33345,33346],{},"    Ok(())\n",[99,33348,33349],{"class":10573,"line":31749},[99,33350,27811],{},[1258,33352,33354],{"id":33353},"swagger-ui-configuration-options","Swagger UI Configuration Options",[10562,33356,33358],{"className":30227,"code":33357,"language":30229,"meta":10567,"style":10567},"SwaggerUi::new(\"\u002Fswagger-ui\")                    \u002F\u002F UI mount path\n    .url(\"\u002Fapi-docs\u002Fopenapi.json\", openapi)     \u002F\u002F OpenAPI JSON path\n    .config(\n        utoipa_swagger_ui::Config::default()\n            \u002F\u002F Configuration options\n            .try_it_out_enabled(true)           \u002F\u002F Enable testing functionality\n            .deep_linking(true)                \u002F\u002F Deep link to specific API\n            .display_request_duration(true)     \u002F\u002F Show request duration\n            .default_models_expand_depth(1)     \u002F\u002F Default model expansion depth\n            .persist_authorization(true)        \u002F\u002F Persist authentication info\n            .filter(true)                       \u002F\u002F Enable search filtering\n    )\n",[10569,33359,33360,33365,33370,33375,33380,33385,33390,33395,33400,33405,33410,33415],{"__ignoreMap":10567},[99,33361,33362],{"class":10573,"line":10574},[99,33363,33364],{},"SwaggerUi::new(\"\u002Fswagger-ui\")                    \u002F\u002F UI mount path\n",[99,33366,33367],{"class":10573,"line":10580},[99,33368,33369],{},"    .url(\"\u002Fapi-docs\u002Fopenapi.json\", openapi)     \u002F\u002F OpenAPI JSON path\n",[99,33371,33372],{"class":10573,"line":10586},[99,33373,33374],{},"    .config(\n",[99,33376,33377],{"class":10573,"line":10592},[99,33378,33379],{},"        utoipa_swagger_ui::Config::default()\n",[99,33381,33382],{"class":10573,"line":10598},[99,33383,33384],{},"            \u002F\u002F Configuration options\n",[99,33386,33387],{"class":10573,"line":10604},[99,33388,33389],{},"            .try_it_out_enabled(true)           \u002F\u002F Enable testing functionality\n",[99,33391,33392],{"class":10573,"line":10610},[99,33393,33394],{},"            .deep_linking(true)                \u002F\u002F Deep link to specific API\n",[99,33396,33397],{"class":10573,"line":10616},[99,33398,33399],{},"            .display_request_duration(true)     \u002F\u002F Show request duration\n",[99,33401,33402],{"class":10573,"line":10622},[99,33403,33404],{},"            .default_models_expand_depth(1)     \u002F\u002F Default model expansion depth\n",[99,33406,33407],{"class":10573,"line":10627},[99,33408,33409],{},"            .persist_authorization(true)        \u002F\u002F Persist authentication info\n",[99,33411,33412],{"class":10573,"line":10633},[99,33413,33414],{},"            .filter(true)                       \u002F\u002F Enable search filtering\n",[99,33416,33417],{"class":10573,"line":10639},[99,33418,31543],{},[1258,33420,33422],{"id":33421},"access-addresses","Access Addresses",[67,33424,33425],{},"After starting the server:",[21736,33427,33428,33437],{},[21739,33429,33430,28233,33433],{},[76,33431,33432],{},"Swagger UI",[27116,33434,33435],{"href":33435,"rel":33436},"http:\u002F\u002Flocalhost:3081\u002Fswagger-ui",[27120],[21739,33438,33439,28233,33442],{},[76,33440,33441],{},"OpenAPI JSON",[27116,33443,33444],{"href":33444,"rel":33445},"http:\u002F\u002Flocalhost:3081\u002Fapi-docs\u002Fopenapi.json",[27120],[86,33447,33449],{"id":33448},"complete-workflow-example","Complete Workflow Example",[1258,33451,33453],{"id":33452},"_1-define-data-models","1. Define Data Models",[10562,33455,33457],{"className":30227,"code":33456,"language":30229,"meta":10567,"style":10567},"\u002F\u002F src\u002Fdocs\u002Fschemas.rs\nuse serde::{Deserialize, Serialize};\nuse utoipa::ToSchema;\n\n#[derive(Debug, Serialize, Deserialize, ToSchema)]\npub struct LoginUserSchema {\n    #[schema(example = \"user@example.com\")]\n    pub email: String,\n\n    #[schema(example = \"password123\")]\n    pub password: String,\n}\n\n#[derive(Debug, Serialize, Deserialize, ToSchema)]\npub struct LoginResponse {\n    pub data: LoginData,\n}\n\n#[derive(Debug, Serialize, Deserialize, ToSchema)]\npub struct LoginData {\n    #[schema(example = \"eyJhbGciOiJIUzI1NiIsInR5cCI6IkpXVCJ9...\")]\n    pub token: String,\n    pub user: FilteredUser,\n}\n",[10569,33458,33459,33464,33468,33472,33476,33480,33485,33490,33494,33498,33503,33507,33511,33515,33519,33523,33527,33531,33535,33539,33543,33547,33551,33555],{"__ignoreMap":10567},[99,33460,33461],{"class":10573,"line":10574},[99,33462,33463],{},"\u002F\u002F src\u002Fdocs\u002Fschemas.rs\n",[99,33465,33466],{"class":10573,"line":10580},[99,33467,32408],{},[99,33469,33470],{"class":10573,"line":10586},[99,33471,32413],{},[99,33473,33474],{"class":10573,"line":10592},[99,33475,10613],{"emptyLinePlaceholder":53},[99,33477,33478],{"class":10573,"line":10598},[99,33479,32422],{},[99,33481,33482],{"class":10573,"line":10604},[99,33483,33484],{},"pub struct LoginUserSchema {\n",[99,33486,33487],{"class":10573,"line":10610},[99,33488,33489],{},"    #[schema(example = \"user@example.com\")]\n",[99,33491,33492],{"class":10573,"line":10616},[99,33493,32451],{},[99,33495,33496],{"class":10573,"line":10622},[99,33497,10613],{"emptyLinePlaceholder":53},[99,33499,33500],{"class":10573,"line":10627},[99,33501,33502],{},"    #[schema(example = \"password123\")]\n",[99,33504,33505],{"class":10573,"line":10633},[99,33506,32520],{},[99,33508,33509],{"class":10573,"line":10639},[99,33510,27811],{},[99,33512,33513],{"class":10573,"line":10645},[99,33514,10613],{"emptyLinePlaceholder":53},[99,33516,33517],{"class":10573,"line":10651},[99,33518,32422],{},[99,33520,33521],{"class":10573,"line":10657},[99,33522,32579],{},[99,33524,33525],{"class":10573,"line":10663},[99,33526,32584],{},[99,33528,33529],{"class":10573,"line":10669},[99,33530,27811],{},[99,33532,33533],{"class":10573,"line":10674},[99,33534,10613],{"emptyLinePlaceholder":53},[99,33536,33537],{"class":10573,"line":10680},[99,33538,32422],{},[99,33540,33541],{"class":10573,"line":10686},[99,33542,32601],{},[99,33544,33545],{"class":10573,"line":10691},[99,33546,32606],{},[99,33548,33549],{"class":10573,"line":10697},[99,33550,32611],{},[99,33552,33553],{"class":10573,"line":31678},[99,33554,32620],{},[99,33556,33557],{"class":10573,"line":31684},[99,33558,27811],{},[1258,33560,33562],{"id":33561},"_2-define-security-schemes","2. Define Security Schemes",[10562,33564,33566],{"className":30227,"code":33565,"language":30229,"meta":10567,"style":10567},"\u002F\u002F src\u002Fdocs\u002Fsecurity.rs\nuse utoipa::{Modify, OpenApi};\nuse utoipa::openapi::security::{SecurityScheme, HttpAuthScheme, Http};\n\npub struct JwtSecurityAddon;\n\nimpl Modify for JwtSecurityAddon {\n    fn modify(&self, openapi: &mut utoipa::openapi::OpenApi) {\n        if let Some(components) = openapi.components.as_mut() {\n            components.add_security_scheme(\n                \"bearerAuth\",\n                SecurityScheme::Http(Http::new(HttpAuthScheme::Bearer))\n            );\n        }\n    }\n}\n",[10569,33567,33568,33572,33576,33581,33585,33589,33593,33597,33601,33605,33609,33613,33618,33622,33626,33630],{"__ignoreMap":10567},[99,33569,33570],{"class":10573,"line":10574},[99,33571,31574],{},[99,33573,33574],{"class":10573,"line":10580},[99,33575,31579],{},[99,33577,33578],{"class":10573,"line":10586},[99,33579,33580],{},"use utoipa::openapi::security::{SecurityScheme, HttpAuthScheme, Http};\n",[99,33582,33583],{"class":10573,"line":10592},[99,33584,10613],{"emptyLinePlaceholder":53},[99,33586,33587],{"class":10573,"line":10598},[99,33588,31598],{},[99,33590,33591],{"class":10573,"line":10604},[99,33592,10613],{"emptyLinePlaceholder":53},[99,33594,33595],{"class":10573,"line":10610},[99,33596,31607],{},[99,33598,33599],{"class":10573,"line":10616},[99,33600,31612],{},[99,33602,33603],{"class":10573,"line":10622},[99,33604,31617],{},[99,33606,33607],{"class":10573,"line":10627},[99,33608,31627],{},[99,33610,33611],{"class":10573,"line":10633},[99,33612,31632],{},[99,33614,33615],{"class":10573,"line":10639},[99,33616,33617],{},"                SecurityScheme::Http(Http::new(HttpAuthScheme::Bearer))\n",[99,33619,33620],{"class":10573,"line":10645},[99,33621,31652],{},[99,33623,33624],{"class":10573,"line":10651},[99,33625,31740],{},[99,33627,33628],{"class":10573,"line":10657},[99,33629,31746],{},[99,33631,33632],{"class":10573,"line":10663},[99,33633,27811],{},[1258,33635,33637],{"id":33636},"_3-implement-api-handlers","3. Implement API Handlers",[10562,33639,33641],{"className":30227,"code":33640,"language":30229,"meta":10567,"style":10567},"\u002F\u002F src\u002Fhandler.rs\nuse crate::docs::schemas::*;\nuse utoipa::path;\n\n#[utoipa::path(\n    post,\n    path = \"\u002Fapi\u002Fauth\u002Flogin\",\n    tag = \"Authentication\",\n    request_body = LoginUserSchema,\n    responses(\n        (status = 200, description = \"Login successful\", body = LoginResponse),\n        (status = 401, description = \"Authentication failed\", body = ErrorResponse)\n    )\n)]\npub async fn login_user_handler(\n    State(data): State\u003CAppState>,\n    Json(body): Json\u003CLoginUserSchema>,\n) -> Result\u003Cimpl IntoResponse, (StatusCode, Json\u003Cserde_json::Value>)> {\n    \u002F\u002F Implement login logic\n}\n",[10569,33642,33643,33648,33653,33657,33661,33665,33669,33673,33677,33682,33686,33690,33694,33698,33702,33707,33711,33716,33720,33725],{"__ignoreMap":10567},[99,33644,33645],{"class":10573,"line":10574},[99,33646,33647],{},"\u002F\u002F src\u002Fhandler.rs\n",[99,33649,33650],{"class":10573,"line":10580},[99,33651,33652],{},"use crate::docs::schemas::*;\n",[99,33654,33655],{"class":10573,"line":10586},[99,33656,31878],{},[99,33658,33659],{"class":10573,"line":10592},[99,33660,10613],{"emptyLinePlaceholder":53},[99,33662,33663],{"class":10573,"line":10598},[99,33664,31887],{},[99,33666,33667],{"class":10573,"line":10604},[99,33668,31897],{},[99,33670,33671],{"class":10573,"line":10610},[99,33672,31902],{},[99,33674,33675],{"class":10573,"line":10616},[99,33676,31916],{},[99,33678,33679],{"class":10573,"line":10622},[99,33680,33681],{},"    request_body = LoginUserSchema,\n",[99,33683,33684],{"class":10573,"line":10627},[99,33685,31973],{},[99,33687,33688],{"class":10573,"line":10633},[99,33689,31978],{},[99,33691,33692],{"class":10573,"line":10639},[99,33693,31983],{},[99,33695,33696],{"class":10573,"line":10645},[99,33697,31543],{},[99,33699,33700],{"class":10573,"line":10651},[99,33701,31548],{},[99,33703,33704],{"class":10573,"line":10657},[99,33705,33706],{},"pub async fn login_user_handler(\n",[99,33708,33709],{"class":10573,"line":10663},[99,33710,32088],{},[99,33712,33713],{"class":10573,"line":10669},[99,33714,33715],{},"    Json(body): Json\u003CLoginUserSchema>,\n",[99,33717,33718],{"class":10573,"line":10674},[99,33719,32098],{},[99,33721,33722],{"class":10573,"line":10680},[99,33723,33724],{},"    \u002F\u002F Implement login logic\n",[99,33726,33727],{"class":10573,"line":10686},[99,33728,27811],{},[1258,33730,33732],{"id":33731},"_4-generate-openapi-documentation","4. Generate OpenAPI Documentation",[10562,33734,33736],{"className":30227,"code":33735,"language":30229,"meta":10567,"style":10567},"\u002F\u002F src\u002Fmain.rs\nuse acrospire_auth::{\n    docs::JwtSecurityAddon,\n    docs::schemas::*,\n    handler::*,\n};\nuse utoipa::OpenApi;\nuse utoipa_swagger_ui::SwaggerUi;\n\n#[derive(OpenApi)]\n#[openapi(\n    paths(\n        health_checker_handler,\n        register_user_handler,\n        login_user_handler,\n    ),\n    components(\n        schemas(\n            HealthCheckResponse,\n            LoginUserSchema,\n            LoginResponse,\n        )\n    ),\n    tags(\n        (name = \"System\", description = \"System health check endpoints\"),\n        (name = \"Authentication\", description = \"User registration and login endpoints\"),\n    ),\n    modifiers(&JwtSecurityAddon),\n    info(\n        title = \"My API\",\n        version = \"1.0.0\"\n    )\n)]\nstruct ApiDoc;\n\n#[tokio::main]\nasync fn main() -> Result\u003C(), Box\u003Cdyn std::error::Error>> {\n    let openapi = ApiDoc::openapi();\n\n    let app = Router::new()\n        \u002F\u002F ... add routes\n        .merge(SwaggerUi::new(\"\u002Fswagger-ui\")\n            .url(\"\u002Fapi-docs\u002Fopenapi.json\", openapi));\n\n    \u002F\u002F Start server...\n}\n",[10569,33737,33738,33742,33746,33750,33754,33758,33762,33766,33770,33774,33778,33782,33786,33790,33794,33798,33802,33806,33810,33814,33818,33822,33826,33830,33834,33839,33844,33848,33853,33857,33862,33867,33871,33875,33879,33883,33887,33891,33895,33899,33904,33909,33914,33919,33923,33928],{"__ignoreMap":10567},[99,33739,33740],{"class":10573,"line":10574},[99,33741,31767],{},[99,33743,33744],{"class":10573,"line":10580},[99,33745,32772],{},[99,33747,33748],{"class":10573,"line":10586},[99,33749,32777],{},[99,33751,33752],{"class":10573,"line":10592},[99,33753,32782],{},[99,33755,33756],{"class":10573,"line":10598},[99,33757,32787],{},[99,33759,33760],{"class":10573,"line":10604},[99,33761,32792],{},[99,33763,33764],{"class":10573,"line":10610},[99,33765,32797],{},[99,33767,33768],{"class":10573,"line":10616},[99,33769,33185],{},[99,33771,33772],{"class":10573,"line":10622},[99,33773,10613],{"emptyLinePlaceholder":53},[99,33775,33776],{"class":10573,"line":10627},[99,33777,31523],{},[99,33779,33780],{"class":10573,"line":10633},[99,33781,31528],{},[99,33783,33784],{"class":10573,"line":10639},[99,33785,32819],{},[99,33787,33788],{"class":10573,"line":10645},[99,33789,32824],{},[99,33791,33792],{"class":10573,"line":10651},[99,33793,32829],{},[99,33795,33796],{"class":10573,"line":10657},[99,33797,32834],{},[99,33799,33800],{"class":10573,"line":10663},[99,33801,31959],{},[99,33803,33804],{"class":10573,"line":10669},[99,33805,32892],{},[99,33807,33808],{"class":10573,"line":10674},[99,33809,32897],{},[99,33811,33812],{"class":10573,"line":10680},[99,33813,32902],{},[99,33815,33816],{"class":10573,"line":10686},[99,33817,32912],{},[99,33819,33820],{"class":10573,"line":10691},[99,33821,32927],{},[99,33823,33824],{"class":10573,"line":10697},[99,33825,33026],{},[99,33827,33828],{"class":10573,"line":31678},[99,33829,31959],{},[99,33831,33832],{"class":10573,"line":31684},[99,33833,33048],{},[99,33835,33836],{"class":10573,"line":31689},[99,33837,33838],{},"        (name = \"System\", description = \"System health check endpoints\"),\n",[99,33840,33841],{"class":10573,"line":31694},[99,33842,33843],{},"        (name = \"Authentication\", description = \"User registration and login endpoints\"),\n",[99,33845,33846],{"class":10573,"line":31699},[99,33847,31959],{},[99,33849,33850],{"class":10573,"line":31705},[99,33851,33852],{},"    modifiers(&JwtSecurityAddon),\n",[99,33854,33855],{"class":10573,"line":31710},[99,33856,33100],{},[99,33858,33859],{"class":10573,"line":31716},[99,33860,33861],{},"        title = \"My API\",\n",[99,33863,33864],{"class":10573,"line":31721},[99,33865,33866],{},"        version = \"1.0.0\"\n",[99,33868,33869],{"class":10573,"line":31727},[99,33870,31543],{},[99,33872,33873],{"class":10573,"line":31732},[99,33874,31548],{},[99,33876,33877],{"class":10573,"line":31737},[99,33878,31553],{},[99,33880,33881],{"class":10573,"line":31743},[99,33882,10613],{"emptyLinePlaceholder":53},[99,33884,33885],{"class":10573,"line":31749},[99,33886,30460],{},[99,33888,33889],{"class":10573,"line":32945},[99,33890,30465],{},[99,33892,33893],{"class":10573,"line":32951},[99,33894,33254],{},[99,33896,33897],{"class":10573,"line":32957},[99,33898,10613],{"emptyLinePlaceholder":53},[99,33900,33901],{"class":10573,"line":32963},[99,33902,33903],{},"    let app = Router::new()\n",[99,33905,33906],{"class":10573,"line":32969},[99,33907,33908],{},"        \u002F\u002F ... add routes\n",[99,33910,33911],{"class":10573,"line":32975},[99,33912,33913],{},"        .merge(SwaggerUi::new(\"\u002Fswagger-ui\")\n",[99,33915,33916],{"class":10573,"line":32981},[99,33917,33918],{},"            .url(\"\u002Fapi-docs\u002Fopenapi.json\", openapi));\n",[99,33920,33921],{"class":10573,"line":32987},[99,33922,10613],{"emptyLinePlaceholder":53},[99,33924,33925],{"class":10573,"line":32993},[99,33926,33927],{},"    \u002F\u002F Start server...\n",[99,33929,33930],{"class":10573,"line":32999},[99,33931,27811],{},[1258,33933,33935],{"id":33934},"_5-using-swagger-ui","5. Using Swagger UI",[27423,33937,33938,33944,33947,33950,33953,33956],{},[21739,33939,33940,33941],{},"Visit ",[27116,33942,33435],{"href":33435,"rel":33943},[27120],[21739,33945,33946],{},"Click 🔓 \"Authorize\" button",[21739,33948,33949],{},"Select authentication method (bearerAuth\u002FcookieAuth\u002FapiKeyAuth)",[21739,33951,33952],{},"Enter authentication credentials",[21739,33954,33955],{},"Click \"Authorize\" → \"Close\"",[21739,33957,33958],{},"Use \"Try it out\" to test APIs",[86,33960,33962],{"id":33961},"common-issues-and-solutions","Common Issues and Solutions",[1258,33964,33966],{"id":33965},"issue-1-authorize-button-not-showing","Issue 1: Authorize Button Not Showing",[67,33968,33969,27783],{},[76,33970,33971],{},"Cause",[27423,33973,33974,33980,33991],{},[21739,33975,33976,33977],{},"No security schemes added via ",[10569,33978,33979],{},"modifiers(&SecurityAddon)",[21739,33981,33982,33983,33986,33987,33990],{},"Incorrect ",[10569,33984,33985],{},"SecurityAddon"," ",[10569,33988,33989],{},"modify"," method implementation",[21739,33992,33993,33995,33996],{},[10569,33994,33985],{}," not referenced in ",[10569,33997,31757],{},[67,33999,34000,27783],{},[76,34001,34002],{},"Solution",[10562,34004,34006],{"className":30227,"code":34005,"language":30229,"meta":10567,"style":10567},"\u002F\u002F Ensure Modify trait is correctly implemented\nimpl Modify for JwtSecurityAddon {\n    fn modify(&self, openapi: &mut utoipa::openapi::OpenApi) {\n        if let Some(components) = openapi.components.as_mut() {\n            components.add_security_scheme(...);\n        }\n    }\n}\n\n\u002F\u002F Use in ApiDoc\n#[openapi(modifiers(&JwtSecurityAddon))]\nstruct ApiDoc;\n",[10569,34007,34008,34013,34017,34021,34025,34030,34034,34038,34042,34046,34051,34056],{"__ignoreMap":10567},[99,34009,34010],{"class":10573,"line":10574},[99,34011,34012],{},"\u002F\u002F Ensure Modify trait is correctly implemented\n",[99,34014,34015],{"class":10573,"line":10580},[99,34016,31607],{},[99,34018,34019],{"class":10573,"line":10586},[99,34020,31612],{},[99,34022,34023],{"class":10573,"line":10592},[99,34024,31617],{},[99,34026,34027],{"class":10573,"line":10598},[99,34028,34029],{},"            components.add_security_scheme(...);\n",[99,34031,34032],{"class":10573,"line":10604},[99,34033,31740],{},[99,34035,34036],{"class":10573,"line":10610},[99,34037,31746],{},[99,34039,34040],{"class":10573,"line":10616},[99,34041,27811],{},[99,34043,34044],{"class":10573,"line":10622},[99,34045,10613],{"emptyLinePlaceholder":53},[99,34047,34048],{"class":10573,"line":10627},[99,34049,34050],{},"\u002F\u002F Use in ApiDoc\n",[99,34052,34053],{"class":10573,"line":10633},[99,34054,34055],{},"#[openapi(modifiers(&JwtSecurityAddon))]\n",[99,34057,34058],{"class":10573,"line":10639},[99,34059,31553],{},[1258,34061,34063],{"id":34062},"issue-2-empty-paths-field","Issue 2: Empty Paths Field",[67,34065,34066,27783],{},[76,34067,33971],{},[27423,34069,34070,34079,34085],{},[21739,34071,34072,34073,34075,34076],{},"Handlers not listed in ",[10569,34074,31757],{},"'s ",[10569,34077,34078],{},"paths(...)",[21739,34080,34081,34082],{},"Handler functions not marked with ",[10569,34083,34084],{},"#[utoipa::path]",[21739,34086,34087],{},"Incorrect path references (function name mismatch)",[67,34089,34090,27783],{},[76,34091,34002],{},[10562,34093,34095],{"className":30227,"code":34094,"language":30229,"meta":10567,"style":10567},"#[openapi(\n    paths(\n        handler::function1,   \u002F\u002F ✅ Correct: List all handlers\n        handler::function2,\n    )\n)]\nstruct ApiDoc;\n",[10569,34096,34097,34101,34105,34110,34115,34119,34123],{"__ignoreMap":10567},[99,34098,34099],{"class":10573,"line":10574},[99,34100,31528],{},[99,34102,34103],{"class":10573,"line":10580},[99,34104,32819],{},[99,34106,34107],{"class":10573,"line":10586},[99,34108,34109],{},"        handler::function1,   \u002F\u002F ✅ Correct: List all handlers\n",[99,34111,34112],{"class":10573,"line":10592},[99,34113,34114],{},"        handler::function2,\n",[99,34116,34117],{"class":10573,"line":10598},[99,34118,31543],{},[99,34120,34121],{"class":10573,"line":10604},[99,34122,31548],{},[99,34124,34125],{"class":10573,"line":10610},[99,34126,31553],{},[1258,34128,34130],{"id":34129},"issue-3-datetime-type-not-supported","Issue 3: DateTime Type Not Supported",[67,34132,34133,27783],{},[76,34134,34135],{},"Problem",[10562,34137,34139],{"className":30227,"code":34138,"language":30229,"meta":10567,"style":10567},"#[derive(ToSchema)]\nstruct MyStruct {\n    pub created_at: DateTime\u003CUtc>,  \u002F\u002F ❌ Might error\n}\n",[10569,34140,34141,34146,34151,34156],{"__ignoreMap":10567},[99,34142,34143],{"class":10573,"line":10574},[99,34144,34145],{},"#[derive(ToSchema)]\n",[99,34147,34148],{"class":10573,"line":10580},[99,34149,34150],{},"struct MyStruct {\n",[99,34152,34153],{"class":10573,"line":10586},[99,34154,34155],{},"    pub created_at: DateTime\u003CUtc>,  \u002F\u002F ❌ Might error\n",[99,34157,34158],{"class":10573,"line":10592},[99,34159,27811],{},[67,34161,34162,27783],{},[76,34163,34002],{},[10562,34165,34167],{"className":30227,"code":34166,"language":30229,"meta":10567,"style":10567},"#[derive(ToSchema)]\nstruct MyStruct {\n    #[schema(value_type = String, format = \"date-time\")]\n    pub created_at: DateTime\u003CUtc>,  \u002F\u002F ✅ Use String type\n}\n",[10569,34168,34169,34173,34177,34181,34186],{"__ignoreMap":10567},[99,34170,34171],{"class":10573,"line":10574},[99,34172,34145],{},[99,34174,34175],{"class":10573,"line":10580},[99,34176,34150],{},[99,34178,34179],{"class":10573,"line":10586},[99,34180,32682],{},[99,34182,34183],{"class":10573,"line":10592},[99,34184,34185],{},"    pub created_at: DateTime\u003CUtc>,  \u002F\u002F ✅ Use String type\n",[99,34187,34188],{"class":10573,"line":10598},[99,34189,27811],{},[1258,34191,34193,34194],{"id":34192},"issue-4-route-conflict-overlapping-method-route","Issue 4: Route Conflict ",[10569,34195,34196],{},"Overlapping method route",[67,34198,34199,27783],{},[76,34200,34201],{},"Error Message",[10562,34203,34206],{"className":34204,"code":34205,"language":582},[10707],"Overlapping method route. Handler for GET \u002Fapi-docs\u002Fopenapi.json already exists\n",[10569,34207,34205],{"__ignoreMap":10567},[67,34209,34210,34212,34213,34216],{},[76,34211,33971],{},":\nAdded ",[10569,34214,34215],{},"SwaggerUi"," in multiple places, causing duplicate routes",[67,34218,34219,34221,34222,2846],{},[76,34220,34002],{},":\nOnly add Swagger UI in one place (recommend ",[10569,34223,34224],{},"main.rs",[10562,34226,34228],{"className":30227,"code":34227,"language":30229,"meta":10567,"style":10567},"\u002F\u002F ❌ Wrong: Added in both route.rs and main.rs\n\u002F\u002F route.rs\nlet app = Router::new().merge(swagger_ui)\n\n\u002F\u002F main.rs\nlet app = create_router().merge(swagger_ui)  \u002F\u002F Conflict!\n\n\u002F\u002F ✅ Correct: Only in main.rs\n\u002F\u002F route.rs - Don't add swagger_ui\n\u002F\u002F main.rs - Add it here\nlet app = create_router().merge(swagger_ui)\n",[10569,34229,34230,34235,34240,34245,34249,34254,34259,34263,34268,34273,34278],{"__ignoreMap":10567},[99,34231,34232],{"class":10573,"line":10574},[99,34233,34234],{},"\u002F\u002F ❌ Wrong: Added in both route.rs and main.rs\n",[99,34236,34237],{"class":10573,"line":10580},[99,34238,34239],{},"\u002F\u002F route.rs\n",[99,34241,34242],{"class":10573,"line":10586},[99,34243,34244],{},"let app = Router::new().merge(swagger_ui)\n",[99,34246,34247],{"class":10573,"line":10592},[99,34248,10613],{"emptyLinePlaceholder":53},[99,34250,34251],{"class":10573,"line":10598},[99,34252,34253],{},"\u002F\u002F main.rs\n",[99,34255,34256],{"class":10573,"line":10604},[99,34257,34258],{},"let app = create_router().merge(swagger_ui)  \u002F\u002F Conflict!\n",[99,34260,34261],{"class":10573,"line":10610},[99,34262,10613],{"emptyLinePlaceholder":53},[99,34264,34265],{"class":10573,"line":10616},[99,34266,34267],{},"\u002F\u002F ✅ Correct: Only in main.rs\n",[99,34269,34270],{"class":10573,"line":10622},[99,34271,34272],{},"\u002F\u002F route.rs - Don't add swagger_ui\n",[99,34274,34275],{"class":10573,"line":10627},[99,34276,34277],{},"\u002F\u002F main.rs - Add it here\n",[99,34279,34280],{"class":10573,"line":10633},[99,34281,34282],{},"let app = create_router().merge(swagger_ui)\n",[1258,34284,34286],{"id":34285},"issue-5-supporting-multiple-authentication-methods","Issue 5: Supporting Multiple Authentication Methods",[10562,34288,34290],{"className":30227,"code":34289,"language":30229,"meta":10567,"style":10567},"\u002F\u002F Declare multiple authentication methods in handler\n#[utoipa::path(\n    get,\n    path = \"\u002Fapi\u002Fusers\u002Fme\",\n    security(\n        (\"bearerAuth\" = []),   \u002F\u002F Method 1\n        (\"cookieAuth\" = [])     \u002F\u002F Method 2\n    )\n)]\npub async fn get_me() {\n    \u002F\u002F Implementation...\n}\n",[10569,34291,34292,34297,34301,34305,34309,34313,34318,34323,34327,34331,34336,34340],{"__ignoreMap":10567},[99,34293,34294],{"class":10573,"line":10574},[99,34295,34296],{},"\u002F\u002F Declare multiple authentication methods in handler\n",[99,34298,34299],{"class":10573,"line":10580},[99,34300,31887],{},[99,34302,34303],{"class":10573,"line":10586},[99,34304,32135],{},[99,34306,34307],{"class":10573,"line":10592},[99,34308,32140],{},[99,34310,34311],{"class":10573,"line":10598},[99,34312,31944],{},[99,34314,34315],{"class":10573,"line":10604},[99,34316,34317],{},"        (\"bearerAuth\" = []),   \u002F\u002F Method 1\n",[99,34319,34320],{"class":10573,"line":10610},[99,34321,34322],{},"        (\"cookieAuth\" = [])     \u002F\u002F Method 2\n",[99,34324,34325],{"class":10573,"line":10616},[99,34326,31543],{},[99,34328,34329],{"class":10573,"line":10622},[99,34330,31548],{},[99,34332,34333],{"class":10573,"line":10627},[99,34334,34335],{},"pub async fn get_me() {\n",[99,34337,34338],{"class":10573,"line":10633},[99,34339,32103],{},[99,34341,34342],{"class":10573,"line":10639},[99,34343,27811],{},[67,34345,34346],{},"Users can choose any authentication method in Swagger UI.",[86,34348,34350],{"id":34349},"best-practices","Best Practices",[1258,34352,34354],{"id":34353},"_1-organize-code-in-layers","1. Organize Code in Layers",[10562,34356,34358],{"className":30227,"code":34357,"language":30229,"meta":10567,"style":10567},"docs\u002F\n├── mod.rs          \u002F\u002F Export interfaces\n├── security.rs     \u002F\u002F Security schemes\n├── schemas.rs      \u002F\u002F Data models\n└── openapi.rs      \u002F\u002F Helper functions\n",[10569,34359,34360,34365,34370,34375,34380],{"__ignoreMap":10567},[99,34361,34362],{"class":10573,"line":10574},[99,34363,34364],{},"docs\u002F\n",[99,34366,34367],{"class":10573,"line":10580},[99,34368,34369],{},"├── mod.rs          \u002F\u002F Export interfaces\n",[99,34371,34372],{"class":10573,"line":10586},[99,34373,34374],{},"├── security.rs     \u002F\u002F Security schemes\n",[99,34376,34377],{"class":10573,"line":10592},[99,34378,34379],{},"├── schemas.rs      \u002F\u002F Data models\n",[99,34381,34382],{"class":10573,"line":10598},[99,34383,34384],{},"└── openapi.rs      \u002F\u002F Helper functions\n",[1258,34386,34388],{"id":34387},"_2-use-full-type-paths","2. Use Full Type Paths",[10562,34390,34392],{"className":30227,"code":34391,"language":30229,"meta":10567,"style":10567},"#[openapi(\n    paths(\n        acrospire_auth::handler::login_handler,  \u002F\u002F ✅ Full path\n        \u002F\u002F login_handler,  \u002F\u002F ❌ Errors if not in scope\n    )\n)]\n",[10569,34393,34394,34398,34402,34407,34415,34419],{"__ignoreMap":10567},[99,34395,34396],{"class":10573,"line":10574},[99,34397,31528],{},[99,34399,34400],{"class":10573,"line":10580},[99,34401,32819],{},[99,34403,34404],{"class":10573,"line":10586},[99,34405,34406],{},"        acrospire_auth::handler::login_handler,  \u002F\u002F ✅ Full path\n",[99,34408,34409,34412],{"class":10573,"line":10592},[99,34410,34411],{},"        \u002F\u002F login_handler,",[99,34413,34414],{},"  \u002F\u002F ❌ Errors if not in scope\n",[99,34416,34417],{"class":10573,"line":10598},[99,34418,31543],{},[99,34420,34421],{"class":10573,"line":10604},[99,34422,31548],{},[1258,34424,34426],{"id":34425},"_3-add-examples-for-all-schemas","3. Add Examples for All Schemas",[10562,34428,34430],{"className":30227,"code":34429,"language":30229,"meta":10567,"style":10567},"#[derive(ToSchema)]\npub struct CreateUserSchema {\n    #[schema(example = \"user@example.com\")]\n    pub email: String,\n\n    #[schema(example = \"StrongPass123!\")]\n    pub password: String,\n}\n",[10569,34431,34432,34436,34441,34445,34449,34453,34458,34462],{"__ignoreMap":10567},[99,34433,34434],{"class":10573,"line":10574},[99,34435,34145],{},[99,34437,34438],{"class":10573,"line":10580},[99,34439,34440],{},"pub struct CreateUserSchema {\n",[99,34442,34443],{"class":10573,"line":10586},[99,34444,33489],{},[99,34446,34447],{"class":10573,"line":10592},[99,34448,32451],{},[99,34450,34451],{"class":10573,"line":10598},[99,34452,10613],{"emptyLinePlaceholder":53},[99,34454,34455],{"class":10573,"line":10604},[99,34456,34457],{},"    #[schema(example = \"StrongPass123!\")]\n",[99,34459,34460],{"class":10573,"line":10610},[99,34461,32520],{},[99,34463,34464],{"class":10573,"line":10616},[99,34465,27811],{},[1258,34467,34469],{"id":34468},"_4-use-descriptive-text","4. Use Descriptive Text",[10562,34471,34473],{"className":30227,"code":34472,"language":30229,"meta":10567,"style":10567},"#[utoipa::path(\n    post,\n    path = \"\u002Fapi\u002Fauth\u002Flogin\",\n    tag = \"Authentication\",\n    summary = \"User login\",           \u002F\u002F ← Add summary\n    description = \"Login to the system using email and password, returns JWT Token on success\",  \u002F\u002F ← Detailed description\n    responses(...)\n)]\n",[10569,34474,34475,34479,34483,34487,34491,34496,34501,34506],{"__ignoreMap":10567},[99,34476,34477],{"class":10573,"line":10574},[99,34478,31887],{},[99,34480,34481],{"class":10573,"line":10580},[99,34482,31897],{},[99,34484,34485],{"class":10573,"line":10586},[99,34486,31902],{},[99,34488,34489],{"class":10573,"line":10592},[99,34490,31916],{},[99,34492,34493],{"class":10573,"line":10598},[99,34494,34495],{},"    summary = \"User login\",           \u002F\u002F ← Add summary\n",[99,34497,34498],{"class":10573,"line":10604},[99,34499,34500],{},"    description = \"Login to the system using email and password, returns JWT Token on success\",  \u002F\u002F ← Detailed description\n",[99,34502,34503],{"class":10573,"line":10610},[99,34504,34505],{},"    responses(...)\n",[99,34507,34508],{"class":10573,"line":10616},[99,34509,31548],{},[1258,34511,34513],{"id":34512},"_5-standardize-error-response-format","5. Standardize Error Response Format",[10562,34515,34517],{"className":30227,"code":34516,"language":30229,"meta":10567,"style":10567},"#[derive(ToSchema)]\npub struct ErrorResponse {\n    pub status: String,\n\n    #[schema(example = \"Operation failed\")]\n    pub message: String,\n}\n\n\u002F\u002F Reuse in all handlers\n#[utoipa::path(\n    responses(\n        (status = 200, description = \"Success\"),\n        (status = 400, description = \"Parameter error\", body = ErrorResponse),  \u002F\u002F Reuse\n        (status = 500, description = \"Server error\", body = ErrorResponse),  \u002F\u002F Reuse\n    )\n)]\n",[10569,34518,34519,34523,34528,34533,34537,34542,34547,34551,34555,34560,34564,34568,34573,34578,34583,34587],{"__ignoreMap":10567},[99,34520,34521],{"class":10573,"line":10574},[99,34522,34145],{},[99,34524,34525],{"class":10573,"line":10580},[99,34526,34527],{},"pub struct ErrorResponse {\n",[99,34529,34530],{"class":10573,"line":10586},[99,34531,34532],{},"    pub status: String,\n",[99,34534,34535],{"class":10573,"line":10592},[99,34536,10613],{"emptyLinePlaceholder":53},[99,34538,34539],{"class":10573,"line":10598},[99,34540,34541],{},"    #[schema(example = \"Operation failed\")]\n",[99,34543,34544],{"class":10573,"line":10604},[99,34545,34546],{},"    pub message: String,\n",[99,34548,34549],{"class":10573,"line":10610},[99,34550,27811],{},[99,34552,34553],{"class":10573,"line":10616},[99,34554,10613],{"emptyLinePlaceholder":53},[99,34556,34557],{"class":10573,"line":10622},[99,34558,34559],{},"\u002F\u002F Reuse in all handlers\n",[99,34561,34562],{"class":10573,"line":10627},[99,34563,31887],{},[99,34565,34566],{"class":10573,"line":10633},[99,34567,31973],{},[99,34569,34570],{"class":10573,"line":10639},[99,34571,34572],{},"        (status = 200, description = \"Success\"),\n",[99,34574,34575],{"class":10573,"line":10645},[99,34576,34577],{},"        (status = 400, description = \"Parameter error\", body = ErrorResponse),  \u002F\u002F Reuse\n",[99,34579,34580],{"class":10573,"line":10651},[99,34581,34582],{},"        (status = 500, description = \"Server error\", body = ErrorResponse),  \u002F\u002F Reuse\n",[99,34584,34585],{"class":10573,"line":10657},[99,34586,31543],{},[99,34588,34589],{"class":10573,"line":10663},[99,34590,31548],{},[86,34592,34594],{"id":34593},"testing-apis-with-swagger-ui","Testing APIs with Swagger UI",[27423,34596,34597,34608,34630],{},[21739,34598,34599,27783,34602],{},[76,34600,34601],{},"Login to Get Token",[10562,34603,34606],{"className":34604,"code":34605,"language":582},[10707],"POST \u002Fapi\u002Fauth\u002Flogin\nBody: { \"email\": \"user@example.com\", \"password\": \"password123\" }\n",[10569,34607,34605],{"__ignoreMap":10567},[21739,34609,34610,27783,34613],{},[76,34611,34612],{},"Configure Authentication",[21736,34614,34615,34618,34624,34627],{},[21739,34616,34617],{},"Click \"Authorize\" button",[21739,34619,34620,34621],{},"Select ",[10569,34622,34623],{},"bearerAuth",[21739,34625,34626],{},"Enter returned Token",[21739,34628,34629],{},"Click \"Authorize\"",[21739,34631,34632,27783,34635],{},[76,34633,34634],{},"Test Protected Endpoints",[21736,34636,34637,34640,34643,34646],{},[21739,34638,34639],{},"Click on protected endpoint",[21739,34641,34642],{},"Click \"Try it out\"",[21739,34644,34645],{},"Click \"Execute\"",[21739,34647,34648],{},"Swagger UI automatically adds Authorization header",[86,34650,30589],{"id":30588},[67,34652,34653],{},"Integrating utoipa with Axum gives you a powerful, type-safe API documentation system. The key steps are:",[27423,34655,34656,34667,34680,34692,34700,34706],{},[21739,34657,34658,34661,34662,926,34664,34666],{},[76,34659,34660],{},"Configure Dependencies"," - Correct ",[10569,34663,31467],{},[10569,34665,31463],{}," versions",[21739,34668,34669,34672,34673,34676,34677],{},[76,34670,34671],{},"Create Modify Implementation"," - Implement ",[10569,34674,34675],{},"JwtSecurityAddon"," in ",[10569,34678,34679],{},"security.rs",[21739,34681,34682,34685,34686,926,34689],{},[76,34683,34684],{},"Mark Handlers"," - Use ",[10569,34687,34688],{},"#[utoipa::path(...)]",[10569,34690,34691],{},"security()",[21739,34693,34694,34685,34697],{},[76,34695,34696],{},"Mark Schemas",[10569,34698,34699],{},"#[derive(ToSchema)]",[21739,34701,34702,34705],{},[76,34703,34704],{},"Define ApiDoc"," - Register paths, schemas, tags, and modifiers",[21739,34707,34708,34711,34712],{},[76,34709,34710],{},"Integrate Swagger UI"," - Mount documentation using ",[10569,34713,34714],{},"SwaggerUi::new()",[67,34716,34717],{},"Following this guide, you'll have beautiful, interactive API documentation with full authentication support in no time. Happy coding!",[86,34719,34721],{"id":34720},"resources","Resources",[21736,34723,34724,34731,34738,34745],{},[21739,34725,34726],{},[27116,34727,34730],{"href":34728,"rel":34729},"https:\u002F\u002Fdocs.rs\u002Futoipa\u002Flatest\u002Futoipa\u002F",[27120],"Utoipa Official Documentation",[21739,34732,34733],{},[27116,34734,34737],{"href":34735,"rel":34736},"https:\u002F\u002Fgithub.com\u002Fjuhaku\u002Futoipa",[27120],"Utoipa GitHub",[21739,34739,34740],{},[27116,34741,34744],{"href":34742,"rel":34743},"https:\u002F\u002Fswagger.io\u002Fspecification\u002F",[27120],"OpenAPI 3.0 Specification",[21739,34746,34747],{},[27116,34748,33432],{"href":34749,"rel":34750},"https:\u002F\u002Fswagger.io\u002Ftools\u002Fswagger-ui\u002F",[27120],[10721,34752,10723],{},{"title":10567,"searchDepth":10580,"depth":10580,"links":34754},[34755,34756,34760,34761,34766,34773,34779,34782,34787,34794,34802,34809,34810,34811],{"id":31302,"depth":10580,"text":31303},{"id":31341,"depth":10580,"text":31342,"children":34757},[34758,34759],{"id":31345,"depth":10586,"text":31346},{"id":31470,"depth":10586,"text":31471},{"id":31483,"depth":10580,"text":31484},{"id":31496,"depth":10580,"text":31497,"children":34762},[34763,34764,34765],{"id":31500,"depth":10586,"text":31501},{"id":31556,"depth":10586,"text":31557},{"id":31800,"depth":10586,"text":31801},{"id":31863,"depth":10580,"text":31864,"children":34767},[34768,34769,34770,34771,34772],{"id":31867,"depth":10586,"text":31868},{"id":32018,"depth":10586,"text":32019},{"id":32110,"depth":10586,"text":32111},{"id":32210,"depth":10586,"text":32211},{"id":32310,"depth":10586,"text":32311},{"id":32393,"depth":10580,"text":32394,"children":34774},[34775,34776,34777,34778],{"id":32397,"depth":10586,"text":32398},{"id":32472,"depth":10586,"text":32473},{"id":32564,"depth":10586,"text":32565},{"id":32627,"depth":10586,"text":32628},{"id":32757,"depth":10580,"text":32758,"children":34780},[34781],{"id":32761,"depth":10586,"text":32762},{"id":33170,"depth":10580,"text":33171,"children":34783},[34784,34785,34786],{"id":33174,"depth":10586,"text":33175},{"id":33353,"depth":10586,"text":33354},{"id":33421,"depth":10586,"text":33422},{"id":33448,"depth":10580,"text":33449,"children":34788},[34789,34790,34791,34792,34793],{"id":33452,"depth":10586,"text":33453},{"id":33561,"depth":10586,"text":33562},{"id":33636,"depth":10586,"text":33637},{"id":33731,"depth":10586,"text":33732},{"id":33934,"depth":10586,"text":33935},{"id":33961,"depth":10580,"text":33962,"children":34795},[34796,34797,34798,34799,34801],{"id":33965,"depth":10586,"text":33966},{"id":34062,"depth":10586,"text":34063},{"id":34129,"depth":10586,"text":34130},{"id":34192,"depth":10586,"text":34800},"Issue 4: Route Conflict Overlapping method route",{"id":34285,"depth":10586,"text":34286},{"id":34349,"depth":10580,"text":34350,"children":34803},[34804,34805,34806,34807,34808],{"id":34353,"depth":10586,"text":34354},{"id":34387,"depth":10586,"text":34388},{"id":34425,"depth":10586,"text":34426},{"id":34468,"depth":10586,"text":34469},{"id":34512,"depth":10586,"text":34513},{"id":34593,"depth":10580,"text":34594},{"id":30588,"depth":10580,"text":30589},{"id":34720,"depth":10580,"text":34721},"2025-01-03","Learn how to integrate utoipa and Swagger UI in Rust Axum projects to enable OpenAPI documentation with JWT, Cookie, and API Key authentication.",{},{"title":38,"description":34813},"89-DdNesAH6hrt9aHnBYQcT7R3xEuZ4jhV0EeD_HP1U",{"id":34818,"title":14,"author":34819,"body":34821,"date":35538,"description":35539,"extension":10734,"image":35540,"meta":35541,"minRead":10604,"navigation":53,"path":15,"seo":35542,"stem":16,"__hash__":35543},"blog\u002Fblog\u002Fdeploying-nuxt-static-site-with-nginx.md",{"name":60,"avatar":34820},{"src":62,"alt":60},{"type":64,"value":34822,"toc":35520},[34823,34826,34830,34833,34865,34869,34875,34919,34925,34929,34932,34947,34950,34968,34971,34988,34992,34996,34999,35025,35029,35032,35178,35181,35185,35188,35352,35355,35361,35365,35373,35393,35398,35409,35414,35422,35426,35429,35437,35444,35448,35452,35472,35476,35485,35487,35490,35511,35514,35517],[67,34824,34825],{},"When it comes to deploying modern web applications, Nuxt 3's static site generation (SSG) offers an excellent balance of performance, SEO, and simplicity. Combined with Nginx's battle-tested serving capabilities, you get a deployment setup that's fast, reliable, and cost-effective. Let's walk through the complete process.",[86,34827,34829],{"id":34828},"why-static-site-generation","Why Static Site Generation?",[67,34831,34832],{},"Static site generation pre-renders your application at build time, producing pure HTML, CSS, and JavaScript files that can be served from any static file server. The benefits are compelling:",[21736,34834,34835,34841,34847,34853,34859],{},[21739,34836,34837,34840],{},[76,34838,34839],{},"Performance",": No server-side rendering overhead means instant page loads",[21739,34842,34843,34846],{},[76,34844,34845],{},"SEO",": Search engines get fully rendered HTML",[21739,34848,34849,34852],{},[76,34850,34851],{},"Simplicity",": No Node.js server required in production",[21739,34854,34855,34858],{},[76,34856,34857],{},"Cost",": Can host on any basic web server",[21739,34860,34861,34864],{},[76,34862,34863],{},"Reliability",": Fewer moving parts means fewer things can break",[86,34866,34868],{"id":34867},"configuring-nuxt-for-static-generation","Configuring Nuxt for Static Generation",[67,34870,34871,34872,27783],{},"First, configure your Nuxt app to generate static files. In your ",[10569,34873,34874],{},"nuxt.config.ts",[10562,34876,34880],{"className":34877,"code":34878,"language":34879,"meta":10567,"style":10567},"language-typescript shiki shiki-themes material-theme-lighter material-theme material-theme-palenight","export default defineNuxtConfig({\n  ssr: false,  \u002F\u002F Disable server-side rendering for static generation\n})\n","typescript",[10569,34881,34882,34897,34912],{"__ignoreMap":10567},[99,34883,34884,34887,34890,34893,34895],{"class":10573,"line":10574},[99,34885,29883],{"class":34886},"s7zQu",[99,34888,34889],{"class":34886}," default",[99,34891,34892],{"class":27617}," defineNuxtConfig",[99,34894,2813],{"class":28232},[99,34896,27768],{"class":27519},[99,34898,34899,34902,34904,34907,34909],{"class":10573,"line":10580},[99,34900,34901],{"class":29089},"  ssr",[99,34903,27783],{"class":27519},[99,34905,34906],{"class":29111}," false",[99,34908,140],{"class":27519},[99,34910,34911],{"class":27395},"  \u002F\u002F Disable server-side rendering for static generation\n",[99,34913,34914,34916],{"class":10573,"line":10586},[99,34915,147],{"class":27519},[99,34917,34918],{"class":28232},")\n",[67,34920,30220,34921,34924],{},[10569,34922,34923],{},"ssr: false"," setting tells Nuxt to generate a static site. This is essential for our use case.",[86,34926,34928],{"id":34927},"building-your-static-site","Building Your Static Site",[67,34930,34931],{},"Generate your static files with a single command:",[10562,34933,34935],{"className":27378,"code":34934,"language":27380,"meta":10567,"style":10567},"pnpm run generate\n",[10569,34936,34937],{"__ignoreMap":10567},[99,34938,34939,34942,34944],{"class":10573,"line":10574},[99,34940,34941],{"class":27387},"pnpm",[99,34943,27661],{"class":27391},[99,34945,34946],{"class":27391}," generate\n",[67,34948,34949],{},"This command:",[27423,34951,34952,34955,34958,34961],{},[21739,34953,34954],{},"Builds your application",[21739,34956,34957],{},"Generates static HTML for all your routes",[21739,34959,34960],{},"Optimizes assets (CSS, JS, images)",[21739,34962,34963,34964,34967],{},"Creates a ",[10569,34965,34966],{},".output\u002Fpublic"," directory ready for deployment",[67,34969,34970],{},"The output will contain:",[21736,34972,34973,34979,34985],{},[21739,34974,34975,34978],{},[10569,34976,34977],{},"index.html"," - Your main entry point",[21739,34980,34981,34984],{},[10569,34982,34983],{},"\u002F_nuxt\u002F"," - Hashed JavaScript and CSS bundles",[21739,34986,34987],{},"Other static assets (images, fonts, etc.)",[86,34989,34991],{"id":34990},"deploying-to-nginx","Deploying to Nginx",[1258,34993,34995],{"id":34994},"step-1-package-your-site","Step 1: Package Your Site",[67,34997,34998],{},"Create a compressed archive of your built site:",[10562,35000,35002],{"className":27378,"code":35001,"language":27380,"meta":10567,"style":10567},"cd .output\u002Fpublic\ntar -czf package.tgz *\n",[10569,35003,35004,35011],{"__ignoreMap":10567},[99,35005,35006,35008],{"class":10573,"line":10574},[99,35007,27618],{"class":27617},[99,35009,35010],{"class":27391}," .output\u002Fpublic\n",[99,35012,35013,35016,35019,35022],{"class":10573,"line":10580},[99,35014,35015],{"class":27387},"tar",[99,35017,35018],{"class":27391}," -czf",[99,35020,35021],{"class":27391}," package.tgz",[99,35023,35024],{"class":28232}," *\n",[1258,35026,35028],{"id":35027},"step-2-upload-and-extract","Step 2: Upload and Extract",[67,35030,35031],{},"On your server, deploy with this script:",[10562,35033,35035],{"className":27378,"code":35034,"language":27380,"meta":10567,"style":10567},"#!\u002Fbin\u002Fbash\n# Check if target directory exists, remove if it does\nif [ -d \"\u002Fvar\u002Fwww\u002Fzhongjing\" ]; then\n    echo \"Removing existing directory: \u002Fvar\u002Fwww\u002Fzhongjing\"\n    rm -rf \u002Fvar\u002Fwww\u002Fzhongjing\nfi\n\n# Create target directory\nmkdir -p \u002Fvar\u002Fwww\u002Fzhongjing\n\n# Extract archive to target directory\ntar -xzf \u002Fvar\u002Fwww\u002Fpackage.tgz -C \u002Fvar\u002Fwww\u002Fzhongjing\n\n# Set proper ownership\nsudo chown -R www-data:www-data zhongjing\u002F\n\necho \"Deployment complete\"\n",[10569,35036,35037,35041,35046,35070,35082,35092,35097,35101,35106,35114,35118,35123,35137,35141,35146,35162,35166],{"__ignoreMap":10567},[99,35038,35039],{"class":10573,"line":10574},[99,35040,30879],{"class":27395},[99,35042,35043],{"class":10573,"line":10580},[99,35044,35045],{"class":27395},"# Check if target directory exists, remove if it does\n",[99,35047,35048,35051,35054,35057,35059,35062,35064,35067],{"class":10573,"line":10586},[99,35049,35050],{"class":34886},"if",[99,35052,35053],{"class":27519}," [",[99,35055,35056],{"class":27519}," -d",[99,35058,27520],{"class":27519},[99,35060,35061],{"class":27391},"\u002Fvar\u002Fwww\u002Fzhongjing",[99,35063,27780],{"class":27519},[99,35065,35066],{"class":27519}," ];",[99,35068,35069],{"class":34886}," then\n",[99,35071,35072,35075,35077,35080],{"class":10573,"line":10592},[99,35073,35074],{"class":27617},"    echo",[99,35076,27520],{"class":27519},[99,35078,35079],{"class":27391},"Removing existing directory: \u002Fvar\u002Fwww\u002Fzhongjing",[99,35081,27526],{"class":27519},[99,35083,35084,35087,35089],{"class":10573,"line":10598},[99,35085,35086],{"class":27387},"    rm",[99,35088,28487],{"class":27391},[99,35090,35091],{"class":27391}," \u002Fvar\u002Fwww\u002Fzhongjing\n",[99,35093,35094],{"class":10573,"line":10604},[99,35095,35096],{"class":34886},"fi\n",[99,35098,35099],{"class":10573,"line":10610},[99,35100,10613],{"emptyLinePlaceholder":53},[99,35102,35103],{"class":10573,"line":10616},[99,35104,35105],{"class":27395},"# Create target directory\n",[99,35107,35108,35110,35112],{"class":10573,"line":10622},[99,35109,28469],{"class":27387},[99,35111,28472],{"class":27391},[99,35113,35091],{"class":27391},[99,35115,35116],{"class":10573,"line":10627},[99,35117,10613],{"emptyLinePlaceholder":53},[99,35119,35120],{"class":10573,"line":10633},[99,35121,35122],{"class":27395},"# Extract archive to target directory\n",[99,35124,35125,35127,35130,35133,35135],{"class":10573,"line":10639},[99,35126,35015],{"class":27387},[99,35128,35129],{"class":27391}," -xzf",[99,35131,35132],{"class":27391}," \u002Fvar\u002Fwww\u002Fpackage.tgz",[99,35134,30681],{"class":27391},[99,35136,35091],{"class":27391},[99,35138,35139],{"class":10573,"line":10645},[99,35140,10613],{"emptyLinePlaceholder":53},[99,35142,35143],{"class":10573,"line":10651},[99,35144,35145],{"class":27395},"# Set proper ownership\n",[99,35147,35148,35150,35153,35156,35159],{"class":10573,"line":10657},[99,35149,28748],{"class":27387},[99,35151,35152],{"class":27391}," chown",[99,35154,35155],{"class":27391}," -R",[99,35157,35158],{"class":27391}," www-data:www-data",[99,35160,35161],{"class":27391}," zhongjing\u002F\n",[99,35163,35164],{"class":10573,"line":10663},[99,35165,10613],{"emptyLinePlaceholder":53},[99,35167,35168,35171,35173,35176],{"class":10573,"line":10669},[99,35169,35170],{"class":27617},"echo",[99,35172,27520],{"class":27519},[99,35174,35175],{"class":27391},"Deployment complete",[99,35177,27526],{"class":27519},[67,35179,35180],{},"This approach ensures clean deployments with no stale files.",[86,35182,35184],{"id":35183},"configuring-nginx","Configuring Nginx",[67,35186,35187],{},"Here's a production-ready Nginx configuration optimized for Nuxt static sites:",[10562,35189,35193],{"className":35190,"code":35191,"language":35192,"meta":10567,"style":10567},"language-nginx shiki shiki-themes material-theme-lighter material-theme material-theme-palenight","server {\n    server_name zhongjing.hitdic.com;\n\n    root \u002Fvar\u002Fwww\u002Fzhongjing;\n    index index.html;\n\n    # 1. Handle Nuxt static assets (highest priority)\n    # Nuxt bundles are in _nuxt folder with hashes, no directory checks needed\n    location ^~ \u002F_nuxt\u002F {\n        alias \u002Fvar\u002Fwww\u002Fzhongjing\u002F_nuxt\u002F;\n        expires 1y;\n        add_header Cache-Control \"public, immutable\";\n        # Only find files, 404 if not found (avoid $uri\u002F redirects)\n        try_files $uri =404;\n    }\n\n    # 2. Handle other static files\n    location ~* \\.(css|js|jpg|jpeg|png|gif|ico|svg|woff|woff2|ttf|eot)$ {\n        expires 1y;\n        add_header Cache-Control \"public, immutable\";\n        try_files $uri =404;\n    }\n\n    # 3. Main site logic (SPA routing)\n    location \u002F {\n        # Remove $uri\u002F to avoid directory redirect interference\n        try_files $uri \u002Findex.html;\n\n        # Disable HTML caching\n        if ($request_uri ~ ^\u002F(.*)\\.(html|htm)$) {\n            expires -1;\n        }\n    }\n}\n","nginx",[10569,35194,35195,35200,35205,35209,35214,35219,35223,35228,35233,35238,35243,35248,35253,35258,35263,35267,35271,35276,35281,35285,35289,35293,35297,35301,35306,35311,35316,35321,35325,35330,35335,35340,35344,35348],{"__ignoreMap":10567},[99,35196,35197],{"class":10573,"line":10574},[99,35198,35199],{},"server {\n",[99,35201,35202],{"class":10573,"line":10580},[99,35203,35204],{},"    server_name zhongjing.hitdic.com;\n",[99,35206,35207],{"class":10573,"line":10586},[99,35208,10613],{"emptyLinePlaceholder":53},[99,35210,35211],{"class":10573,"line":10592},[99,35212,35213],{},"    root \u002Fvar\u002Fwww\u002Fzhongjing;\n",[99,35215,35216],{"class":10573,"line":10598},[99,35217,35218],{},"    index index.html;\n",[99,35220,35221],{"class":10573,"line":10604},[99,35222,10613],{"emptyLinePlaceholder":53},[99,35224,35225],{"class":10573,"line":10610},[99,35226,35227],{},"    # 1. Handle Nuxt static assets (highest priority)\n",[99,35229,35230],{"class":10573,"line":10616},[99,35231,35232],{},"    # Nuxt bundles are in _nuxt folder with hashes, no directory checks needed\n",[99,35234,35235],{"class":10573,"line":10622},[99,35236,35237],{},"    location ^~ \u002F_nuxt\u002F {\n",[99,35239,35240],{"class":10573,"line":10627},[99,35241,35242],{},"        alias \u002Fvar\u002Fwww\u002Fzhongjing\u002F_nuxt\u002F;\n",[99,35244,35245],{"class":10573,"line":10633},[99,35246,35247],{},"        expires 1y;\n",[99,35249,35250],{"class":10573,"line":10639},[99,35251,35252],{},"        add_header Cache-Control \"public, immutable\";\n",[99,35254,35255],{"class":10573,"line":10645},[99,35256,35257],{},"        # Only find files, 404 if not found (avoid $uri\u002F redirects)\n",[99,35259,35260],{"class":10573,"line":10651},[99,35261,35262],{},"        try_files $uri =404;\n",[99,35264,35265],{"class":10573,"line":10657},[99,35266,31746],{},[99,35268,35269],{"class":10573,"line":10663},[99,35270,10613],{"emptyLinePlaceholder":53},[99,35272,35273],{"class":10573,"line":10669},[99,35274,35275],{},"    # 2. Handle other static files\n",[99,35277,35278],{"class":10573,"line":10674},[99,35279,35280],{},"    location ~* \\.(css|js|jpg|jpeg|png|gif|ico|svg|woff|woff2|ttf|eot)$ {\n",[99,35282,35283],{"class":10573,"line":10680},[99,35284,35247],{},[99,35286,35287],{"class":10573,"line":10686},[99,35288,35252],{},[99,35290,35291],{"class":10573,"line":10691},[99,35292,35262],{},[99,35294,35295],{"class":10573,"line":10697},[99,35296,31746],{},[99,35298,35299],{"class":10573,"line":31678},[99,35300,10613],{"emptyLinePlaceholder":53},[99,35302,35303],{"class":10573,"line":31684},[99,35304,35305],{},"    # 3. Main site logic (SPA routing)\n",[99,35307,35308],{"class":10573,"line":31689},[99,35309,35310],{},"    location \u002F {\n",[99,35312,35313],{"class":10573,"line":31694},[99,35314,35315],{},"        # Remove $uri\u002F to avoid directory redirect interference\n",[99,35317,35318],{"class":10573,"line":31699},[99,35319,35320],{},"        try_files $uri \u002Findex.html;\n",[99,35322,35323],{"class":10573,"line":31705},[99,35324,10613],{"emptyLinePlaceholder":53},[99,35326,35327],{"class":10573,"line":31710},[99,35328,35329],{},"        # Disable HTML caching\n",[99,35331,35332],{"class":10573,"line":31716},[99,35333,35334],{},"        if ($request_uri ~ ^\u002F(.*)\\.(html|htm)$) {\n",[99,35336,35337],{"class":10573,"line":31721},[99,35338,35339],{},"            expires -1;\n",[99,35341,35342],{"class":10573,"line":31727},[99,35343,31740],{},[99,35345,35346],{"class":10573,"line":31732},[99,35347,31746],{},[99,35349,35350],{"class":10573,"line":31737},[99,35351,27811],{},[67,35353,35354],{},"Deplot nginx configuation",[10562,35356,35359],{"className":35357,"code":35358,"language":582},[10707],"sudo ln -sf \u002Fetc\u002Fnginx\u002Fsites-available\u002Fdata.hitdic.com \u002Fetc\u002Fnginx\u002Fsites-enabled\u002F\n",[10569,35360,35358],{"__ignoreMap":10567},[1258,35362,35364],{"id":35363},"key-configuration-points","Key Configuration Points",[67,35366,35367],{},[76,35368,35369,35370,35372],{},"Asset Caching (",[10569,35371,34983],{}," and static files)",[21736,35374,35375,35381,35387],{},[21739,35376,35377,35380],{},[10569,35378,35379],{},"expires 1y",": Long cache lifetime for hashed assets",[21739,35382,35383,35386],{},[10569,35384,35385],{},"Cache-Control \"public, immutable\"",": Tells browsers assets won't change",[21739,35388,35389,35392],{},[10569,35390,35391],{},"try_files $uri =404",": Directly return 404 for missing assets (no redirects)",[67,35394,35395],{},[76,35396,35397],{},"SPA Routing",[21736,35399,35400,35406],{},[21739,35401,35402,35405],{},[10569,35403,35404],{},"try_files $uri \u002Findex.html",": Falls back to index.html for non-file routes",[21739,35407,35408],{},"This enables client-side routing to work correctly",[67,35410,35411],{},[76,35412,35413],{},"HTML Caching",[21736,35415,35416],{},[21739,35417,35418,35421],{},[10569,35419,35420],{},"expires -1",": Prevents HTML caching to ensure fresh content",[86,35423,35425],{"id":35424},"clearing-browser-cache","Clearing Browser Cache",[67,35427,35428],{},"Very important: clear your browser cache! ERR_TOO_MANY_REDIRECTS (301) errors are aggressively cached by browsers. Make sure to:",[21736,35430,35431,35434],{},[21739,35432,35433],{},"Use Incognito Mode to test the page",[21739,35435,35436],{},"Or open DevTools (F12) and right-click the refresh button to select \"Empty Cache and Hard Reload\"",[67,35438,35439,35440,35443],{},"If you still see errors, check the browser's Network panel to see what URLs are being requested (look for double slashes ",[10569,35441,35442],{},"\u002F\u002F"," or unusual paths).",[86,35445,35447],{"id":35446},"performance-optimization-tips","Performance Optimization Tips",[1258,35449,35451],{"id":35450},"_1-enable-gzip-compression","1. Enable Gzip Compression",[10562,35453,35455],{"className":35190,"code":35454,"language":35192,"meta":10567,"style":10567},"gzip on;\ngzip_types text\u002Fplain text\u002Fcss application\u002Fjson application\u002Fjavascript text\u002Fxml application\u002Fxml application\u002Fxml+rss text\u002Fjavascript;\ngzip_min_length 1000;\n",[10569,35456,35457,35462,35467],{"__ignoreMap":10567},[99,35458,35459],{"class":10573,"line":10574},[99,35460,35461],{},"gzip on;\n",[99,35463,35464],{"class":10573,"line":10580},[99,35465,35466],{},"gzip_types text\u002Fplain text\u002Fcss application\u002Fjson application\u002Fjavascript text\u002Fxml application\u002Fxml application\u002Fxml+rss text\u002Fjavascript;\n",[99,35468,35469],{"class":10573,"line":10586},[99,35470,35471],{},"gzip_min_length 1000;\n",[1258,35473,35475],{"id":35474},"_2-use-http2","2. Use HTTP\u002F2",[10562,35477,35479],{"className":35190,"code":35478,"language":35192,"meta":10567,"style":10567},"listen 443 ssl http2;\n",[10569,35480,35481],{"__ignoreMap":10567},[99,35482,35483],{"class":10573,"line":10574},[99,35484,35478],{},[86,35486,30589],{"id":30588},[67,35488,35489],{},"Deploying a Nuxt static site with Nginx gives you a fast, reliable, and cost-effective hosting solution. The key is proper configuration:",[27423,35491,35492,35497,35500,35503,35508],{},[21739,35493,35494,35495],{},"Generate static files with ",[10569,35496,34923],{},[21739,35498,35499],{},"Use proper Nginx location blocks for asset routing",[21739,35501,35502],{},"Implement aggressive caching for hashed assets",[21739,35504,35505,35506],{},"Handle SPA routing with ",[10569,35507,35404],{},[21739,35509,35510],{},"Clear browser cache when troubleshooting redirect issues",[67,35512,35513],{},"This setup scales well, handles high traffic, and provides an excellent user experience with minimal maintenance overhead. Whether you're deploying a personal portfolio or a production application, this configuration has you covered.",[67,35515,35516],{},"Happy deploying!",[10721,35518,35519],{},"html .light .shiki span {color: var(--shiki-light);background: var(--shiki-light-bg);font-style: var(--shiki-light-font-style);font-weight: var(--shiki-light-font-weight);text-decoration: var(--shiki-light-text-decoration);}html.light .shiki span {color: var(--shiki-light);background: var(--shiki-light-bg);font-style: var(--shiki-light-font-style);font-weight: var(--shiki-light-font-weight);text-decoration: var(--shiki-light-text-decoration);}html .default .shiki span {color: var(--shiki-default);background: var(--shiki-default-bg);font-style: var(--shiki-default-font-style);font-weight: var(--shiki-default-font-weight);text-decoration: var(--shiki-default-text-decoration);}html .shiki span {color: var(--shiki-default);background: var(--shiki-default-bg);font-style: var(--shiki-default-font-style);font-weight: var(--shiki-default-font-weight);text-decoration: var(--shiki-default-text-decoration);}html .dark .shiki span {color: var(--shiki-dark);background: var(--shiki-dark-bg);font-style: var(--shiki-dark-font-style);font-weight: var(--shiki-dark-font-weight);text-decoration: var(--shiki-dark-text-decoration);}html.dark .shiki span {color: var(--shiki-dark);background: var(--shiki-dark-bg);font-style: var(--shiki-dark-font-style);font-weight: var(--shiki-dark-font-weight);text-decoration: var(--shiki-dark-text-decoration);}html pre.shiki code .s7zQu, html code.shiki .s7zQu{--shiki-light:#39ADB5;--shiki-light-font-style:italic;--shiki-default:#89DDFF;--shiki-default-font-style:italic;--shiki-dark:#89DDFF;--shiki-dark-font-style:italic}html pre.shiki code .s2Zo4, html code.shiki .s2Zo4{--shiki-light:#6182B8;--shiki-default:#82AAFF;--shiki-dark:#82AAFF}html pre.shiki code .sTEyZ, html code.shiki .sTEyZ{--shiki-light:#90A4AE;--shiki-default:#EEFFFF;--shiki-dark:#BABED8}html pre.shiki code .sMK4o, html code.shiki .sMK4o{--shiki-light:#39ADB5;--shiki-default:#89DDFF;--shiki-dark:#89DDFF}html pre.shiki code .swJcz, html code.shiki .swJcz{--shiki-light:#E53935;--shiki-default:#F07178;--shiki-dark:#F07178}html pre.shiki code .sfNiH, html code.shiki .sfNiH{--shiki-light:#FF5370;--shiki-default:#FF9CAC;--shiki-dark:#FF9CAC}html pre.shiki code .sHwdD, html code.shiki .sHwdD{--shiki-light:#90A4AE;--shiki-light-font-style:italic;--shiki-default:#546E7A;--shiki-default-font-style:italic;--shiki-dark:#676E95;--shiki-dark-font-style:italic}html pre.shiki code .sBMFI, html code.shiki .sBMFI{--shiki-light:#E2931D;--shiki-default:#FFCB6B;--shiki-dark:#FFCB6B}html pre.shiki code .sfazB, html code.shiki .sfazB{--shiki-light:#91B859;--shiki-default:#C3E88D;--shiki-dark:#C3E88D}",{"title":10567,"searchDepth":10580,"depth":10580,"links":35521},[35522,35523,35524,35525,35529,35532,35533,35537],{"id":34828,"depth":10580,"text":34829},{"id":34867,"depth":10580,"text":34868},{"id":34927,"depth":10580,"text":34928},{"id":34990,"depth":10580,"text":34991,"children":35526},[35527,35528],{"id":34994,"depth":10586,"text":34995},{"id":35027,"depth":10586,"text":35028},{"id":35183,"depth":10580,"text":35184,"children":35530},[35531],{"id":35363,"depth":10586,"text":35364},{"id":35424,"depth":10580,"text":35425},{"id":35446,"depth":10580,"text":35447,"children":35534},[35535,35536],{"id":35450,"depth":10586,"text":35451},{"id":35474,"depth":10586,"text":35475},{"id":30588,"depth":10580,"text":30589},"2025-01-02","Learn how to generate static sites with Nuxt 3 and deploy them to Nginx, handling routing, caching, and avoiding common pitfalls like redirect loops.","https:\u002F\u002Fppm-sources.oss-cn-hongkong.aliyuncs.com\u002Fzj\u002F3rd\u002Fnuxt.png",{},{"title":14,"description":35539},"7YXz6Jj-JrARYeFiUfMlykf3ey5l2N8CiSG07nmkUJ8",1792686184627]