{"id":7146,"date":"2016-09-11T03:30:44","date_gmt":"2016-09-10T19:30:44","guid":{"rendered":"http:\/\/www.andrewsun.net\/panta_rhei\/?p=7146"},"modified":"2016-09-11T03:30:44","modified_gmt":"2016-09-10T19:30:44","slug":"%e9%9a%8f%e6%9c%ba%e8%a1%8c%e8%b5%b0%e8%bd%a8%e8%bf%b9%e7%9a%84%e5%9d%87%e6%96%b9%e5%9b%9e%e8%bd%ac%e5%8d%8a%e5%be%84","status":"publish","type":"post","link":"https:\/\/www.andrewsun.net\/panta_rhei\/archives\/7146","title":{"rendered":"\u968f\u673a\u884c\u8d70\u8f68\u8ff9\u7684\u5747\u65b9\u56de\u8f6c\u534a\u5f84"},"content":{"rendered":"<div class=\"kcite-section\" kcite-section-id=\"7146\">\n<p>[latexpage]<br 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S^2\\right\\rangle_\\alpha$\u3002\u5c31\u7b97\u8bba\u6587\u7684\u6b63\u6587\u6ca1\u6709\u7ed9\u51fa\u503c\uff0c\u53ea\u8981\u7ed9\u4e86\u6570\u636e\u56fe\uff0c\u4f60\u81ea\u5df1\u4e5f\u53ef\u4ee5\u4ece\u56fe\u4e2d\u5f97\u5230\u3002\u8fd9\u90e8\u5206\u7684\u539f\u7406\u6bd4\u8f83\u57fa\u672c\uff0c\u4e00\u822c\u7684\u9ad8\u5206\u5b50\u6eb6\u6db2\u7406\u8bba\u7684\u4e66\u7684\u8bb2\u8ff0\u4e0d\u4f1a\u6709\u4ec0\u4e48\u4ee4\u4eba\u56f0\u60d1\u7684\u5dee\u5f02\uff0c\u5c31\u4e0d\u5728\u6b64\u89e3\u91ca\u4e86\u3002\u5982\u679c\u627e\u5230\u6587\u732e\u505a\u4e86\u4e0d\u6b62\u4e00\u4e2a\u5206\u5b50\u91cf\u7684\u6837\u54c1\uff0c\u4f46\u662f\u6ca1\u6709\u6d4b\u5b83\u4eec\u7684\u7279\u6027\u7c98\u6570$\\left[\\eta\\right]_\\alpha$\u56e0\u6b64\u8fd8\u662f\u4e0d\u77e5\u9053Mark\u2014Houwink\u7cfb\u6570\uff0c\u90a3\u4f60\u4ecd\u7136\u53ef\u4ee5\u65b9\u4fbf\u5730\u6839\u636e$\\left\\langle S^2\\right\\rangle^{1\/2}_\\alpha\\sim M^{\\nu_\\alpha}$\u5f97\u5230\u6587\u732e\u6761\u4ef6\u4e0b\u7684$\\nu_\\alpha$\uff08\u54ea\u6015\u6587\u732e\u6ca1\u505a\u4f60\u4e5f\u53ef\u4ee5\u7528\u5b83\u7684\u6570\u636e\u81ea\u5df1\u505a\uff0c\u8fd9\u4e00\u70b9\u5728\u4e0b\u6587\u4e2d\u5c31\u4e0d\u518d\u91cd\u590d\u63d0\u793a\u4e86\uff09\u3002 \u5982\u679c\u6587\u732e\u53ea\u505a\u4e86\u4e00\u4e2a\u5206\u5b50\u91cf\u7684\u6837\u54c1\uff0c\u81f3\u5c11\u4e5f\u5df2\u7ecf\u6709$M$\u548c$A_2$\u4e86\u3002\u8fd9\u65f6\u53ef\u4ee5\u901a\u8fc7\u6269\u5f20\u7cfb\u6570\u6765\u6c42Flory\u6307\u6570\u3002\u5982\u679c\u6269\u5f20\u7cfb\u6570\u662f\u5173\u4e8e\u5747\u65b9\u672b\u7aef\u8ddd\u7684\uff0c\u5c31\u6709\uff1a$\\alpha_\\alpha=\\left\\langle h^2\\right\\rangle^{1\/2}_\\alpha\/\\left\\langle h^2\\right\\rangle_\\theta^{1\/2}$\uff0c\u5176\u4e2d\uff0c$\\left\\langle h^2\\right\\rangle^{1\/2} = b_\\alpha N_\\alpha^\\nu_\\alpha$\uff0c$\\left\\langle h^2\\right\\rangle_\\theta^{1\/2} = b_\\alpha N_\\alpha^{1\/2}$\uff0c$b_\\alpha$\u662fKuhn\u94fe\u6bb5\u957f\u5ea6\uff0c$N_\\alpha$\u662fKuhn\u94fe\u6bb5\u7684\u4e2a\u6570\u3002$N_\\alpha=M\/\\left(M_1 b_\\alpha\\right)$\u3002\u90a3\u4e48\u5c31\u53ef\u4ee5\u7531\u6269\u5f20\u7cfb\u6570\u8ba1\u7b97Flory\u6307\u6570\u4e86\uff0c\u6240\u7f3a\u7684\u53c2\u6570\u662f$\\alpha_\\alpha$\u548c$b_alpha$\u3002 $b_\\alpha$\u4e5f\u662f\u8981\u627e\u6587\u732e\u7684\u3002\u6587\u732e\u4e00\u822c\u6709\u4e24\u79cd\u505a\u6cd5\uff1a\u4e00\u662f\u5149\u6563\u5c04\u5f97\u5230\u4e86\u6bd4\u8f83\u5bbd\u6ce2\u77e2\u8303\u56f4\u7684form factor\uff0c\u53ef\u4ee5\u770b\u5230coil\u884c\u4e3a\u5411rod\u884c\u4e3a\u7684\u8f6c\u53d8\uff0c\u8fd9\u4e2a\u8f6c\u53d8\u6240\u5bf9\u5e94\u7684\u5c3a\u5ea6\u5c31\u662f$b$\u3002\u4e8c\u662f\u901a\u8fc7\u4e00\u4e9b\u542b\u6709\u6301\u7eed\u957f\u5ea6$l_\\mathrm{p}$\u53c2\u6570\u7684\u94fe\u6a21\u578b\u6765\u62df\u5408\u6d4b\u5f97\u7684$\\left\\langle S^2\\right\\rangle$\u6570\u636e\u5f97\u5230$l_\\mathrm{p}$\u4ece\u800c\u5f97\u5230$b$\u3002\u4e0d\u7ba1\u600e\u4e48\u6837\u4f60\u8981\u67e5\u5230\u8fd9\u4e2a\u6570\u636e\u3002\u7531\u4e8e$b_\\alpha$\u7684\u503c\u662f\u4f9d\u8d56\u6761\u4ef6\uff0c\u6240\u4ee5\u6700\u597d\u662f\u540c\u4e00\u4e2a\u62a5\u9053\u91cc\u4e0d\u4ec5\u4f5c\u4e86Zimm\u56fe\uff0c\u8fd8\u628a\u5149\u5f3a\u548c\u6ce2\u77e2\u66f2\u7ebf\u7ed9\u51fa\u6765\uff0c\u7136\u540e\u4f9b\u4f60\u7528\u7b2c\u4e00\u79cd\u65b9\u6cd5\u4f30\u7b97\u51fa$b$\u3002\u6587\u732e\u81ea\u5df1\u628a\u8fd9\u4ef6\u4e8b\u505a\u4e86\u7684\u8bdd\u5c31\u66f4\u597d\u4e86\u3002 \u81f3\u4e8e\u6269\u5f20\u7cfb\u6570\uff0c\u662f\u8fd9\u6837\u5f97\u5230\u7684\uff1a\u901a\u8fc7\u6bd4\u8f83\u53e6\u4e00\u79cd\u9ad8\u5206\u5b50B\u7684$M_\\mathrm{B}$\u3001$A_{2,\\mathrm{B}}$\u548c\u6269\u5f20\u7cfb\u6570$\\alpha_{B\\beta}$\u6765\u4f30\u7b97\u5f53\u524d\u7684\u9ad8\u5206\u5b50\u5728\u6761\u4ef6\u03b1\u7684\u6269\u5f20\u7cfb\u6570$\\alpha_\\alpha$\u3002\u5177\u4f53\u5730\u8bb2\uff0c\u4f60\u9700\u8981\u67e5\u627e\u53e6\u4e00\u79cd\u7814\u7a76\u5f97\u6bd4\u8f83\u591a\u7684\u9ad8\u5206\u5b50B\u7684\u6570\u636e\uff0c\u8fd9\u6837\u5c31\u6709\u671b\u627e\u5230\u540c\u65f6\u62a5\u9053\u4e86\u5176\u5206\u5b50\u91cf$M_\\mathrm{B}$\u548c\u67d0\u6761\u4ef6\uff08\u8bb0\u4e3a\u03b2\uff09\u4e0b\u7684$A_{2,\\mathrm{B}}$\u548c\u6269\u5f20\u6bd4$\\alpha_\\mathrm{B\\beta}$\u7684\u6587\u732e\u3002\u7136\u540e\uff0c\u6839\u636eFlory\u7684\u6269\u5f20\u7cfb\u6570\u5173\u7cfb\u5f0f$\\alpha^5-\\alpha^3=2C_\\mathrm{M}\\psi\\left(1-\\Theta\/T\\right)M^{1\/2}$\u53ef\u77e5\uff0c\u4e0d\u540c\u9ad8\u5206\u5b50\u5728\u540c\u4e00\u7b2c\u4e8c\u7ef4\u5229\u7cfb\u6570\u4e0b\u7684$\\left(\\alpha^5-\\alpha^3\\right)\/M^{1\/2}$\u503c\u662f\u5dee\u522b\u5f88\u5c0f\u7684\u3002\u4e8e\u662f\u4f60\u5c31\u53ef\u4ee5\u901a\u8fc7$\\frac{\\alpha_\\alpha^5-\\alpha_\\alpha^3}{M^{1\/2}}=\\frac{\\alpha_\\mathrm{B\\beta}^5-\\alpha_\\mathrm{B\\beta}^3}{M_\\mathrm{B}^{1\/2}}$\u6765\u8ba1\u7b97\u4f60\u8981\u7684\u6269\u5f20\u7cfb\u6570$\\alpha_\\alpha$\u4e86\u3002\u6709\u4e86$\\alpha_\\alpha$\u548c$b_\\alpha$\uff0c\u5c31\u53ef\u4ee5\u6c42$\\nu_\\alpha$\u4e86\u3002 \u77e5\u9053\u4e86$\\nu_\\alpha$\uff0c\u4e0b\u4e00\u6b65\u5c31\u662f\u8ba1\u7b97\u6211\u4eec\u624b\u5934\u4e0a\u7684\u6837\u54c1\u7684\u5206\u5b50\u91cf$M^\\prime$\u3002\u8fd9\u65f6\u5c31\u9700\u8981\u4f7f\u7528\u7279\u6027\u7c98\u6570\u7684\u6570\u636e\u4e86\u3002\u4f60\u9700\u8981\u518d\u4ece\u6587\u732e\u4e2d\u627e\u5230\u76f8\u540c\u6761\u4ef6\u4e0b\u7684\u7279\u6027\u7c98\u6570$\\left[\\eta\\right]_\\alpha$\u3002\u4e5f\u5c31\u662f\u8bf4\uff0c\u4f60\u4ece\u6587\u732e\u4e2d\u4e00\u5171\u8981\u627e\u5230\u5bf9\u67d0\u5206\u5b50\u91cf\u4e3a$M$\u7684\u6837\u54c1\u5728\u540c\u4e00\u6761\u4ef6\u03b1\u4e0b\u7684\uff1a$b_\\alpha$\u548c$\\left[\\eta\\right]_\\alpha$\uff0c\u6309\u4e0a\u8ff0\u7684\u8ba1\u7b97\u65b9\u6cd5\u7b97\u51fa$\\nu_\\alpha$\u3002\u540c\u65f6\uff0c\u4f60\u624b\u5934\u4e0a\u7684\u6837\u54c1\u4e5f\u8981\u81ea\u5df1\u62ff\u53bb\u5728\u76f8\u540c\u7684\u6761\u4ef6\u4e0b\u6d4b\u7279\u6027\u7c98\u6570\uff0c\u5f97\u5230$\\left[\\eta\\right]^\\prime_\\alpha$\u3002\u8fd9\u65f6\u6839\u636eFlory\u2014Fox\u5173\u7cfb\u6709$\\left[\\eta\\right]_\\alpha\/\\left[\\eta\\right]^\\prime_\\alpha=\\left(M\/M^\\prime\\right)^{\\left(3\\nu_\\alpha-1\\right)}$\uff0c\u4ece\u800c\u5f97\u5230\u4f60\u624b\u5934\u4e0a\u6837\u54c1\u7684\u5206\u5b50\u91cf$M^\\prime$\u3002 \u5728\u6b64\u57fa\u7840\u4e0a\uff0c\u5982\u679c\u8981\u4f30\u7b97\u53e6\u4e00\u79cd\u6eb6\u5242\u6216\u6e29\u5ea6\u6761\u4ef6\uff08\u8bb0\u4e3a\u03b3\uff09\u4e0b\u7684\u5404\u79cd\u5c3a\u5bf8\uff0c\u5c31\u5fc5\u987b\u77e5\u9053\u65b0\u6761\u4ef6\u4e0b\u8fd9\u4e00\u9ad8\u5206\u5b50\u6837\u54c1\u7684\u7279\u6027\u7c98\u6570$\\left[\\eta\\right]_\\gamma$\u548c\u5206\u5b50\u91cf$M$\uff0c\u8fd9\u540c\u6837\u8981\u4ece\u6587\u732e\u91cc\u627e\u3002\u7b80\u5355\u5730\u8bf4\uff0c\u5c31\u662f\u4f60\u60f3\u83b7\u5f97\u4f60\u624b\u5934\u4e0a\u6837\u54c1\u6761\u4ef6\u03b3\u7684\u4fe1\u606f\uff0c\u4f60\u5c31\u8981\u627e\u5230\u6709\u4eba\u4e5f\u5728\u6761\u4ef6\u03b3\u4e0b\u505a\u8fc7\u540c\u79cd\u9ad8\u5206\u5b50\u7684\u5b9e\u9a8c\uff0c\u5426\u5219\u5c31\u6ca1\u620f\u4e86\u3002\u5982\u679c\u6709\uff0c\u90a3\u4f60\u53ea\u9700\u8981\u518d\u5728\u6761\u4ef6\u03b3\u4e0b\u6d4b\u4e00\u6b21\u624b\u5934\u4e0a\u6837\u54c1\u7684\u7279\u6027\u7c98\u6570$\\left[\\eta\\right]^\\prime_\\gamma$\uff0c\u5c31\u53ef\u4ee5\u7c7b\u4f3c\u5730\u7528\u5173\u7cfb$\\left[\\eta\\right]_\\gamma\/\\left[\\eta\\right]^\\prime_\\gamma=\\left(M\/M^\\prime\\right)^{\\left(3\\nu_\\gamma-1\\right)}$\u5f97\u5230\u65b0\u6761\u4ef6\u7684Flory\u6307\u6570\u3002\u7136\u540e\u53ef\u4ee5\u5229\u7528Flory\u2014Fox\u5173\u7cfb\u672c\u8eab\u5f97\u5230\u65b0\u6761\u4ef6\u4e0b\u7684Kuhn\u94fe\u6bb5\u6570\u91cf$N^\\prime_\\gamma$\u548c\u957f\u5ea6$b_\\gamma$\uff0c\u8fdb\u800c\u5f97\u5230\u5747\u65b9\u672b\u7aef\u8ddd$\\left\\langle h^2\\right\\rangle_\\gamma^\\prime$\u3002 \u6eb6\u80c0\u94fe\u7684\u5747\u65b9\u56de\u8f6c\u534a\u5f84$\\left\\langle S^2\\right\\rangle^{1\/2}$\u4e0e\u5747\u65b9\u672b\u7aef\u8ddd$\\left\\langle h^2\\right\\rangle^{1\/2}$\u4e4b\u95f4\u6ca1\u6709\u7b80\u5355\u7684\u7cbe\u786e\u5173\u7cfb\u3002\u4f46\u4ecd\u7136\u53ef\u4ee5\u6309\u6587\u672b\u5173\u4e8e\u6269\u5f20\u7cfb\u6570\u7684\u8865\u5145\u8bf4\u660e\u53ef\u4ee5\u4f5c\u6b64\u6362\u7b97\uff0c\u5f97\u5230\u4f60\u624b\u5934\u4e0a\u6837\u54c1\u7684\u5747\u65b9\u56de\u8f6c\u534a\u5f84$\\left\\langle S^2\\right\\rangle^\\prime_\\gamma$\u3002\u6709\u4e86\u5747\u65b9\u56de\u8f6c\u534a\u5f84\uff0c\u4f60\u5c31\u53ef\u4ee5\u8ba1\u7b97\u65b0\u6761\u4ef6\u4e0b\u5f53\u524d\u6837\u54c1\u7684\u5f88\u591a\u4fe1\u606f\uff0c\u4f8b\u5982\u534a\u6d53\u6eb6\u6db2\u7684\u63a5\u89e6\u6d53\u5ea6$c^*=3M\/\\left(4\\pi N_\\mathrm{A}\\left\\langle S^2\\right\\rangle^{1\/2}\\right)$\uff0c\u4ee5\u53ca\u76f8\u5173\u957f\u5ea6\uff08blob size\uff09$\\xi=\\left\\langle S^2\\right\\rangle^{1\/2}\\left(c\/c^*\\right)^{-\\nu\/\\left(3\\nu-1\\right)}$\u3002\u6ce8\u610f\u5f0f\u4e2d\u4f9d\u8d56\u6761\u4ef6\u7684\u91cf\u8981\u53d6\u540c\u4e00\u6761\u4ef6\u4e0b\u7684\u503c\u3002 \u5bf9\u4e8e\u9ad8\u5206\u5b50\u6eb6\u6db2\u4ea4\u8054\u5f62\u6210\u7684\u51dd\u80f6\uff0c\u4e5f\u53ef\u4ee5\u5728\u540c\u6837\u7684\u6eb6\u5242\u548c\u6e29\u5ea6\uff08\u5982\u6761\u4ef6\u03b3\uff0c\u4e0d\u518d\u6807\u793a\u4e86\uff09\u4e0b\u6d4b\u91cf\u5e73\u53f0\u6a21\u91cf$G_\\mathrm{p}$\uff0c\u7136\u540e\u7528Nijenhuis\u7684\u5f0f\u5b50\uff0c\u5f97\u5230\u4ea4\u8054\u70b9\u95f4\u5206\u5b50\u91cf$M_\\mathrm{c}$\u3002 \\begin{equation}G_\\mathrm{p}=\\frac{2cRT}{M}\\left(\\frac{M}{M_\\mathrm{c}}\\frac{f-1}{f}-1\\right)\\left(1-w_\\mathrm{s}\\right)\\end{equation}\\begin{equation}\\frac{M}{M_\\mathrm{c}}=-\\frac{\\mathrm{ln}w_\\mathrm{s}}{1-w_\\mathrm{s}}\\frac{1-w_\\mathrm{s}^{0.5f}}{1-w_\\mathrm{s}^{0.5f-1}}\\end{equation} $M$\u662f\u9ad8\u5206\u5b50\u7684\u5206\u5b50\u91cf\uff0c$c$\u662f\u9ad8\u5206\u5b50\u6d53\u5ea6\uff08\u5355\u4f4d\u4f53\u79ef\u7684\u9ad8\u5206\u5b50\u8d28\u91cf\uff09\u3002$f$\u662f\u4ea4\u8054\u70b9\u7684\u5b98\u80fd\u5ea6\uff0c$w_\\mathrm{s}$\u662f\u51dd\u80f6\u4e2d\u7684sol fraction\u3002 \u5f97\u5230\u4e86\u4ea4\u8054\u70b9\u95f4\u5e73\u5747\u5206\u5b50\u91cf\uff0c\u5c31\u53ef\u4ee5\u901a\u8fc7\u4e4b\u524d\u5f97\u5230\u7684\u540c\u6837\u6761\u4ef6\u4e0b\u7684\u6837\u54c1\u7684$M$\u3001$M_1$\u3001$\\nu$\u3001$b$\u8ba1\u7b97\u4ea4\u8054\u70b9\u95f4\u5e73\u5747Kuhn\u94fe\u6bb5\u6570$N_\\mathrm{c}$\uff0c\u8fdb\u800c\u5047\u8bbe\u7f51\u773c\u5c3a\u5bf8\u8fd1\u4f3c\u7b49\u4e8e\u4ea4\u8054\u70b9\u95f4\u94fe\u6bb5\u7684\u5747\u65b9\u672b\u7aef\u8ddd\uff0c\u53ef\u5f97\u7f51\u773c\u5c3a\u5bf8$\\xi=bN_\\mathrm{c}^\\nu$\u3002 \u529f\u80fd\u6027\u6c34\u51dd\u80f6\u7684\u6eb6\u5242\u6761\u4ef6\u5343\u53d8\u4e07\u5316\u3002\u6e29\u5ea6\u4f9d\u8d56\u6027\u5c1a\u4e14\u6709\u70ed\u529b\u5b66\u4e00\u822c\u5173\u7cfb\u53ef\u4f9d\u8d56\uff0c\u4f46\u662f\u4e0d\u540cpH\u6216\u76d0\u7684\u79cd\u7c7b\u3001\u6d53\u5ea6\uff0c\u4e0d\u53ef\u80fd\u90fd\u6709\u4eba\u505a\u8fc7\u5149\u6563\u5c04\u5b9e\u9a8c\u3002\u54ea\u6015\u81ea\u5df1\u6709\u5149\u6563\u5c04\uff0c\u4e5f\u4e0d\u53ef\u80fd\u53d8\u4e00\u4e0b\u76d0\u6d53\u5ea6\u5c31\u6d4b\u4e00\u6b21\u6216\u8005\u641e\u51fa\u4ec0\u4e48\u5de5\u4f5c\u66f2\u7ebf\u6765\u3002\u8fd9\u65f6\u6211\u4eec\u8981\u6709\u4e00\u79cd\u4e0d\u90a3\u4e48\u7ea0\u7ed3\u7684\u65b9\u5f0f\u3002\u5728\u5904\u7406\u8fd9\u79cd\u95ee\u9898\u7684\u65f6\u5019\uff0c\u53ea\u80fd\u628a\u6761\u4ef6\u4f9d\u8d56\u7684\u53c2\u6570\u90fd\u5f53\u4f5c\u53d8\u91cf\uff0c\u770b\u80fd\u4e0d\u80fd\u641e\u4e00\u4e9b\u62df\u5408\u4e86\u3002 \u5173\u4e8e\u6269\u5f20\u7cfb\u6570\u7684\u8865\u5145\u8bf4\u660e \u524d\u9762\u63d0\u5230\u5bf9\u4e8e\u6eb6\u80c0\u94fe\u7684\u5747\u65b9\u56de\u8f6c\u534a\u5f84$\\left\\langle S^2\\right\\rangle^{1\/2}$\u4e0e\u5747\u65b9\u672b\u7aef\u8ddd$\\left\\langle h^2\\right\\rangle^{1\/2}$\u4e4b\u95f4\u6ca1\u6709\u7b80\u5355\u7684\u7cbe\u786e\u5173\u7cfb\uff0c\u6269\u5f20\u7cfb\u6570\u4e5f\u9700\u8981\u5206\u5f00\u5b9a\u4e49\u3002\u5747\u65b9\u672b\u7aef\u8ddd\u7684\u6269\u5f20\u7cfb\u6570\u662f$\\alpha_h\\equiv\\left\\langle h^2\\right\\rangle^{1\/2}\/\\left\\langle h^2\\right\\rangle_\\mathrm{\\theta} ^{1\/2}$\uff1b\u5747\u65b9\u56de\u8f6c\u534a\u5f84\u7684\u6269\u5f20\u7cfb\u6570\u662f$\\alpha_S\\equiv\\left\\langle S^2\\right\\rangle^{1\/2}\/\\left\\langle\u2026","rel":"","context":"In &quot;\u4ee5tag\u5206\u7c7b\u7684\u6587\u7ae0&quot;","block_context":{"text":"\u4ee5tag\u5206\u7c7b\u7684\u6587\u7ae0","link":"https:\/\/www.andrewsun.net\/panta_rhei\/archives\/category\/tagged"},"img":{"alt_text":"","src":"","width":0,"height":0},"classes":[]},{"id":7025,"url":"https:\/\/www.andrewsun.net\/panta_rhei\/archives\/7025","url_meta":{"origin":7146,"position":1},"title":"\u6781\u5750\u6807\u4e0b\u7684\u4e8c\u7ef4\u65e0\u89c4\u884c\u8d70","author":"Andrew","date":"2016\u5e746\u670811\u65e5","format":false,"excerpt":"[latexpage] \u8fd9\u51e0\u5929\u6211\u5728\u674e\u4fca\u6770\u3001Mathematica\u7684\u5e2e\u52a9\u4e0b\u63a8\u5bfc\u4e86\u6781\u5750\u6807\u4e0b\u7684\u4e8c\u7ef4\u5e03\u6717\u8fd0\u52a8\u7684\u7edf\u8ba1\u3002\u4e00\u5f00\u59cb\u6211\u5c31\u89c9\u5f97\uff0c\u8fd9\u662f\u5f88\u57fa\u672c\u7684\u95ee\u9898\uff0c\u5e94\u8be5\u4f1a\u6709\u76f8\u5e94\u7684\u4f8b\u9898\u6216\u8bfe\u4ef6\u76f4\u63a5\u7ed9\u51fa\u7b54\u6848\u3002\u4f46\u662f\u4e00\u5f00\u59cb\u641c\u90fd\u641c\u4e0d\u5230\u3002\u6211\u7528\u4f53\u80b2\u8001\u5e08\u6559\u7684\u6570\u5b66\u63a8\u4e86\u534a\u5929\uff0c\u51fa\u7ed3\u679c\u4e4b\u540e\uff0c\u5c31\u7acb\u9a6c\u641c\u5230\u8d44\u6599\u4e86\u3002\u53ea\u5f53\u4f5c\u4e0a\u5929\u903c\u6211\u7ec3\u4e60\u4e00\u4e0b\u5927\u5b66\u7684\u6570\u5b66\u5427\u3002 \u6211\u8981\u8003\u8651\u7684\u95ee\u9898\u662f\u4e8c\u7ef4\u65e0\u89c4\u884c\u8d70\u7684\u6781\u5750\u6807\u7684\u7edf\u8ba1\uff0c\u5373\u6781\u5f84\u548c\u6781\u89d2\u7684\u5206\u5e03\u3002\u4e4b\u524d\u6211\u603b\u7ed3\u8fc7\u4e86\u4e8c\u7ef4\u548c\u4e09\u7ef4\u65e0\u89c4\u884c\u8d70\u7684\u6781\u5f84\u5206\u5e03\u5206\u522b\u662fRayleigh\u5206\u5e03\u548cMaxwell\u5206\u5e03\uff0c\u8fd9\u90fd\u662f\u76f4\u89d2\u5750\u6807\u7684\u671f\u671b\u503c\u4e3a\u96f6\u7684\u60c5\u51b5\u3002\u672c\u6587\u4e00\u662f\u8981\u8003\u8651\u671f\u671b\u503c\u4e0d\u4e3a\u96f6\u7684\u60c5\u51b5\uff0c\u4e8c\u662f\u4e0d\u5149\u8003\u8651\u6781\u5f84\u7684\u5206\u5e03\uff0c\u8fd8\u8981\u8003\u8651\u6781\u89d2\u7684\u3002 \u4e8c\u7ef4\u65e0\u89c4\u884c\u8d70\u7684\u201c\u8f68\u8ff9\u4e2d\u5fc3\u201d \u4e00\u4e2a\u8d70\u4e86N\u6b65\u7684\u4e8c\u7ef4\u65e0\u89c4\u884c\u8d70\u8f68\u8ff9\u5e94\u8be5\u662f\u6709\u5176\u4e2d\u5fc3\u7684\u3002\u4f8b\u5982\uff0c\u53ef\u4ee5\u5b9a\u4e49\u8fd9\u4e2a\u4e2d\u5fc3\u4e3a\u65e0\u89c4\u884c\u8d70\u7684x\u5750\u6807\u548cy\u5750\u6807\u7684\u671f\u671b\u503c$\\mu_X$\u548c$\\mu_Y$\u3002\u8fd9\u6837\u7684\u5b9a\u4e49\u4e25\u683c\u6765\u8bf4\u5e76\u4e0d\u5b9e\u7528\uff0c\u56e0\u4e3a\u5bf9\u4e8e\u7ed9\u5b9a\u7684\u6709\u9650\u6b65\u6570\u7684\u8f68\u8ff9\uff0c\u6211\u4eec\u65e0\u6cd5\u77e5\u9053\u671f\u671b\u503c\uff0c\u53ea\u80fd\u8ba1\u7b97\u5747\u503c\u3002\u540e\u8005\u53ea\u6709$N\\rightarrow\\infty$\u65f6\u624d\u662f\u671f\u671b\u503c\u3002\u4e3a\u4e86\u5b9e\u9a8c\u65b9\u4fbf\uff0c\u6211\u5b9a\u4e49\u4e8c\u7ef4\u65e0\u89c4\u884c\u8d70\u7684\u8f68\u8ff9\u201c\u4e2d\u5fc3\u201d\u662f\u5176\u8d77\u59cb\u5750\u6807$\\left(x_0,y_0\\right)$\u3002\u8fd9\u6837\uff0c\u4e0d\u4ec5\u5bf9\u4efb\u610f\u4e00\u4e2a\u7ed9\u5b9a\u7684\u8f68\u8ff9\u90fd\u80fd\u76f4\u63a5\u8bf4\u51fa\u5176\u201c\u4e2d\u5fc3\u201d\uff0c\u8fd8\u80fd\u4e3b\u52a8\u5b9e\u73b0\u4e00\u4e2a\u7ed9\u5b9a\u4e2d\u5fc3\u7684\u201c\u65e0\u89c4\u884c\u8d70\u201d\u2014\u2014\u53ea\u8981\u4ece\u4f60\u7684\u884c\u8d70\u662f\u4ece\u90a3\u4e2a\u4e2d\u5fc3\u5f00\u59cb\u7684\u5c31\u884c\u3002\u51ed\u76f4\u89c2\u60f3\u8c61\uff0c\u4e00\u4e2a\u4ece\u70b9$\\left(x_0,y_0\\right)$\u51fa\u53d1\u7684\u65e0\u89c4\u884c\u8d70\uff0c\u53ea\u8981\u6b65\u6570$N$\u8db3\u591f\u5927\uff0c\u5c31\u6709$\\mu_X=x_0$\u548c$\\mu_Y=y_0$\u3002\u5f53\u7136\uff0c\u8fd9\u662f\u4e3a\u4e86\u5b9e\u9a8c\u7684\u601d\u8003\u3002\u63a5\u4e0b\u6765\u7684\u63a8\u5bfc\u90fd\u662f\u8c08\u671f\u671b\u503c \u671f\u671b\u503c\u4e3a\u96f6\u7684\u60c5\u51b5 \u9996\u5148\uff0c\u8003\u8651\u4e00\u4e2a\u201c\u5728\u539f\u70b9\u5904\u201d\u7684\u65e0\u89c4\u884c\u8d70\uff0c\u5373\u5176x\u5750\u6807\u548cy\u5750\u6807\u7684\u671f\u671b\u503c$\\mu_X=\\mu_Y=0$\uff0c\u65b9\u5dee\u90fd\u662f$\\sigma^2$\uff08\u5404\u5411\u540c\u6027\uff09\u3002\u8fd9\u65f6\u5176\u6781\u5750\u6807\u7684\u6781\u5f84\u548c\u6781\u89d2$r$\u548c$\\theta$\u7684\u5206\u5e03\u5206\u522b\u4e3a\u4e00\u4e2aRayleigh\u5206\u5e03\u548c\u4e00\u4e2a\u5747\u5300\u5206\u5e03\uff1a \\begin{equation}\\label{eq:1} p_R\\left(r\\right)=\\frac{r}{\\sigma^2}\\exp\\left[-\\frac{r^2}{2\\sigma^2}\\right] \\end{equation} \\begin{equation}\\label{eq:2} p_\\Theta\\left(\\theta\\right)=\\frac{1}{2\\pi} \\end{equation} \u671f\u671b\u503c\u4e0d\u4e3a\u96f6\u7684\u60c5\u51b5 \u8003\u8651\u201c\u4f4d\u4e8e\u6781\u5750\u6807\u4e2d\u70b9$\\left(\\mu_r,\\mu_\\theta\\right)$\u5904\u7684\u65e0\u89c4\u884c\u8d70\uff0c\u5373\u5176\u76f4\u89d2\u5750\u6807x\u548cy\u7684\u671f\u671b\u503c\u4e3a$\\mu_X\u548c\\mu_Y$\uff0c\u65b9\u5dee\u90fd\u662f$\\sigma^2$\uff08\u5404\u5411\u540c\u6027\uff09\u3002\u4e8e\u662f \\begin{equation}\\label{eq:3} \\begin{aligned} \\mu_r&=\\sqrt{\\mu_X^2+\\mu_Y^2} \\\\ \\mu_\\theta&=\\left\\{\\begin{matrix} \\arctan\\frac{\\mu_Y}{\\mu_X}, & x>0\\\\ \\arctan\\frac{\\mu_Y}{\\mu_X}+\\pi, &x<0 \\end{matrix}\\right. \\end{aligned}\\end{equation} \u5219\u6781\u5f84$r$\u548c\u6781\u89d2$\\theta$\u7684\u8054\u5408\u5206\u5e03\u4e3a \\begin{equation}\\label{eq:4} p_{R\\Theta}\\left(r,\\theta\\right)=\\frac{r}{2\\pi\\sigma^2}\\exp\\left[-\\frac{r^2+\\mu_r^2-2r\\mu_r\\cos\\left(\\theta-\\mu_\\theta\\right)}{2\\sigma^2}\\right] \\end{equation} \u7531\u4e8e\u65e0\u89c4\u884c\u8d70\u7684\u6781\u5f84\u548c\u6781\u89d2\u662f\u76f8\u4e92\u72ec\u7acb\u7684\u968f\u673a\u91cf\uff0c\u6240\u4ee5\u6c42\u4e24\u4e2a\u8fb9\u7f18\u5206\u5e03\u5c31\u53ef\u4ee5\u4e86\u3002 \\begin{equation} \\begin{aligned} p_R\\left(r\\right)&=\\int_0^{2\\pi}p_{R\\Theta}d\\theta\\\\ p_\\Theta\\left(\\theta\\right)&=\\int_0^\\infty p_{R\\Theta}dr \\end{aligned} \\end{equation} \u8fd9\u4e24\u4e2a\u79ef\u5206\u90fd\u65e0\u6cd5\u7528\u521d\u7b49\u51fd\u6570\u8868\u793a\u3002\u6211\u662f\u7528Mathematica\u6765\u7b97\u7684\uff0c\u7ed3\u679c\u5982\u4e0b\uff1a \\begin{equation}\\label{eq:6} p_R\\left(r\\right)=\\frac{r}{\\sigma^2}I_0\\left(\\frac{r\\mu_r}{\\sigma^2}\\right)\\exp\\left(-\\frac{r^2+\\mu_r^2}{2\\sigma^2}\\right) \\end{equation} \\begin{equation}\\label{eq:7} \\begin{aligned} p_\\Theta\\left(\\theta\\right)=&\\frac{1}{\\sqrt{8\\pi\\sigma^2}}\\mu_r\\cos\\left(\\theta-\\mu_\\theta\\right)\\exp\\left[-\\frac{\\mu_r^2\\sin^2\\left(\\theta-\\mu_\\theta\\right)}{2\\sigma^2}\\right]\\times \\\\ &\\left[\\mathrm{erf}}\\left(\\frac{\\mu_r\\cos\\left(\\theta-\\mu_\\theta\\right)}{\\sqrt{2\\sigma^2}}\\right)+1\\right]+\\frac{1}{2\\pi}\\exp\\left(-\\frac{\\mu_r^2}{2\\sigma^2}\\right) \\end{aligned} \\end{equation}\u2026","rel":"","context":"In &quot;\u4ee5tag\u5206\u7c7b\u7684\u6587\u7ae0&quot;","block_context":{"text":"\u4ee5tag\u5206\u7c7b\u7684\u6587\u7ae0","link":"https:\/\/www.andrewsun.net\/panta_rhei\/archives\/category\/tagged"},"img":{"alt_text":"Rice distributions of varying 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\u901a\u8fc7\u80f6\u4f53\u7c92\u5b50\u7684\u70ed\u8fd0\u52a8\u7edf\u8ba1\u89c4\u5f8b\u53cd\u63a8\u60ac\u6d6e\u4ecb\u8d28\u7684\u6d41\u53d8\u6027\u8d28\u7684\u4e00\u79cd\u5b9e\u9a8c\u7814\u7a76\u3002\u8fd9\u4e5f\u662f\u6211\u73b0\u5728\u7814\u7a76\u65b9\u5411\u4e4b\u4e00\u3002\u4f46\u662f\uff0c\u8fd9\u4e2a\u672f\u8bed\u6700\u65e9\u7684\u610f\u4e49\u8ddf\u73b0\u5728\u6709\u4e9b\u533a\u522b\u3002 \u6839\u636e\u6211\u67e5\u5230\u7684\u7ed3\u679c\uff0c\u201cmicrorheology\u201d\u4e00\u8bcd\u6700\u65e9\u51fa\u73b0\u5728M. Reiner\u7684\u6d41\u53d8\u5b66\u8bb2\u4e49\uff08Markus Reiner (1943), Ten Lectures on Theoretical Rheology, Rubin Mass\uff09\u4e2d\u7684\u7b2c\u4e03\u8bb2\u3002\u8fd9\u4e2a\u5957\u8bb2\u4e49\u540e\u6765\u5206\u522b\u57281949\u5e74\u548c1960\u5e74\u51fa\u4e86\u7b2c\u4e8c\u548c\u7b2c\u4e09\u7248\u3002\u7b2c\u4e09\u7248\u6709\u4e2d\u8bd1\u672c\uff1aM. \u96f7\u8bb7\u8457\uff0c\u90ed\u6709\u4e2d\u7b49\u8bd1\u300a\u7406\u8bba\u6d41\u53d8\u5b66\u8bb2\u4e49\u300b\uff0c\u7531\u79d1\u5b66\u51fa\u7248\u793e\u4e8e1965\u51fa\u7248\u3002\u5728\u5f53\u65f6\u8fd9\u4e2a\u8bcd\u5927\u6982\u662f\u6307I. \u4ece\u5fae\u89c2\u7ed3\u6784\u63a8\u51fa\u5b8f\u89c2\u7cfb\u7edf\u6d41\u53d8\u5b66\u6027\u8d28\u7684\u7406\u8bba\u7814\u7a76\uff0c\u4f3c\u4e4e\u662f\u7528\u4e8e\u4e0e\u57fa\u4e8e\u8fde\u7eed\u4ecb\u8d28\u5047\u5b9a\u7684\u7406\u8bba\u76f8\u533a\u522b\u3002\u540e\u8005\u88ab\u79f0\u4f5c\u201cmacrorheology\u201d\u3002 \u5927\u6982\u76f8\u540c\u7684\u65f6\u671f\uff0c\u80f6\u4f53\u7c92\u5b50\u60ac\u6d6e\u6db2\u6d41\u53d8\u5b66\u7684\u5148\u9a71Stanley G. Mason\uff081914-1987\uff09\u5927\u91cf\u4f7f\u7528\u8fd9\u4e2a\u8bcd\u6765\u63cf\u8ff0\u4ed6\u7814\u7a76\u7684\u95ee\u9898\u3002\u5173\u4e8eMason\u7ecf\u5386\u7684\u4e00\u4e9b\u8d44\u6599\u53ef\u89c1\u4ed6\u7684\u81ea\u8ff0\u548c\u540e\u8f88\u5199\u7684appreciation\u3002Mason\u57281950\u5e74\u4ee3\u5c31\u5f00\u59cb\u6b63\u5f0f\u7814\u7a76\u60ac\u6d6e\u7c92\u5b50\u7684\u6d41\u4f53\u52a8\u529b\u5b66\u3002\u4ed6\u521b\u7acb\u7684\u7814\u7a76\u65b9\u6cd5\u662fII. \u901a\u8fc7\u5b9e\u9a8c\u89c2\u5bdf\u7c92\u5b50\u5468\u56f4\u7684\u6d41\u573a\u6765\u9a8c\u8bc1\u6d41\u4f53\u52a8\u529b\u5b66\u7406\u8bba\u3002\u56e0\u6b64\uff0c\u5230\u4e86Mason\u8fd9\u91cc\uff0c\u201cmicrorheology\u201d\u7684\u610f\u4e49\u5c31\u4ece\u7406\u8bba\u6a21\u578b\u53d8\u4e3a\u5b9e\u9a8c\u624b\u6bb5\u3002Mason\u4e5f\u63a8\u5bfc\u8fc7\u80f6\u4f53\u6d41\u53d8\u5b66\u7406\u8bba\uff0c\u4f46\u4ed6\u548c\u4ed6\u7684\u5b66\u751f\u4e0d\u7528\u201cmicrorheology\u201d\u4e00\u8bcd\u63cf\u8481\u8fd9\u4e9b\u7406\u8bba\u5de5\u4f5c\u3002 Mason\u7684\u53ca\u5176\u5b66\u751f\u7684\u540e\u7eed\u5de5\u4f5c\u4e00\u76f4\u6301\u7eed\u52301970\u5e74\u4ee3\u3002\u5728\u8fd9\u6bb5\u65f6\u95f4\uff0c\u201cmicrorheology\u201d\u4e00\u8bcd\u51e0\u4e4e\u53ea\u51fa\u73b0\u5728\u4ed6\u4eec\u53d1\u8868\u7684\u5de5\u4f5c\u5f53\u4e2d\u3002\u4e5f\u6709\u96f6\u661f\u613f\u610f\u4f7f\u7528Reiner\u8bb2\u4e49\u7684\u8001\u610f\u4e49\u7684\u8bba\u6587\uff0c\u5305\u62ec\u51af\u5143\u6862\u5148\u751f\u30021970\u5e74\u4ee3\uff0c\u201cmicrorheology\u201d\u4e00\u8bcd\u88ab\u8840\u6db2\u6d41\u53d8\u5b66\u9886\u57df\u5927\u91cf\u91c7\u7528\uff0c\u8fd9\u4e5f\u4ecd\u662f\u5f52\u56e0\u4e8eMason\u7684\u5de5\u4f5c\u5bf9\u8fd9\u4e00\u9886\u57df\u7684\u5f71\u54cd\u529b\u3002 \u6211\u80fd\u627e\u5230\u7684\u7b2c\u4e00\u4e2a\u610f\u4e49\u53d8\u6210\u73b0\u5728\u7684\u7b2cIII\u79cd\u7684\u6700\u65e9\u8bba\u6587\u662f1985\u5e74\u7684\u4e00\u7bc7\u8bba\u6587\u3002 \u4e0e\u201cmicrorheology\u201d\u4e00\u8bcd\u5341\u5206\u76f8\u5173\u7684\u8fd8\u6709\u201cmicroviscosity\u201d\u3002\u8fd9\u4e2a\u8bcd\u53cd\u800c\u6700\u65e9\u5c31\u8fbe\u5230\u4e86\u4eca\u5929\u5bf9microrheology\u5e94\u8be5\u8fbe\u5230\u7684\u7406\u89e3\u3002\u57281929\u5e74\u7684\u7b2c\u4e00\u5c4a\u7f8e\u56fd\u6d41\u53d8\u5b66\u5e74\u4f1a\u4e0a\uff0cE. Kraemer & R. Williamson\u533a\u5206\u4e86\u51e0\u4e2a\u5c42\u6b21\u7684\u201c\u6469\u64e6\u201d\uff08friction\uff09\u3002\u4e00\u662f\u5b8f\u89c2\u4f53\u7cfb\u7684\u7c98\u5ea6\uff0c\u4e8c\u662f\u7c92\u5b50\u4e0e\u5468\u56f4\u6d41\u573a\u754c\u9762\u5904\u7684\u6469\u64e6\uff0c\u4e09\u662f\u7c92\u5b50\u5f62\u53d8\u7684\u5185\u90e8\u6469\u64e6\u3002\u201cmicroviscosity\u201d\u6307\u7684\u5c31\u662f\u5728IV. \u5fae\u89c2\u5c3a\u5ea6\u4e0b\u7684\u7c98\u5ea6\u2014\u2014\u5b83\u5e38\u5e38\u4e0e\u5b8f\u89c2\u5c3a\u5ea6\u4e0b\u5bf9\u540c\u4e00\u7cfb\u7edf\u6d4b\u5f97\u7684\u7c98\u5ea6\u660e\u663e\u4e0d\u540c\u3002\u8fd9\u4ef6\u4e8b\u65e9\u5728\u201c\u80f6\u4f53\u201d\uff08colloid\uff09\u4e00\u8bcd\u7684\u675c\u64b0\u8005Thomas Graham\u57281861\u5e74\u7684\u7814\u7a76\u4e2d\u5c31\u53d1\u73b0\u4e86\u3002\u76d0\u5728\u660e\u80f6\u6216\u743c\u8102\u51dd\u80f6\u4e2d\u7684\u6269\u6563\u6bd4\u5c11\u6162\u4e0d\u4e86\u591a\u5c11\uff0c\u4f46\u524d\u8005\u7684\u7c98\u5ea6\u6bd4\u6c34\u9ad8\u597d\u51e0\u4e2a\u6570\u91cf\u7ea7\u3002\u56e0\u6b64\u8fd9\u4ee4\u4eba\u76f8\u4fe1\uff0c\u5fae\u89c2\u5c3a\u5ea6\u7269\u4f53\u611f\u53d7\u5230\u7684\u6db2\u4f53\u7684\u7c98\u5ea6\u662f\u8ddf\u5b8f\u89c2\u6d4b\u91cf\u503c\u4e0d\u540c\u7684\u3002\u5177\u4f53\u5728\u8fd9\u4e00\u5b9e\u9a8c\u73b0\u8c61\u4e2d\uff0c\u7814\u7a76\u8005\u751a\u81f3\u662f\u901a\u8fc7\u6269\u6563\u7684\u6548\u679c\u6765\u7406\u89e3\u7c98\u5ea6\u3002\u8fd9\u662f\u5728Einstein--Stokes\u5173\u7cfb\u7684\u7406\u8bba\u57fa\u7840\u4e0a\u7684\u8ba4\u8bc6\u89d2\u5ea6\uff0c\u628a\u5b9e\u9a8c\u7ed3\u679c\u5173\u4e8eEinstein--Stokes\u5173\u7cfb\u7684\u504f\u79bb\u5f53\u4f5c\u7c98\u5ea6\u4e0d\u540c\u3002\u4eca\u5929\u6211\u4eec\u8fd8\u6709\u53e6\u4e00\u79cd\u505a\u6cd5\uff0c\u90a3\u5c31\u662f\u628a\u5b9e\u9a8c\u7ed3\u679c\u5173\u4e8eEinstein--Stokes\u5173\u7cfb\u7684\u504f\u79bb\u5f53\u4f5c\u534a\u5f84\u4e0d\u540c\uff0c\u5b9a\u4e49\u51fa\u201c\u6d41\u4f53\u52a8\u529b\u5b66\u534a\u5f84\u201d\u3002\u8fd9\u4e24\u54b1\u505a\u6cd5\u7684\u4eba\u4e4b\u95f4\u5f88\u5c11\u770b\u5230\u6709\u4ea4\u53c9\u7684\uff0c\u66f4\u522b\u8bf4\u6709\u4eba\u53bbreconcile\u8fd9\u4e24\u8005\u3002\u8fd9\u53ef\u80fd\u662f\u7531\u4e8e\u5b9e\u9a8c\u65b9\u6cd5\u4e0d\u540c\u3002\u4e00\u6d3e\u4eba\u6d4b\u91cf\u5b8f\u89c2\u7cfb\u7edf\u7684\u7c98\u5ea6\uff0c\u548c\u5206\u5b50\u7684\u6269\u6563\u7cfb\u6570\u3002\u7531\u4e8e\u5206\u5b50\u7ed3\u6784\u662f\u660e\u786e\u7684\uff0c\u8fd9\u6d3e\u4eba\u662f\u4e0d\u4f1a\u6000\u7591\u5206\u5b50\u8fd8\u6709\u53e6\u4e00\u79cd\u201c\u534a\u5f84\u201d\u3002\u53e6\u4e00\u6d3e\u4eba\u7528\u52a8\u6001\u5149\u6563\u5c04\u6d4b\u80f6\u4f53\u7c92\u5b50\u5728\u60ac\u6d6e\u6db2\u4e2d\u6216\u805a\u5408\u7269\u5728\u6eb6\u6db2\u4e2d\u7684\u534a\u5f84\uff0c\u5e76\u4e0e\u7535\u5b50\u663e\u5fae\u955c\u6216\u89d2\u5ea6\u4f9d\u8d56\u6563\u5c04\u7684\u7ed3\u679c\uff08\u5747\u65b9\u56de\u8f6c\u534a\u5f84\uff09\u76f8\u6bd4\u8f83\u3002\u7279\u522b\u662f\u5bf9\u4e8e\u805a\u5408\u7269\u8bd5\u6837\uff0c\u7531\u4e8e\u5176\u5206\u5b50\u5c3a\u5bf8\u53ea\u6709\u5e73\u5747\u6982\u5ff5\uff0c\u5728\u6eb6\u6db2\u4e2d\u7684\u5e73\u5747\u5c3a\u5bf8\u8fd8\u53d7\u6eb6\u5242\u6eb6\u8d28\u76f8\u4e92\u4f5c\u7528\u4ee5\u53ca\u6d41\u4f53\u52a8\u529b\u5b66\u76f8\u4e92\u4f5c\u7528\u7684\u5f71\u54cd\u3002\u800c\u6269\u6563\u7cfb\u6570\u88ab\u9690\u542b\u5728\u52a8\u6001\u5149\u6563\u5c04\u7684\u57fa\u672c\u539f\u7406\u5f53\u4e2d\u3002","rel":"","context":"In &quot;\u4ee5tag\u5206\u7c7b\u7684\u6587\u7ae0&quot;","block_context":{"text":"\u4ee5tag\u5206\u7c7b\u7684\u6587\u7ae0","link":"https:\/\/www.andrewsun.net\/panta_rhei\/archives\/category\/tagged"},"img":{"alt_text":"","src":"","width":0,"height":0},"classes":[]}],"jetpack_likes_enabled":true,"_links":{"self":[{"href":"https:\/\/www.andrewsun.net\/panta_rhei\/wp-json\/wp\/v2\/posts\/7146","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.andrewsun.net\/panta_rhei\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.andrewsun.net\/panta_rhei\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.andrewsun.net\/panta_rhei\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.andrewsun.net\/panta_rhei\/wp-json\/wp\/v2\/comments?post=7146"}],"version-history":[{"count":14,"href":"https:\/\/www.andrewsun.net\/panta_rhei\/wp-json\/wp\/v2\/posts\/7146\/revisions"}],"predecessor-version":[{"id":7160,"href":"https:\/\/www.andrewsun.net\/panta_rhei\/wp-json\/wp\/v2\/posts\/7146\/revisions\/7160"}],"wp:attachment":[{"href":"https:\/\/www.andrewsun.net\/panta_rhei\/wp-json\/wp\/v2\/media?parent=7146"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.andrewsun.net\/panta_rhei\/wp-json\/wp\/v2\/categories?post=7146"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.andrewsun.net\/panta_rhei\/wp-json\/wp\/v2\/tags?post=7146"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}