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https:\/\/i0.wp.com\/www.andrewsun.net\/panta_rhei\/wp-content\/uploads\/2023\/08\/20230808_012812896_iOS-%E5%A4%A7.jpg?resize=1400%2C800&ssl=1 4x"},"classes":[]},{"id":9108,"url":"https:\/\/www.andrewsun.net\/panta_rhei\/archives\/9108","url_meta":{"origin":4328,"position":1},"title":"Leon B. Lucy","author":"Andrew","date":"2024\u5e7412\u670814\u65e5","format":false,"excerpt":"[latexpage] \u80cc\u666f \u5728\u6570\u503c\u8ba1\u7b97\u9886\u57df\u6709\u4e00\u4e2a\u6bd4\u8f83\u77e5\u540d\u7684\u53bb\u5377\u79ef\u8fed\u4ee3\u7b97\u6cd5\u2014\u2014Lucy--Richardson\u7b97\u6cd5\uff0c\u5b83\u88ab\u540e\u4e16\u96c6\u4e2d\u7528\u4e8e\u56fe\u50cf\u53bb\u566a\u3002\u4f8b\u5982\uff0cMATLAB\u7684Image Processing Toolbox\u6709\u4e00\u4e2adeconvlucy\u547d\u4ee4\uff0c\u58f0\u79f0\u5c31\u662f\u7528Lucy--Richardson\u7b97\u6cd5\u5bf9\u7ed9\u5b9a\u56fe\u7247\uff08\u50cf\u7d20\u77e9\u9635\uff09\u4f5c\u7ed9\u5b9a\u70b9\u6269\u6563\u51fd\u6570\u7684\u53bb\u566a\u3002 \u4f46\u662f\uff0cLucy\u7684\u539f\u6587\u6240\u9488\u5bf9\u7684\u95ee\u9898\uff0c\u6bd4\u73b0\u5728\u4e00\u822c\u5e94\u7528\u66f4\u5e7f\u4e49\u3002\u5047\u5b9a$X$\u662f\u4e00\u4e2a\u8fde\u7eed\u53d6\u503c\u968f\u673a\u53d8\u91cf\u3002\u5b83\u7406\u5e94\u6309\u7167\u5206\u5e03\u5bc6\u5ea6\u51fd\u6570$\\phi\\left(x\\right)$\u3002\u6211\u4eec\u60f3\u628a$\\phi\\left(x\\right)$\u89c6\u4e3a\u67d0\u79cd\u7b80\u5355\u5206\u5e03$P\\left(x\\middle|\\xi\\right)$\u6309\u6743\u91cd\u8c31$\\psi\\left(\\xi\\right)$\u7684\u53e0\u52a0\u7ed3\u679c\uff1a \\begin{equation}\\label{eq:original_phi_expression}\\phi\\left(x\\right)=\\int P\\left(x\\middle|\\xi\\right)\\psi\\left(\\xi\\right)\\mathrm{d}\\xi\\end{equation} \u800c\u6211\u4eec\u60f3\u5f97\u77e5\u7ed9\u5b9a\u5f62\u5f0f\u7684\u6838$P\\left(x\\middle|\\xi\\right)$\u6240\u5bf9\u5e94\u7684\u6743\u91cd\u8c31$\\psi\\left(\\xi\\right)$\u3002\u5728\u8fd9\u91cc\uff0c$\\xi$\u662f\u6838\u51fd\u6570$P$\u7684\u53c2\u6570\u3002\u6bd4\u5982\uff0c\u6211\u4eec\u5173\u5fc3\u9ad8\u65af\u6838\u51fd\u6570\u7684\u60c5\u51b5\uff0c\u90a3\u4e48$P\\left(x\\middle|\\xi\\right)$\u53ef\u80fd\u662f\u4ee5$\\xi$\u4e3a\u6807\u51c6\u5dee\u7684\u9ad8\u65af\u51fd\u6570 \\[P\\left(x\\middle|\\xi\\right)=\\frac{1}{\\sqrt{2\\pi\\xi^2}}\\exp\\left[-\\frac{\\left(x-\\mu\\right)^2}{2\\xi^2}\\right]\\] \u5728\u56fe\u50cf\u53bb\u566a\u7684\u4e0a\u4e0b\u6587\u4e2d\uff0c\u4ee5deconvlucy\u4e3a\u4f8b\uff0c\u6838\u51fd\u6570$P\\left(x\\right)$\u662f\u4e00\u4e2a\u56fa\u5b9a\u53c2\u6570$\\xi$\u7684\u51fd\u6570\uff0c\u4e14$\\xi$\u7684\u53d6\u503c\u8303\u56f4\uff08\u5373$P\\left(x\\right)$\u7684\u201c\u5bbd\u5ea6\u201d\uff09\u8fdc\u7a84\u4e8e$x$\u7684\u8303\u56f4\uff08\u5728\u56fe\u50cf\u8bed\u5883\u4e2d\u662f\u56fe\u50cf\u7684\u5927\u5c0f\uff09\u3002\u4f46\u5728Lucy\u539f\u6587\u7684\u8bed\u5883\u4e2d\uff0c$\\phi\\left(x\\right)$\u3001$P\\left(x\\middle|\\xi\\right)$\u548c$\\psi\\left(\\xi\\right)$\u90fd\u662f\u652f\u6491\u4e3a\u6574\u4e2a\u5b9e\u6570\u7684\u5206\u5e03\u5bc6\u5ea6\u51fd\u6570\u3002\u53ef\u4ee5\u8bf4\uff0c\u56fe\u50cf\u53bb\u566a\u5e94\u7528\uff0c\u53ea\u662fLucy\u539f\u6587\u7b97\u6cd5\u7684\u5176\u4e2d\u4e00\u4e2a\u5f88\u7279\u6b8a\u7684\u4f8b\u5b50\u3002 \u6570\u503c\u8ba1\u7b97\u7684\u8bbe\u8ba1\u827a\u672f 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&quot;\u4e2a\u4eba\u6587\u96c6&quot;","block_context":{"text":"\u4e2a\u4eba\u6587\u96c6","link":"https:\/\/www.andrewsun.net\/panta_rhei\/archives\/category\/featured"},"img":{"alt_text":"","src":"","width":0,"height":0},"classes":[]},{"id":9177,"url":"https:\/\/www.andrewsun.net\/panta_rhei\/archives\/9177","url_meta":{"origin":4328,"position":2},"title":"\u5728\u7535\u5b50\u8ba1\u7b97\u673a\u4e4b\u524d\u7684Fourier\u5206\u6790","author":"Andrew","date":"2025\u5e743\u670830\u65e5","format":"aside","excerpt":"[latexpage] \u5982\u679c\u6211\u4eec\u8981\u5bf9\u4e00\u4e2a\u5468\u671f\u4fe1\u53f7\u8fdb\u884cFourier\u7ea7\u6570\u5206\u6790\uff0c\u90a3\u4e48\u6211\u4eec\u662f\u5047\u5b9a\u8be5\u4fe1\u53f7\u53ef\u4ee5\u8868\u793a\u6210\\[f\\left(x\\right)=\\sum_{n=-\\infty}^\\infty c_n e^{\\mathrm{i}2\\pi n x\/P}\\]\u5176\u4e2d\\[c_n=\\frac{1}{P}\\int_0^P f\\left(x\\right)e^{-\\mathrm{i} 2\\pi n x\/P}\\mathrm{d}x\\] 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\u5c0f\u91ce\u6728\u91cd\u6cbb\uff08Shigeharu Onogi\uff09\u53ef\u80fd\u662f\u65e5\u672c\u6700\u65e9\u5bf9\u975e\u7ebf\u6027\u7c98\u5f39\u6027\u6d41\u4f53\u7684\u6b63\u5f26\u632f\u8361\u6d4b\u8bd5\u7ed3\u679c\u4f5c\u8c10\u6ce2\u5206\u6790\u7684\u7814\u7a76\u8005\u3002\u4ed6\u5f53\u65f6\u4f30\u8ba1\u5c31\u662f\u8fd9\u4e48\u505a\u7684\u3002 \u5728\u7f8e\u56fd\uff0cW. Philippoff\u5f88\u65e9\u5c31\u5f00\u53d1\u5bbd\u9891\u8303\u56f4\u7684\u52a8\u6001\u6d4b\u8bd5\u4eea\u5668\u3002\u4ed6\u57281966\u5e74\u53d1\u8868\u7684\u6587\u7ae0\u4e2d\uff0c\u7528\u4e00\u4e2a\u7279\u522b\u6784\u5efa\u7684\u53ef\u8c03\u8282\u6a21\u62df\u8ba1\u7b97\u5668\uff0c\u53bb\u540c\u65f6\u751f\u6210\u4e00\u4e2a\u57fa\u9891\u548c3\u500d\u9891\u7684\u6b63\u5f26\u4fe1\u53f7\uff0c\u7136\u540e\u4f5c\u52a0\u548c\u3002\u4ed6\u901a\u8fc7\u8c03\u8282\u8fd9\u4e2a\u6a21\u62df\u8ba1\u7b97\u5668\uff0c\u51d1\u51fa\u4e0e\u5b9e\u9a8c\u7ed3\u679c\u5f62\u72b6\u76f8\u4f3c\u7684Lissajous\u66f2\u7ebf\uff0c\u4ece\u800c\u5f97\u77e5\u8be5\u66f2\u7ebf\u76843\u500d\u9891\u8c10\u6ce2\u5e45\u503c\u548c\u76f8\u4f4d\u3002 1960\u5e74\u4ee3\uff0c\u6070\u597d\u662f\u6a21\u62df\u6280\u672f\u7684\u98a0\u5cf0\u65f6\u671f\u3002\u6a21\u62df\u8ba1\u7b97\u7535\u8def\u80fd\u80fd\u505a\u5f88\u591a\u4e8b\u60c5\u3002\u7531\u6d41\u53d8\u4eea\u5f97\u51fa\u7684\u6ce2\u5f62\u4fe1\u53f7\uff0c\u53ef\u901a\u8fc7\u76f8\u5173\u5668\u4e0e\u7ed9\u5b9a\u7684\u6ce2\u5f62\u6bd4\u8f83\uff0c\u8f93\u51fa\u7684\u7ed3\u679c\u662f\u4e0e\u7ed9\u5b9a\u6ce2\u5f62\u7684\u5185\u79ef\u3002\u8fd9\u6837\u5c31\u53ef\u4ee5\u901a\u8fc7\u8bbe\u5b9a\u53c2\u8003\u6ce2\u5f62\u4fe1\u53f7\uff0c\u4ece\u539f\u59cb\u4fe1\u53f7\u4e2d\u63d0\u53d6\u76f8\u5e94\u7684\u5206\u91cf\uff0c\u4ece\u800c\u5b9e\u73b0\u8c10\u6ce2\u5206\u6790\u3002\u4f8b\u5982\uff0cQueen's Collage\u673a\u68b0\u5de5\u7a0b\u7cfb\u7684Harris\u548cBogie\u3002 1967\u5e74\uff0cBrenner\u7684\u6797\u80af\u5b9e\u9a8c\u5ba4\u62a5\u544a\u7ed9\u51fa\u4e86Cooley\u548cTukey\u7684\u5feb\u901fFourier\u53d8\u6362\u7684Fortran\u7a0b\u5e8f\u3002\u51ef\u65af\u897f\u50a8\u5927\u5b66\u5316\u5b66\u7cfb\u7684Dodge\u548cKrieger\u57281971\u5e74\u5c31\u7528\u4e0a\u8fd9\u4e2a\u65b9\u6cd5\u6765\u8fdb\u884c\u8c10\u6ce2\u5206\u6790\u4e86\uff0c\u6b63\u5f0f\u8fdb\u5165\u4e86\u6570\u5b57\u65f6\u4ee3\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":[]},{"id":9191,"url":"https:\/\/www.andrewsun.net\/panta_rhei\/archives\/9191","url_meta":{"origin":4328,"position":3},"title":"Flory\u7684\u201c\u53e6\u4e00\u672c\u4e66\u201d","author":"Andrew","date":"2025\u5e744\u670820\u65e5","format":false,"excerpt":"\u67d0\u6821\u300a\u9ad8\u5206\u5b50\u7269\u7406\u300b\u8bfe\u671f\u672b\u8003\u8bd5\u7684\u201c\u82f1\u6587\u540d\u8bcd\u89e3\u91ca\u201d\u9898\u4e2d\uff0c\u8003\u5230\u201crotational isomeric state\u201d\uff08\u65cb\u8f6c\u5f02\u6784\u6001\uff09\u8fd9\u4e2a\u672f\u8bed\u3002\u6211\u611f\u5230\u5f88\u56f0\u60d1\u3002\u56e0\u4e3a\u8fd9\u4e2a\u672f\u8bed\u662f\u6bd4\u8f83\u6df1\u7684\u3002\u6211\u4eec\u6240\u91c7\u7528\u7684\u672c\u79d1\u9ad8\u5206\u5b50\u7269\u7406\u6559\u6750\uff0c\u6839\u672c\u6ca1\u6709\u6d89\u53ca\u5230\u8fd9\u4e2a\u6982\u5ff5\u3002\u8fd9\u4e2a\u6982\u5ff5\u751a\u81f3\u6ca1\u6709\u51fa\u73b0\u5728P. J. Flory\u7684\u201c\u90a3\u672c\u4e66\u201d\u2014\u2014Principles of Polymer Chemistry\u4e2d\uff08\u51fa\u7248\u4e8e1953\u5e74\uff09\uff0c\u56e0\u4e3a\u8fd9\u4e2a\u6982\u5ff5\u662f\u7531\u041c\u0438\u0445\u0430\u0438\u0301\u043b \u0412\u043b\u0430\u0434\u0438\u0301\u043c\u0438\u0440\u043e\u0432\u0438\u0447 \u0412\u043e\u043b\u044c\u043a\u0435\u043d\u0448\u0442\u0435\u0301\u0439\u043d\uff08M. V. Volkenstein\uff09\u57281959\u5e74\u53d1\u8868\u7684\u8457\u4f5c\u041a\u043e\u043d\u0444\u0438\u0433\u0443\u0440\u0430\u0446\u0438\u043e\u043d\u043d\u0430\u044f \u0441\u0442\u0430\u0442\u0438\u0441\u0442\u0438\u043a\u0430 \u043f\u043e\u043b\u0438\u043c\u0435\u0440\u043d\u044b\u0445 \u0446\u0435\u043f\u0435\u0439\uff08\u805a\u5408\u7269\u94fe\u7684\u6784\u8c61\u7edf\u8ba1\uff09\u4e2d\u6b63\u5f0f\u63d0\u51fa\u7684\u30021963\u5e74\uff0c\u8be5\u4e66\u7684\u82f1\u6587\u7ffb\u8bd1\u5728\u7f8e\u56fd\u51fa\u7248\uff0cP. J. Flory\u5728\u5e8f\u4e2d\u9ad8\u5ea6\u8d5e\u8d4f\u4e86\u8be5\u8457\u4f5c\u3002\u540e\u8005\u7684\u201c\u53e6\u4e00\u672c\u4e66\u201d\u2014\u2014Statistical Mechanics of Chain Molecules\u4e5f\u4e8e1969\u5e74\u51fa\u7248\uff0c\u4f7f\u5f97\u65cb\u8f6c\u5f02\u6784\u6001\u2014\u2014\u8ba1\u7b97\u771f\u5b9e\u805a\u5408\u7269\u94fe\u7edf\u8ba1\u6027\u8d28\u7684\u4e00\u79cd\u8fd1\u4f3c\u601d\u60f3\u2014\u2014\u5f97\u5230\u66f4\u52a0\u4e3a\u4eba\u6240\u77e5\uff08\u5c3d\u7ba1\u8fd9\u672c\u4e66\u4ecd\u7136\u662f\u5c11\u6709\u4eba\u9605\u8bfb\u7684\uff09\u3002 M. Volkenstein\u539f\u8457\u5c01\u9762 \u65cb\u8f6c\u5f02\u6784\u6001\u5047\u8bbe\uff0c\u4f7f\u5f97\u63cf\u8ff0\u771f\u5b9e\u94fe\u7684\u5316\u5b66\u952e\u8282\u590d\u6742\u6027\u2014\u2014\u4f8b\u5982\u4e0d\u5bf9\u79f0\u4ee5\u53ca\u5404\u81ea\u4e0d\u72ec\u7acb\u7684\u952e\u8282\u65cb\u8f6c\u52bf\u80fd\u66f2\u7ebf\u2014\u2014\u6709\u4e86\u53ef\u5199\u4e0b\u7684\u7edf\u4e00\u6570\u5b66\u5f62\u5f0f\u3002\u4ece\u4eca\u5929\u7684\u89d2\u5ea6\u770b\uff0c\u8fd9\u4e00\u5047\u8bbe\u9020\u6210\u7684\u597d\u5904\u662f\u6570\u5b66\u63cf\u8ff0\u7684\u79bb\u6563\u5316\u3002\u8fd9\u5f88\u50cf\u7531\u201c\u968f\u673a\u8fc7\u7a0b\u201d\u5230\u201c\u65f6\u95f4\u5e8f\u5217\u201d\u7684\u53d8\u5316\u65b9\u5f0f\u3002 \u4e0a\u4e16\u7eaa60\u5e74\u4ee3\u6070\u597d\u662f\u7535\u5b50\u8ba1\u7b97\u673a\u95ee\u4e16\u7684\u65f6\u4ee3\u3002\u590d\u6742\u7684\u8ba1\u7b97\u5982\u679c\u53ef\u4ee5\u88ab\u4ee5\u4e00\u79cd\u79bb\u6563\u5316\u7684\u65b9\u5f0f\u63cf\u8ff0\uff0c\u5c31\u53ef\u4ee5\u901a\u8fc7\u7535\u5b50\u8ba1\u7b97\u673a\u6765\u89e3\u51b3\u3002\u57fa\u4e8e\u77e9\u9635\u8fd0\u7b97\u7684\u7ebf\u6027\u4ee3\u6570\u5728\u8fd9\u4e2a\u8fc7\u7a0b\u4e2d\u53d1\u6325\u4e86\u91cd\u8981\u7684\u4f5c\u7528\u3002\u6bd4\u5982\uff0c\u4ee5\u9a6c\u5c14\u53ef\u592b\u8fc7\u7a0b\u4e3a\u6a21\u578b\u7684\u9884\u6d4b\uff0c\u5176\u5b9e\u662f\u843d\u5b9e\u5230\u8f6c\u79fb\u77e9\u9635\u7684\u8fd0\u7b97\u4e0a\u3002\u540c\u7406\uff0c\u57fa\u4e8e\u65cb\u8f6c\u5f02\u6784\u6001\u5047\u8bbe\u5bf9\u771f\u5b9e\u94fe\u8fdb\u884c\u79bb\u6563\u5316\u63cf\u8ff0\u540e\uff0c\u6709\u671b\u901a\u8fc7\u8ba1\u7b97\u673a\uff0c\u7ed9\u5b9a\u5316\u5b66\u5f0f\uff0c\u9884\u6d4b\u51fa\u94fe\u7edf\u8ba1\u7ed3\u679c\u2014\u2014\u8fd9\u5c06\u8fdb\u4e00\u6b65\u7528\u4e8e\u9884\u6d4b\u805a\u5408\u7269\u6750\u6599\u7684\u8bb8\u591a\u6027\u8d28\u3002\u8fd9\u65e0\u7591\u662f\u4ee4\u4eba\u5174\u594b\u7684\u3002\u4f46\u662f\u4f5c\u4e3a\u4e00\u95e8\u79d1\u5b66\uff0c\u8fd9\u4e00\u5047\u8bbe\u662f\u5426\u7b26\u5408\u5b9e\u9645\uff0c\u9700\u8981\u5b9e\u9a8c\u9a8c\u8bc1\u3002\u800c\u5b9e\u9a8c\u7684\u53ef\u9a8c\u8bc1\u6027\u7406\u8bba\uff0c\u662f\u4efb\u4f55\u4e00\u9879\u7406\u8bba\u5de5\u4f5c\u7684\u201c\u53e6\u591650%\u52aa\u529b\u201d\u3002Volkenstein\u539f\u4e66\u603b\u7ed3\u4e86\u5927\u91cf\u53ef\u80fd\u7528\u4e8e\u9a8c\u8bc1\u8fd9\u4e00\u7406\u8bba\u7684\u5b9e\u9a8c\u65b9\u6cd5\u2014\u2014\u5305\u62ec\u5076\u6781\u77e9\u6d4b\u91cf\u3001\u5149\u6563\u5c04\u3001Kerr\u6548\u5e94\u7b49\u3002\u4f46\u662f\u8fd9\u4e9b\u5b9e\u9a8c\u65b9\u6cd5\u4e0e\u65cb\u8f6c\u5f02\u6784\u6001\u5047\u8bbe\u6b63\u786e\u6027\u7684\u8054\u7cfb\uff0c\u4f9d\u7136\u85cf\u5728\u590d\u6742\u800c\u95f4\u63a5\u7684\u6570\u91cf\u5173\u7cfb\u4ee5\u53ca\u66f4\u591a\u5b9e\u9a8c\u5047\u5b9a\uff08\u6bd4\u5982valence-optical scheme\uff09\u4e4b\u4e0b\u3002 \u4ece\u4eca\u5929\u7684\u89d2\u5ea6\u770b\uff0c\u9ad8\u5206\u5b50\u7269\u7406\u7406\u8bba\u7684\u53d1\u5c55\u4e0e\u6db2\u4f53\u7269\u7406\u7684\u53d1\u5c55\u82e5\u4e0d\u80fd\u8bf4\u662f\u540c\u65f6\u7684\uff0c\u5219\u524d\u8005\u751a\u81f3\u8d85\u524d\u4e8e\u540e\u8005\u3002\u56e0\u6b64\uff0c\u6210\u529f\u7684\u9ad8\u5206\u5b50\u7269\u7406\u5b66\u5bb6\uff0c\u514d\u4e0d\u4e86\u8981\u5728\u6db2\u4f53\u7269\u7406\u95ee\u9898\u4e0a\u6709\u5148\u950b\u5f0f\u7684\u6b63\u786e\u8ba4\u8bc6\u3002\u8fd9\u5728Flory\u7684Principles in Polymer Chemistry\u4e00\u4e66\u4e2d\u662f\u6709\u6240\u4f53\u73b0\u7684\u3002\u4f8b\u5982\u5728\u6eb6\u6db2\u70ed\u529b\u5b66\u7684\u683c\u5b50\u7edf\u8ba1\u90e8\u5206\uff0cFlory\u201c\u5570\u55e6\u201d\u4e86\u4e00\u6bb5\u8bdd\uff08p. 497 sec. 1a\u7684\u7b2c2\u81ea\u7136\u6bb5\uff09\uff0c\u5b9e\u9645\u4e0a\u9053\u51fa\u4e86\u6db2\u4f53\u7684\u5f84\u5411\u5206\u5e03\u51fd\u6570\u6982\u5ff5\uff01\u53cd\u4e4b\uff0cVolkenstein\u7684\u539f\u4e66\uff0c\u53cd\u6620\u4e86\u524d\u82cf\u8054\u79d1\u5b66\u5bb6\u5728\u0412\u0430\u043b\u0435\u043d\u0442\u0438\u043d \u0410\u043b\u0435\u043a\u0441\u0435\u0435\u0432\u0438\u0447 \u041a\u0430\u0440\u0433\u0438\u043d\uff08V. A. Kargin\uff09\u5173\u4e8e\u6db2\u6001\u7684\u843d\u540e\u8ba4\u8bc6\u7684\u5f71\u54cd\u3002\u5728Kargin\u5f53\u9886\u5bfc\u7684\u671f\u95f4\uff0c\u8fd9\u4e9b\u89c2\u70b9\u662f\u7528\u6765\u5bf9\u6297\u6765\u81ea\u7f8e\u56fd\u540c\u884c\u7684\u4e0d\u540c\u89c2\u70b9\u7684\u3002\u0418\u043b\u044c\u044f\u0301 \u041c\u0438\u0445\u0430\u0301\u0439\u043b\u043e\u0432\u0438\u0447 \u041b\u0438\u0301\u0444\u0448\u0438\u0446\uff08I. M. Lifshitz\uff09\u7684\u66f4\u52a0\u6b63\u786e\u7684\u9ad8\u5206\u5b50\u7269\u7406\u89c2\u70b9\uff081968\u5e74\uff09\u88ab\u63a8\u8fdf\u5230\u65af\u5927\u6797\u65f6\u4ee3\u4e4b\u540e\u624d\u4e3a\u4eba\u6240\u77e5\u3002\u56e0\u6b64\uff0c\u4eca\u5929\u518d\u60f3\u4e86\u89e3\u8fd9\u90e8\u5206\u5185\u5bb9\uff0c\u5e94\u8be5\u76f4\u63a5\u770bFlory\u7684\u8457\u4f5c\u3002Flory\u7684\u8457\u4f5c\u5305\u62ec\u4e86\u4ed6\u672c\u4eba\u548c\u540e\u671f\u7684\u51e0\u4e2a\u540c\u4e8b\u548c\u5b66\u751f\uff1aJ. Mark\u3001A. Abe\u3001R. Jernigan\u3001A. Tonelli\u7684\u540e\u7eed\u5de5\u4f5c\uff1b\u4ed6\u4eec\u53d1\u8868\u4e86\u540c\u4e00\u7269\u7406\u91cf\u7684\u7406\u8bba\u8ba1\u7b97\u548c\u5b9e\u9a8c\u6d4b\u91cf\u7ed3\u679c\u6bd4\u8f83\uff0c\u5341\u5206\u5b8c\u7f8e\u7684\u5370\u8bc1\u4e86Volkenstein\u94fe\u7edf\u8ba1\u7406\u8bba\u7684\u6210\u529f\uff0c\u6bd4\u5982\u4ee5\u4e0b\u8457\u540d\u63d2\u56fe\u3002 \u7528Monte Carlo\u6a21\u62df\u751f\u6210\u7684\u7acb\u4f53\u5f02\u6784\u65e0\u89c4\u94fe\u7279\u5f81\u6bd4\uff0c\u4e0e\u7406\u8bba\u8ba1\u7b97\u7279\u5f81\u6bd4\u7684\u6bd4\u8f83\u56fe","rel":"","context":"In &quot;\u4e2a\u4eba\u6587\u96c6&quot;","block_context":{"text":"\u4e2a\u4eba\u6587\u96c6","link":"https:\/\/www.andrewsun.net\/panta_rhei\/archives\/category\/featured"},"img":{"alt_text":"","src":"https:\/\/i0.wp.com\/www.andrewsun.net\/panta_rhei\/wp-content\/uploads\/2025\/04\/1.jpg?resize=350%2C200&ssl=1","width":350,"height":200,"srcset":"https:\/\/i0.wp.com\/www.andrewsun.net\/panta_rhei\/wp-content\/uploads\/2025\/04\/1.jpg?resize=350%2C200&ssl=1 1x, https:\/\/i0.wp.com\/www.andrewsun.net\/panta_rhei\/wp-content\/uploads\/2025\/04\/1.jpg?resize=525%2C300&ssl=1 1.5x, https:\/\/i0.wp.com\/www.andrewsun.net\/panta_rhei\/wp-content\/uploads\/2025\/04\/1.jpg?resize=700%2C400&ssl=1 2x, https:\/\/i0.wp.com\/www.andrewsun.net\/panta_rhei\/wp-content\/uploads\/2025\/04\/1.jpg?resize=1050%2C600&ssl=1 3x, https:\/\/i0.wp.com\/www.andrewsun.net\/panta_rhei\/wp-content\/uploads\/2025\/04\/1.jpg?resize=1400%2C800&ssl=1 4x"},"classes":[]},{"id":6002,"url":"https:\/\/www.andrewsun.net\/panta_rhei\/archives\/6002","url_meta":{"origin":4328,"position":4},"title":"\u5173\u4e8efirst principle","author":"Andrew","date":"2014\u5e746\u67082\u65e5","format":"aside","excerpt":"\u8fd9\u4e2a\u8bcd\u5e38\u5e38\u5f53\u4f5c\u5f62\u5bb9\u8bcd\u6765\u7528\uff0c\u56e0\u4e3a\u5b83\u662f\u63cf\u8ff0\u4e00\u4e2a\u7406\u8bba\u7684\u7279\u6027\u7684\u8bcd\u3002\u5b83\u4e5f\u4e0d\u5177\u4f53\u8ddf\u4ec0\u4e48\u91cf\u5b50\u529b\u5b66\u76f8\u5173\uff0c\u5b83\u662f\u4e00\u4e2a\u4e00\u822c\u6027\u7684\u903b\u8f91\u6982\u5ff5\u3002Wikipedia\u6709\u8bcd\u6761First principle\uff0c\u7b2c\u4e00\u53e5\u8bdd\u5c31\u5f88\u6e05\u695a\uff1aa first principle is a basic, foundational proposition or assumption that cannot be deduced from any other proposition or assumption. \u5728\u7269\u7406\u5b66\u4e2d\uff0cfirst principle\u8fd9\u4e2a\u8bcd\u4e5f\u4e0d\u4ec5\u4ec5\u662f\u8ba1\u7b97\u7269\u7406\u7684\u6982\u5ff5\u3002\u5b83\u53ef\u4ee5\u7528\u6765\u5f62\u5bb9\u4efb\u4f55\u4e00\u4e2a\u7406\u8bba\u6a21\u578b\u662f\u5426\u7b26\u5408\u4e0a\u9762\u8fd9\u53e5\u8bdd\u3002\u4f46\u662f\uff0c\u8fd8\u539f\u8bba\u7684\u7406\u60f3\u662f\u65e0\u7a77\u65e0\u5c3d\u7684\uff08\u4f11\u8c1f\u95ee\u9898\uff09\uff0c\u4e00\u4e2a\u7406\u8bba\u6a21\u578b\u662f\u5426first principle\u3001\u5b83\u7684foundation\u662f\u5426\u5df2\u7ecfcannot be deduced from any other assumption\uff0c\u90a3\u4e5f\u53ea\u80fd\u662f\u4e2a\u76f8\u5bf9\u7a0b\u5ea6\u95ee\u9898\u3002\u8fd9\u4e2a\u8bcd\u5f80\u5f80\u53ea\u662f\u7528\u4e8e\u4e0e\u201c\u7ecf\u9a8c\u201d\uff08empirical\uff09\u6216\u8005\u201c\u552f\u8c61\u201d\uff08phenomenological\uff09\u8fd9\u4e24\u4e2a\u8bcd\u76f8\u5bf9\u5e94\uff0c\u8bf4\u660e\u4e00\u4e2a\u7406\u8bba\u4e0d\u662f\u7ecf\u9a8c\u6216\u552f\u8c61\u7684\u3002\u4f46\u662f\u4e0d\u662f\u4e00\u5b9a\u8981\u201c\u4ece\u91cf\u5b50\u529b\u5b66\u51fa\u53d1\u201d\u624d\u53ebfirst principle\uff0c\u8fd9\u4e2a\u662f\u8981\u770b\u5177\u4f53\u7814\u7a76\u9886\u57df\u7684\u3002\u4f8b\u5982\uff0c\u6709\u4e00\u4e2a\u63cf\u8ff0\u73bb\u7483\u6001\u7269\u8d28\u7684\u52a8\u6001\uff08dynamics\uff09\u7684\u7406\u8bba\u6a21\u578b\u53eb\u505amode-coupling theory\uff08MCT\uff09\uff0c\u5b83\u4e3b\u8981\u89e3\u51b3\u7684\u95ee\u9898\u662f\u7269\u8d28\u7684\u52a8\u6001\uff0c\u800c\u4ed6\u7684\u51fa\u53d1\u70b9\u662f\u7269\u8d28\u7684\u7ed3\u6784\uff08structure\uff09\u3002\u7b80\u5355\u5730\u8bf4\uff0c\u5b83\u662f\u4ece\u9759\u6b62\u7ed3\u6784\u51fa\u53d1\uff0c\u9884\u6d4b\u7279\u5b9a\u7684\u8fd0\u52a8\u3002\u4e1a\u754c\u516c\u8ba4\u8fd9\u4e2a\u7406\u8bba\u662ffirst principle\u7684\uff0c\u56e0\u4e3a\u5b83\u9700\u8981\u7684\u5c31\u662f\u5df2\u77e5\u7684\u529b\u5b66\uff0c\u4f46\u5e76\u6ca1\u6709\u7528\u91cf\u5b50\u529b\u5b66\u3002 \u8bf4\u5230\u8fd9\u91cc\u5c31\u8981\u533a\u5206\u4e00\u4e0b\u201c\u9884\u6d4b\u201d\u548c\u201c\u6a21\u62df\u201d\u3002\u867d\u7136\u6211\u4eec\u5df2\u7ecf\u77e5\u9053\u4e86\u5f88\u591a\u529b\u5b66\uff0c\u4f46\u662f\u5927\u81ea\u7136\u8fd8\u662f\u592a\u590d\u6742\uff08\u590d\u6742\u6027complexity\uff09\uff0c\u56e0\u6b64\u6211\u4eec\u8fd8\u9700\u8981\u5f88\u591aassumption\u624d\u80fd\u5efa\u7acb\u66f4\u5177\u4f53\u7684\u7406\u8bba\u6a21\u578b\u89e3\u91ca\u5404\u79cd\u7ec6\u8282\u3002\u4f8b\u5982\u73bb\u7483\u6001\u7269\u8d28\u7684\u884c\u4e3a\u3002\u8fd9\u65f6\uff0c\u5c31\u53ef\u4ee5\u6709\u4e24\u79cd\u52a8\u4f5c\u3002 \u7b2c\u4e00\u79cd\uff08\u9884\u6d4b\uff09\u5c31\u662f\u6211\u5728\u5df2\u6709\u529b\u5b66\u7684\u57fa\u7840\u4e0a\u63d0\u51fa\u5c3d\u53ef\u80fd\u5c11\u4f46\u4ecd\u7136\u5fc5\u8981\u7684\u989d\u5916\u7684assumption\u6216\u8005approximation\uff0c\u5efa\u7acb\u4e00\u4e2a\u7406\u8bba\u6a21\u578b\uff0c\u5b83\u4e5f\u8bb8\u662f\u4e00\u7ec4\u65b9\u7a0b\u3002\u8fd9\u4e2a\u6a21\u578b\u7684\u9884\u6d4b\u5c31\u662f\u8fd9\u7ec4\u65b9\u7a0b\u7684\u89e3\u3002\u8fd9\u6837\u7684\u7406\u8bba\u6a21\u578b\u4e5f\u8bb8\u4f1a\u88ab\u8ba4\u4e3a\u662ffirst principle\u7684\uff0c\u56e0\u4e3a\u5b83\u989d\u5916\u7684assumption\u5f88\u5c11\u3002 \u53e6\u4e00\u79cd\u52a8\u4f5c\uff08\u6a21\u62df\uff09\u662f\uff0c\u6211\u4ec0\u4e48\u989d\u5916\u7684assumption\/approximation\u90fd\u4e0d\u7528\uff0c\u6211\u4e0d\u5efa\u7acb\u7406\u8bba\u6a21\u578b\u3002\u6211\u53ea\u57fa\u4e8e\u6700\u57fa\u672c\u7684\u529b\u5b66\uff0c\u5229\u7528\u5f53\u4eca\u8ba1\u7b97\u673a\u5f3a\u5927\u7684\u8ba1\u7b97\u80fd\u529b\u53bb\u8ba9\u8fd9\u4e2a\u4f53\u7cfb\u6309\u7167\u57fa\u672c\u529b\u5b66\u53bb\u6f14\u5316\u3002\u8fd9\u6837\u5f97\u5230\u7684\u7ed3\u679c\uff0c\u4ecd\u7136\u662f\u65e0\u6cd5\u89e3\u91ca\u7684\uff0c\u5b83\u76f8\u5f53\u4e8e\u4e00\u6b21\u5b9e\u9a8c\uff08\u6982\u5ff5\u4e0a\u6a21\u62dfsimulation\u662f\u5b9e\u9a8c\u7684\u4e00\u79cd\uff09\u3002\u4f46\u662f\uff0c\u4e0d\u7ba1\u600e\u4e48\u8bf4\uff0c\u8fd9\u4e2a\u505a\u6cd5\u8fd8\u662f\u7528\u5230\u4e86\u57fa\u672c\u529b\u5b66\uff08\u6ca1\u529e\u6cd5\u4ec0\u4e48\u529b\u5b66\u90fd\u4e0d\u7528\u5c31\u8ba9\u8ba1\u7b97\u673a\u53bb\u6a21\u62df\uff09\uff0c\u6240\u4ee5\u4e25\u683c\u6765\u8bf4\uff0c\u8fd9\u4e2a\u52a8\u4f5c\u4ecd\u7136\u5c5e\u4e8e\u57fa\u672c\u529b\u5b66\u7684\u9884\u6d4b\uff0c\u53ea\u4e0d\u8fc7\u4e0d\u662f\u901a\u8fc7\u89e3\u65b9\u7a0b\u7ec4\u800c\u5df2\u3002\u7136\u800c\uff0c\u8ddf\u7b2c\u4e00\u79cd\u601d\u60f3\u76f8\u6bd4\uff0c\u7b2c\u4e8c\u79cd\u52a8\u4f5c\u5bf9\u989d\u5916assumption\u7684\u5bb9\u5fcd\u5ea6\u5c31\u5e95\u5f97\u591a\u3002\u4f60\u4e0d\u80fd\u518d\u5728\u57fa\u672c\u529b\u5b66\u4e0a\u5047\u8bbe\u4ec0\u4e48\uff0c\u5426\u5219\u4eba\u4eec\u5c31\u8bf4\u4f60\u6a21\u62df\u7684\u65b9\u6cd5\u4e0d\u591ffirst principle\u3002 \u6240\u4ee5\uff0c\u5f53\u6211\u4eec\u4f7f\u7528\u6216\u770b\u5230first principle\u8fd9\u4e2a\u8bcd\u7684\u65f6\u5019\uff0c\u9996\u5148\u8981\u77e5\u9053\u5b83\u53ea\u80fd\u662f\u4e2a\u7a0b\u5ea6\u95ee\u9898\uff0c\u7136\u540e\u8981\u533a\u5206\u5b83\u5230\u5e95\u5f62\u5bb9\u7684\u5bf9\u8c61\u662f\u4ec0\u4e48\u52a8\u4f5c\uff0c\u662f\u5f62\u5bb9\u4e00\u4e2a\u7406\u8bba\u6a21\u578b\uff0c\u8fd8\u662f\u5f62\u5bb9\u4e00\u79cd\u6a21\u62df\u5b9e\u9a8c\u7684\u65b9\u6cd5\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":[]},{"id":9352,"url":"https:\/\/www.andrewsun.net\/panta_rhei\/archives\/9352","url_meta":{"origin":4328,"position":5},"title":"\u968f\u4fbf\u5199\u7684","author":"Andrew","date":"2026\u5e741\u670828\u65e5","format":false,"excerpt":"\u5728 1960 \u5e74\u4ee3\uff0c\u5927\u5bb6\u666e\u904d\u76f8\u4fe1\uff1a\u5bf9\u67d0\u4e00\u7279\u5b9a\u5316\u5b66\u7269\u79cd\u7684\u9ad8\u5206\u5b50\u94fe\uff0c\u201c\u65e0\u6270\u5c3a\u5bf8\u201d\uff08unperturbed dimension\uff09\u662f\u552f\u4e00\u7684\uff0c\u7b49\u6548\u9ad8\u65af\u94fe\u6bb5\u957f\u5ea6\u4e0e\u94fe\u6bb5\u6570\u8fd9\u4e9b\u53c2\u6570\u5e94\u8be5\u662f\u56fa\u5b9a\u4e0d\u53d8\u7684\uff1b\u56e0\u6b64\u7528\u4efb\u4f55\u5b9e\u9a8c\u624b\u6bb5\u6d4b\u51fa\u6765\u7684\u65e0\u6270\u5c3a\u5bf8\u90fd\u5e94\u8be5\u4e00\u81f4\u3002 \u90a3\u4e2a\u5e74\u4ee3\u6700\u5e38\u7528\u7684\u8def\u7ebf\u662f\u7a00\u6eb6\u6db2\u7c98\u5ea6\u6cd5\uff1b\u800c\u4ece\u7406\u8bba\u4e0a\u8bb2\uff0c\u65e0\u6270\u5c3a\u5bf8\u4e3b\u8981\u53d7\u952e\u89d2\u4e0e\u5185\u65cb\u8f6c\u53d7\u9650\u6027\u5f71\u54cd\uff0c\u6240\u4ee5\u914d\u5408 \u65cb\u8f6c\u5f02\u6784\u6001\uff08RIS\uff09\u7406\u8bba \u8ba1\u7b97\u5c31\u53ef\u4ee5\u505a\u51fa\u9884\u6d4b\u3002 \u4f46\u662f\u5230\u5927\u7ea61970\u5e74\u524d\u540e\uff0c\u8d8a\u6765\u8d8a\u591a\u73b0\u8c61\u63d0\u793a\uff1a\u5373\u4f7f\u628a\u6eb6\u5242\u8c03\u5230theta\u6761\u4ef6\uff0c\u6eb6\u6db2\u7c98\u5ea6\u6d4b\u5230\u7684\u201c\u65e0\u6270\u5c3a\u5bf8\u201d\u4ecd\u53ef\u80fd\u968f\u6eb6\u5242\u800c\u53d8\uff0c\u8fd9\u7b49\u4e8e\u5728\u63d0\u9192\u6211\u4eec\u2014\u2014\u6eb6\u5242\u5e76\u975e\u53ea\u662f\u628a\u6392\u65a5\u4f53\u79ef\u6548\u5e94\u201c\u5173\u6389\u201d\uff0c\u5b83\u8fd8\u53ef\u80fd\u901a\u8fc7\u5f71\u54cd\u94fe\u7684\u5185\u65cb\u8f6c\u52bf\u80fd\u5206\u5e03\u800c\u6539\u53d8\u6784\u8c61\u7edf\u8ba1\u3002 \u90a3\u4e48\u95ee\u9898\u5c31\u53d8\u6210\uff1a\u6240\u8c13\u201c\u65e0\u6270\u201d\u7a76\u7adf\u5e94\u8be5\u4ee5\u4ec0\u4e48\u72b6\u6001\u6765\u5b9a\u4e49\uff1f\u5982\u679c\u56de\u5230RIS\u8ba1\u7b97\u7684\u51fa\u53d1\u70b9\u2014\u2014\u5355\u94fe\u7edf\u8ba1\u2014\u2014\u53bb\u5b9a\u4e49\u4e00\u79cd\u201c\u7406\u60f3\u7684\u65e0\u6270\u72b6\u6001\u201d\uff0c\u4f46\u8fd9\u79cd\u72b6\u6001\u5728\u539f\u5219\u4e0a\u672a\u5fc5\u5bf9\u5e94\u4efb\u4f55\u73b0\u5b9e\u4e2d\u53ef\u76f4\u63a5\u5236\u5907\u7684\u8bd5\u6837\uff0c\u56e0\u4e3a\u9ad8\u5206\u5b50\u6ca1\u6709\u6c14\u6001\u3002 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\u8fd9\u7c7b\u5b9e\u9a8c\u7684\u5173\u952e\u6280\u5de7\u4e4b\u4e00\uff0c\u662f\u628a\u5c11\u91cf\u6c18\u5316\u94fe\u63ba\u5230\u672a\u6c18\u5316\u7684\u57fa\u4f53\u4e2d\uff0c\u5229\u7528\u6c22\/\u6c18\u5728\u4e2d\u5b50\u6563\u5c04\u622a\u9762\u4e0a\u7684\u5de8\u5927\u5dee\u5f02\uff0c\u4ece\u800c\u5728\u201c\u7ed3\u6784\u4e0a\u51e0\u4e4e\u4e0d\u6539\u53d8\u4f53\u7cfb\u201d\u7684\u524d\u63d0\u4e0b\u628a\u5355\u94fe\u4fe1\u53f7\u201c\u663e\u5f71\u201d\u51fa\u6765\uff0c\u8fdb\u800c\u63d0\u53d6\u5747\u65b9\u56de\u8f6c\u534a\u5f84\u7b49\u91cf\u3002 \u5728\u6ca1\u6709SANS\u4e4b\u524d\uff0c\u786e\u5b9e\u7f3a\u5c11\u8fd9\u6837\u76f4\u63a5\u3001\u5e72\u51c0\u5730\u5728\u51dd\u805a\u76f8\u91cc\u770b\u5355\u94fe\u7edf\u8ba1\u5c3a\u5bf8\u7684\u529e\u6cd5\u3002 \u4f46\u5b9e\u9a8c\u5e76\u6ca1\u6709\u628a\u4e8b\u60c5\u7b80\u5355\u5316\uff1a\u67d0\u4e9b\u6781\u6027\u805a\u5408\u7269\u7684\u7194\u4f53\u7ed3\u679c\u4e0e\u7406\u8bba\u9884\u6d4b\u5dee\u5f97\u5f88\u8fdc\uff0c\u751a\u81f3\u4e5f\u4e0e theta 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