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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]\\] 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Structure and Rheology of Complex Fluids\uff08Ronald G. Larson, Oxford University Press, 1999\uff09\u4e00\u4e66\u91cc\u5df2\u7ecf\u6709\u5f88\u7cfb\u7edf\u7684\u603b\u7ed3\u4e86\u3002\u6211\u5728\u8fd9\u91cc\u662f\u628a\u5b9e\u9645\u5927\u5bb6\u6700\u559c\u6b22\u7528\u7684\u5f0f\u5b50\u6311\u51fa\u6765\uff0c\u4e5f\u5bf9\u8be5\u4e66\u6ca1\u8bb2\u5230\u7684\u90e8\u5206\u505a\u4e86\u4e00\u4e9b\u8865\u5145\u3002\u65e0\u76f8\u4e92\u4f5c\u7528\u786c\u7403\u4f53\u7cfb\u96f6\u5207\u7c98\u5ea6\\(\\eta_0\\sim\\phi\\)\uff0c\u4e09\u4e2a\u65b9\u7a0b\uff1aEinstein\u3001Bachelor\u3001Krieger-Dougherty\u3002\u8fd9\u4e09\u4e2a\u65b9\u7a0b\u975e\u5e38\u5e38\u89c1\uff0c\u4e0a\u7f51\u641c\u4e00\u4e0b\u90fd\u6709\u3002\u4e8b\u5b9e\u4e0a\u53ea\u6709Einstein\u662ffirst principle\u7684\u3002\u8fd9\u4e09\u4e2a\u65b9\u7a0b\u5e38\u5e38\u88ab\u7528\u6765\u6807\u5b9a\u60ac\u6d6e\u6db2\u7684\u4f53\u79ef\u5206\u6570\u3002\u6211\u4e2a\u4eba\u89c9\u5f97\u53ea\u6709\u4fdd\u8bc1\u4f53\u7cfb\u662f\u5178\u578b\u7684\u65e0\u76f8\u4e92\u4f5c\u7528\u5355\u5206\u6563\u786c\u7403\u624d\u53ef\u9760\u3002\u4f46\u5f80\u5f80\u7528\u7684\u573a\u5408\u90fd\u662f\u5fae\u51dd\u80f6\u6216\u8005\u4e73\u6db2\u7684\u60c5\u51b5\u3002\u800c\u4e14\uff0c\u7528Krieger-Dougherty\u6765\u6807\u5b9a\u6d53\u60ac\u6d6e\u6db2\u4f53\u79ef\u5206\u6570\u7684\u65f6\u5019\uff0c\u4f60\u5fc5\u987b\u5148\u5047\u5b9a\u4e00\u4e2a\u6700\u5927\u4f53\u79ef\u5206\u6570\\(\\phi_\\textrm{max}\\)\uff08\u5b9e\u9645\u4e0a\u5c31\u662f\u4f7fKrieger-Dougherty\u5f0f\u4e2d\u7684\u7c98\u5ea6\u53d1\u6563\u7684\u4f53\u79ef\u5206\u6570\uff09\uff0c\u4f46\u662f\u8fd9\u4e2a\\(\\phi_\\textrm{max}\\)\u7684\u53d6\u503c\u6709\u4efb\u610f\u6027\uff0c\u75280.58\u30010.64\u3001\\(\\pi\\sqrt{2}\/6\\)\u7684\u90fd\u6709\uff0c\u90fd\u6709\u7406\u7531\uff08\u4f9d\u6b21\u662f\u73bb\u7483\u5316\u3001random close packing\u548crhomboidal dodecahedron packing\uff09\u3002\u6211\u5012\u662f\u6ca1\u8bd5\u8fc7\u5bf9\u4e8e\u540c\u4e00\u5957\u6570\u636e\uff0c\u5047\u5b9a\u4e0d\u540c\u7684\\(\\phi_\\textrm{max}\\)\u503c\u6765\u6807\u5b9a\\(\\phi\\)\u4f1a\u5dee\u591a\u5c11\u3002\u8ddf\u8fd9\u4e00\u5173\u7cfb\u76f8\u5e76\u5217\u7684\uff0c\u662f\u5f53\\(\\phi>\\phi_\\textrm{max}\\)\u65f6\u5e73\u53f0\u6a21\u91cf\\(G_\\textrm{p}\\)\u5bf9\\(\\phi\\)\u7684\u5173\u7cfb\u3002\u5012\u662f\u6709\u4e00\u4e2a\u8ddf\u7c92\u5b50\u76f8\u4e92\u4f5c\u7528\u52bf\u80fd\u6709\u5173\u7684\u7b80\u5355\u5173\u7cfb\uff1a$$G_\\textrm{p}\\propto\\frac{1}{r}\\left(\\frac{\\partial^2U\\left(r\\right)}{\\partial r^2}\\right)$$\u526a\u5207\u7c98\u5ea6\\(\\eta_\\textrm{r}\\sim\\textrm{Pe}\\)\u3002\u8fd9\u4e2a\u5173\u7cfb\uff0c\u597d\u50cf\u53ea\u6709\u8f83\u6d53\u7684\u60ac\u6d6e\u6db2\uff08\u53d1\u751f\u526a\u5207\u53d8\u7a00\uff09\u624d\u6709\u610f\u4e49\u3002\u552f\u8c61\u7684\u7eaf\u526a\u5207\u7684\u6d41\u53d8\u5b66\u6a21\u578b\u5f88\u5e38\u7528\u7684\u662fCasson\u6216\u8005Cross\u3002Casson\u65b9\u7a0b\u542b\u6709\u4e00\u4e2a\u201c\u5c48\u670d\u5e94\u529b\u201d$$\\sigma^{\\frac{1}{2}}=\\sigma_\\textrm{y}^{\\frac{1}{2}}+c\\dot{\\gamma}^{\\frac{1}{2}}$$\u4f46\u662f\u7528\u8fd9\u4e2a\u65b9\u7a0b\u62df\u5408\u5f97\u5230\u7684\u5c48\u670d\u5e94\u529b\u8ddf\u505a\u8815\u53d8\u5f97\u5230\u7684\u9759\u6001\u5c48\u670d\u5e94\u529b\u5f80\u5f80\u6709\u5dee\u3002Cross\u65b9\u7a0b\uff1a$$\\eta_\\textrm{r}=\\eta_{\\textrm{r}\\infty}+\\frac{\\eta_\\textrm{r0}-\\eta_{\\textrm{r}\\infty}}{1+\\left(b\\sigma_\\textrm{r}\\right)^m}$$\u5176\u4e2d\\(\\sigma_\\textrm{r}=a^3\\sigma\/k_\\textrm{B}T\\)\u3002\u81f3\u4e8e\u7ed3\u6784\u6a21\u578b\u5c31\u6d89\u53ca\u5230\u80f6\u4f53\u73bb\u7483\u7684\u95ee\u9898\u4e86\u3002\u5982\u679c\u662f\u786c\u7403\u4f53\u7cfb\u53ef\u4ee5\u5229\u7528schematic MCT\u7684\u7ed3\u679c\u6765\u8bd5\u8bd5\u3002\u7ebf\u6027\u7c98\u5f39\u6027\u5bf9\u4e8e\u6d53\u4f53\u7cfb\u8fd8\u662f\u53ef\u4ee5\u8bd5\u7528schematic MCT\u7684\uff0c\u6216\u8005\u7528\u8fd9\u4e00\u4e2a\u66f4\u7b80\u5355\u7684\u7248\u672c\uff1aPRL 75, 2770 (1995)\u3002\u8fd9\u4e2a\u5f0f\u5b50\u5b9e\u9645\u62df\u5408\u53c2\u6570\u5f88\u591a\uff0c\u4efb\u610f\u5ea6\u5f88\u5927\u3002\u7a00\u548c\u534a\u7a00\u4f53\u7cfb\u7684\u7ebf\u6027\u7c98\u5f39\u6027\u600e\u6837\uff0c\u6211\u6ca1\u6709\u67e5\u9605\u548c\u603b\u7ed3\u3002\u975e\u7ebf\u6027\u77ac\u6001\u884c\u4e3a\u540c\u6837\uff0cschematic MCT\u7684\u63a8\u5e7f\u4e5f\u6709\u5230time-dependent shear\u7684\u60c5\u5f62\uff0c\u6240\u4ee5\u80fd\u628aschematic MCT\u770b\u61c2\u7684\u8bdd\uff0c\u65e0\u76f8\u4e92\u4f5c\u7528\u786c\u7403jamming\u4f53\u7cfb\u7684\u6d41\u53d8\u5b66\u662f\u53ef\u4ee5\u83b7\u5f97\u7406\u8bba\u63cf\u8ff0\u7684\u3002\u95ee\u9898\u662f\uff0c\u5177\u6709\u7c7b\u4f3c\u6d41\u53d8\u5b66\u884c\u4e3a\u7684\u8fd8\u6709\u80f6\u4f53\u51dd\u80f6\u4f53\u7cfb\uff0c\u7528MCT\u53bb\u7b97\u5c31\u6ca1\u4ec0\u4e48\u7406\u7531\u3002\u6211\u6ca1\u6709\u67e5\u6700\u8fd1\u7684\u6587\u732e\u3002\u4eceLarson\u7684\u4e66\u91cc\u770b\u5230\uff0c\u51dd\u80f6\u4f53\u7cfb\u4e5f\u6709\u4e00\u4e9b\u4ece\u7c92\u5b50\u76f8\u4e92\u4f5c\u7528\u51fa\u53d1\u534a\u7ecf\u9a8c\u7684\u7ed3\u6784\u6a21\u578b\uff0c\u4f46\u591a\u6570\u662f\u9884\u6d4b\u4e00\u4e0b\u5c48\u670d\u5e94\u529b\uff0c\u6ca1\u6709\u5230\u9884\u6d4btime-dependent shear\u8fd9\u4e48\u5b8c\u6574\u3002\u7528\u6d41\u53d8\u5b66\u672c\u6784\u65b9\u7a0b\u7684\u5c31\u4e0d\u5728\u6b64\u603b\u7ed3\u4e86\uff0c\u6211\u7684\u5174\u8da3\u662f\u5982\u4f55\u80fd\u5c06\u6d41\u53d8\u5b66\u8ddf\u7ed3\u6784\u8054\u7cfb\u8d77\u6765\u3002\u4e73\u6db2\u4f53\u7cfb\u4e73\u6db2\u4f53\u7cfb\u8981\u8003\u8651Ca\u503c\u3002\u6211\u4e3b\u8981\u603b\u7ed3\\(\\textrm{Ca}\\ll1\\)\u7684\u60c5\u51b5\u3002\u96f6\u5207\u7c98\u5ea6\u7a00\u4e73\u6db2\uff0c\u8ddf\u786c\u7403\u5df2\u7ecf\u5f88\u63a5\u8fd1\u4e86\u3002Talor\u8003\u8651\u4e86\u6db2\u6ef4\u76f8\u672c\u8eab\u5728\u6d41\u573a\u4e2d\u4f1a\u6253\u8f6c\uff0c\u4f7f\u7c98\u5ea6\u964d\u4f4e\uff0c\u5f0f\u5b50\u662f\uff1a$$\\eta_\\textrm{r}=1+\\frac{1+\\frac{5}{2}M}{1+M}\\phi$$\u5176\u4e2d\\(M=\\eta_\\textrm{d}\/\\eta_\\textrm{s}\\)\u3002\u6d53\u4e00\u70b9\u7684\uff0c\u7528Pal\u7684\u51e0\u4e2a\u5f0f\u5b50\u3002\u6d53\u6d6e\u6db2\u4ea7\u751f\u7684\u53e6\u4e00\u4e2a\u4e0e\u786c\u7403\u4e0d\u540c\u7684\u56e0\u7d20\u5c31\u662f\u6db2\u6ef4\u7c98\u5728\u4e00\u8d77\u6709\u4e00\u5b9a\u7684\u63a5\u89e6\u89d2\uff0c\u63a5\u89e6\u754c\u9762\u7531\u4e24\u5c42\u6d3b\u6027\u5242\u5206\u5b50\uff0c\u6709\u4e00\u5b9a\u539a\u5ea6\u3002\u6709\u6548\u4f53\u79ef\u5206\u6570\u7684\u8ba8\u8bba\u89c1Princen\u7b49\u3002\u53e6\u5916\uff0c\u867d\u7136\\(\\textrm{Ca}\\ll1\\)\uff0c\u4f46\u662f\u6d53\u4e86\u4e4b\u540e\u6db2\u6ef4\u8fd8\u662f\u4f1a\u6324\u538b\u53d1\u751f\u53d8\u5f62\uff0c\u8fd9\u65f6\u54ea\u6015\u4e0d\u53d8\u5f62\u65f6\u5df2\u8fbe\u5230\u751a\u81f3\u8d85\u8fc7\\(\\phi_\\textrm{max}\\)\uff0c\u4f46\u901a\u8fc7\u53d8\u5f62\u4ecd\u7136\u53ef\u4ee5\u6ed1\u79fb\uff0c\u6240\u4ee5\u7c98\u5ea6\u4e0d\u4f1a\u53d1\u6563\u3002\u8fd9\u4e00\u6548\u5e94\u6ca1\u6709\u8fd8\u6ca1\u67e5\u5230\u7ed3\u6784\u7406\u8bba\u6a21\u578b\uff0c\u5b9e\u9a8c\u53ef\u53c2\u8003Colloids Surf. A 299, 65 (2007)\u3002\\(\\phi_\\textrm{max}\\)\u4ee5\u4e0a\uff0c\u6a21\u91cf\u968f\\(\\phi\\)\u7684\u53d8\u5316\uff0c\u53c2\u89c1J. Non-Newt. Fluid Mech. 105, 21 (2002)\u3002\u6216\u8005Princen\u526a\u5207\u7c98\u5ea6Princen\u3002\u7ebf\u6027\u7c98\u5f39\u6027\u7a00\u7684\u7528Palierne\u7684\u6a21\u578b\uff0c\u592a\u51fa\u540d\u4e86\uff0c\u4e0d\u5f15\u4e86\u3002\u6d53\u7684\u6ca1\u6709\uff0c\u53ef\u80fd\u53ef\u4ee5\u7528MCT\uff1f\u975e\u7ebf\u6027\u77ac\u6001\u884c\u4e3a\u518d\u6b21\u5f3a\u8c03\u6211\u53ea\u603b\u7ed3\\(\\textrm{Ca}\\ll1\\)\u7684\u60c5\u51b5\u3002\u6db2\u6ef4\u53d8\u5f62\u90a3\u4e00\u5927\u5757\u6709\u5f88\u591a\u6a21\u578b\u53ef\u4ee5\u505a\u5230time-dependent shear\u3002Princen\u7ed9\u8fc7\u4e00\u4e2a\u6d53\u6d6e\u6db2\u5c48\u670d\u5e94\u529b\u7684\u5f0f\u5b50[backref name=\"118\"]\u3002\u800c\u5bf9\u4e8etime-dependent shear\uff0c\u6211\u627e\u5230\u4e00\u7bc7J. Fluid Mech. 463, 1 (2002)\u662f\u8003\u8651\u7a00\u6d6e\u6db2\u7684\u3002\u4f46\u597d\u50cf\u8fd8\u6ca1\u6709\u4eba\u53bb\u4f7f\u7528\u3002","rel":"","context":"In 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transition\uff09\uff0c\u6240\u8c13\u52a8\u529b\u5b66\u675f\u7f1a\uff08dynamic arrest\uff09\u3002nonergodic transition\uff0c\u662f\u4e00\u79cdtransition\u5417\uff1ftransition\u662f\u4ec0\u4e48\uff1f\u4e13\u6307\u76f8\u53d8\uff08phase transition\uff09\u5462\uff1f\u8fd8\u662f\u968f\u4fbf\u7528\u4e00\u4e0b\u8fd9\u4e2a\u8bcd\u800c\u5df2\uff1f\u82e5\u8bf4\u662f\u76f8\u53d8\uff0c\u53c8\u6ca1\u6709\u770b\u5230\u6587\u7ae0\u8bf4\u5728nonergodic 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