{"id":33955,"date":"2022-04-19T22:39:27","date_gmt":"2022-04-19T14:39:27","guid":{"rendered":"https:\/\/swarma.org\/?p=33955"},"modified":"2022-04-19T22:39:27","modified_gmt":"2022-04-19T14:39:27","slug":"%e6%b6%8c%e7%8e%b0%e4%ba%8e%e4%ba%a4%e5%8f%89%e7%a7%91%e5%ad%a6%e7%9a%84%e6%96%b0%e6%96%b9%e5%90%91-%e6%b4%bb%e6%80%a7%e7%89%a9%e8%b4%a8","status":"publish","type":"post","link":"https:\/\/swarma.org\/?p=33955","title":{"rendered":"\u6d8c\u73b0\u4e8e\u4ea4\u53c9\u79d1\u5b66\u7684\u65b0\u65b9\u5411\u2014\u2014\u6d3b\u6027\u7269\u8d28"},"content":{"rendered":"
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\u7406\u89e3\u6d3b\u6027\u4e2a\u4f53\u81ea\u9a71\u52a8\u7684\u529b\u5b66\u673a\u5236\u5f80\u5f80\u662f\u7814\u7a76\u6d3b\u6027\u7269\u8d28\u7684\u7b2c\u4e00\u6b65\u3002\u4ee5\u5b58\u5728\u4e8e\u6d41\u4f53<\/span>(\u7a7a\u6c14\u6216\u8005\u6c34)<\/span>\u73af\u5883\u4e2d\u7684\u6d3b\u6027\u7269\u8d28<\/span>(\u5982\u9e1f\u3001\u9c7c\u3001\u8fd0\u52a8\u5fae\u751f\u7269\u7b49)<\/span>\u4e3a\u4f8b\uff0c\u6d3b\u6027\u4e2a\u4f53\u901a\u8fc7\u548c\u6d41\u4f53\u73af\u5883\u76f8\u4e92\u4f5c\u7528\u83b7\u5f97\u9a71\u52a8\u529b\u3002\u7136\u800c\u4e0d\u540c\u7cfb\u7edf\u4ea7\u751f\u9a71\u52a8\u7684\u529b\u5b66\u673a\u5236\u5374\u53ef\u80fd\u5927\u76f8\u5f84\u5ead[11]\uff0c\u6bd4\u5982\u5b8f\u89c2\u5c3a\u5ea6\u7684\u9e1f\u548c\u9c7c\u53ef\u4ee5\u901a\u8fc7\u5468\u671f\u6027\u6446\u52a8\u7fc5\u8180\u6216\u8005\u9c7c\u9ccd\u83b7\u5f97\u9a71\u52a8\u529b\uff0c\u800c\u5fae\u89c2\u5c3a\u5ea6\u7684\u7ec6\u83cc\u5374\u662f\u901a\u8fc7\u65cb\u8f6c\u87ba\u65cb\u5f62\u7684\u97ad\u6bdb\u800c\u524d\u8fdb[12]\u3002\u8fd9\u4e9b\u9a71\u52a8\u65b9\u5f0f\u7684\u4e0d\u540c\u53ef\u4ee5\u901a\u8fc7\u6d41\u4f53\u529b\u5b66\u6548\u5e94\u7406\u89e3\u3002\u6d41\u4f53\u8fd0\u52a8\u7531\u7eb3\u7ef4\u2014\u65af\u6258\u514b\u65af\u65b9\u7a0b\u63cf\u8ff0\uff0c\u8be5\u65b9\u7a0b\u4e2d\u60ef\u6027\u9879\u548c\u7c98\u6ede\u9879\u7684\u6bd4\u503c\u5b9a\u4e49\u4e86\u4e00\u4e2a\u540d\u4e3a\u96f7\u8bfa\u6570\u7684\u65e0\u91cf\u7eb2\u6570\uff0c\u5b83\u7684\u5b9a\u4e49\u4e3a\uff1aRe=UL\/\u03bd\uff0c\u5176\u4e2dU\u662f\u6d41\u901f\uff0cL\u662f\u6d3b\u6027\u4e2a\u4f53\u7684\u5c3a\u5bf8\uff0c\u03bd\u662f\u52a8\u529b\u7c98\u6ede\u7cfb\u6570<\/span>(kinematic viscosity)<\/span>\uff0c\u5ba4\u6e29\u4e0b\u6c34\u7684\u52a8\u529b\u7c98\u6ede\u7cfb\u6570\u03bd \u22481\u00d710-6 m2\/s\u3002\u6211\u4eec\u5148\u8003\u8651\u4e00\u4e2a\u5b8f\u89c2\u751f\u7269\uff1a\u4e00\u6761\u4f53\u957f10 cm\u7684\u9c7c\uff0c\u4ee510 cm\/s\u901f\u5ea6\u6e38\u52a8\u65f6\u7684\u96f7\u8bfa\u6570\u4e3aRe=10000\uff0c\u6b64\u65f6\u60ef\u6027\u529b\u4e3b\u5bfc\u6d41\u4f53\u8fd0\u52a8\uff0c\u5e76\u5e2e\u52a9\u5468\u671f\u6446\u52a8\u7684\u9c7c\u9ccd\u4ea7\u751f\u9a71\u52a8\u529b\u3002\u4e0b\u9762\u6211\u4eec\u518d\u8003\u8651\u4e00\u4e2a10 \u03bcm\u957f\u7684\u5fae\u751f\u7269\u4ee510 \u03bcm\/s\u7684\u901f\u5ea6\u8fd0\u52a8\uff0c\u6b64\u65f6\u96f7\u8bfa\u6570\u4e3aRe=0.0001\uff0c\u8fd9\u4e2a\u533a\u95f4\u6d41\u4f53\u7c98\u6ede\u529b\u5360\u4e3b\u5bfc\uff0c\u7eb3\u7ef4\u2014\u65af\u6258\u514b\u65af\u65b9\u7a0b\u4e2d\u7684\u65f6\u95f4\u5bfc\u6570\u53ef\u5ffd\u7565\uff0c\u53d8\u6210\u4e0d\u542b\u65f6\u7684\u65af\u6258\u514b\u65af\u65b9\u7a0b\uff0c\u8868\u73b0\u51fa\u8fd0\u52a8\u5b66\u65f6\u95f4\u53ef\u9006\u6027\u3002\u56fe2(a)\u4e2d\u7684\u5b9e\u9a8c\u662f\u5bf9\u65f6\u95f4\u53ef\u9006\u6027\u7684\u751f\u52a8\u5c55\u793a\uff1a\u8f6c\u52a8\u7684\u5185\u7b52\u548c\u9759\u6b62\u7684\u5916\u7b52\u5728\u7c98\u6ede\u6d41\u4f53\u4e2d\u4ea7\u751f\u4e00\u4e2a\u526a\u5207\u6d41\u573a\uff0c\u62c9\u4f38\u4e09\u6ef4\u7d2b\u8272\u67d3\u6599\uff0c\u4f7f\u4e4b\u989c\u8272\u53d8\u6de1\uff1b\u4e4b\u540e\u5185\u7b52\u53cd\u8f6c\uff0c\u7a00\u91ca\u7684\u67d3\u6599\u6e10\u6e10\u6c47\u805a\uff0c\u6700\u7ec8\u795e\u5947\u5730\u51fa\u73b0\u5728\u521d\u59cb\u7684\u4f4d\u7f6e\u3002\u8fd9\u8bf4\u660e\u5f53\u5185\u7b52\u8fd0\u52a8\u56de\u5230\u521d\u59cb\u4f4d\u7f6e\u540e\uff0c\u7cfb\u7edf\u5176\u4ed6\u6027\u8d28\u4e5f\u6062\u590d\u539f\u72b6[13]\u3002\u57fa\u4e8e\u65f6\u95f4\u53ef\u9006\u6027\u7684\u8003\u8651\uff0c\u73c0\u585e\u5c14\u63d0\u51fa\u4e86\u4e00\u4e2a\u6709\u8da3\u7684\u201c\u6247\u8d1d\u5b9a\u7406\u201d[14]\u3002\u56fe2(b)\u4e2d\u5398\u7c73\u5c3a\u5ea6\u7684\u6247\u8d1d\u5229\u7528\u5728\u6c34\u4e2d\u7f13\u6162\u5f20\u5f00\u8d1d\u58f3\u4e4b\u540e\u8fc5\u901f\u5408\u62e2\u4ea7\u751f\u7684\u51b2\u51fb\u529b\u6e38\u52a8[15]\u3002\u7136\u800c\u5982\u679c\u6211\u4eec\u628a\u6247\u8d1d\u7f29\u5c0f\u5230\u5fae\u7c73\u91cf\u7ea7\uff0c\u8fd9\u79cd\u65b9\u5f0f\u5c31\u4e0d\u80fd\u4ea7\u751f\u9a71\u52a8\u529b\u4e86\uff1a\u8d1d\u58f3\u5f20\u5f00\u548c\u95ed\u62e2\u7684\u5f62\u53d8\u8fc7\u7a0b\u5728\u65f6\u95f4\u4e0a\u662f\u5bf9\u79f0\u7684\uff0c\u8d1d\u58f3\u5f20\u5f00\u65f6\u4f1a\u524d\u8fdb\uff0c\u4f46\u95ed\u62e2\u65f6\u76f8\u53cd\u7684\u529b\u4f1a\u8ba9\u5b83\u56de\u5230\u539f\u4f4d\uff0c\u7c7b\u4f3c\u4e8e\u56fe2(a)\u4e2d\u7684\u67d3\u6599\u3002\u6839\u636e\u540c\u6837\u7684\u539f\u7406\uff0c\u6211\u4eec\u4e5f\u53ef\u4ee5\u7406\u89e3\u5468\u671f\u6027\u6446\u52a8\u9c7c\u9ccd\u65e0\u6cd5\u5728\u4f4e\u96f7\u8bfa\u6570\u73af\u5883\u4e0b\u9a71\u52a8\u3002<\/span><\/p>\n<\/section>\n<\/section>\n<\/section>\n


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<\/p>\n

\u56fe2 (a)\u4f4e\u96f7\u8bfa\u6570\u6d41\u4f53\u4e2d\u65f6\u95f4\u53ef\u9006\u6027\u7684\u5b9e\u9a8c\u5c55\u793a\uff1a\u7c98\u6027\u6db2\u4f53\u5728\u5185\u5916\u5706\u7b52\u4e4b\u95f4\uff0c\u521d\u59cb(T = 0 s)\u6709\u4e09\u6ef4\u7d2b\u8272\u67d3\u6599\uff0c\u5728\u5185\u7b52\u8f6c\u52a8\u4ea7\u751f\u7684\u526a\u5207\u6d41\u4e2d\u67d3\u6599\u88ab\u62c9\u4f38\u3001\u88ab\u7a00\u91ca\u5230 T = 20 s\uff0c\u4e4b\u540e\u5185\u7b52\u53cd\u8f6c\u5230\u521d\u59cb\u4f4d\u7f6e\uff0c\u67d3\u6599\u4e5f\u968f\u4e4b\u56de\u5230\u521d\u59cb\u4f4d\u7f6e(T = 40 s)[13]\uff1b(b)\u6247\u8d1d\u4f7f\u7528\u7684\u65f6\u95f4\u53ef\u9006\u4f4d\u578b\u53d8\u5316[15]\uff1b(c)\u8fd0\u52a8\u7cbe\u5b50\u7684\u7167\u7247[17]\uff1b(d)\u8fd0\u52a8\u7ec6\u83cc\u7684\u8367\u5149\u7167\u7247[19]\uff1b(e)\u7ec6\u83cc\u5468\u56f4\u7684\u6d41\u573a\uff0c\u989c\u8272\u5bf9\u5e94\u901f\u5ea6\u5927\u5c0f\uff0c\u7ebf\u6761\u5bf9\u5e94\u6d41\u7ebf[20]<\/span><\/p>\n


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\u4e3a\u4e86\u5728\u4f4e\u96f7\u8bfa\u6570\u73af\u5883\u4e0b\u6e38\u52a8\uff0c\u5fae\u751f\u7269\u9700\u8981\u4e00\u4e2a\u65f6\u95f4\u53cd\u6f14\u975e\u5bf9\u79f0\u7684\u9a71\u52a8\u65b9\u5f0f\u6765\u6446\u8131\u201c\u6247\u8d1d\u5b9a\u7406\u201d\u7684\u675f\u7f1a[16]\u3002\u884c\u6ce2\u662f\u5fae\u751f\u7269\u6700\u5e38\u4f7f\u7528\u7684\u65b9\u6cd5\uff1a\u56fe2(c)\u4e2d\u7cbe\u5b50\u97ad\u6bdb\u5728\u5206\u5b50\u9a6c\u8fbe\u7684\u9a71\u52a8\u4e0b\u6709\u89c4\u5219\u7684\u5f2f\u66f2\uff0c\u4ea7\u751f\u4e86\u4e00\u4e2a\u4ece\u8eab\u4f53\u4f20\u5411\u97ad\u6bdb\u5c3e\u7aef\u7684\u884c\u6ce2\u5f0f\u5f62\u53d8\uff0c\u4ece\u800c\u4ea7\u751f\u4e00\u4e2a\u4e0e\u6ce2\u7684\u4f20\u64ad\u65b9\u5411\u76f8\u53cd\u7684\u6d41\u4f53\u529b\uff0c\u9a71\u52a8\u7cbe\u5b50\u7684\u8fd0\u52a8[17]\u3002\u8fd9\u79cd\u7ec6\u957f\u578b\u97ad\u6bdb\u914d\u5408\u884c\u6ce2\u9a71\u52a8\u7684\u65b9\u5f0f\u5728\u5fae\u751f\u7269\u4e2d\u5f88\u5e38\u89c1[18]\uff1a\u56fe2(d)\u4e2d\u7684\u7ec6\u83cc\u8f6c\u52a8\u87ba\u65cb\u5f62\u7684\u521a\u6027\u97ad\u6bdb\uff0c\u4ea7\u751f\u4e00\u4e2a\u5411\u5c3e\u90e8\u4f20\u64ad\u7684\u5f62\u53d8\u6ce2\uff0c\u6253\u7834\u5bf9\u79f0\u6027[19]\u3002\u8fd0\u52a8\u7684\u7ec6\u83cc\u80fd\u5728\u5468\u56f4\u6d41\u4f53\u4e2d\u4ea7\u751f\u6d41\u573a\uff0c\u6d41\u573a\u5404\u5411\u5f02\u6027\uff0c\u968f\u7740\u8ddd\u79bb\u7684\u5e73\u65b9\u8870\u51cf\uff0c\u5982\u56fe2(e)\u6240\u793a\u3002\u901a\u8fc7\u8fd9\u6837\u7684\u6d41\u573a\uff0c\u7ec6\u83cc\u4e4b\u95f4\u53ef\u4ee5\u76f8\u4e92\u4f5c\u7528\uff0c\u6539\u53d8\u5f7c\u6b64\u7684\u8eab\u4f53\u53d6\u5411\u548c\u8fd0\u52a8\u901f\u5ea6[20]\u3002  <\/span><\/p>\n

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3.<\/strong><\/strong><\/strong><\/strong>\u6d3b\u6027\u7269\u8d28\u7684\u76f8\u53d8<\/span><\/strong><\/strong><\/strong><\/p>\n<\/section>\n

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<\/section>\n

<\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/h3>\n


<\/p>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n

\u6d3b\u6027\u7269\u8d28\uff0c\u4f5c\u4e3a\u4e00\u7c7b\u7269\u8d28\u4f53\u7cfb\uff0c\u5176\u5fc5\u7136\u5177\u6709\u4e30\u5bcc\u7684\u7269\u8d28\u76f8\u6001\u7ed3\u6784\u3002\u5f53\u5927\u91cf\u5177\u6709\u76f8\u4e92\u4f5c\u7528\u7684\u6d3b\u6027\u7c92\u5b50\u5f62\u6210\u591a\u4f53\u7cfb\u7edf\u65f6\uff0c\u6d3b\u6027\u7269\u8d28\u4f53\u7cfb\u4e0d\u4f46\u53ef\u80fd\u5448\u73b0\u4e00\u822c\u5e73\u8861\u6001\u7269\u8d28\u5e38\u6709\u7684\u76f8\u53d8\u884c\u4e3a\uff0c\u540c\u65f6\u5728\u8fd9\u7c7b\u7cfb\u7edf\u4e2d\u901a\u8fc7\u96c6\u4f53\u6a21\u5f0f\u7684\u975e\u7ebf\u6027\u76f8\u4e92\u4f5c\u7528\uff0c\u53ef\u4ee5\u6fc0\u53d1\u51fa\u66f4\u4e3a\u4e30\u5bcc\u7684\u5b8f\u89c2\u52a8\u529b\u5b66\u7ed3\u6784\u3002\u8fd9\u4e9b\u4e30\u5bcc\u7684\u76f8\u6001\u53ca\u4e0e\u4e4b\u4f34\u968f\u7684\u96c6\u4f53\u52a8\u529b\u5b66\uff0c\u6b63\u662f\u6d3b\u6027\u7269\u8d28\u7269\u7406\u7684\u9b45\u529b\u6240\u5728\u3002<\/span><\/p>\n


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3.1 \u6d3b\u6027\u7269\u8d28\u4e2d\u7684\u4e8c\u7ef4\u957f\u7a0b\u5e8f<\/span><\/strong><\/span><\/p>\n


<\/span><\/strong><\/span><\/p>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n

1995\u5e74\uff0cT.Vicsek\u7b49\u4eba\u8bd5\u56fe\u8003\u8651\u4e00\u7c7b\u975e\u5e73\u8861\u4f53\u7cfb\u7684\u76f8\u53d8\u884c\u4e3a[21]\u3002\u7c7b\u6bd4\u4e8e\u5e73\u8861\u6001\u7684XY\u6a21\u578b\uff0c\u540c\u65f6\u53d7\u5230\u751f\u7269\u4f53\u7cfb\u7fa4\u4f53\u884c\u4e3a\u7684\u542f\u53d1\uff0c\u6a21\u578b\u4e2d\u7684\u81ea\u65cb\u6307\u5411\u9664\u4e86\u4ee3\u8868\u6781\u5316\u65b9\u5411\u540c\u65f6\u8fd8\u88ab\u8d4b\u4e88\u7c92\u5b50\u8fd0\u52a8\u7684\u901f\u5ea6\u65b9\u5411\uff0c\u76f8\u4e92\u4f5c\u7528\u5219\u91c7\u7528\u7b80\u5355\u7684\u5c40\u57df\u901f\u5ea6\u5bf9\u9f50\u3002\u7531\u4e8e\u7c92\u5b50\u5728\u4e8c\u7ef4\u5e73\u9762\u5185\u8fc1\u79fb\uff0c\u5b83\u4eec\u7684\u4f4d\u7f6e\u4e0d\u65ad\u53d8\u5316\uff0c\u5728\u4e0d\u540c\u7684\u566a\u58f0\u6761\u4ef6\u4e0b\uff0c\u5c55\u73b0\u51fa\u6781\u4e3a\u4e0d\u540c\u7684\u52a8\u529b\u5b66\u884c\u4e3a\u3002\u53d7\u76f8\u53d8\u4e34\u754c\u884c\u4e3a\u7684\u542f\u53d1\uff0cT. Vicsek\u7b49\u4eba\u8ba1\u7b97\u4e86\u7cfb\u7edf\u7684\u6781\u5316\u5e8f\u53c2\u91cf\uff0c\u5e76\u901a\u8fc7\u4e00\u7cfb\u5217\u7684\u6807\u5ea6\u5206\u6790\uff0c\u786e\u8ba4\u7cfb\u7edf\u4e2d\u5b58\u5728\u4e00\u7c7b\u65b0\u578b\u7684\u6709\u5e8f\u2014\u65e0\u5e8f\u76f8\u53d8\uff0c\u4f53\u7cfb\u5728\u76f8\u53d8\u70b9\u9075\u5b88\u4e00\u5b9a\u7684\u6807\u5ea6\u7387[21]\u3002\u7136\u800c\uff0c\u7531\u4e8e\u5f53\u65f6\u8ba1\u7b97\u901f\u5ea6\u7684\u9650\u5236\uff0c\u4ed6\u4eec\u6a21\u62df\u7684\u4f53\u7cfb\u5927\u5c0f\u79bb\u7cfb\u7edf\u7684\u70ed\u529b\u5b66\u6781\u9650\u884c\u4e3a\u7684\u6807\u5ea6\u533a\u95f4\u4f3c\u4e4e\u8fd8\u5dee\u5f97\u5f88\u8fdc\u3002\u4e4b\u540eH. Chat\u00e9\u7b49\u4eba\u7684\u4e00\u7cfb\u5217\u5de5\u4f5c\u8868\u660e\uff0c\u4f53\u7cfb\u5728\u76f8\u53d8\u70b9\u9644\u8fd1\u7684\u8f6c\u53d8\u5e76\u975e\u4e00\u822c\u7684\u8fde\u7eed\u76f8\u53d8\uff0c\u8f6c\u53d8\u70b9\u9644\u8fd1\u7684\u6709\u5e8f\u6001\u51fa\u73b0\u6761\u5e26\u72b6\u76f8\u5206\u79bb\u7ed3\u6784\uff0c\u6781\u5316\u5e8f\u53c2\u91cf\u51fa\u73b0\u4e0d\u8fde\u7eed\u8df3\u53d8[22]\u3002<\/span><\/p>\n


<\/p>\n

\u4e8b\u5b9e\u4e0aVicsek\u6a21\u578b\u4e2d\u7684\u6709\u5e8f\u6001\u5728\u4e8c\u7ef4\u60c5\u51b5\u4e0b\u5c55\u73b0\u51fa\u4e86\u5e73\u8861\u6001\u4e0d\u53ef\u80fd\u5b9e\u73b0\u7684\u957f\u7a0b\u5e8f\uff0c\u867d\u7136\u5728\u4ed6\u4eec1995\u5e74\u7684\u8bba\u6587\u4e2d\u5e76\u6ca1\u6709\u63d0\u53ca\u8fd9\u4e2a\u91cd\u8981\u7684\u7ed3\u679c[23]\uff0c\u4f46\u901a\u8fc7J.Toner\u548c\u6d82\u8c6b\u6d77\u5bf9\u5e8f\u53c2\u91cf\u573a\u6d41\u4f53\u52a8\u529b\u5b66\u65b9\u7a0b\u7684\u52a8\u529b\u5b66\u91cd\u6574\u5316\u7fa4\u7684\u7406\u8bba\u5206\u6790\uff0c\u8fd9\u4e00\u884c\u4e3a\u5f88\u5feb\u5f97\u4ee5\u8bc1\u5b9e[24]\u3002\u5bf9\u4e8e\u5e73\u8861\u6001\u4f53\u7cfb\uff0c1966\u5e74Mermin\u2014Wagner\u5b9a\u7406\u6307\u51fa\u5177\u6709\u8fde\u7eed\u65cb\u8f6c\u5bf9\u79f0\u6027\u7684\u4f53\u7cfb\u5728\u4e8c\u7ef4\u60c5\u51b5\u4e0b\u662f\u4e0d\u53ef\u80fd\u5b58\u5728\u957f\u7a0b\u5e8f\u7684\uff0c\u8fd9\u5728\u6570\u5b66\u4e0a\u53ef\u4ee5\u88ab\u4e25\u683c\u8bc1\u660e\u3002\u800c20\u4e16\u7eaa70\u5e74\u4ee3\u7684Berezinskii\u2014Kosterlitz\u2014Thouless<\/span>(BKT)<\/span>\u7406\u8bba\u5219\u6307\u51fa\u8fd9\u6837\u7684\u4f53\u7cfb\u53ef\u4ee5\u5b58\u5728\u5e8f\u53c2\u91cf\u5173\u8054\u51fd\u6570\u5448\u5e42\u6307\u6570\u8870\u51cf\u7684\u51c6\u957f\u7a0b\u5e8f\uff0c\u5728\u70ed\u529b\u5b66\u6781\u9650\u4e0b\u6709\u5e8f\u6001\u7684\u5e8f\u53c2\u91cf\u4f9d\u7136\u8d8b\u4e8e0\u3002\u5bf9\u4e8eVicsek\u6a21\u578b\u8fd9\u6837\u7684\u81ea\u9a71\u52a8\u4f53\u7cfb\uff0c\u4e2a\u4f53\u7684\u81ea\u9a71\u52a8\u884c\u4e3a\u663e\u7136\u7834\u574f\u4e86\u5e73\u8861\u6001\u6761\u4ef6\uff0cMermin\u2014Wagner\u5b9a\u7406\u7684\u524d\u63d0\u5c31\u4e0d\u80fd\u6210\u7acb\u3002\u7269\u7406\u4e0a\u7684\u5173\u952e\u5728\u4e8e\u6781\u5316\u5e8f\u53c2\u91cf\u573a\u5bf9\u5e94\u7684\u81ea\u9a71\u52a8\u901f\u5ea6\u573a\u5fc5\u7136\u5bfc\u81f4\u975e\u7ebf\u6027\u7684\u5bf9\u6d41\u9879\uff0c\u8fd9\u4e00\u5bf9\u6d41\u9879\u7684\u4f5c\u7528\u4e0d\u4ec5\u63ed\u793a\u4e86\u8be5\u4f53\u7cfb\u4e0e\u5e73\u8861\u6001\u5b8f\u89c2\u6d41\u4f53\u52a8\u529b\u5b66\u7684\u672c\u8d28\u533a\u522b\uff0c\u5e76\u4e14\u8d77\u5230\u4e86\u76f4\u63a5\u7a33\u5b9a\u957f\u7a0b\u5e8f\u7684\u4f5c\u7528[25]\u3002<\/span><\/p>\n


<\/p>\n

T. Vicsek\uff0cJ. Toner\u548c\u6d82\u8c6b\u6d77\u5bf9\u4e8e\u81ea\u9a71\u52a8\u4f53\u7cfb\u7684\u7814\u7a76\u582a\u79f0\u6d3b\u6027\u7269\u8d28\u7814\u7a76\u7684\u5960\u57fa\u6027\u5de5\u4f5c<\/span>(\u4e09\u4eba\u4e00\u8d77\u88ab\u6388\u4e88\u4e862020\u5e74\u5ea6\u7684\u6602\u8428\u683c\u5956\uff0c\u8be5\u5956\u8868\u5f70\u7edf\u8ba1\u7269\u7406\u7406\u8bba\u65b9\u9762\u7684\u6770\u51fa\u7814\u7a76\u5de5\u4f5c)<\/span>\uff0c\u4e0d\u8bba\u662fVicsek\u6a21\u578b\uff0c\u8fd8\u662f\u6d41\u4f53\u52a8\u529b\u5b66\u7406\u8bba\u90fd\u5bf9\u540e\u7eed\u7684\u5de5\u4f5c\u5177\u6709\u975e\u5e38\u91cd\u8981\u7684\u542f\u53d1\u610f\u4e49[2\uff0c25\u201427]\u3002\u8fd9\u7c7b\u975e\u5e73\u8861\u4f53\u7cfb\u76f8\u53d8\u4e2d\u4f9d\u7136\u53ef\u80fd\u5b58\u5728\u666e\u9002\u6027\u7684\u7406\u5ff5\uff0c\u4f7f\u7269\u7406\u5b66\u5bb6\u4e50\u4e8e\u5c1d\u8bd5\u65b0\u7684\u6a21\u578b\u53bb\u63cf\u8ff0\u5e26\u6709\u666e\u904d\u610f\u4e49\u7684\u6d3b\u6027\u7269\u8d28\u4f53\u7cfb\u3002<\/span><\/p>\n


<\/p>\n

\n
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3.2 \u6d3b\u6027\u7269\u8d28\u7684\u5bf9\u79f0\u6027\u5206\u7c7b\u53ca\u76f8\u6001<\/span><\/strong><\/span><\/p>\n


<\/span><\/strong><\/span><\/p>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n

\u7c7b\u6bd4\u4e8e\u8f6f\u7269\u8d28\u4f53\u7cfb\u4e2d\u901a\u8fc7\u76f8\u4e92\u4f5c\u7528\u53d6\u5411\u5bf9\u79f0\u6027\u5212\u5206\u4e3a\u6781\u5316\u6db2\u6676\u3001\u5411\u5217\u578b\u6db2\u6676\uff0c\u5728\u6d3b\u6027\u7269\u8d28\u4f53\u7cfb\u901a\u8fc7\u589e\u52a0\u81ea\u9a71\u52a8\u53d6\u5411\uff0c\u6211\u4eec\u53ef\u4ee5\u7b80\u5355\u5212\u5206\u51fa\u56db\u7c7b\u6d3b\u6027\u7269\u8d28\u7684\u5bf9\u79f0\u7c7b\u578b<\/span>(\u56fe3)<\/span>[2\uff0c26]\u3002\u56fe\u4e2d\u7c92\u5b50\u7684\u8f6e\u5ed3\u4ee3\u8868\u76f8\u4e92\u4f5c\u7528\u7684\u7c7b\u578b\uff0c\u800c\u7bad\u5934\u4ee3\u8868\u67d0\u4e2a\u65f6\u523b\u53ef\u80fd\u7684\u8fd0\u52a8\u65b9\u5411\u3002<\/span><\/p>\n


<\/p>\n

\u6240\u6709\u8fd9\u4e9b\u7c7b\u578b\u7684\u6a21\u578b\u90fd\u6709\u4e00\u4e2a\u7279\u70b9\uff0c\u5373\u8fd0\u52a8\u65b9\u5411\u548c\u6781\u5316\u65b9\u5411\u5b58\u5728\u6781\u5176\u7d27\u5bc6\u7684\u5173\u7cfb\u3002\u5373\u4f7f\u5bf9\u4e8e\u56fe\u4e2d\u7684\u53cc\u5411\u7bad\u5934\uff0c\u7c92\u5b50\u7684\u8fd0\u52a8\u4e3b\u8981\u4e5f\u662f\u6cbf\u7740\u8f74\u5411\u6269\u6563\uff0c\u800c\u4e0d\u662f\u4fa7\u5411\u8fd0\u52a8\u3002\u7531\u6b64\u53ef\u89c1\uff0c\u5728\u8fd9\u7c7b\u6d3b\u6027\u7269\u8d28\u4f53\u7cfb\uff0c\u5c40\u90e8\u96c6\u4f53\u8fd0\u52a8\u548c\u7cfb\u7edf\u7684\u53d6\u5411\u573a\u7d27\u5bc6\u76f8\u5173\u3002\u540c\u65f6\u7c92\u5b50\u7684\u8fd0\u52a8\u5fc5\u7136\u5e26\u6765\u5bc6\u5ea6\u573a\u7684\u6f14\u5316\uff0c\u800c\u5bc6\u5ea6\u7684\u9ad8\u4f4e\u53c8\u5c06\u76f4\u63a5\u51b3\u5b9a\u5c40\u90e8\u7684\u6709\u5e8f\u5ea6\u3002\u8fd9\u5bfc\u81f4\u5728\u63cf\u8ff0\u7cfb\u7edf\u7684\u5b8f\u89c2\u6d41\u4f53\u52a8\u529b\u5b66\u65b9\u7a0b\u4e2d\uff0c\u5bc6\u5ea6\u573a\u548c\u5e8f\u53c2\u91cf\u573a\u6709\u7d27\u5bc6\u7684\u8026\u5408\u5173\u7cfb\uff0c\u5728\u5f88\u591a\u60c5\u51b5\u4e0b\u8fd9\u4f1a\u8bf1\u53d1\u5747\u5300\u6709\u5e8f\u6001\u7684\u957f\u6ce2\u5931\u7a33\u3002<\/span><\/p>\n


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<\/section>\n
\u56fe3 (a)\u6839\u636e\u7c92\u5b50\u76f8\u4e92\u4f5c\u7528\u5bf9\u79f0\u6027\u53ca\u8f74\u5411\u8fd0\u52a8\u65b9\u5f0f\u5206\u7c7b\u7684\u4e8c\u7ef4\u6d3b\u6027\u7269\u8d28\u793a\u610f\u56fe\u3002\u4e0a\u6392\u84dd\u8272\u7b26\u53f7\u4ee3\u8868\u76f8\u4e92\u4f5c\u7528\u5bf9\u79f0\u6027\uff0c\u5de6\u6392\u7ea2\u8272\u7bad\u5934\u4ee3\u8868\u8fd0\u52a8\u65b9\u5f0f\uff0c\u53cc\u5411\u7bad\u5934\u4ee3\u8868\u9a71\u52a8\u65b9\u5411\u53ef\u53d1\u751f\u81ea\u53d1\u53cd\u8f6c\uff1b(b)\u2014(e)\u76f8\u5bf9\u5e94\u7684\u7cfb\u7edf\u4e2d\u53ef\u80fd\u51fa\u73b0\u7684\u6f14\u5316\u56fe\u6848\u3002(b)\u7ecf\u5178 Vicsek \u6a21\u578b\u4e2d\u5728\u76f8\u53d8\u70b9\u9644\u8fd1\u51fa\u73b0\u7684\u6761\u5e26\u72b6\u7ed3\u6784\u3002\u989c\u8272\u53d8\u5316\u4ee3\u8868\u5bc6\u5ea6\uff0c\u84dd\u8272\u4e3a\u4f4e\u5bc6\u5ea6\u4f4e\u6709\u5e8f\u5ea6\u533a\u57df\uff0c\u9ec4\u8272\u4e3a\u9ad8\u5bc6\u5ea6\u9ad8\u6709\u5e8f\u5ea6\u533a\u57df\uff0c\u767d\u8272\u7bad\u5934\u4ee3\u8868\u5168\u5c40\u8fd0\u52a8\u65b9\u5411[26]\uff1b(c)\u9a71\u52a8\u6746\u72b6\u7c92\u5b50\u6a21\u578b\u4e2d\u51fa\u73b0\u7684\u6781\u5316\u96c6\u56e2\u7ed3\u6784\uff0c\u989c\u8272\u53d8\u5316\u4ee3\u8868\u9a71\u52a8\u65b9\u5411\u53d8\u5316[33]\uff1b(d)\u968f\u673a\u6643\u52a8\u7684\u6781\u5316\u7c92\u5b50\u6709\u5e8f\u6001\u4e2d\u7f3a\u9677\u5bf9\u6f14\u5316\u5bfc\u81f4\u7684+1\u7f3a\u9677\u65b9\u5411\u7684\u5bc6\u5ea6\u7a7a\u6d1e\uff0c\u7834\u574f\u4e86\u5e8f\u53c2\u91cf\u573a\u7684\u5c40\u90e8\u6709\u5e8f\u6027\uff0c\u989c\u8272\u53d8\u5316\u4ee3\u8868\u7a7a\u95f4\u53d6\u5411\u53d8\u5316[34]\uff1b(e)\u6d3b\u6027\u5411\u5217\u578b\u4f53\u7cfb\u6709\u5e8f\u2014\u65e0\u5e8f\u8f6c\u53d8\u70b9\u9644\u8fd1\u7684\u65f6\u7a7a\u6df7\u6c8c\u6f14\u5316\uff0c\u989c\u8272\u4ee3\u8868\u5bc6\u5ea6\u53d8\u5316[29\uff0c31]<\/span><\/section>\n


<\/p>\n

\u5728\u76f8\u53d8\u70b9\u9644\u8fd1\uff0c\u4f53\u7cfb\u7684\u6709\u5e8f\u5ea6\u5bf9\u5bc6\u5ea6\u6709\u975e\u5e38\u654f\u611f\u7684\u4f9d\u8d56\u5173\u7cfb\uff0c\u5bfc\u81f4\u5747\u5300\u6709\u5e8f\u6001\u6700\u5bb9\u6613\u5728\u76f8\u53d8\u70b9\u9644\u8fd1\u53d1\u751f\u5931\u7a33[28\uff0c29]\u3002\u6b63\u662f\u8fd9\u4e00\u673a\u5236\u5bfc\u81f4Vicsek\u6a21\u578b\u5728\u6709\u5e8f\u2014\u65e0\u5e8f\u8f6c\u53d8\u533a\u95f4\u5f62\u6210\u7c7b\u4f3c\u4e8e\u8fd1\u6676\u76f8\u7684\u6761\u5e26\u7ed3\u6784<\/span>(\u56fe3(b))<\/span>[22\uff0c28]\uff0c\u800c\u5728\u6d3b\u6027\u5411\u5217\u578b<\/span>(\u56fe3(e))<\/span>\u548c\u81ea\u9a71\u52a8\u68d2\u72b6\u7c92\u5b50\u4f53\u7cfb<\/span>(\u56fe3(c))<\/span>\uff0c\u5219\u5448\u73b0\u51fa\u6761\u5e26\u7ed3\u6784\u6216\u8005\u62d3\u6251\u7f3a\u9677\u7684\u65f6\u7a7a\u6df7\u6c8c\u52a8\u529b\u5b66[29\u201433]\u3002\u8fd9\u4e9b\u975e\u7ebf\u6027\u52a8\u529b\u5b66\u7ed3\u6784\u90fd\u76f4\u63a5\u7834\u574f\u4e86\u4f53\u7cfb\u5728\u76f8\u53d8\u70b9\u9644\u8fd1\u7684\u4e34\u754c\u6027[22\uff0c30]\u3002\u4ece\u8fd9\u65b9\u9762\u770b\uff0c\u8f74\u5411\u968f\u673a\u6643\u52a8\u7684\u6781\u5316\u7c92\u5b50\u662f\u4e2a\u4f8b\u5916<\/span>(\u56fe3(d))<\/span>\uff0c\u6a21\u62df\u548c\u5bf9\u4f53\u7cfb\u6d41\u4f53\u52a8\u529b\u5b66\u65b9\u7a0b\u7684\u5206\u6790\u90fd\u8868\u660e\uff0c\u8fd9\u4e2a\u4f53\u7cfb\u5728\u76f8\u53d8\u70b9\u9644\u8fd1\u5747\u5300\u6001\u53ef\u4ee5\u662f\u7a33\u5b9a\u7684[34]\uff0c\u6b63\u662f\u8fd9\u4e00\u7279\u6027\u4f7f\u8be5\u7cfb\u7edf\u6210\u4e3a\u8fd9\u56db\u7c7b\u6a21\u578b\u4e2d\u552f\u4e00\u53ef\u4ee5\u7814\u7a76\u76f8\u53d8\u4e34\u754c\u884c\u4e3a\u7279\u6027\u7684\u6d3b\u6027\u7269\u8d28\u4f53\u7cfb\u3002<\/span><\/p>\n


<\/p>\n

\n
\n
\n
\n

3.3 \u6d3b\u6027\u5e03\u6717\u7c92\u5b50\u7684\u6c14\u6db2\u76f8\u5206\u79bb<\/span><\/strong><\/p>\n


<\/span><\/strong><\/p>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n

\u63cf\u8ff0\u4e0a\u8ff0\u6d3b\u6027\u7269\u8d28\u4f53\u7cfb\u5927\u5c3a\u5ea6\u884c\u4e3a\u7684\u5e8f\u53c2\u91cf\u573a\u9700\u8981\u662f\u4e00\u4e2a\u77e2\u91cf\u573a\u6216\u8005\u5f20\u91cf\u573a\uff0c\u5728\u6570\u5b66\u4e0a\u662f\u6bd4\u8f83\u590d\u6742\u7684\uff0c\u4e00\u822c\u9700\u8981\u591a\u4e2a\u76f8\u4e92\u8026\u5408\u7684\u6d41\u4f53\u52a8\u529b\u5b66\u65b9\u7a0b\u624d\u80fd\u523b\u753b\u5176\u70ed\u529b\u5b66\u6781\u9650\u884c\u4e3a\u3002\u7531\u4e8e\u81ea\u9a71\u52a8\u7c92\u5b50\u672c\u8eab\u7684\u9a71\u52a8\u65b9\u5411\u662f\u4e2a\u77e2\u91cf\uff0c\u8fd9\u79cd\u590d\u6742\u6027\u4f3c\u4e4e\u662f\u65e0\u6cd5\u907f\u514d\u7684\u3002\u5982\u679c\u6211\u4eec\u8003\u8651\u81ea\u9a71\u52a8\u7684\u7403\u5f62\u9897\u7c92\uff0c\u76f8\u4e92\u4f5c\u7528\u53ea\u5b58\u5728\u6392\u65a5\u6548\u5e94\uff0c\u90a3\u4e48\u5728\u957f\u65f6\u95f4\u4e0a\u770b\u81ea\u9a71\u52a8\u6548\u5e94\u7531\u4e8e\u89d2\u5ea6\u7684\u65cb\u8f6c\u6269\u6563\u53ea\u80fd\u8d21\u732e\u4e00\u4e2a\u6709\u6548\u7684\u7c92\u5b50\u6269\u6563\uff0c\u63cf\u8ff0\u8fd9\u7c7b\u4f53\u7cfb\u7684\u6d41\u4f53\u52a8\u529b\u5b66\u53d8\u91cf\u53ea\u9700\u8981\u4e00\u4e2a\u6807\u91cf\u573a\u5bc6\u5ea6[35]\u3002\u8fd9\u5c31\u662f\u6d3b\u6027\u7269\u8d28\u4e2d\u5e38\u88ab\u63d0\u53ca\u7684\u6d3b\u6027\u5e03\u6717\u7c92\u5b50<\/span>(active Brownian particles)<\/span>[36]\u3002 <\/span><\/p>\n


<\/p>\n

\u7531\u4e8e\u7c92\u5b50\u95f4\u76f8\u4e92\u6392\u65a5\uff0c\u81ea\u9a71\u52a8\u5bfc\u81f4\u7684\u6709\u6548\u6269\u6563\u5c06\u53d6\u51b3\u4e8e\u5468\u56f4\u7684\u7c92\u5b50\u5bc6\u5ea6\uff0c\u5904\u4e8e\u5c40\u90e8\u9ad8\u5bc6\u5ea6\u533a\u57df\u7684\u7c92\u5b50\u6709\u6548\u6269\u6563\u4f1a\u76f8\u5bf9\u8f83\u6162\u3002\u5f53\u4f53\u7cfb\u7684\u672c\u4f53\u5bc6\u5ea6\u6216\u8005\u4f53\u7cfb\u7684\u89d2\u5ea6Pectlet\u6570<\/span>(\u4ee5\u7c92\u5b50\u76f4\u5f84\u4e3a\u5355\u4f4d\u957f\u5ea6\u7ea6\u5316\u7684\u81ea\u9a71\u52a8\u901f\u5ea6\u548c\u89d2\u5ea6\u6269\u6563\u7684\u6bd4\u503c)<\/span>\u5230\u8fbe\u4e00\u5b9a\u9608\u503c\u65f6\u7cfb\u7edf\u4f1a\u4ea7\u751f\u81ea\u53d1\u7684\u76f8\u5206\u79bb\u3002\u503c\u5f97\u6ce8\u610f\u7684\u662f\uff0c\u8fd9\u91cc\u53d1\u751f\u76f8\u5206\u79bb\u7684\u4f53\u7cfb\u4e2d\u7c92\u5b50\u95f4\u53ea\u5b58\u5728\u6392\u65a5\u76f8\u4e92\u4f5c\u7528\uff0c\u8fd9\u5728\u5e73\u8861\u6001\u4e0b\u662f\u4e0d\u53ef\u80fd\u7684\u3002\u8fd9\u4e00\u73b0\u8c61\u53ef\u4ee5\u88ab\u8ba4\u4e3a\u662f\u4e00\u79cd\u8fd0\u52a8\u8bf1\u5bfc\u7684\u76f8\u5206\u79bb[36\u201439]\u3002 <\/span><\/p>\n


<\/p>\n

\u5bf9\u8fd9\u79cd\u7279\u6b8a\u7684\u6d3b\u6027\u5e03\u6717\u7c92\u5b50\u4f53\u7cfb\u7684\u76f8\u5206\u79bb\u884c\u4e3a\u7684\u7814\u7a76\u6d89\u53ca\u5230\u591a\u4e2a\u91cd\u8981\u7684\u95ee\u9898\uff0c\u6bd4\u5982\u4f53\u7cfb\u4e2d\u6c14\u6db2\u754c\u9762\u8868\u9762\u5f20\u529b\u7684\u6b63\u8d1f\u53f7\u95ee\u9898[40\u201442]\u3001\u76f8\u5206\u79bb\u7684\u751f\u957f\u52a8\u529b\u5b66\u6162\u5316[43]\u4ee5\u53ca\u76f8\u5206\u79bb\u4e34\u754c\u70b9\u7684\u666e\u9002\u7c7b[44\uff0c45]\u7b49\u7b49\u3002\u63cf\u8ff0\u8fd9\u4e9b\u95ee\u9898\u7684\u5173\u952e\u662f\u627e\u5230\u51c6\u786e\u7684\u63cf\u8ff0\u4f53\u7cfb\u5927\u5c3a\u5ea6\u884c\u4e3a\u7684\u6d41\u4f53\u52a8\u529b\u5b66\u65b9\u7a0b\u3002\u76ee\u524d\u5df2\u7ecf\u53d1\u73b0\uff0c\u6709\u522b\u4e8e\u5e73\u8861\u6001\u7684\u76f8\u5206\u79bb\u7406\u8bba\uff0c\u6d41\u4f53\u52a8\u529b\u5b66\u65b9\u7a0b\u4e2d\u5fc5\u987b\u5f15\u5165\u9ad8\u9636\u7684\u975e\u7ebf\u6027\u9879[46]\u3002\u8fd9\u4e9b\u9879\u7684\u5b58\u5728\u6765\u6e90\u4e8e\u81ea\u9a71\u52a8\u6548\u5e94\u5e76\u4e14\u4e0e\u7c92\u5b50\u95f4\u7684\u6392\u65a5\u4f5c\u7528\u4ee5\u53ca\u7c92\u5b50\u95f4\u7684\u7a7a\u95f4\u5173\u8054\u6709\u5173\uff0c\u5e76\u4e14\u4e0d\u80fd\u901a\u8fc7\u6709\u6548\u7684\u81ea\u7531\u80fd\u6cdb\u51fd\u5f97\u5230\u3002\u8fd9\u5bf9\u5b9a\u4e49\u4f53\u7cfb\u7684\u8868\u9762\u5f20\u529b\u7b49\u70ed\u529b\u5b66\u91cf\u9020\u6210\u4e86\u56f0\u96be\u3002\u5373\u4f7f\u5728\u9ad8\u5bc6\u5ea6\u6db2\u76f8\uff0c\u5927\u5c3a\u5ea6\u7684\u6a21\u62df\u8ba1\u7b97\u8868\u660e\u4f53\u7cfb\u4e2d\u4f1a\u81ea\u53d1\u4ea7\u751f\u6c14\u6ce1[47]\uff0c\u5e76\u5177\u6709\u81ea\u7ec4\u7ec7\u4e34\u754c\u6027[43]\u3002\u6709\u5e8f\u76f8\u7684\u5947\u5f02\u6027\u80fd\u5426\u5f71\u54cd\u548c\u6539\u53d8\u4f53\u7cfb\u76f8\u5206\u79bb\u4e34\u754c\u70b9\u7684\u666e\u9002\u7c7b\uff0c\u76ee\u524d\u5c1a\u5f85\u89c2\u5bdf\uff0c\u7406\u89e3\u8fd9\u7c7b\u4f53\u7cfb\u7684\u76f8\u5206\u79bb\u672c\u8d28\u53ef\u80fd\u5c1a\u9700\u65f6\u95f4\u3002<\/span><\/p>\n


<\/p>\n

\n
\n
\n
\n

3.4 \u6d3b\u6027\u6e4d\u6d41\u53ca\u7f3a\u9677\u8fd0\u52a8\u884c\u4e3a<\/span><\/strong><\/span><\/p>\n


<\/span><\/p>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n

\u5982\u679c\u6211\u4eec\u8003\u8651\u81ea\u9a71\u52a8\u7c92\u5b50\u5904\u4e8e\u6d41\u4f53\u4e4b\u4e2d\uff0c\u90a3\u4e48\u5b83\u4eec\u7684\u81ea\u9a71\u52a8\u884c\u4e3a\u5fc5\u7136\u5bfc\u81f4\u6d41\u4f53\u7684\u8fd0\u52a8\u3002\u5728\u81ea\u9a71\u52a8\u7c92\u5b50\u548c\u6d41\u4f53\u7684\u6df7\u5408\u4f53\u7cfb\u7684\u672c\u4f53\u76f8\u4e2d\uff0c\u4efb\u4f55\u5185\u90e8\u4f5c\u7528\u5fc5\u7136\u9075\u5b88\u52a8\u91cf\u5b88\u6052\uff0c\u8fd9\u5bfc\u81f4\u7c92\u5b50\u7684\u81ea\u9a71\u52a8\u8fd0\u52a8\u5bf9\u6d41\u4f53\u65bd\u52a0\u7684\u4f5c\u7528\u4ece\u8fdc\u8ddd\u79bb\u770b\u662f\u4e00\u5bf9\u529b\u5076[27]\u3002\u5927\u91cf\u53d6\u5411\u6709\u5e8f\u81ea\u9a71\u52a8\u7c92\u5b50\u7684\u9a71\u52a8\u884c\u4e3a\uff0c\u901a\u8fc7\u8fd9\u4e9b\u529b\u5076\u53e0\u52a0\uff0c\u53ea\u8981\u7c92\u5b50\u6392\u5217\u4e0d\u662f\u5b8c\u7f8e\u5bf9\u9f50\uff0c\u5c31\u4f1a\u5bfc\u81f4\u6d41\u4f53\u5728\u5927\u5c3a\u5ea6\u4e0a\u4ea7\u751f\u6d41\u52a8<\/span>(\u56fe4(a))<\/span>\u3002\u800c\u81ea\u9a71\u52a8\u7c92\u5b50\u672c\u8eab\u5c31\u5728\u6d41\u4f53\u4e4b\u4e2d\uff0c\u5176\u5e73\u52a8\u548c\u8f6c\u52a8\u90fd\u5c06\u53d7\u5236\u4e8e\u6d41\u573a\u7684\u5f3a\u5ea6\u53ca\u5c40\u90e8\u7684\u6da1\u5ea6\u548c\u5e94\u53d8[48]\u3002\u8fd9\u5bf9\u7c92\u5b50\u53d6\u5411\u7684\u4f5c\u7528\u5f62\u6210\u4e00\u5957\u6b63\u53cd\u9988\u7684\u673a\u5236\uff0c\u5bfc\u81f4\u9ad8\u5bc6\u5ea6\u6709\u5e8f\u6001\u4e5f\u4f1a\u53d1\u751f\u65f6\u7a7a\u5931\u7a33[49]\u3002\u8fd9\u5728\u9ad8\u5bc6\u5ea6\u7684\u6d3b\u6027\u76f8\u5217\u76f8\u4e2d\u975e\u5e38\u660e\u663e\uff0c\u5f62\u6210\u6240\u8c13\u7684\u6d3b\u6027\u6e4d\u6d41[6]\u3002\u4e8b\u5b9e\u4e0a\u5373\u4f7f\u6ca1\u6709\u76f4\u63a5\u7684\u6d41\u4f53\u76f8\u4e92\u4f5c\u7528\uff0c\u5982\u679c\u9ad8\u5bc6\u5ea6\u65f6\u7c92\u5b50\u8fc1\u79fb\u5bfc\u81f4\u7684\u6324\u538b\u548c\u6392\u65a5\u5bf9\u7c92\u5b50\u7684\u53d6\u5411\u6709\u76f4\u63a5\u7684\u4f5c\u7528\uff0c\u6709\u5e8f\u6001\u4e5f\u4f1a\u53d1\u751f\u7c7b\u4f3c\u7684\u5931\u7a33[32\uff0c50\uff0c51]\u3002<\/span><\/p>\n


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4.<\/strong><\/strong>\u6d3b\u6027\u7269\u8d28\u7684\u70ed\u529b\u5b66<\/span><\/strong><\/p>\n<\/section>\n

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<\/p>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n

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5.<\/strong><\/strong>\u6d3b\u6027\u7269\u8d28\u7684<\/span><\/strong>\u62d3\u6251\u8fb9\u7f18\u6001<\/span><\/strong><\/span><\/p>\n<\/section>\n

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\u56fe8 (a)\u6d3b\u6027\u8f6c\u5b50\u7cfb\u7edf\u53ca\u5176\u7a33\u6001\u7684\u8fb9\u754c\u6d41\u573a\u5206\u5e03[81]\uff1b(b)\u5f53\u7cfb\u7edf\u8fb9\u754c\u5b58\u5728\u969c\u788d\u7269\u65f6\uff0c\u6d3b\u6027\u8f6c\u5b50\u7684\u8fb9\u7f18\u6d41\u80fd\u591f\u5355\u5411\u3001\u4e0d\u53d7\u6563\u5c04\u5730\u7ed5\u8fc7\u969c\u788d\u7269[83]\uff1b(c)\u5728\u8017\u5c3d\u529b\u7684\u4f5c\u7528\u4e0b\uff0c\u624b\u6027\u6d3b\u6027\u6d41\u4f53\u7684\u8fb9\u7f18\u6d41\u53ef\u4ee5\u5bf9\u60ac\u6d6e\u7684\u975e\u6d3b\u6027\u8d27\u7269\u8fdb\u884c\u62d3\u6251\u4fdd\u62a4\u7684\u8fb9\u754c\u8f93\u8fd0[84]\uff0c\u5176\u4e2d\u975e\u6d3b\u6027\u8d27\u7269(\u5927\u9897\u7c92)\u53ef\u4ee5\u5355\u5411\u9c81\u68d2\u5730\u7ed5\u8fc7\u8fb9\u754c\u5904\u7684\u969c\u788d\u7269
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6.<\/strong><\/strong>\u8ba8\u8bba\u548c\u5c55\u671b<\/span><\/strong><\/span><\/p>\n<\/section>\n

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