{"id":31293,"date":"2021-12-24T19:33:49","date_gmt":"2021-12-24T11:33:49","guid":{"rendered":"https:\/\/swarma.org\/?p=31293"},"modified":"2021-12-24T19:33:49","modified_gmt":"2021-12-24T11:33:49","slug":"%e5%89%8d%e6%b2%bf%e9%80%9f%e9%80%92%ef%bc%9a%e7%94%9f%e5%91%bd%e7%b3%bb%e7%bb%9f%e9%9b%86%e4%bd%93%e8%a1%8c%e4%b8%ba%e7%9a%84%e8%bf%9e%e7%bb%ad%e5%92%8c%e4%b8%8d%e8%bf%9e%e7%bb%ad%e7%9b%b8%e5%8f%98","status":"publish","type":"post","link":"https:\/\/swarma.org\/?p=31293","title":{"rendered":"\u524d\u6cbf\u901f\u9012\uff1a\u751f\u547d\u7cfb\u7edf\u96c6\u4f53\u884c\u4e3a\u7684\u8fde\u7eed\u548c\u4e0d\u8fde\u7eed\u76f8\u53d8"},"content":{"rendered":"
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Vicsek\u6a21\u578b<\/span><\/strong>[1]\u662f\u7814\u7a76\u751f\u547d\u7cfb\u7edf\u96c6\u4f53\u8fd0\u52a8\u7684\u4e00\u4e2a\u7b80\u7ea6\u6a21\u578b\uff0c\u7531\u81ea\u6211\u63a8\u8fdb\u7684\u70b9\u72b6\u7c92\u5b50\u7ec4\u6210\u3002\u5728\u5f3a\u566a\u58f0\u6216\u4f4e\u5bc6\u5ea6\u65f6\uff0c\u7c92\u5b50\u603b\u4f53\u4e0a\u968f\u673a\u8fd0\u52a8\uff0c\u6574\u4e2a\u7cfb\u7edf\u5c31\u50cf\u662f\u65e0\u5e8f\u7684\u6c14\u4f53\u3002\u800c\u5728\u9ad8\u5bc6\u5ea6\u6216\u4f4e\u566a\u58f0\u60c5\u51b5\u4e0b\uff0c\u7c92\u5b50\u7684\u901f\u5ea6\u503e\u5411\u4e8e\u4e0e\u76f8\u90bb\u7c92\u5b50\u4fdd\u6301\u4e00\u81f4\uff0c\u6574\u4f53\u671d\u5411\u540c\u4e00\u4e2a\u65b9\u5411\u8fd0\u52a8\uff0c\u4ece\u800c\u6d8c\u73b0\u51fa\u96c6\u4f53\u8fd0\u52a8\uff0c\u7ecf\u5386\u4ece\u65e0\u5e8f\u5230\u6709\u5e8f\u7684\u76f8\u53d8\u3002<\/span><\/p>\n


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\u5728\u63d0\u51faVicsek\u6a21\u578b\u7684\u539f\u6587\u4e2d\uff0c\u4e0a\u8ff0\u7fa4\u4f53\u8fd0\u52a8\u7684\u76f8\u53d8\u88ab\u8ba4\u4e3a\u662f\u8fde\u7eed\u7684[1]\u3002\u4f46\u540e\u7eed\u8fdb\u4e00\u6b65\u7814\u7a76\u5bf9\u8fd9\u4e00\u89c2\u70b9\u63d0\u51fa\u4e86\u8d28\u7591\uff0c\u8fd9\u4e9b\u7814\u7a76\u8005\u8ba4\u4e3a\uff0cViscek\u7b49\u4eba\u89c2\u6d4b\u5230\u7684\u8fde\u7eed\u76f8\u53d8\u5b9e\u9645\u4e0a\u662f\u7531\u4e8e\u6709\u9650\u5c3a\u5bf8\u6548\u5e94<\/span>\uff08finite-size effect\uff09<\/span>\u5bfc\u81f4\u7684\uff0c\u96c6\u4f53\u8fd0\u52a8\u7684\u76f8\u53d8\u5b9e\u9645\u4e0a\u662f\u4e0d\u8fde\u7eed\u7684[2]\u3002\u7531\u4e8e\u8fd9\u4e9b\u7814\u7a76\u4e0d\u80fd\u91c7\u7528\u96c6\u4f53\u8fd0\u52a8\u76f8\u53d8\u7cbe\u786e\u7684\u5e8f\u53c2\u91cf\uff0c\u4e5f\u6ca1\u6709\u8fdb\u884c\u6709\u9650\u5c3a\u5ea6\u6807\u5ea6\u6027\u7684\u7cfb\u7edf\u5206\u6790\uff0c\u5b83\u4eec\u5173\u4e8e\u76f8\u53d8\u6027\u8d28\u7684\u7ed3\u8bba\u65e0\u6cd5\u6210\u4e3a\u5b9a\u8bba\u3002<\/span><\/p>\n


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\u5728\u4e34\u754c\u70b9\u9644\u8fd1\uff0c\u03c3I<\/sub><\/span> \u9075\u5faa\u6709\u9650\u5c3a\u5bf8\u6807\u5ea6\u5f62\u5f0f\uff08finite-size scaling form\uff09<\/span>\uff1a<\/span><\/p>\n


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\u8fd9\u91cc L \u662f\u7cfb\u7edf\u7684\u5c3a\u5bf8\uff0c\u662f\u7ea6\u5316\u566a\u58f0\uff0c\u03b2 \u662f\u5e8f\u53c2\u91cf \u03c3I<\/sub><\/span> \u7684\u4e34\u754c\u6307\u6570\uff0c\u03bd \u662f\u5173\u8054\u957f\u5ea6\u7684\u4e34\u754c\u6307\u6570\u3002\u03b2>0 \u65f6\uff0c\u7cfb\u7edf\u53d1\u751f\u8fde\u7eed\u76f8\u53d8\uff1b\u03b2=0 \u65f6\uff0c\u5e8f\u53c2\u91cf\u51fa\u73b0\u8df3\u53d8\uff0c\u7cfb\u7edf\u53d1\u751f\u4e0d\u8fde\u7eed\u76f8\u53d8\u3002<\/span><\/p>\n


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\u6700\u8fd1\uff0c\u672c\u5f81\u5fae\u89c2\u6001\u65b9\u6cd5\u88ab\u7528\u4e8e\u7814\u7a76Vicsek\u6a21\u578b\u7684\u76f8\u53d8\u4e0e\u4e34\u754c\u73b0\u8c61\u3002\u5f53\u7cfb\u7edf\u5904\u5728\u5f3a\u566a\u58f0\u73af\u5883\u7684\u65f6\u5019\uff0c\u7c92\u5b50\u7684\u4f4d\u7f6e\u548c\u901f\u5ea6\u65b9\u5411\u90fd\u662f\u968f\u673a\u7684\uff0c\u5b83\u4eec\u7684\u672c\u5f81\u5fae\u89c2\u6001\u4e5f\u6ca1\u6709\u54ea\u4e2a\u5360\u636e\u4e3b\u5bfc\uff0c\u7cfb\u7edf\u5904\u4e8e\u65e0\u5e8f\u72b6\u6001\u3002<\/span><\/p>\n


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\u968f\u7740\u566a\u58f0\u964d\u4f4e\uff0c\u7b2c\u4e00\u5927\u672c\u5f81\u5fae\u89c2\u6001\u7684\u5e8f\u53c2\u91cf \u03c31<\/sub><\/span> \u53d8\u4e3a\u6709\u9650\uff0c\u7cfb\u7edf\u6d8c\u73b0\u51fa\u4e00\u4e2a\u65b0\u7684\u76f8\uff0c\u5373\u672c\u5f81\u5fae\u89c2\u6001 <\/span>u1<\/sub><\/span> <\/span>\uff0c\u5bf9\u5e94\u7684\u4e34\u754c\u6307\u6570 \u03b2=0\u3002\u5982\u56fe1\u6240\u793a\uff0c\u968f\u7740\u566a\u58f0\u51cf\u5f31\uff0c\u7c92\u5b50\u4e4b\u95f4\u7684\u6709\u6548\u76f8\u4e92\u4f5c\u7528\u589e\u5f3a\uff0c\u5f7c\u6b64\u4e4b\u95f4\u8ddd\u79bb\u53d8\u5c0f\uff0c\u5e73\u5747\u90bb\u8fd1\u5bc6\u5ea6\u589e\u5927\uff1b\u566a\u58f0\u51cf\u5c0f\u5230\u67d0\u4e2a\u503c\u7684\u65f6\u5019\uff0c\u4e0e\u6c14-\u6db2\u76f8\u53d8\u76f8\u4f3c\uff0c\u7cfb\u7edf\u4f1a\u53d1\u751f\u4e00\u4e2a\u5bc6\u5ea6\u7684\u4e0d\u8fde\u7eed\u76f8\u53d8<\/strong>\u3002<\/span><\/p>\n


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<\/section>\n

\u56fe1. \u4ece\u4e0a\u5230\u4e0b\u4e3a\u566a\u58f0 \u03b7=6, 3.95, 0.25 \u65f6\uff0c\u7b2c\u4e00\u5927\u672c\u5f81\u5fae\u89c2\u6001 u1<\/sub><\/span> \u7684\u901f\u5ea6\u7a7a\u95f4\u5206\u5e03\uff08a, c, e\uff09\u548c\u90bb\u8fd1\u5bc6\u5ea6\u6da8\u843d\uff08b, d, f\uff09\u3002\u5f53\u566a\u58f0 \u03b71c<\/sub><\/span>=3. 95 \u65f6\uff0c\u5e73\u5747\u90bb\u8fd1\u5bc6\u5ea6\u589e\u5927\uff0c\u7c92\u5b50\u53d1\u751f\u51dd\u805a\uff0c\u7cfb\u7edf\u7ecf\u5386\u5bc6\u5ea6\u7684\u975e\u8fde\u7eed\u76f8\u53d8\u3002<\/span><\/p>\n


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\u5728\u66f4\u5c0f\u7684\u566a\u58f0\u73af\u5883\u4e0b\uff0c\u5982\u56fe2\u6240\u793a\uff0c\u7531\u4e8e\u90bb\u8fd1\u5bc6\u5ea6\u8fdb\u4e00\u6b65\u589e\u5927\uff0c\u7c92\u5b50\u4e4b\u95f4\u7684\u6709\u6548\u76f8\u4e92\u4f5c\u7528\u7ee7\u7eed\u589e\u5f3a\uff0c\u4ece\u800c\u5bfc\u81f4\u7c92\u5b50\u901f\u5ea6\u65b9\u5411\u8d8b\u5411\u4e00\u81f4\uff0c\u7cfb\u7edf\u53d1\u751f\u96c6\u4f53\u8fd0\u52a8\u7684\u76f8\u53d8<\/strong>\u3002\u901a\u8fc7\u6709\u9650\u5c3a\u5ea6\u6807\u5ea6\u6027\u5206\u6790\uff0c\u5f97\u5230\u4e34\u754c\u6307\u6570 \u03b2>0\uff0c\u56e0\u6b64\u8be5\u96c6\u4f53\u8fd0\u52a8\u76f8\u53d8\u662f\u8fde\u7eed\u7684\u3002\u6b64\u76f8\u53d8\u53d1\u751f\u65f6\uff0c\u7cfb\u7edf\u540c\u65f6\u6d8c\u73b0\u4e24\u4e2a\u5e8f\u53c2\u91cf\u76f8\u540c\u3001\u901f\u5ea6\u65b9\u5411\u76f8\u4e92\u5782\u76f4\u7684\u672c\u5f81\u5fae\u89c2\u6001 u<\/span>2<\/sub><\/span> <\/span>\u548c u<\/span>3<\/sub><\/span> <\/span>\u3002<\/span><\/p>\n


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<\/section>\n

\u56fe2. \u566a\u58f0 \u03b7=6, 3.69, 0.25 \u65f6\uff0c\u7b2c\u4e8c\u5927\u672c\u5f81\u5fae\u89c2\u6001 u<\/span>2<\/sub><\/span> \u7684\u901f\u5ea6\u7a7a\u95f4\u5206\u5e03\uff08a, c, e\uff09\u548c\u90bb\u8fd1\u5bc6\u5ea6\u6da8\u843d\uff08b, d, f\uff09\u3002\u5f53\u566a\u58f0 \u03b72c<\/sub><\/span>=3.69 \u65f6\uff0c\u7c92\u5b50\u901f\u5ea6\u65b9\u5411\u53d8\u5f97\u4e00\u81f4\uff0c\u7cfb\u7edf\u7ecf\u5386\u8fde\u7eed\u76f8\u53d8\u3002<\/span><\/p>\n


<\/p>\n

\u4e0a\u8ff0\u7814\u7a76\u8868\u660e\uff0c\u7531Vicsek\u6a21\u578b\u63cf\u8ff0\u7684\u975e\u5e73\u8861\u751f\u547d\u7cfb\u7edf\u80fd\u591f\u51fa\u73b0\u4e24\u79cd\u76f8\u53d8<\/strong>\u3002\u968f\u7740\u566a\u58f0\u51cf\u5f31\uff0c\u9996\u5148\u53d1\u751f\u5bc6\u5ea6\u4e3b\u5bfc\u7684\u6c14-\u6db2\u4e0d\u8fde\u7eed\u76f8\u53d8\uff0c\u5bfc\u81f4\u7c92\u5b50\u95f4\u8ddd\u51cf\u5c0f\u3001\u76f8\u4e92\u4f5c\u7528\u589e\u5f3a\uff0c\u7136\u540e\u7c92\u5b50\u72b6\u6001<\/span>\uff08\u901f\u5ea6\uff09<\/span>\u8d8b\u540c\uff0c\u53d1\u751f\u96c6\u4f53\u8fd0\u52a8\u7684\u8fde\u7eed\u76f8\u53d8\u3002\u5229\u7528\u6709\u9650\u5c3a\u5ea6\u6807\u5ea6\u6027\uff0c\u5f97\u5230\u4e0d\u540cVicsek\u6a21\u578b\u8fde\u7eed\u76f8\u53d8\u7684\u4e34\u754c\u6307\u6570\u76f8\u540c\uff0c\u8868\u660e\u5b83\u4eec\u5c5e\u4e8e\u540c\u4e00\u4e2a\u666e\u9002\u7c7b\u3002\u8fd9\u91cc\u53d1\u73b0\u7684\u76f8\u53d8\u673a\u5236\u4e0e\u7279\u6027\u5bf9\u751f\u547d\u7cfb\u7edf\u53ef\u80fd\u5177\u6709\u666e\u904d\u6027\u3002<\/span><\/p>\n


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\u672c\u5f81\u5fae\u89c2\u6001\u65b9\u6cd5\u5728\u751f\u547d\u7cfb\u7edf\u7684\u6210\u529f\u5e94\u7528\uff0c\u8868\u660e\u5176\u5bf9\u4e8e\u975e\u5e73\u8861\u6001\u7684\u9002\u7528\u6027\u3002\u672a\u6765\u8fd8\u53ef\u5c06\u5176\u5e94\u7528\u4e8e\u66f4\u5e7f\u6cdb\u7684\u590d\u6742\u7cfb\u7edf\uff0c\u6bd4\u5982\u6c14\u5019\u7cfb\u7edf\u3001\u751f\u6001\u7cfb\u7edf\u548c\u6d41\u4f53\u7cfb\u7edf\u7b49\u3002<\/span><\/p>\n


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

\u4ee5\u4e0a\u7ed3\u679c\u4f5c\u4e3a Rapid Communication \u53d1\u8868\u5728 Chin. Phys. B 30, 128703 (2021).<\/span><\/p>\n


<\/p>\n

\u53c2\u8003\u6587\u732e<\/strong><\/span><\/p>\n

[1] Vicsek T,  Czirok A, Ben-Jacob E, Cohenl I, and Shochet O 1995 Phys. Rev. Lett. 75, 1226.<\/span><\/p>\n

[2] Gregoire G and Chate H 2004 Phys. Rev. Lett. 92, 025702.<\/span><\/p>\n

[3] Sun Y, Hu G, Zhang Y, Lu B, Lu Z, Fan J, Li X, Deng Q, and Chen X 2021 Commun. Theor. Phys. 73, 065603.<\/span><\/p>\n


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\u96c6\u667a\u6591\u56fe\u9876\u520a\u8bba\u6587\u901f\u9012\u680f\u76ee\u4e0a\u7ebf\u4ee5\u6765\uff0c\u6301\u7eed\u6536\u5f55\u6765\u81eaNature\u3001Science<\/span>\u7b49\u9876\u520a\u7684\u6700\u65b0\u8bba\u6587\uff0c\u8ffd\u8e2a\u590d\u6742\u7cfb\u7edf\u3001\u7f51\u7edc\u79d1\u5b66\u3001\u8ba1\u7b97\u793e\u4f1a\u79d1\u5b66\u7b49\u9886\u57df\u7684\u524d\u6cbf\u8fdb\u5c55\u3002\u73b0\u5728\u6b63\u5f0f\u63a8\u51fa\u8ba2\u9605\u529f\u80fd\uff0c\u6bcf\u5468\u901a\u8fc7\u5fae\u4fe1\u670d\u52a1\u53f7\u300c\u96c6\u667a\u6591\u56fe\u300d\u63a8\u9001\u8bba\u6587\u4fe1\u606f\u3002\u626b\u63cf\u4e0b\u65b9\u4e8c\u7ef4\u7801\u5373\u53ef\u4e00\u952e\u8ba2\u9605\uff1a<\/span>
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