{"id":1184,"date":"2018-06-29T01:00:00","date_gmt":"2018-06-28T17:00:00","guid":{"rendered":"http:\/\/swarma.org\/%swarma-paper%\/"},"modified":"2018-12-06T15:05:32","modified_gmt":"2018-12-06T07:05:32","slug":"%e4%b8%ba%e4%bb%80%e4%b9%88%e9%b8%9f%e7%9c%8b%e5%88%b0%e7%9a%84%e4%b8%96%e7%95%8c%e4%bd%a0%e4%bd%93%e4%bc%9a%e4%b8%8d%e4%ba%86%ef%bc%9f%e5%9b%a0%e4%b8%ba%e5%ae%83%e4%bb%ac%e7%9a%84%e7%9c%bc%e9%87%8c","status":"publish","type":"post","link":"https:\/\/swarma.org\/?p=1184","title":{"rendered":"\u4e3a\u4ec0\u4e48\u9e1f\u770b\u5230\u7684\u4e16\u754c\u4f60\u4f53\u4f1a\u4e0d\u4e86\uff1f\u56e0\u4e3a\u5b83\u4eec\u7684\u773c\u91cc\u9690\u85cf\u7740\u79d8\u5bc6"},"content":{"rendered":"
\n

\"\u96c6\u667a\"<\/p>\n

\u9e21\u7684\u89c6\u9525\u7ec6\u80de\u56fe\u8c31<\/strong><\/span><\/p>\n


<\/p>\n


<\/p>\n

\n

\u5bfc\u8bed<\/span><\/strong><\/span><\/p>\n

\n
\n
\n

\u548c\u4eba\u7c7b\u76f8\u6bd4\uff0c\u9e1f\u7c7b\u6709\u66f4\u591a\u79cd\u7c7b\u7684\u89c6\u9525\u7ec6\u80de\uff0c\u800c\u8fd9\u4e9b\u7ec6\u80de\u7684\u6392\u5217\u65b9\u5f0f\u4e2d\u9690\u85cf\u7740\u8fdb\u5316\u5965\u79d8\u3002<\/span>\u4e00\u8d77\u9605\u8bfb\u672c\u6587\uff0c\u4e86\u89e3\u8fd9\u4e2a\u6a2a\u8de8\u6570\u5b66\u3001\u7269\u7406\u3001\u5316\u5b66\u3001\u751f\u7269\u7684\u795e\u79d8\u95ee\u9898\u3002<\/span><\/p>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n


<\/p>\n

\n

\u7f16\u8bd1\uff1a\u96c6\u667a\u7ffb\u8bd1\u7ec4<\/span><\/p>\n

\u6765\u6e90\uff1a<\/span>quantamagazine.org<\/span><\/p>\n

\u539f\u9898\uff1a<\/span>A Bird\u2019s-Eye View of Nature\u2019s Hidden Order<\/span><\/p>\n<\/blockquote>\n

\n
\n
\n


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

\u5728\u9e1f\u7c7b\u7684\u773c\u775b\u3001\u76d2\u88c5\u7684\u73bb\u7483\u5f39\u73e0\u548c\u5176\u4ed6\u532a\u5937\u6240\u601d\u7684\u5730\u65b9\u51fa\u73b0\u7684\u795e\u79d8\u6392\u5217\u6a21\u5f0f\u5f15\u8d77\u4e86\u79d1\u5b66\u5bb6\u4eec\u7684\u5173\u6ce8\u3002<\/span><\/p>\n

 <\/span><\/p>\n

\u4e03\u5e74\u524d\uff0cJoe Corbo\u4ece\u9e21\u7684\u773c\u775b\u4e2d\u770b\u5230\u4e86\u60ca\u4eba\u7684\u4e1c\u897f\u3002\u8986\u76d6\u89c6\u7f51\u819c\u7684\u3001\u5bf9\u989c\u8272\u654f\u611f\u7684\u89c6\u9525\u7ec6\u80de\uff08\u4ece\u9e21\u7684\u773c\u775b\u4e2d\u5206\u79bb\u800c\u6765\uff09\uff0c\u5728\u663e\u5fae\u955c\u4e0b\u5448\u73b0\u4e3a\u4e94\u79cd\u4e0d\u540c\u989c\u8272\u4e0e\u5927\u5c0f\u7684\u6ce2\u5361\u5706\u70b9\u3002\u7136\u800cCorbo\u89c2\u5bdf\u5230\uff0c\u4e0d\u540c\u4e8e\u4eba\u7c7b\u89c6\u9525\u7ec6\u80de\u7684\u968f\u673a\u5206\u6563\u4ee5\u53ca\u9c7c\u7c7b\u89c6\u9525\u7ec6\u80de\u7684\u6574\u9f50\u6392\u5217\uff0c\u9e21\u89c6\u9525\u7ec6\u80de\u7684\u5206\u5e03\u770b\u4f3c\u6742\u4e71\u65e0\u7ae0\u5374\u53c8\u76f8\u5f53\u5747\u5300\u3002\u5c3d\u7ba1\u8fd9\u4e9b\u7ec6\u80de\u7684\u6392\u5e03\u6ca1\u6709\u660e\u663e\u7684\u89c4\u5f8b\uff0c\u4f46\u5b83\u4eec\u4e4b\u95f4\u7684\u8ddd\u79bb\u4e0d\u4f1a\u592a\u8fd1\u6216\u592a\u8fdc\u3002\u4e94\u79cd\u89c6\u9525\u7ec6\u80de\u6563\u5e03\u5728\u89c6\u7f51\u819c\u4e0a\uff0c\u5982\u660e\u6697\u4e0d\u540c\u7684\u661f\u661f\u70b9\u7f00\u5728\u591c\u7a7a\u91cc\uff0c\u65e0\u8bba\u662f\u5176\u4e2d\u4efb\u4f55\u4e00\u79cd\u89c6\u9525\u7ec6\u80de\uff0c\u8fd8\u662f\u6240\u6709\u89c6\u9525\u7ec6\u80de\u7684\u96c6\u5408\uff0c\u90fd\u5448\u73b0\u51fa\u540c\u6837\u5f15\u4eba\u6ce8\u76ee\u7684\u968f\u673a\u6027\u4e0e\u89c4\u5f8b\u6027\u7684\u7ed3\u5408\u3002<\/strong>\u5723\u8def\u6613\u65af\u534e\u76db\u987f\u5927\u5b66<\/span>\uff08Washington University in St. Louis\uff09\u751f\u7269\u5b9e\u9a8c\u5ba4\u7684Corbo\u5b8c\u5168\u88ab\u8fd9\u4e00\u73b0\u8c61\u8ff7\u4f4f\u4e86\u3002<\/span><\/p>\n

 <\/span><\/p>\n

\u201c\u4ec5\u4ec5\u770b\u7740\u8fd9\u4e9b\u56fe\u6848\uff0c\u5c31\u80fd\u611f\u53d7\u5230\u5b83\u4eec\u7684\u7f8e\u4e3d\uff01\u6211\u4eec\u88ab\u8fd9\u7f8e\u4e3d\u5438\u5f15\uff0c\u7eaf\u7cb9\u51fa\u4e8e\u597d\u5947\u800c\u6e34\u671b\u66f4\u597d\u5730\u7406\u89e3\u8fd9\u4e9b\u56fe\u6848\u3002\u201dCorbo\u548c\u4ed6\u7684\u5408\u4f5c\u8005\u5e0c\u671b\u80fd\u591f\u627e\u5bfb\u51fa\u56fe\u6848\u7684\u529f\u80fd\u4ee5\u53ca\u5f62\u6210\u8fc7\u7a0b\u3002\u4f46\u662f\u5f53\u65f6\u4ed6\u5e76\u4e0d\u77e5\u9053\uff0c\u539f\u6765\u540c\u6837\u7684\u95ee\u9898\u5728\u4f17\u591a\u5176\u4ed6\u7684\u8bed\u5883\u4e2d\u5c61\u88ab\u63d0\u53ca\u3002\u4ed6\u7684\u53d1\u73b0\uff0c\u4f7f\u5f97\u5728\u6570\u5b66\u548c\u7269\u7406\u4e2d\u5c61\u5c61\u51fa\u73b0\u7684\u9690\u85cf\u79e9\u5e8f\uff0c\u7b2c\u4e00\u6b21\u627e\u5230\u4e86\u751f\u7269\u8868\u73b0\u5f62\u5f0f\u3002<\/span><\/p>\n

 <\/span><\/p>\n

Corbo\u6240\u786e\u4fe1\u7684\u662f\uff0c\u8fd9\u4e2a\u95ee\u9898\u7684\u7b54\u6848\u5e94\u8be5\u4ece\u9e1f\u7c7b\u89c6\u7f51\u819c\u672c\u8eab\u7684\u529f\u80fd\u5165\u624b\u3002\u9e1f\u7c7b\u5177\u6709\u60ca\u4eba\u7684\u89c6\u89c9\u529f\u80fd\uff0c\u4f8b\u5982\uff0c\u8001\u9e70\u53ef\u4ee5\u4ece\u4e00\u82f1\u91cc\u5916\u7684\u9ad8\u7a7a\u641c\u5bfb\u5230\u8001\u9f20\u7684\u8e2a\u8ff9\u3002\u4ed6\u7684\u5b9e\u9a8c\u5ba4\u6b63\u81f4\u529b\u4e8e\u7814\u7a76\u9e1f\u7c7b\u83b7\u5f97\u51fa\u8272\u89c6\u89c9\u80fd\u529b\u7684\u8fdb\u5316\u9002\u5e94\u6027\u673a\u5236\u3002<\/span>
<\/p>\n

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


<\/p>\n

1.\u9e1f\u7c7b\u773c\u775b\u4e2d\u7684<\/strong><\/strong><\/span><\/strong><\/span><\/p>\n

\u8d85\u9f50\u6784\u4f53<\/strong><\/strong><\/span><\/strong><\/span>
<\/p>\n

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

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

3\u4ebf\u5e74\u524d\uff0c\u4e00\u79cd\u7c7b\u4f3c\u8725\u8734\u7684\u751f\u7269\u9010\u6e10\u8fdb\u5316\u4e3a\u6050\u9f99\u548c\u539f\u59cb\u54fa\u4e73\u52a8\u7269\u3002\u800c\u6050\u9f99\u6b63\u662f\u9e1f\u7c7b\u7684\u7956\u5148\uff0c\u56e0\u800c\uff0c\u9e1f\u7c7b\u89c6\u89c9\u8bb8\u591a\u4ee4\u4eba\u60ca\u5f02\u7684\u5c5e\u6027\uff0c\u88ab\u8ba4\u4e3a\u662f\u4ece\u8fd9\u4e9b\u7c7b\u4f3c\u8725\u8734\u7684\u751f\u7269\u90a3\u91cc\u7ee7\u627f\u800c\u6765\u3002\u5728\u6050\u9f99\u7edf\u6cbb\u5730\u7403\u4e0a\u6816\u606f\u5730\u7684\u6f2b\u957f\u65f6\u95f4\u91cc\uff0c\u6211\u4eec\u7684\u54fa\u4e73\u52a8\u7269\u8fd1\u4eb2\u53ea\u80fd\u5728\u9ed1\u6697\u4e2d\u4ed3\u7687\u5954\u8d70\uff0c\u6210\u4e3a\u6218\u6218\u5162\u5162\u7684\u591c\u884c\u751f\u7269\uff0c\u9010\u6e10\u4e27\u5931\u4e86\u8fa8\u522b\u8272\u5f69\u7684\u80fd\u529b\u3002\u5728\u90a3\u65f6\uff0c\u54fa\u4e73\u52a8\u7269\u7684\u89c6\u9525\u7ec6\u80de\u51cf\u5c11\u5230\u4e86\u4e24\u4e2a\u2014\u2014\u8fd9\u662f\u4e00\u4e2a\u8fdb\u5316\u53f2\u4e0a\u7684\u4f4e\u8c37\uff0c\u81f3\u4eca\u4eba\u7c7b\u4ecd\u7136\u8bd5\u56fe\u4ece\u8fd9\u4e00\u4f4e\u8c37\u4e2d\u6446\u8131\u51fa\u6765\u3002\u5e78\u8fd0\u7684\u662f\uff0c\u5927\u7ea63000\u4e07\u5e74\u524d\uff0c\u6211\u4eec\u7684\u4e00\u652f\u7075\u957f\u7c7b\u7956\u5148\u7684\u89c6\u9525\u7ec6\u80de\u5206\u88c2\u51fa\u7ea2\u3001\u7eff\u4e24\u79cd\u989c\u8272\u7684\u611f\u77e5\u529f\u80fd\uff0c\u4e0e\u539f\u672c\u5c31\u5b58\u5728\u7684\u611f\u77e5\u84dd\u8272\u7684\u89c6\u9525\u7ec6\u80de\u4e00\u8d77\uff0c\u5f62\u6210\u4e86\u4eba\u7c7b\u7684\u4e09\u8272\u89c6\u89c9\u3002\u7136\u800c\u4eba\u7c7b\u7684\u89c6\u9525\u7ec6\u80de\uff0c\u5c24\u5176\u662f\u8f83\u5e74\u8f7b\u7684\u611f\u77e5\u7ea2\u8272\u4e0e\u7eff\u8272\u7684\u89c6\u9525\u7ec6\u80de\uff0c\u5206\u5e03\u5448\u5757\u72b6\u4e14\u6742\u4e71\u65e0\u7ae0\uff0c\u5bf9\u4e8e\u5149\u7684\u63a2\u6d4b\u4e5f\u4e0d\u5747\u5300\u3002<\/span><\/p>\n

 <\/span><\/p>\n

\u4e0e\u54fa\u4e73\u52a8\u7269\u4e0d\u540c\uff0c\u9e1f\u7c7b\u7684\u773c\u775b\u7ecf\u8fc7\u4e86\u4ebf\u4e07\u5e74\u65f6\u95f4\u7684\u4f18\u5316\u3002\u968f\u7740\u89c6\u9525\u7ec6\u80de\u6570\u76ee\u7684\u589e\u52a0\uff0c\u5176\u7a7a\u95f4\u6392\u5e03\u66f4\u4e3a\u89c4\u5f8b\u3002\u7136\u800c\uff0cCorbo\u548c\u540c\u4e8b\u4eec\u597d\u5947\uff0c\u4e3a\u4ec0\u4e48\u89c6\u9525\u7ec6\u80de\u7684\u5206\u5e03\u6ca1\u6709\u8fdb\u5316\u4e3a\u7f51\u683c\u6216\u201c\u6676\u683c\u201d\u90a3\u6837\u5b8c\u5168\u89c4\u5f8b\u6027\u7684\u6392\u5217\u65b9\u5f0f\uff1f\u4e00\u79cd\u770b\u8d77\u6765\u6700\u6709\u53ef\u80fd\u7684\u89e3\u91ca\u662f\uff0c\u4ed6\u4eec\u5728\u89c6\u7f51\u819c\u89c2\u5bdf\u5230\u7684\u5947\u602a\u7684\u3001\u96be\u4ee5\u5206\u7c7b\u7684\u56fe\u6848\uff0c\u662f\u5728\u67d0\u79cd\u672a\u77e5\u7ea6\u675f\u6761\u4ef6\u4e0b\u7684\u6700\u4f18\u72b6\u6001\u3002\u8fd9\u4e9b\u7ea6\u675f\u6761\u4ef6\u662f\u4ec0\u4e48\uff1f\u56fe\u6848\u610f\u5473\u7740\u4ec0\u4e48\uff1f\u9e1f\u7c7b\u89c6\u89c9\u7cfb\u7edf\u662f\u5982\u4f55\u6f14\u5316\u6210\u73b0\u5728\u7684\u6837\u5b50\u7684\uff1f\u8fd9\u4e9b\u95ee\u9898\u4ecd\u7136\u4e0d\u6e05\u695a\u3002\u751f\u7269\u5b66\u5bb6\u5df2\u7ecf\u5c3d\u529b\u91cf\u5316\u89c6\u7f51\u819c\u7684\u89c4\u5f8b\u6027\uff0c\u7136\u800c\u8fd9\u662f\u4e00\u4e2a\u4ed6\u4eec\u4e0d\u719f\u6089\u7684\u9886\u57df\uff0c\u4ed6\u4eec\u9700\u8981\u5e2e\u52a9\u3002<\/span><\/p>\n

 <\/span><\/p>\n

2012\u5e74\uff0cCorbo\u8054\u7cfb\u4e86\u666e\u6797\u65af\u987f\u5927\u5b66\u7684\u7406\u8bba\u5316\u5b66\u6559\u6388Salvatore Torquato\uff0c\u4ed6\u662f\u7814\u7a76\u201c\u5806\u79ef\u201d\u95ee\u9898\uff08Packing problem\uff09\u7684\u4e13\u5bb6\u3002\u6240\u8c13\u7684\u201c\u5806\u79ef\u201d\u95ee\u9898\uff0c\u662f\u6307\u5728\u7ed9\u5b9a\u7684\u7a7a\u95f4\u7ef4\u5ea6\u4e0b\uff0c\u5982\u4f55\u6392\u5e03\u7269\u4f53\u4ee5\u6700\u5927\u9650\u5ea6\u5730\u585e\u6ee1\u6709\u9650\u7a7a\u95f4\uff0c\u5728\u9e1f\u7c7b\u89c6\u89c9\u95ee\u9898\u4e2d\uff0c\u5c31\u662f\u5982\u4f55\u5c06\u4e94\u79cd\u4e0d\u540c\u5c3a\u5bf8\u7684\u89c6\u9525\u7ec6\u80de\u6700\u81f4\u5bc6\u5730\u6392\u5e03\u5728\u4e8c\u7ef4\u7684\u89c6\u7f51\u819c\u4e0a\u3002<\/strong><\/span><\/p>\n

 <\/span><\/p>\n

\u201c\u6211\u60f3\u77e5\u9053\u9e1f\u7c7b\u89c6\u89c9\u7cfb\u7edf\u662f\u5426\u662f\u5c5e\u4e8e\u6700\u4f18\u7684\u6392\u5e03\u65b9\u5f0f\u3002\u201dCorbo\u8bf4\u9053\u3002Torquato\u5bf9\u8fd9\u4e2a\u95ee\u9898\u540c\u6837\u611f\u5230\u597d\u5947\uff0c\u4ed6\u5728\u89c6\u7f51\u819c\u56fe\u6848\u7684\u6570\u5b57\u56fe\u50cf\u4e0a\u8fd0\u884c\u4e86\u4e00\u4e9b\u7b97\u6cd5\uff0c\u7ed3\u679c\u8ba9\u4ed6\u201c\u611f\u5230\u9707\u60ca\u201d\uff0cCorbo\u56de\u5fc6\u8bf4\uff0c\u201c\u4ed6\u53d1\u73b0\uff0c\u539f\u672c\u5728\u65e0\u673a\u7269\u6216\u7269\u7406\u7cfb\u7edf\u4e2d\u770b\u89c1\u7684\u73b0\u8c61\uff0c\u7adf\u7136\u540c\u6837\u51fa\u73b0\u5728\u9e1f\u7c7b\u89c6\u89c9\u7cfb\u7edf\u4e2d\u3002\u201d<\/span><\/p>\n


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

\"\u96c6\u667a\"<\/p>\n

\u9e21\u773c\u4e2d\u7684\u8d85\u9f50\u6784\u4f53<\/span><\/strong><\/span><\/p>\n

\uff08Hyperuniformity\uff09<\/span><\/strong><\/span><\/p>\n

 <\/span><\/p>\n

\u4ece21\u4e16\u7eaa\u521d\uff0cTorquato\u5df2\u7ecf\u5f00\u59cb\u5bf9\u8fd9\u4e00\u5168\u65b0\u7684\u5206\u5e03\u6a21\u5f0f\u8fdb\u884c\u7814\u7a76\uff0c\u4ed6\u5c06\u5176\u79f0\u4e3a\u201c\u8d85\u9f50\u6784\u4f53\u201d\uff08hyperuniformity\uff09\u3002<\/span>\uff08\u76f8\u6bd4\u4e8e\u540c\u4e00\u65f6\u671f\u7531\u7f57\u683c\u65af\u5927\u5b66\uff08Rutgers University\uff09\u7684Joel Lebowitz\u63d0\u51fa\u7684\u201c\u8d85\u540c\u8d28\u4f53\u201d\uff08superhomogeneity\uff09\uff0c\u8fd9\u4e00\u540d\u79f0\u66f4\u4e3a\u5408\u9002\u3002\uff09<\/span>\u4ece\u90a3\u65f6\u8d77\uff0c\u8d85\u9f50\u6784\u4f53\u73b0\u8c61\u5f00\u59cb\u5e7f\u6cdb\u51fa\u73b0\u5728\u4e0d\u540c\u7684\u7cfb\u7edf\u4e2d\u3002\u9664\u4e86\u9e1f\u7c7b\u7684\u773c\u775b\uff0c\u8d85\u9f50\u6784\u4f53\u4e5f\u51fa\u73b0\u5728\u51c6\u6676\u6750\u6599\u3001\u968f\u673a\u6570\u77e9\u9635\u3001\u5b87\u5b99\u7684\u5927\u5c3a\u5ea6\u7ed3\u6784\u3001\u91cf\u5b50\u7cfb\u7efc\u4ee5\u53ca\u4e73\u6d4a\u6db2\u4e0e\u80f6\u4f53\u7b49\u8f6f\u7269\u8d28\u7cfb\u7edf\u4e2d\u3002<\/strong><\/span><\/p>\n

 <\/span><\/p>\n

\u5f53\u67d0\u4e9b\u73b0\u8c61\u51fa\u73b0\u5728\u4e00\u4e9b\u65b0\u7684\u9886\u57df\u4e2d\u65f6\uff0c\u79d1\u5b66\u5bb6\u4eec\u5f80\u5f80\u4f1a\u4e3a\u4e4b\u60ca\u559c\uff0c\u8fd9\u79cd\u611f\u89c9\u5c31\u597d\u50cf\u548c\u5b87\u5b99\u73a9\u201d\u6253\u5730\u9f20\u201c\u6e38\u620f\u4e00\u6837\u3002\u63a2\u7d22\u8fd9\u79cd\u73b0\u8c61\u80cc\u540e\u9690\u85cf\u7684\u666e\u904d\u771f\u7406\u662f\u79d1\u5b66\u5bb6\u95e8\u6700\u4e3a\u70ed\u8877\u7684\u5de5\u4f5c\u3002\u5728\u8fd9\u4e2a\u8fc7\u7a0b\u4e2d\uff0c\u4ed6\u4eec\u53d1\u73b0\u4e86\u5f88\u591a\u8d85\u9f50\u6784\u6750\u6599\u5177\u6709\u5b9e\u7528\u4ef7\u503c\u7684\u65b0\u7279\u6027\u3002<\/span><\/p>\n

 <\/span><\/p>\n

\u4ece\u6570\u5b66\u7684\u89d2\u5ea6\u6765\u770b\uff0c\u8d85\u9f50\u6784\u4f53\u7684\u7814\u7a76\u4e5f\u5f88\u6709\u4ef7\u503c\u3002\u201c\u6211\u5bf9\u5b83\u7684\u7814\u7a76\u8d8a\u6df1\u5165\uff0c\u5c31\u8d8a\u80fd\u611f\u53d7\u5230\u5b83\u539f\u7406\u4e0a\u7684\u4f18\u96c5\u4ee5\u53ca\u8fd9\u4e00\u6982\u5ff5\u4ee4\u4eba\u60ca\u53f9\u7684\u5730\u65b9\u3002\u201d\u65b0\u82f1\u683c\u5170\u5fae\u8f6f\u7814\u7a76\u6240\u7684\u6570\u5b66\u5bb6\u3001\u7814\u7a76\u5806\u79ef\u95ee\u9898\u7684\u4e13\u5bb6Henry Cohn\u8bf4\u3002\u201c\u53e6\u4e00\u65b9\u9762\uff0c\u8ba9\u6211\u60ca\u8bb6\u7684\u662f\u8d85\u9f50\u6784\u4f53\u5e7f\u6cdb\u7684\u5e94\u7528\u524d\u666f\u3002<\/strong>\u201d<\/span>
<\/p>\n


<\/p>\n

\n

13\u5e74\u524d\uff0cTorquato\u548c\u4e00\u4f4d\u540c\u4e8b\u53d1\u8d77\u4e86\u8d85\u9f50\u6784\u4f53\u7684\u7814\u7a76\uff0c\u4ed6\u4eec\u4ece\u7406\u8bba\u4e0a\u63cf\u8ff0\u4e86\u8fd9\u4e2a\u95ee\u9898\uff0c\u5e76\u7ed9\u51fa\u4e86\u4e00\u4e2a\u7b80\u5355\u800c\u53c8\u4ee4\u4eba\u60ca\u8bb6\u7684\u4f8b\u5b50\uff1a\u201c\u5c06\uff08\u5404\u79cd\u5927\u5c0f\u7684\uff09\u73bb\u7483\u5f39\u73e0\u653e\u8fdb\u4e00\u4e2a\u5bb9\u5668\u91cc\uff0c\u6447\u52a8\u5b83\u4eec\u76f4\u5230\u585e\u6ee1\u5bb9\u5668\u4e3a\u6b62\uff0c\u8fd9\u65f6\u5019\u7cfb\u7edf\u662f\u8d85\u9f50\u6784\u7684\u3002\u201d\u4eca\u5e74\u6625\u5929\uff0cTorquato\u5728\u4ed6\u666e\u6797\u65af\u987f\u5927\u5b66\u7684\u529e\u516c\u5ba4\u8bf4\u9053\u3002<\/span><\/p>\n<\/section>\n

 <\/span><\/p>\n

\u4e0a\u8ff0\u73bb\u7483\u5f39\u73e0\u7684\u6392\u5e03\u6a21\u5f0f\u5728\u5b66\u672f\u4e0a\u88ab\u79f0\u4e3a\u201c\u6700\u5927\u968f\u673a\u6ee1\u585e\u5806\u79ef\u201d\uff08maximally random jammed packing\uff09\uff0c\u8fd9\u79cd\u6392\u5e03\u65b9\u5f0f\u53ef\u4ee5\u586b\u514564%\u7684\u7a7a\u95f4\uff08\u5176\u4f59\u90e8\u5206\u662f\u7a7a\u6c14\uff09\u3002\u8fd9\u6bd4\u7403\u4f53\u53ef\u80fd\u7684\u6700\u5bc6\u5806\u79ef\u8981\u5c0f\u2014\u2014\u5728\u7bb1\u5b50\u91cc\u586b\u6ee1\u6854\u5b50\u7684\u6676\u683c\u5806\u79ef\uff08lattice packing\uff09\uff0c\u53ef\u4ee5\u586b\u514574%\u7684\u7a7a\u95f4\u3002\u4f46\u662f\u6676\u683c\u5806\u79ef\u5e76\u975e\u603b\u80fd\u5b9e\u73b0\uff0c\u6211\u4eec\u5e76\u4e0d\u80fd\u8f7b\u6613\u5730\u5c06\u4e00\u7bb1\u73bb\u7483\u5f39\u73e0\u6447\u52a8\u6210\u6676\u683c\u5806\u79ef\u3002\u540c\u6837\u5730\uff0c\u4e94\u79cd\u4e0d\u540c\u5c3a\u5bf8\u7684\u7269\u4f53\u4e5f\u5f88\u96be\u6392\u5217\u5f62\u6210\u6676\u683c\u7ed3\u6784\uff0c\u4f8b\u5982\u9e21\u773c\u4e2d\u7684\u89c6\u9525\u7ec6\u80de\uff0c<\/strong>Torquato\u89e3\u91ca\u8bf4\u3002<\/span> <\/span><\/p>\n


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

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

\"\u96c6\u667a\"<\/p>\n

\u5806\u79ef\u95ee\u9898<\/span><\/strong>
<\/p>\n

 <\/span><\/p>\n

\u6211\u4eec\u8003\u8651\u7528\u6c34\u5e73\u684c\u9762\u4e0a\u7684\u786c\u5e01\u6765\u4ee3\u66ff\u89c6\u9525\u7ec6\u80de\u3002\u201c\u5982\u679c\u538b\u7f29\u4e00\u5806\u4e00\u7f8e\u5206\u786c\u5e01\uff0c\u786c\u5e01\u4f1a\u5f62\u6210\u4e09\u89d2\u6676\u683c\u5806\u79ef\uff1b\u7136\u800c\uff0c\u5982\u679c\u5411\u5176\u4e2d\u52a0\u5165\u4e00\u4e9b\u4e0e\u4e4b\u5c3a\u5bf8\u4e0d\u540c\u7684\u4e94\u7f8e\u5206\u786c\u5e01\uff0c\u5219\u4f1a\u963b\u6b62\u786c\u5e01\u5f62\u6210\u6676\u683c\u5806\u79ef\u3002\u5982\u679c\u6709\u4e94\u79cd\u4e0d\u540c\u5c3a\u5bf8\u7684\u786c\u5e01\uff0c\u6bd4\u5982\u7ee7\u7eed\u52a0\u516525\u7f8e\u5206\u786c\u5e01\uff0c50\u7f8e\u5206\u786c\u5e01\uff0c\u6216\u8005\u5176\u4ed6\u4e0d\u540c\u5c3a\u5bf8\u7684\u786c\u5e01\u2014\u2014\u4f1a\u8fdb\u4e00\u6b65\u6291\u5236\u6676\u683c\u5806\u79ef\u7684\u5f62\u6210\u3002\u201dTorquato\u8bf4\u3002<\/span><\/p>\n

 <\/span><\/p>\n

\u7c7b\u4f3c\u5730\uff0c\u51e0\u4f55\u5b66\u539f\u7406\u8981\u6c42\u9e21\u7684\u89c6\u9525\u7ec6\u80de\u5448\u65e0\u5e8f\u6392\u5217\u3002\u7136\u800c\uff0c\u8fdb\u5316\u8fc7\u7a0b\u4e2d\u7684\u6fc0\u70c8\u7ade\u4e89\u53c8\u8981\u6c42\u89c6\u7f51\u819c\u5c3d\u53ef\u80fd\u5747\u5300\u5730\u63a5\u6536\u5149\u7ebf\uff1a\u63a5\u6536\u84dd\u5149\u7684\u89c6\u9525\u7ec6\u80de\u5f7c\u6b64\u8fdc\u79bb\uff0c\u63a5\u6536\u7ea2\u5149\u7684\u89c6\u9525\u7ec6\u80de\u5219\u5f7c\u6b64\u8fdc\u79bb\uff0c\u7b49\u7b49\u3002\u8fd9\u4e9b\u8981\u6c42\u7684\u5e73\u8861\u4f1a\u4f7f\u7cfb\u7edf\u6700\u7ec8\u201c\u5448\u73b0\u51fa\u65e0\u5e8f\u8d85\u9f50\u6784\u4f53\u7684\u7279\u5f81\u201d\u3002<\/span><\/p>\n

 <\/span><\/p>\n

\u8d85\u9f50\u6784\u4f53\u4f7f\u9e1f\u7c7b\u7684\u89c6\u89d2\u5177\u5907\u4e86\u4e24\u79cd\u4f18\u52bf\uff1a\u65e2\u6709\u591a\u8fbe\u4e94\u79cd\u7684\u611f\u77e5\u989c\u8272\u7684\u89c6\u9525\u7ec6\u80de\uff0c\u53c8\u8ba9\u6bcf\u79cd\u7ec6\u80de\u8fd1\u4e4e\u5747\u5300\u5730\u6392\u5e03\u5728\u89c6\u7f51\u819c\u4e0a\uff0c\u4e3a\u9e1f\u7c7b\u63d0\u4f9b\u4e86\u663e\u8457\u7684\u989c\u8272\u5206\u8fa8\u80fd\u529b\u3002<\/span><\/strong>\u7136\u800c\uff0c\u8fd9\u79cd\u201c\u9690\u85cf\u7684\u79e9\u5e8f\uff0c\u4eba\u7c7b\u65e0\u6cd5\u901a\u8fc7\u81ea\u5df1\u7684\u773c\u775b\u611f\u53d7\u5230\u3002\u201c\u4ed6\u8bf4\u3002<\/span><\/p>\n

 <\/span><\/p>\n

\"\u96c6\u667a\"
<\/span><\/strong><\/p>\n

\n

\u9a6c\u8d5b\u514b\u56fe\u6848\uff1a\u770b\u4f3c\u65e0\u5e8f\u6392\u5217\uff08\u5c0f\u5c3a\u5ea6\u7684\u65e0\u5e8f\uff09\u7684\u5f69\u8272\u5c0f\u77f3\u5b50\u62fc\u63a5\u51fa\u751f\u52a8\u7684\u56fe\u6848\uff08\u5927\u5c3a\u5ea6\u7684\u89c4\u5f8b\uff09 | \u6765\u6e90\uff1aWikipedia<\/span><\/p>\n<\/blockquote>\n

 <\/span><\/p>\n

\u786e\u5b9a\u4e00\u4e2a\u7cfb\u7edf\u662f\u5426\u662f\u8d85\u9f50\u6784\u4f53\u6240\u9700\u8981\u7684\u7b97\u6cd5\u7c7b\u4f3c\u4e8e\u5957\u5708\u5708\u90a3\u6837\u7684\u6e38\u620f\u3002<\/span><\/p>\n

 <\/span><\/p>\n

\"\u96c6\u667a\"<\/p>\n

 <\/span><\/p>\n

\uff081\uff09\u9996\u5148\uff0cTorquato\u89e3\u91ca\u9053\uff0c\u60f3\u8c61\u5c06\u5706\u73af\u53cd\u590d\u6254\u5230\u6709\u5e8f\u7684\u6676\u683c\u4e0a\uff0c\u6bcf\u4e00\u6b21\u5706\u73af\u843d\u5730\u65f6\uff0c\u8ba1\u7b97\u5706\u73af\u5185\u7684\u70b9\u6570\u3002\u5706\u73af\u6355\u83b7\u7684\u5706\u70b9\u6570\u91cf\u4ece\u4e00\u6b21\u6295\u63b7\u5230\u4e0b\u4e00\u6b21\u6295\u63b7\u6709\u6240\u6ce2\u52a8\uff0c\u4f46\u662f\u6ce2\u52a8\u5e76\u4e0d\u5927\u3002\u8fd9\u662f\u56e0\u4e3a\u5706\u73af\u5185\u90e8\u603b\u662f\u8986\u76d6\u56fa\u5b9a\u6570\u91cf\u7684\u5706\u70b9\uff0c\u6355\u83b7\u70b9\u6570\u7684\u552f\u4e00\u53d8\u5316\u53d1\u751f\u5728\u5706\u73af\u5916\u56f4\u3002\u5982\u679c\u589e\u52a0\u5706\u73af\u7684\u5c3a\u5bf8\uff0c\u6ce2\u52a8\u5c06\u4f1a\u53d1\u751f\u5728\u66f4\u957f\u7684\u5706\u5468\u4e0a\u3002\u56e0\u6b64\uff0c\u5bf9\u4e8e\u6676\u683c\u5206\u5e03\uff0c\u6355\u83b7\u7684\u70b9\u6570\uff08\u6216\u6676\u683c\u4e2d\u7684\u201c\u5bc6\u5ea6\u6ce2\u52a8\u201d\uff09\u7684\u6ce2\u52a8\u4e0e\u5706\u73af\u5468\u957f\u6210\u6b63\u6bd4\u3002<\/strong>\uff08\u5728\u66f4\u9ad8\u7ef4\u5ea6\uff0c\u5bc6\u5ea6\u6ce2\u52a8\u4e5f\u4e0e\u7ef4\u6570\u51cf\u53bb\u4e00\u6210\u6b63\u6bd4\u3002\uff09<\/span><\/p>\n

 <\/span><\/p>\n

\uff082\uff09\u73b0\u5728\u518d\u6765\u60f3\u8c61\u5728\u4e00\u4e9b\u968f\u673a\u5206\u5e03\u7684\u70b9\u4e0a\u73a9\u5957\u5708\u5708\u6e38\u620f\u3002\u968f\u673a\u5206\u5e03\u7684\u70b9\u5f80\u5f80\u5f62\u6210\u7a7a\u9699\u4e0e\u56e2\u7c07\uff0c\u5e76\u4e0d\u5747\u5300\u3002\u968f\u673a\u5206\u5e03\u7684\u4e00\u4e2a\u7279\u70b9\u662f\uff0c\u5f53\u5706\u73af\u53d8\u5927\u65f6\uff0c\u88ab\u6355\u83b7\u7684\u70b9\u6570\u4e0e\u5706\u73af\u9762\u79ef\u6210\u6b63\u6bd4\uff0c\u800c\u4e0d\u662f\u5468\u957f\u3002\u7ed3\u679c\u5c31\u662f\uff0c\u5728\u5927\u5c3a\u5ea6\u4e0a\uff0c\u5728\u4e0d\u540c\u6b21\u6295\u63b7\u4e4b\u95f4\uff0c\u5bc6\u5ea6\u6ce2\u52a8\u6bd4\u6676\u683c\u5206\u5e03\u8981\u6781\u7aef\u5f97\u591a\u3002<\/strong><\/span><\/p>\n

 <\/span><\/p>\n

\uff083\uff09\u5f53\u6d89\u53ca\u5230\u8d85\u9f50\u6784\u5206\u5e03\u65f6\uff0c\u6e38\u620f\u53d8\u5f97\u66f4\u52a0\u6709\u8da3\u3002\u56e0\u4e3a\u70b9\u7684\u5206\u5e03\u662f\u5c40\u90e8\u65e0\u5e8f\u7684\uff0c\u6240\u4ee5\u5bf9\u4e8e\u5c0f\u5706\u73af\uff0c\u76f8\u90bb\u4e24\u6b21\u6295\u63b7\u6355\u83b7\u70b9\u6570\u7684\u6ce2\u52a8\u6bd4\u6676\u683c\u5206\u5e03\u7684\u8981\u5927\uff0c\u4e0e\u968f\u673a\u5206\u5e03\u76f8\u4f3c\u3002\u7136\u800c\u968f\u7740\u5706\u73af\u53d8\u5927\uff0c\u5bc6\u5ea6\u6ce2\u52a8\u7684\u589e\u957f\u9010\u6e10\u4e0e\u5706\u73af\u7684\u5468\u957f\u6210\u6b63\u6bd4\uff0c\u800c\u4e0d\u662f\u5706\u73af\u7684\u9762\u79ef\u3002\u8fd9\u610f\u5473\u7740\uff0c\u5927\u5c3a\u5ea6\u4e0b\uff0c\u8d85\u9f50\u6784\u5206\u5e03\u4e0e\u6676\u683c\u5206\u5e03\u4e00\u6837\u5747\u5300\u3002<\/strong><\/span><\/p>\n

 <\/span><\/p>\n

\u666e\u6797\u65af\u987f\u5927\u5b66\u7684\u7269\u7406\u5b66\u5bb6Paul Steinhardt\u8bf4\uff0c\u5728\u8d85\u9f50\u6784\u7cfb\u7edf\u4e2d\uff0c\u7814\u7a76\u4eba\u5458\u53d1\u73b0\u4e86\u66f4\u591a\u201c\u7ed3\u6784\u751f\u6001\u89c4\u5f8b\u201d\uff1a\u5728\u8d85\u9f50\u6784\u7cfb\u7edf\u4e2d\uff0c\u5bc6\u5ea6\u7684\u6ce2\u52a8\u4e0e\u5706\u73af\u5468\u957f\u7684n\u6b21\u5e42\u6210\u6b63\u6bd4\uff0c\u5e42\u6307\u6570n\u901a\u5e38\u57281\u548c2\u4e4b\u95f4\uff0c\u5e76\u4e14\u4e58\u4ee5\u4e0d\u540c\u7684\u7cfb\u6570\u3002<\/strong><\/span><\/p>\n

 <\/span><\/p>\n

\u201c\u8fd9\u4e00\u5207\u610f\u5473\u7740\u4ec0\u4e48\u5462\uff1f\u6211\u4eec\u4e0d\u77e5\u9053\u3002\u7814\u7a76\u4ecd\u5728\u8fdb\u884c\u4e2d\uff0c\u5f88\u591a\u8bba\u6587\u6709\u5f85\u53d1\u8868\u3002\u201dTorquato\u8bf4\u3002<\/span><\/p>\n

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


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

2. \u6750\u6599\u5927\u89c2\u56ed<\/strong><\/span><\/strong><\/span><\/p>\n

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


<\/p>\n

\u8d85\u9f50\u6784\u4f53\u663e\u7136\u662f\u5f88\u591a\u4e0d\u540c\u7cfb\u7edf\u5171\u6709\u7684\u4e00\u79cd\u72b6\u6001\uff0c\u7136\u800c\uff0c\u5bf9\u4e8e\u5176\u666e\u904d\u6027\u7684\u89e3\u91ca\u4ecd\u662f\u4e00\u9879\u6b63\u5728\u8fdb\u884c\u7684\u5de5\u4f5c\u3002\u201c\u6211\u8ba4\u4e3a\uff0c\u8d85\u9f50\u6784\u4f53\u672c\u8d28\u4e0a\u662f\u67d0\u79cd\u66f4\u6df1\u5c42\u4f18\u5316\u8fc7\u7a0b\u7684\u6807\u5fd7\u201d\uff0cCohn\u8bf4\uff0c\u81f3\u4e8e\u8fd9\u4e9b\u8fc7\u7a0b\u662f\u4ec0\u4e48\uff0c\u201c\u5bf9\u4e8e\u4e0d\u540c\u95ee\u9898\u53ef\u80fd\u5dee\u522b\u5f88\u5927\u3002\u201d<\/span><\/section>\n<\/section>\n<\/section>\n

 <\/span><\/p>\n

\u8d85\u9f50\u6784\u7cfb\u7edf\u5206\u4e3a\u4e24\u5927\u7c7b\u3002\u7b2c\u4e00\u7c7b\uff0c\u662f\u7cfb\u7edf\u8fbe\u5230\u5e73\u8861\u65f6\u81ea\u53d1\u5f62\u6210\u7684\u8d85\u9f50\u6784\u4f53\u3002<\/strong>\u4f8b\u5982\u51c6\u6676\u2014\u2014\u4e00\u79cd\u5947\u5f02\u7684\u56fa\u4f53\uff0c\u5176\u5185\u90e8\u5f7c\u6b64\u8fde\u7ed3\u7684\u539f\u5b50\u4e0d\u9075\u5faa\u91cd\u590d\u89c4\u5f8b\u6392\u5e03\uff0c\u4f46\u80fd\u5f62\u6210\u5bc6\u94fa\u7a7a\u95f4\uff08tessellate space\uff09\u2014\u2014\u7cfb\u7edf\u8fbe\u5230\u5e73\u8861\u65f6\uff0c\u8868\u73b0\u4e3a\u8d85\u9f50\u6784\u4f53\u3002<\/span><\/p>\n

 <\/span><\/p>\n

\u5728\u8fd9\u4e9b\u5e73\u8861\u7cfb\u7edf\u4e2d\uff0c\u662f\u7c92\u5b50\u95f4\u7684\u65a5\u529b\u5c06\u5f7c\u6b64\u5206\u5f00\uff0c\u5e76\u5f62\u6210\u5168\u5c40\u7684\u8d85\u9f50\u6784\u4f53\u3002\u4e0e\u4e4b\u76f8\u4f3c\u7684\u6570\u5b66\u539f\u7406\u6216\u8bb8\u80fd\u591f\u89e3\u91ca\u9e1f\u7c7b\u773c\u4e2d\u8d85\u9f50\u6784\u4f53\u7684\u51fa\u73b0\uff0c\u968f\u673a\u6570\u77e9\u9635\u7684\u672c\u5f81\u503c\u5206\u5e03\uff0c\u4ee5\u53ca\u9ece\u66fcZeta\u51fd\u6570\uff08\u5c31\u662f\u90a3\u4e2a\u53ef\u4ee5\u63a8\u51fa\u7d20\u6570\u6709\u65e0\u9650\u591a\u4e2a\u7684\u51fd\u6570\uff09\u7684\u96f6\u70b9\u5206\u5e03\u7b49\u6570\u5b66\u95ee\u9898\u3002<\/span><\/p>\n

 <\/span><\/p>\n

\u53e6\u4e00\u7c7b\u8d85\u9f50\u6784\u7cfb\u7edf\u662f\u201c\u975e\u5e73\u8861\u201d\u7cfb\u7edf\uff0c\u6643\u52a8\u540e\u7684\u73bb\u7483\u5f39\u73e0\u3001\u4e73\u6d4a\u6db2\u3001\u80f6\u4f53\u4ee5\u53ca\u51b7\u539f\u5b50\u7cfb\u7efc\u90fd\u5c5e\u4e8e\u8fd9\u7c7b\u7cfb\u7edf\u3002<\/span><\/strong>\u7ec4\u6210\u7cfb\u7edf\u7684\u7c92\u5b50\u76f8\u4e92\u78b0\u649e\uff0c\u4f46\u4e0d\u5b58\u5728\u76f8\u4e92\u65a5\u529b\u3002\u7cfb\u7edf\u5fc5\u987b\u5728\u5916\u529b\u4f5c\u7528\u4e0b\uff0c\u624d\u80fd\u5f62\u6210\u8d85\u9f50\u6784\u72b6\u6001\u3002\u800c\u5728\u8fd9\u7c7b\u975e\u5e73\u8861\u7cfb\u7edf\u4e2d\uff0c\u8fd8\u5b58\u5728\u7740\u66f4\u4e3a\u68d8\u624b\u7684\u5206\u7c7b\u3002<\/span><\/p>\n

 <\/span><\/p>\n

\u53bb\u5e74\u79cb\u5929\uff0c\u4ee5\u6cd5\u56fd\u91cc\u6602\u9ad8\u7b49\u5e08\u8303\u5b66\u6821Denis Bartolo\u4e3a\u4ee3\u8868\u7684\u7269\u7406\u5b66\u5bb6\u4eec\uff0c\u5728Physical Review Letters\u4e0a\u53d1\u8868\u6587\u7ae0\u79f0\uff0c\u4ee5\u7cbe\u786e\u7684\u7279\u5b9a\u632f\u5e45\u6643\u52a8\u4e73\u6db2\uff0c\u53ef\u4ee5\u5f62\u6210\u8d85\u9f50\u6784\u4f53\uff0c<\/strong>\u8fd9\u4e00\u7279\u5f81\u632f\u5e45\u6807\u5fd7\u7740\u6750\u6599\u53ef\u9006\u6027\u4e0e\u4e0d\u53ef\u9006\u6027\u7684\u4e34\u754c\u8f6c\u53d8\uff1a\u5982\u679c\u6643\u52a8\u6bd4\u4e34\u754c\u632f\u5e45\u8f7b\uff0c\u4e73\u6db2\u4e2d\u60ac\u6d6e\u7684\u7c92\u5b50\u5728\u6643\u52a8\u4e4b\u540e\u4f1a\u56de\u5230\u4e4b\u524d\u7684\u76f8\u5bf9\u4f4d\u7f6e\u3002\u5982\u679c\u6643\u52a8\u6bd4\u4e34\u754c\u632f\u5e45\u5267\u70c8\uff0c\u7c92\u5b50\u7684\u8fd0\u52a8\u5219\u4e0d\u53ef\u9006\u8f6c\u3002<\/span><\/p>\n

 <\/span><\/p>\n

Bartolo\u7684\u5de5\u4f5c\u8868\u660e\uff0c\u5728\u975e\u5e73\u8861\u7cfb\u7edf\u4e2d\uff0c\u53ef\u9006\u6027\u7684\u5f00\u59cb\u4e0e\u8d85\u9f50\u6784\u4f53\u7684\u51fa\u73b0\u4e4b\u95f4\u5b58\u5728\u7740\u6839\u672c(\u5c3d\u7ba1\u4e0d\u662f\u5b8c\u5168)\u7684\u8054\u7cfb\u3002\u7136\u800c\uff0c\u6700\u5927\u968f\u673a\u6ee1\u585e\u5806\u79ef\u7684\u539f\u7406\u5219\u662f\u5b8c\u5168\u4e0d\u540c\u7684\u7406\u8bba\u3002<\/span><\/p>\n

 <\/span><\/p>\n

\u201c\u6211\u4eec\u80fd\u8fde\u63a5\u8fd9\u4e24\u79cd\u7cfb\u7edf\u7684\u7269\u7406\u73b0\u8c61\u5417\uff1f\u201dBartolo\u95ee\u9053\uff0c\u201c\u6839\u672c\u4e0d\u884c\u3002\u5bf9\u4e8e\u8d85\u9f50\u6784\u4f53\u4e3a\u4ec0\u4e48\u4f1a\u5728\u4e24\u79cd\u622a\u7136\u4e0d\u540c\u7684\u7269\u7406\u7cfb\u7edf\u4e2d\u51fa\u73b0\uff0c\u6211\u4eec\u4e00\u65e0\u6240\u77e5\u3002\u201d<\/span><\/p>\n

 <\/span>
<\/span><\/p>\n

\u5f53\u79d1\u5b66\u5bb6\u4eec\u52aa\u529b\u4e32\u8054\u8fd9\u4e9b\u7ebf\u7d22\u65f6\uff0c\u4ed6\u4eec\u53d1\u73b0\u4e86\u8d85\u9f50\u6784\u6750\u6599\u4ee4\u4eba\u60ca\u8bb6\u7684\u7279\u6027\u2014\u2014\u8d85\u9f50\u6784\u6750\u6599\u5177\u5907\u4e00\u4e9b\u6676\u4f53\u7684\u7279\u6027\uff0c\u800c\u4e14\u4e0d\u5bb9\u6613\u53d7\u5230\u5236\u9020\u8bef\u5dee\u7684\u5f71\u54cd\uff0c\u5b83\u4eec\u66f4\u7c7b\u4f3c\u4e8e\u73bb\u7483\uff0c\u6216\u5176\u4ed6\u6ca1\u6709\u76f8\u5173\u6027\u7684\u7269\u8d28\u3002<\/strong><\/span><\/p>\n

 <\/span><\/p>\n

\u5728Optica\u4e0a\u65b0\u53d1\u8868\u7684\u4e00\u7bc7\u8bba\u6587\u4e2d\uff0c\u4ee5R\u00e9mi Carminati\u4e3a\u4ee3\u8868\u7684\u6cd5\u56fd\u7269\u7406\u5b66\u5bb6\u62a5\u544a\u8bf4\uff0c\u81f4\u5bc6\u7684\u8d85\u9f50\u6784\u6750\u6599\u53ef\u4ee5\u5236\u4f5c\u6210\u900f\u660e\u6750\u6599\uff0c\u7136\u800c\uff0c\u540c\u6837\u5bc6\u5ea6\u7684\u975e\u5173\u8054\u65e0\u5e8f\u6750\u6599\u5374\u662f\u4e0d\u900f\u660e\u7684\uff0c\u9690\u85cf\u5728\u7c92\u5b50\u76f8\u5bf9\u4f4d\u7f6e\u4e2d\u7684\u89c4\u5f8b\u5bfc\u81f4\u6563\u5c04\u5149\u5e72\u6d89\u5e76\u4e14\u62b5\u6d88\u3002\u201c\u5e72\u6d89\u4f1a\u7834\u574f\u6563\u5c04\u3002\u5149\u7a7f\u8fc7\u6750\u6599\uff0c\u4eff\u4f5b\u6750\u6599\u662f\u5747\u5300\u7684\u3002\u201dCarminati\u89e3\u91ca\u9053\u3002\u73b0\u5728\u8981\u77e5\u9053\u8fd9\u79cd\u81f4\u5bc6\u3001\u900f\u660e\u3001\u975e\u6676\u4f53\u7684\u6750\u6599\u4f1a\u6709\u4ec0\u4e48\u5e94\u7528\uff0c\u8fd8\u4e3a\u65f6\u5c1a\u65e9\u3002\u4f46\u662f\u201c\u80af\u5b9a\u6709\u6f5c\u5728\u7684\u5e94\u7528\u201d\uff0c\u5c24\u5176\u5728\u5149\u5b50\u5b66\u9886\u57df\u3002<\/span><\/p>\n

 <\/span><\/p>\n

Bartolo\u6700\u8fd1\u5173\u4e8e\u8d85\u9f50\u6784\u4f53\u5982\u4f55\u5728\u4e73\u6db2\u4e2d\u5f62\u6210\u7684\u53d1\u73b0\uff0c\u53ef\u4ee5\u8f6c\u5316\u6210\u7b80\u6613\u914d\u65b9\uff0c\u7528\u4e8e\u6405\u62cc\u6df7\u51dd\u571f\u3001\u5316\u5986\u54c1\u818f\u4f53\u3001\u73bb\u7483\u548c\u98df\u7269\u7b49\u3002\u201c\u6bcf\u5f53\u8981\u5206\u6563\u7cca\u72b6\u7269\u5185\u7684\u7c92\u5b50\u65f6\uff0c\u5c31\u9700\u8981\u5904\u7406\u56fa\u4f53\u9897\u7c92\u7684\u6df7\u5408\u95ee\u9898\u3002\u8fd9\u53ef\u4ee5\u4f5c\u4e3a\u5747\u5300\u5206\u6563\u56fa\u4f53\u9897\u7c92\u7684\u4e00\u79cd\u65b9\u6cd5\u3002\u201d<\/span><\/p>\n

 <\/span><\/p>\n

\u9996\u5148\uff0c\u786e\u5b9a\u6750\u6599\u7684\u7279\u5f81\u632f\u5e45\uff0c\u7136\u540e\u591a\u6b21\u4ee5\u8fd9\u4e00\u632f\u5e45\u6643\u52a8\u6750\u6599\uff0c\u8fd9\u6837\uff0c\u5747\u5300\u6df7\u5408\u7684\u8d85\u9f50\u6784\u5206\u5e03\u5c31\u51fa\u73b0\u4e86\u3002<\/span><\/strong>\u201c\u6211\u4e0d\u5e94\u8be5\u514d\u8d39\u544a\u8bc9\u4f60\u8fd9\u4e9b\uff0c\u800c\u5e94\u8be5\u521b\u5efa\u4e00\u4e2a\u516c\u53f8\uff01\u201dBartolo\u8bf4\u3002<\/span><\/p>\n


<\/p>\n

\"\u96c6\u667a\"<\/p>\n

\n

Salvatore Torquato\uff0c\u666e\u6797\u65af\u987f\u5927\u5b66\u7684\u7406\u8bba\u5316\u5b66\u5bb6\uff0c\u4ece21\u4e16\u7eaa\u521d\u5c31\u5f00\u59cb\u7814\u7a76\u8d85\u9f50\u6784\u4f53\u3002<\/span><\/p>\n<\/blockquote>\n

 <\/span><\/p>\n

\u4e8b\u5b9e\u4e0a\uff0cTorquato\u3001Steinhardt\u548c\u540c\u4e8b\u4eec\u5df2\u7ecf\u8fd9\u6837\u505a\u4e86\u3002\u4ed6\u4eec\u521b\u5efa\u7684\u516c\u53f8Etaphase\uff0c\u5c06\u751f\u4ea7\u8d85\u9f50\u6784\u5149\u5b50\u7535\u8def\u2014\u2014\u4e00\u79cd\u901a\u8fc7\u5149\u800c\u975e\u7535\u5b50\u4f20\u8f93\u6570\u636e\u7684\u8bbe\u5907\u3002\u51e0\u5e74\u524d\uff0c\u666e\u6797\u65af\u987f\u5927\u5b66\u7684\u79d1\u5b66\u5bb6\u53d1\u73b0\uff0c\u8d85\u9f50\u6784\u6750\u6599\u5b58\u5728\u201c\u5e26\u9699\u201d\uff08band gap\uff09\uff0c\u53ef\u4ee5\u963b\u6b62\u7279\u5b9a\u9891\u7387\u7684\u4f20\u64ad\u3002\u5e26\u9699\u4f7f\u5f97\u6570\u636e\u7684\u53d7\u63a7\u4f20\u8f93\u6210\u4e3a\u53ef\u80fd\uff0c\u56e0\u4e3a\u88ab\u963b\u6321\u7684\u9891\u7387\u53ef\u4ee5\u88ab\u6ce2\u5bfc\uff08waveguide\uff09\u5bb9\u7eb3\u548c\u5f15\u5bfc\u3002<\/span><\/p>\n

 <\/span><\/p>\n

\u5e26\u9699\u66fe\u88ab\u8ba4\u4e3a\u662f\u6676\u683c\u7279\u6709\u7684\uff0c\u5176\u4f20\u8f93\u65b9\u5411\u5fc5\u987b\u4e0e\u6676\u4f53\u7684\u5bf9\u79f0\u8f74\u65b9\u5411\u4e00\u81f4\u3002\u8fd9\u610f\u5473\u7740\uff0c\u5149\u5b50\u6ce2\u5bfc\u53ea\u80fd\u5728\u7279\u5b9a\u7684\u65b9\u5411\u4e0a\u4f20\u64ad\uff0c\u9650\u5236\u4e86\u5b83\u4f5c\u4e3a\u7535\u8def\u7684\u7528\u9014\u3002<\/strong><\/span><\/p>\n

 <\/span><\/p>\n

\u56e0\u4e3a\u8d85\u9f50\u6784\u6750\u6599\u6ca1\u6709\u4f20\u8f93\u65b9\u5411\u65b9\u5411\u7684\u9650\u5236\uff0c\u6211\u4eec\u77e5\u4e4b\u751a\u5c11\u7684\u5e26\u9699\u53ef\u80fd\u4f1a\u66f4\u6709\u5b9e\u9645\u7528\u9014\uff0c\u4f7f\u201c\u5f2f\u66f2\u7684\u6ce2\u5bfc\uff0c\u5e76\u4e14\u662f\u4efb\u4f55\u5e0c\u671b\u7684\u6ce2\u5bfc\u201d\u6210\u4e3a\u53ef\u80fd\uff0cSteinhardt\u8bf4\u3002<\/span><\/p>\n

 <\/span><\/p>\n

\u9e1f\u7c7b\u773c\u4e2d\u4e94\u79cd\u989c\u8272\u7684\u9a6c\u8d5b\u514b\u56fe\u6848\u88ab\u79f0\u4e3a\u201c\u591a\u89c6\u9525\u8d85\u9f50\u6784\u4f53\u201d \uff08multihyperuniform\uff09<\/strong>\uff0c\u81f3\u4eca\u4e3a\u6b62\uff0c\u5728\u81ea\u7136\u754c\u662f\u72ec\u4e00\u65e0\u4e8c\u7684\u3002<\/span><\/p>\n

 <\/span><\/p>\n

Corbo\u4ecd\u7136\u6ca1\u6709\u7cbe\u786e\u5730\u8bf4\u660e\u8fd9\u4e9b\u56fe\u6848\u662f\u5982\u4f55\u5f62\u6210\u7684\u3002\u5b83\u662f\u56e0\u4e3a\u89c6\u9525\u7ec6\u80de\u7684\u5f7c\u6b64\u6392\u65a5\u800c\u51fa\u73b0\uff1f\u8fd8\u662f\u56e0\u4e3a\u89c6\u9525\u7ec6\u80de\u50cf\u73bb\u7483\u5f39\u73e0\u4e00\u6837\u88ab\u6643\u52a8\u6210\u5982\u6b64\u5f62\u6001\uff1f\u4ed6\u66f4\u503e\u5411\u4e8e\u524d\u8005\u3002<\/span><\/p>\n

 <\/span><\/p>\n

\u7ec6\u80de\u53ef\u4ee5\u5206\u6ccc\u5206\u5b50\uff0c\u6392\u65a5\u540c\u4e00\u7c7b\u578b\u7684\u7ec6\u80de\uff0c\u4f46\u5bf9\u5176\u4ed6\u7c7b\u578b\u7684\u7ec6\u80de\u6ca1\u6709\u5f71\u54cd\u3002\u6216\u8bb8\u5728\u80da\u80ce\u53d1\u80b2\u8fc7\u7a0b\u4e2d\uff0c\u6bcf\u4e2a\u89c6\u9525\u7ec6\u80de\u90fd\u4f1a\u53d1\u51fa\u4fe1\u53f7\uff0c\u8868\u660e\u5b83\u5c06\u5206\u5316\u6210\u67d0\u79cd\u7c7b\u578b\uff0c\u4ee5\u9632\u6b62\u4e34\u8fd1\u7684\u7ec6\u80de\u505a\u540c\u6837\u7684\u4e8b\u60c5\u3002\u201c\u8fd9\u4e0d\u8fc7\u662f\u4e00\u4e2a\u89e3\u91ca\u4e8b\u60c5\u53ef\u80fd\u662f\u5982\u4f55\u53d1\u5c55\u7684\u7b80\u5355\u6a21\u578b\u3002\u6bcf\u4e00\u4e2a\u7ec6\u80de\u7684\u5c40\u90e8\u884c\u4e3a\u521b\u9020\u4e86\u5168\u5c40\u6a21\u5f0f\u3002\u201d<\/span><\/p>\n

 <\/span><\/p>\n

\u9664\u4e86\u9e21\u8fd9\u79cd\u6700\u5bb9\u6613\u83b7\u5f97\u7684\u3001\u7528\u4e8e\u5b9e\u9a8c\u5ba4\u7814\u7a76\u7684\u5bb6\u79bd\uff0c\u540c\u6837\u7684\u201c\u591a\u89c6\u9525\u8d85\u9f50\u6784\u4f53\u201d\u56fe\u6848\u4e5f\u51fa\u73b0\u5728Corbo\u7814\u7a76\u8fc7\u7684\u5176\u4ed6\u4e09\u79cd\u9e1f\u7c7b\u7684\u89c6\u7f51\u819c\u4e2d\uff0c\u8868\u660e\u8fd9\u79cd\u8fdb\u5316\u9002\u5e94\u6027\u662f\u666e\u904d\u7684\uff0c\u800c\u975e\u67d0\u79cd\u7279\u5b9a\u73af\u5883\u4e0b\u7684\u4ea7\u7269\u3002<\/span><\/p>\n

 <\/span><\/p>\n

\"\u96c6\u667a\"<\/div>\n

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

\u4ed6\u5f88\u597d\u5947\uff0c\u591c\u884c\u7269\u79cd\u662f\u5426\u5728\u8fdb\u5316\u8fc7\u7a0b\u4e2d\u4ea7\u751f\u4e86\u4e86\u4e00\u79cd\u4e0d\u540c\u7684\u89c6\u89c9\u7cfb\u7edf\u7684\u6700\u4f18\u7ed3\u6784\u3002\u201c\u8fd9\u5c06\u975e\u5e38\u6709\u8da3\uff0c\u4f46\u662f\uff0c\u62ff\u5230\u732b\u5934\u9e70\u7684\u773c\u775b\u96be\u5ea6\u662f\u5f88\u5927\u7684\u3002\u201d<\/span>
<\/p>\n


<\/p>\n

\n
\n

\u7ffb\u8bd1\uff1a\u6881\u91d1<\/span><\/p>\n

\u5ba1\u6821\uff1a\u738b\u4f1f\u5609<\/span><\/p>\n

\u7f16\u8f91\uff1a\u674e\u6c9b\u6b23<\/span>
<\/p>\n

\u539f\u6587\uff1a<\/span><\/p>\n

https:\/\/www.quantamagazine.org\/hyperuniformity-found-in-birds-math-and-physics-20160712\/<\/span><\/p>\n<\/blockquote>\n<\/section>\n

<\/section>\n


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

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

\u63a8\u8350\u9605\u8bfb<\/strong><\/span><\/p>\n

<\/strong><\/section>\n<\/section>\n<\/section>\n<\/section>\n<\/section>\n

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

\u535a\u7269\u5b66\u89c6\u89d2\u4e0b\u7684\u8fdb\u5316\u3001\u71b5\u4e0e\u81ea\u7136\u79e9\u5e8f<\/strong><\/span><\/a><\/p>\n

\u81ea\u7136\u4e3a\u4ec0\u4e48\u949f\u60c5\u4e8e\u6b63\u516d\u8fb9\u5f62\uff1f<\/strong><\/span><\/a><\/p>\n

\u8d28\u6570\u5206\u5e03\u3001\u6676\u4f53\u884d\u5c04\u548c\u5206\u5f62\u51e0\u4f55<\/strong><\/span><\/a><\/p>\n

<\/span>\u52a0\u5165\u96c6\u667a\uff0c\u4e00\u8d77\u590d\u6742\uff01\u96c6\u667a\u4ff1\u4e50\u90e8\u56e2\u961f\u62db\u65b0\u5566\uff01<\/a><\/strong><\/strong><\/span><\/p>\n


<\/p>\n

\n
\n
\n
\u63a8\u8350\u8bfe\u7a0b<\/strong><\/section>\n<\/section>\n<\/section>\n


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

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

\"\u96c6\u667a\"<\/p>\n

\u626b\u7801\u542c\u8bfe<\/strong><\/span><\/p>\n

\n
\n
\n
\n
\n
\n
\n
\n


<\/p>\n


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

\n

\"\u96c6\u667a\"
<\/p>\n


<\/p>\n

\n
\n
\n
\n
\n
\n

\u96c6\u667aQQ\u7fa4\uff5c292641157<\/span><\/strong><\/p>\n

\u5546\u52a1\u5408\u4f5c\u53ca\u6295\u7a3f\u8f6c\u8f7d\uff5cswarma@swarma.org
<\/span><\/strong><\/p>\n


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

\n

\u25c6 <\/span>\u25c6 <\/span>\u25c6<\/span><\/span><\/strong><\/strong><\/h1>\n<\/section>\n

\u641c\u7d22\u516c\u4f17\u53f7\uff1a\u96c6\u667a\u4ff1\u4e50\u90e8<\/span><\/strong><\/span><\/p>\n


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

\u52a0\u5165\u201c\u6ca1\u6709\u56f4\u5899\u7684\u7814\u7a76\u6240\u201d<\/span><\/strong><\/span><\/p>\n

\n

\"\u96c6\u667a\"<\/p>\n<\/section>\n

\u8ba9\u82f9\u679c\u7838\u5f97\u66f4\u731b\u70c8\u4e9b\u5427\uff01<\/span><\/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

\n

\u59cb\u53d1\u4e8e\u5fae\u4fe1\u516c\u4f17\u53f7\uff1a \u96c6\u667a\u4ff1\u4e50\u90e8 <\/p>\n<\/blockquote>\n<\/div>\n","protected":false},"excerpt":{"rendered":"

\u9e21\u7684\u89c6\u9525\u7ec6\u80de\u56fe\u8c31 \u5bfc\u8bed \u548c\u4eba\u7c7b\u76f8\u6bd4\uff0c\u9e1f\u7c7b\u6709\u66f4\u591a\u79cd\u7c7b\u7684\u89c6\u9525\u7ec6\u80de\uff0c\u800c\u8fd9\u4e9b\u7ec6\u80de\u7684\u6392\u5217\u65b9\u5f0f\u4e2d\u9690\u85cf\u7740\u8fdb\u5316\u5965\u79d8\u3002\u4e00\u8d77\u9605\u8bfb\u672c\u6587\uff0c\u4e86\u89e3\u8fd9\u4e2a\u6a2a\u8de8\u6570\u5b66\u3001\u7269\u7406\u3001\u5316\u5b66\u3001\u751f\u7269\u7684\u795e\u79d8\u95ee\u9898\u3002 \u7f16\u8bd1\uff1a\u96c6\u667a\u7ffb\u8bd1\u7ec4 \u6765\u6e90\uff1aquantamagazine.org \u539f\u9898\uff1aA Bird\u2019s-Eye View of Nature\u2019s Hidde…<\/p>\n","protected":false},"author":1,"featured_media":1185,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":[],"categories":[17],"tags":[],"special":[],"_links":{"self":[{"href":"https:\/\/swarma.org\/index.php?rest_route=\/wp\/v2\/posts\/1184"}],"collection":[{"href":"https:\/\/swarma.org\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/swarma.org\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/swarma.org\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/swarma.org\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=1184"}],"version-history":[{"count":1,"href":"https:\/\/swarma.org\/index.php?rest_route=\/wp\/v2\/posts\/1184\/revisions"}],"predecessor-version":[{"id":1200,"href":"https:\/\/swarma.org\/index.php?rest_route=\/wp\/v2\/posts\/1184\/revisions\/1200"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/swarma.org\/index.php?rest_route=\/wp\/v2\/media\/1185"}],"wp:attachment":[{"href":"https:\/\/swarma.org\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=1184"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/swarma.org\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=1184"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/swarma.org\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=1184"},{"taxonomy":"special","embeddable":true,"href":"https:\/\/swarma.org\/index.php?rest_route=%2Fwp%2Fv2%2Fspecial&post=1184"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}