{"id":646,"date":"2009-12-17T03:29:47","date_gmt":"2009-12-16T19:29:47","guid":{"rendered":"http:\/\/xiangge.andrewsun.net\/?p=646"},"modified":"2021-06-04T20:51:53","modified_gmt":"2021-06-04T12:51:53","slug":"%e8%b0%81%e6%9c%80%e5%85%88%e5%af%b9%e6%9d%90%e6%96%99%e6%96%bd%e5%8a%a0%e6%ad%a3%e5%bc%a6%e5%bd%a2%e5%8f%98%ef%bc%9fw-philippoff%e3%80%82","status":"publish","type":"post","link":"https:\/\/www.andrewsun.net\/panta_rhei\/archives\/646","title":{"rendered":"\u8c01\u6700\u5148\u5bf9\u6750\u6599\u65bd\u52a0\u6b63\u5f26\u5f62\u53d8\uff1fW. 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Philippoff\u3002\u8fd9\u4e2a\u4eba\u4f60\u5728Google\u4e0a\u9664\u4e86\u4ed6\u5199\u7684\u6587\u7ae0\u4e4b\u5916\u57fa\u672c\u4e0a\u641c\u4e0d\u5230\u4efb\u4f55\u76f8\u5173\u4fe1\u606f\uff0c\u6ca1\u4eba\u7ed9\u4ed6\u9881\u5956\u3001\u5199\u8ba3\u544a\u6216\u8005\u7eaa\u5ff5\u4f5c\u4f20\u3002<\/p>\n\n\n\n<p>\u4f46\u662f\uff0cW. Philippoff\u7edd\u5bf9\u662f\u725b\u4eba\u3002\u80fd\u5728Weissenberg\u516b\u5341\u5c81\u8bde\u8fb0\u7eaa\u5ff5\u96c6\u4e2d\u5199\u6587\u7ae0\u7684\u90fd\u662f\u6d41\u53d8\u5b66\u7684\u725b\u4eba\uff0c\u800c\u4e14\u6211\u4e5f\u6709\u597d\u51e0\u7bc7Philippoff\u7684\u6587\u7ae0\u3002\u6211\u8bb0\u5f97\u8fd9\u4e2a\u540d\u5b57\uff0c\u6700\u521d\u662f\u89c9\u5f97\u8fd9\u4e2a\u8bcd\u5f88\u53ef\u7231\u3002\u7ecf\u8fc7\u52aa\u529b\uff0c\u7ec8\u4e8e\u641c\u5230R. Tanner\u66fe\u7ecf\u5728Korea-Austr. Rheol. J.\u4e0a\u4ecb\u7ecd\u8fc7\u8fd9\u4e00\u6bb5\u5386\u53f2\uff0c\u53ef\u4f5c\u4e3a\u5bf9Philippoff\u81f4\u656c\u7684\u4ee3\u8868\u6027\u6587\u4ef6\u6dfb\u52a0\u5230W. Philippoff\u7684\u94fe\u63a5\u3002\u6709\u5174\u8da3\u7684\u670b\u53cb\u53ef\u4ee5\u5728\u5de6\u8fb9\u70b9\u51fbW. Philippoff\u7684\u94fe\u63a5\u770b\u770b\u8fd9\u7bc7\u6587\u7ae0\u3002\u539f\u6765\uff0c\u662fW. Philippoff\u5168\u540d\u662fWladimir Philippoff\uff0c\u7528\u5168\u540d\u53bbGoogle\u5012\u8fd8\u80fd\u627e\u5230\u4ed6<a href=\"http:\/\/dx.doi.org\/10.1122\/1.548938\">\u83b7\u9881Bingham\u5956<\/a>\u7684\u4fe1\u606f\u3002\u6211\u4e00\u76f4\u8fd8\u4ee5\u4e3a\u6700\u521d\u7528\u6b63\u5f26\u632f\u8361\u5f62\u53d8\u7684\u662fWeissenberg\u5462\u3002\u4e0d\u8fc7\u4e5f\u5dee\u4e0d\u591a\uff0c\u56e0\u4e3aWeissenber\u5728\u90a3\u65f6\u662fPhilippoff\u7684\u540c\u4e8b\u3002<\/p>\n\n\n\n<p>\u4e4b\u6240\u4ee5\u4f1a\u60f3\u5230\u7528\u6b63\u5f26\u5f62\u53d8\uff0c\u5176\u5b9e\u662f\u6709\u80cc\u666f\u7684\uff0c1850\u5e74\u5de6\u53f3\uff0c\u5f00\u59cb\u6709\u7535\u8bdd\u3002\u7531\u4e8e\u97f3\u9891\u662f\u5feb\u901f\u53d8\u5316\u7684\u7535\u6d41\uff0c\u8ddd\u79bb\u4e00\u957f\u4e86\u7684\u8bdd\u4ecb\u7535\u635f\u8017\u7684\u5f71\u54cd\u5c31\u5f88\u53ef\u89c2\uff0c\u4e8e\u662f\u91c7\u7528\u6b63\u5f26\u4ea4\u53d8\u7535\u538b\u7814\u7a76\u6750\u6599\u7684\u4ecb\u7535\u635f\u8017\u5c31\u6162\u6162\u5174\u8d77\u4e86\uff0c\u635f\u8017\u89d2\u6b63\u5207tan\u03b4\u4e4b\u7c7b\u7684\u6982\u5ff5\u4e5f\u662f\u4ece\u90a3\u91cc\u6765\u7684\u3002\u8fd9\u79cd\u77e5\u8bc6\u5230\u4e861933\u5e74Philippoff\u53d1\u660e\u6b63\u5f26\u5f62\u53d8\u7684\u65f6\u5019\u5df2\u7ecf\u662f\u7535\u6c14\u5de5\u7a0b\u7684\u57fa\u672c\u77e5\u8bc6\u4e86\uff0c\u800cPhilippoff\u6070\u6070\u662f\u5b66\u7535\u7684\uff0c\u6240\u4ee5\u4ed6\u60f3\u5230\u628a\u8fd9\u4e00\u5957\u4e1c\u897f\u8fd0\u7528\u5230\u6d41\u53d8\u5b66\u4e0a\u9762\u53bb\u3002\u7167\u8fd9\u6837\u7684\u8bf4\u6cd5\uff0c\u90a3\u4e48\u4e94\uff0c\u516d\u5341\u5e74\u4ee3\u7684\u6587\u7ae0\u4e2d\u51fa\u73b0\u7528Lissajous\u66f2\u7ebf\u8868\u5f81\u6750\u6599\u975e\u7ebf\u6027\u54cd\u5e94\u7684\u505a\u6cd5\uff0c\u5c31\u66f4\u52a0\u4e0d\u7b97\u4ec0\u4e48\u521b\u4e3e\u4e86\u2014\u2014Lissajous\u66f2\u7ebf\u5c31\u662f\u4ea4\u6d41\u7535\u65b9\u9762\u7684\u57fa\u672c\u77e5\u8bc6\u3002\u5230\u73b0\u5728\uff0c\u6211\u4eec\u8fd8\u5728\u7528\u52a8\u6001\u626b\u9891\u5b9e\u9a8c\u6765\u63a2\u6d4b\u8bb8\u8bb8\u591a\u591a\u7684\u6750\u6599\u7ed3\u6784\uff0c\u51e0\u6761Lissajous\u66f2\u7ebf\u8fd8\u8db3\u4ee5\u8ba9McKinley\u4ed6\u4eec\u5728Soft Matter\u4e0a\u53d1\u6587\u7ae0\uff0c\u8db3\u89c1Philippoff\u7ed9\u540e\u4eba\u63d0\u4f9b\u4e86\u4e00\u4e2a\u591a\u4e48\u5927\u7684\u996d\u7897\uff01\u7ed9\u540e\u4eba\u63d0\u4f9b\u5f88\u591a\u996d\u7897\u7684\u4eba\uff0c\u5176\u5b9e\u5c31\u662f\u8bfa\u8d1d\u5c14\u5956\u7ea7\u522b\u7684\u4eba\uff08\u90a3\u4e9b\u8bfa\u5956\u5f97\u4e3b\u65e0\u975e\u4e0d\u5c31\u662f\u4e3a\u540e\u9762\u7684\u5e73\u5eb8\u540c\u884c\u521b\u9020\u4e86\u4e2a\u6301\u4e45\u8010\u7528\u7684\u996d\u7897\u4e48\uff09\u3002<\/p>\n\n\n\n<p>\u6240\u4ee5Philippoff\u662f\u725b\u4eba\u662f\u7edd\u5bf9\u4e0d\u5dee\u7684\u3002<\/p>\n\n\n\n<p>\u6211\u8fd8\u65e0\u610f\u4e2d\u627e\u5230\u4e86Philippoff\u7684\u4eb2\u7b14\u7b7e\u540d\uff01\u90a3\u662f\u5728G. Natta\u7684\u7eaa\u5ff5\u7f51\u7ad9\u4e0a\u627e\u5230\u7684\u3002G. Natta\u5c31\u662f\u9f50\u683c\u52d2-\u7eb3\u5854\u7684\u90a3\u4e2a\u7eb3\u5854\u3002\u5728\u4ed6\u7f51\u7ad9\u6536\u4e86\u4ed6\u7684\u4e66\u4fe1\uff0c\u5e76\u6309\u53bb\u4fe1\u7684\u5355\u4f4d\u5206\u4e86\u7c7b\uff0c\u5176\u4e2d\u4e00\u4e2a\u5c31\u662fEsso Research &amp; Engineering\uff08\u5c31\u662f\u57c3\u7d22\u6c7d\u6cb9\u5427\uff09\uff0c\u800cPhilippoff\u5c31\u6b63\u662fEsso\u7684\u4eba\u3002\u4e66\u4fe1\u96c6\u91cc\u6536\u96c6\u4e86\u4e5f\u8bb8\u662f\u6240\u6709Esso\u4eba\u5458\u4e0eNatta\u7684\u4e66\u4fe1\u6765\u5f80\uff0c\u591a\u6570\u662f\u4e0eNatta\u8054\u7cfb\u5b66\u672f\u8bbf\u95ee\u7684\uff0c\u770b\u770b\u90a3\u65f6\u5019\u7684\u4eba\u4e92\u76f8\u5b66\u672f\u8bbf\u95ee\u641e\u8bb2\u5ea7\u7684\u6f6e\u6d41\u4e5f\u4e0d\u5931\u79cd\u8da3\u5473\u3002\u5176\u6b21\u5c31\u662f\u5411Natta\u7d22\u8981\u7b49\u89c4\u805a\u4e19\u70ef\u6837\u54c1\u6765\u73a9\u7684\u3002\u7b49\u89c4\u805a\u4e19\u70ef\u6070\u6070\u5c31\u662fZ-N\u50ac\u5316\u5242\u7684\u4e3e\u4e16\u6210\u679c\uff0c\u5728\u90a3\u4e2a\u65f6\u5019\u4e5f\u8bb8\u53ea\u6709Natta\u7684\u5b9e\u9a8c\u5ba4\u624d\u80fd\u505a\u5f97\u51fa\u6765\u3002\u6709\u8da3\u7684\u662f\uff0cNatta\u4e5f\u6c42\u8fc7Esso\u7814\u7a76\u6240\u5e2e\u4ed6\u6d4b\u7b49\u89c4\u805a\u4e19\u70ef\u7684\u5206\u5b50\u91cf\uff0c\u7ed3\u679cEsso\u7814\u7a76\u6240\u56de\u4fe1\u8bf4\u6ca1\u6709\u4eea\u5668\uff0c\u6d4b\u4e0d\u4e86\u3002\u54c8\u54c8\uff0c\u8ddf\u73b0\u5728\u6bd4\u8d77\u6765\uff0c\u90a3\u4e2a\u65f6\u5019\u771f\u83dc\u554a\uff01<\/p>\n\n\n\n<p>\u6240\u4ee5\uff0c\u5728\u4e66\u4fe1\u96c6\u91cc\u6211\u5c31\u627e\u5230\u4e86Philippoff\u7684\u4fe1\uff0c\u53ea\u6709\u4e00\u5c01\uff0c\u662f\u8054\u7cfb\u8bbf\u95eeNatta\u7684\u5b9e\u9a8c\u5ba4\u3002Philippoff\u7684\u56de\u4fe1\u672b\u5c3e\uff0c\u5c31\u9644\u4e86\u4e00\u4e2a\u4eb2\u7b14\u7b7e\u540d\uff1a<\/p>\n\n\n\n<figure class=\"wp-block-image\"><a href=\"http:\/\/www.andrewsun.net\/panta_rhei\/wp-content\/uploads\/2009\/12\/W.jpg\"><img loading=\"lazy\" decoding=\"async\" width=\"300\" height=\"95\" data-attachment-id=\"647\" data-permalink=\"https:\/\/www.andrewsun.net\/panta_rhei\/archives\/646\/w\" data-orig-file=\"https:\/\/www.andrewsun.net\/panta_rhei\/wp-content\/uploads\/2009\/12\/W.jpg\" data-orig-size=\"961,305\" data-comments-opened=\"1\" data-image-meta=\"{&quot;aperture&quot;:&quot;0&quot;,&quot;credit&quot;:&quot;&quot;,&quot;camera&quot;:&quot;&quot;,&quot;caption&quot;:&quot;&quot;,&quot;created_timestamp&quot;:&quot;0&quot;,&quot;copyright&quot;:&quot;&quot;,&quot;focal_length&quot;:&quot;0&quot;,&quot;iso&quot;:&quot;0&quot;,&quot;shutter_speed&quot;:&quot;0&quot;,&quot;title&quot;:&quot;&quot;}\" data-image-title=\"W. Philippoff\u7684\u7b7e\u540d\" data-image-description=\"\" data-image-caption=\"&lt;p&gt;W. Philippoff\u7684\u7b7e\u540d&lt;\/p&gt;\n\" data-large-file=\"https:\/\/www.andrewsun.net\/panta_rhei\/wp-content\/uploads\/2009\/12\/W.jpg\" src=\"http:\/\/www.andrewsun.net\/panta_rhei\/wp-content\/uploads\/2009\/12\/W-300x95.jpg\" alt=\"W. Philippoff\u7684\u7b7e\u540d\" class=\"wp-image-647\" title=\"W. Philippoff\u7684\u7b7e\u540d\" srcset=\"https:\/\/www.andrewsun.net\/panta_rhei\/wp-content\/uploads\/2009\/12\/W-300x95.jpg 300w, https:\/\/www.andrewsun.net\/panta_rhei\/wp-content\/uploads\/2009\/12\/W.jpg 961w\" sizes=\"auto, (max-width: 300px) 100vw, 300px\" \/><\/a><\/figure>\n\n\n\n<p>Update 2021\uff1a\u539f\u6587\u6240\u8bf4\u7684\u201cG. Natta\u7684\u7eaa\u5ff5\u7f51\u7ad9\u201d\uff0c\u73b0\u5728\u627e\u4e0d\u5230\u4e86\u3002<a rel=\"noreferrer noopener\" href=\"http:\/\/www.giulionatta.it\" data-type=\"URL\" data-id=\"http:\/\/www.giulionatta.it\" target=\"_blank\">\u8fd9\u4e2a\u7f51\u7ad9<\/a>\u662f\u66f4\u52a0\u5168\u9762\u7684G. Natta\u751f\u524d\u8d44\u6599\u5b58\u6863\u7f51\u7ad9\uff0c\u4f46\u4e5f\u5f88\u96be\u627e\u51fa\u539f\u6587\u6240\u8bf4\u7684\u90a3\u4e9b\u4fe1\u606f\u4e86\u3002<\/p>\n<!-- kcite active, but no citations found -->\n<\/div> <!-- kcite-section 646 -->","protected":false},"excerpt":{"rendered":"<p>\u6211\u5207\u5165\u5927\u5e45\u632f\u8361\u526a\u5207\u6d41\u53d8\u5b66\u8fd9\u4e00\u9886\u57df\u7684\u65f6\u5019\uff0c\u4ece1835\u5e74Webber\u7684\u90a3\u7bc7\u8bb2\u8695\u4e1d\u8815\u53d8\u7684\u6587\u7ae0\u8d77\uff0c\u4e00\u5171\u6536\u96c6\u4e86\u8fd1500\u7bc7paper\uff08\u5305\u62ec1841\u5e74\u67ef\u897f\u5728\u6570\u5b66\u4e0a\u63cf\u8ff0\u6750\u6599\u5f62\u53d8\u7684\u8bb0\u5fc6\u6548\u5e94\u7684\u6587\u7ae0\uff09\u3002\u6211\u4e3b\u8981\u6536\u96c6\u7684\u662f\u805a\u5408\u7269\u7684\u975e\u7ebf\u6027\u6d41\u53d8\u5b66\u7406\u8bba\u548c\u5b9e\u9a8c\u7684\u6587\u732e\uff0c\u5c24\u5176\u662f\u632f\u8361\u5f62\u53d8\u6cd5\u3002\u867d\u7136\u8fd9\u4e48\u591a\u7bc7\u6587\u7ae0\u7684\u5185\u5bb9\u6211\u4e0d\u4e00\u5b9a\u90fd\u8bb0\u5f97\uff0c\u4f46\u662f\u4e00\u4e9b\u7ecf\u5e38\u51fa\u73b0\u7684\u4eba\u540d\uff0c\u8fd8\u6709\u4e00\u4e9b\u867d\u7136\u51fa\u73b0\u5f97\u5c11\u4f46\u88ab\u516c\u8ba4\u4e3a\u5927\u725b\u6216\u5143\u8001\u7684\u4eba\uff0c\u6211\u8fd8\u662f\u77e5\u9053\u7684\u3002\u4eca\u5929\u6211\u628a\u672c\u535a\u5ba2\u4e3b\u9875\u53f3\u8fb9\u7684\u201c\u6d41\u53d8\u5b66\u5bb6\u201d\u680f\u76ee\u5b8c\u5584\u4e86\uff0c\u6839\u636e\u7684\u5c31\u662f\u6211\u4ece\u770bpaper\u8fc7\u7a0b\u4e2d\u4e86\u89e3\u5230\u7684\u4e00\u4e9b\u725b\u4eba\uff0c\u6709\u6b7b\u4e86\u7684\u6709\u6ca1\u6b7b\u7684\u3002\u5176\u94fe\u63a5\u90fd\u662f\u627e\u7684\u6700\u6709\u4ee3\u8868\u6027\u7684\u7f51\u9875\u6216\u6587\u4ef6\u3002\u5176\u4e2d\u6709\u4e00\u4e2a\u4eba\u8ba9\u6211\u627e\u5f97\u6700\u8f9b\u82e6\uff0c\u90a3\u5c31\u662fW. Philippoff\u3002\u8fd9\u4e2a\u4eba\u4f60\u5728Google\u4e0a\u9664\u4e86\u4ed6\u5199\u7684\u6587\u7ae0\u4e4b\u5916\u57fa\u672c\u4e0a\u641c\u4e0d\u5230\u4efb\u4f55\u76f8\u5173\u4fe1\u606f\uff0c\u6ca1\u4eba\u7ed9\u4ed6\u9881\u5956\u3001\u5199\u8ba3\u544a\u6216\u8005\u7eaa\u5ff5\u4f5c\u4f20\u3002 \u4f46\u662f\uff0cW. Philippoff\u7edd\u5bf9\u662f\u725b\u4eba\u3002\u80fd\u5728Weissenberg\u516b\u5341\u5c81\u8bde\u8fb0\u7eaa\u5ff5\u96c6\u4e2d\u5199\u6587\u7ae0\u7684\u90fd\u662f\u6d41\u53d8\u5b66\u7684\u725b\u4eba\uff0c\u800c\u4e14\u6211\u4e5f\u6709\u597d\u51e0\u7bc7Philippoff\u7684\u6587\u7ae0\u3002\u6211\u8bb0\u5f97\u8fd9\u4e2a\u540d\u5b57\uff0c\u6700\u521d\u662f\u89c9\u5f97\u8fd9\u4e2a\u8bcd\u5f88\u53ef\u7231\u3002\u7ecf\u8fc7\u52aa\u529b\uff0c\u7ec8\u4e8e\u641c\u5230R. Tanner\u66fe\u7ecf\u5728Korea-Austr. Rheol. J.\u4e0a\u4ecb\u7ecd\u8fc7\u8fd9\u4e00\u6bb5\u5386\u53f2\uff0c\u53ef\u4f5c\u4e3a\u5bf9Philippoff\u81f4\u656c\u7684\u4ee3\u8868\u6027\u6587\u4ef6\u6dfb\u52a0\u5230W. 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Giacomin\u57282012\u5e74\u6587\u7ae0\u7684\u6807\u9898\u66f4\u503c\u5f97\u5173\u5fc3\u7684\u4e00\u4e2a\u95ee\u9898\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":374,"url":"https:\/\/www.andrewsun.net\/panta_rhei\/archives\/374","url_meta":{"origin":646,"position":1},"title":"\u6d41\u53d8\u5b66\u8bb2\u4e60\u73ed\u2014\u2014\u51e0\u672c\u6d41\u53d8\u5b66\u65b9\u9762\u7684\u4e66","author":"Andrew","date":"2009\u5e747\u67088\u65e5","format":false,"excerpt":"\u5728\u6d41\u53d8\u5b66\u8bb2\u4e60\u73ed\u4e0a\u6709\u5f88\u591a\u4eba\u63d0\u51fa\u627e\u4e0d\u5230\u6d41\u53d8\u5b66\u65b9\u9762\u7684\u6559\u6750\u3002\u6211\u77e5\u9053\u7684\u6559\u6750\u4e5f\u4e0d\u591a\uff0c\u6211\u4e5f\u6ca1\u6709\u90fd\u5168\u90e8\u770b\u5b8c\u3002\u4f46\u662f\u53cd\u6b63\u6211\u8ba4\u4e3a\u6d41\u53d8\u5b66\u5e76\u4e0d\u7f3a\u4e66\u3002\u6211\u73b0\u5728\u51b3\u5b9a\u82b1\u65f6\u95f4\u770b\uff0c\u5e76\u4e14\u6b63\u5728\u770b\u7684\u662fBird\u5199\u7684\u4e66Dynamics of Polymeric Liquids\uff08\u5171\u4e24\u5377\uff09\u3002\u8fd9\u5957\u4e66\u53ef\u4ee5\u8bf4\u662f\u6d41\u53d8\u5b66\u7684\u201c\u4ece\u5165\u95e8\u5230\u7cbe\u901a\u201d\u3002\u5982\u679c\u60f3\u53ea\u770b\u4e00\u672c\u4e66\uff0c\u5e94\u8be5\u770b\u8fd9\u672c\u3002\u5982\u679c\u8981\u4e13\u6ce8\u672c\u6784\u65b9\u7a0b\uff0cLarson\u6709\u4e00\u672cConstitutive Equations for Polymer Metls and Solutions\u3002\u4ed6\u8fd8\u6709\u4e00\u672cThe Structure and Rheology of Complex Fluids\uff0c\u5305\u62ec\u4e86\u9664\u9ad8\u805a\u7269\u4e4b\u5916\u7684\u5176\u4ed6\u590d\u6742\u6d41\u4f53\u7684\u6d41\u53d8\u73b0\u8c61\uff0c\u662f\u4e00\u4e2a\u5927\u89c2\u56ed\u3002\u5feb\u901f\u5165\u95e8\uff0c\u53ef\u4ee5\u770bPhan-Thien\u7684Understanding 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Rheology\uff0c\u5185\u5bb9\u975e\u5e38\u7684\u5168\uff0c\u53ef\u4ee5\u7528\u6765\u8865\u77e5\u8bc6\u3002\u540c\u65f6\uff0c\u6211\u8fd8\u6709\u4e00\u4e2a\u611f\u60f3\u3002\u4ee5\u5927\u5e45\u632f\u8361\u51cf\u5207\uff08LAOS\uff09\u4e3a\u4f8b\uff0c\u73b0\u5728\u5f88\u591a\u4eba\u90fd\u8ba4\u4e3a\u8fd9\u662f\u5f88\u65b0\u7684\u4e1c\u897f\uff0c\u6d41\u53d8\u5b66\u8bb2\u4e60\u73ed\u4e0a\u7684\u8001\u5e08\u4e5f\u4e0d\u4f8b\u5916\u3002\u5176\u5b9eWeissenberg\u5728\u53d1\u660e\u5b83\u7684\u6d41\u53d8\u4eea\u7684\u65f6\u5019\u5c31\u5df2\u7ecf\u63d0\u51fa\u8fc7\u8c10\u6ce2\u5206\u6790\u4e86\uff0c\u5207\u5b9e\u505a\u8c10\u6ce2\u5206\u6790\u7684\u6587\u7ae0\u65e9\u5728\u4e03\u5341\u5e74\u4ee3\u4e5f\u90fd\u6709\u4e86\u3002\u53ea\u662f\u56e0\u4e3a\u8fd9\u4e2a\u8c10\u6ce2\u5206\u6790\u6ca1\u6709\u7269\u7406\u610f\u4e49\uff0c\u4e00\u76f4\u4e0d\u53d7\u91cd\u89c6\u3002\u5230\u4eca\u5929\u5b83\u53d7\u91cd\u89c6\u4e86\uff0c\u65e0\u975e\u662f\u56e0\u4e3a\u79d1\u5b66\u5728\u4eca\u5929\u8fd9\u4e2a\u65f6\u4ee3\u975e\u5e38\u6d6e\u8e81\u7684\u7f18\u6545\u3002\u73b0\u5728\u7684\u7814\u7a76\u751f\u770b\u6765\u770b\u53bb\u90fd\u662f\u8fd1\u51e0\u5e74\u7684paper\uff0c\u5927\u591a\u90fd\u57f9\u517b\u51fa\u8fd9\u79cd\u6d6e\u8e81\u7684\u5fc3\u6001\uff0c\u8001\u4e00\u4ee3\u79d1\u5b66\u5148\u9a71\u7684\u90a3\u79cd\u4e25\u8c28\u5b66\u98ce\u548c\u5b66\u672f\u54c1\u5473\u5df2\u7ecf\u6240\u5269\u65e0\u51e0\u4e86\u3002\u6211\u89c9\u5f97\u641e\u6d41\u53d8\u5b66\u7814\u7a76\u4e5f\u597d\uff0c\u641e\u4efb\u4f55\u5316\u5b66\u7814\u7a76\u4e5f\u597d\uff0c\u4e0d\u8981\u4f9d\u8d56review\u548c\u4e66\uff0c\u8981\u4eb2\u81ea\u770b\u51e0\u5341\u5e74\u524d\u7684\u53e4\u8001\u6587\u732e\uff0c\u53d7\u4e00\u4e0b\u90a3\u4e2a\u65f6\u4ee3\u7684\u5b66\u98ce\u7684\u85b0\u9676\uff0c\u8981\u4e86\u89e3\u5b66\u79d1\u7684\u53d1\u5c55\u5386\u53f2\u3002\u4ee5\u4e0a\u63a8\u8350\u7684\u4e66\uff0c\u4f5c\u8005\u672c\u8eab\u90fd\u662f\u6d41\u53d8\u5b66\u5148\u9a71\uff0c\u4eb2\u8eab\u7ecf\u5386\u4e86\u6d41\u53d8\u5b66\u7684\u53d1\u5c55\uff0c\u56e0\u6b64\u4e66\u4e2d\u900f\u9732\u7740\u5386\u53f2\u6c14\u8d28\u3002\u6d41\u53d8\u5b66\u8fd8\u6709\u5f88\u591a\u6700\u8fd1\u51fa\u7248\u7684\u6559\u6750\uff0c\u6211\u90fd\u4e0d\u53bb\u770b\uff0c\u5c31\u662f\u56e0\u4e3a\u5b83\u4eec\u6ca1\u6709\u6c14\u8d28\u3002\u9664\u6b64\u4e4b\u5916\uff0c\u8fd8\u6709\u5f88\u591a\u4e13\u95e8\u201c\u5fc6\u82e6\u601d\u751c\u201d\u7684\u8d44\u6599\uff0c\u4f8b\u5982\u82f1\u56fd\u6d41\u53d8\u5b66\u4f1a\u7684\u7eaa\u5ff5K. Weissenberg\u8bde\u8fb080\u5468\u5e74\u7684\u4e13\u9898\uff0cLarson\u3001Giesekus\u3001Lodge\u3001Philippoff\u3001Markovitz\u7b49\u6d41\u53d8\u5b66\u5143\u8001\u4eb2\u81ea\u6267\u7b14\u5199\u6587\u7ae0\uff0c\u975e\u5e38\u6709\u4ef7\u503c\u3002\u5176\u6b21\u5c31\u662fWaters\u548cPhan-Thien\u4e3b\u7f16\u7684Rheology Series Vol. 7\uff1aRheology - An Historical Perspective\uff0c\u8bb2\u8ff0\u4e86\u6574\u4e2a\u6d41\u53d8\u5b66\u7684\u53d1\u5c55\u53f2\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":9177,"url":"https:\/\/www.andrewsun.net\/panta_rhei\/archives\/9177","url_meta":{"origin":646,"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\\] \u5728\u4eca\u5929\uff0c\u6211\u4eec\u7684\u5b9e\u9a8c\u4fe1\u53f7\u57fa\u672c\u90fd\u5df2\u7ecf\u6570\u5b57\u5316\uff0c\u5728\u7535\u5b50\u8ba1\u7b97\u673a\u4e2d\u4e00\u79d2\u949f\u4e0d\u5230\u5c31\u505a\u5b8c\u4e86\u4e00\u4e2a\u5feb\u901fFourier\u53d8\u6362\u8ba1\u7b97\u3002\u4f46\u662f\u5728\u4e0a\u4e16\u7eaa50~60\u5e74\u4ee3\uff0c\u7535\u5b50\u8ba1\u7b97\u673a\u8fd8\u6ca1\u53d1\u660e\u4e4b\u524d\uff0c\u5b9e\u9a8c\u7ed3\u679c\u672c\u8eab\u5c31\u53ef\u80fd\u662f\u901a\u8fc7X-Y\u8bb0\u5f55\u4eea\u6216\u53cc\u7b14\u8bb0\u5f55\u4eea\u753b\u5728\u5750\u6807\u7eb8\u4e0a\u7684\u3002\u5f53\u65f6\u7684\u4eba\u662f\u600e\u6837\u5bf9\u8fd9\u4e48\u4e00\u6bb5\u58a8\u8ff9\u8fdb\u884cFourier\u7ea7\u6570\u5206\u6790\u7684\u5462\uff1f\u6211\u4eec\u53ef\u4ee5\u770b\u5230\uff0cFourier\u7ea7\u6570\u7684\u5404\u4e2a\u7cfb\u6570$c_n$\u662f\u4e00\u4e2a\u79ef\u5206\u3002\u5728\u90a3\u4e2a\u5e74\u4ee3\uff0c\u79ef\u5206\u53ef\u4ee5\u4f7f\u7528\u6b27\u62c9\u6cd5\u6570\u503c\u6c42\u89e3\u3002\u5728\u6b64\u4e4b\u524d\uff0c\u9700\u8981\u5c06\u88ab\u79ef\u51fd\u6570\u8fdb\u884c\u4eba\u5de5\u91c7\u6837\uff08sampling\uff09\u79bb\u6563\u5316\u3002\u56e0\u6b64\u8fd9\u662f\u4e00\u4e2a\u5f88\u7e41\u7410\u7684\u4efb\u52a1\u3002 \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":353,"url":"https:\/\/www.andrewsun.net\/panta_rhei\/archives\/353","url_meta":{"origin":646,"position":3},"title":"\u4f55\u8c13\u5927\u5e45\uff1f\u53e6\u4e00\u79cd\u5b9a\u4e49\u3002","author":"Andrew","date":"2009\u5e748\u670817\u65e5","format":false,"excerpt":"\u6211\u7684\u8bfe\u9898\u662f\u5173\u4e8e\u5927\u5e45\u632f\u8361\u526a\u5207\uff08Large Amplitude Oscillatory Shearing, LAOS\uff09\u6d41\u53d8\u5b9e\u9a8c\u3002\u6240\u8c13\u632f\u8361\u526a\u5207\uff08Oscillatory Shearing\uff09\u6307\u7684\u5176\u5b9e\u5c31\u662f\u52a8\u6001\u529b\u5b66\u6d4b\u8bd5\u7684\u526a\u5207\u5f62\u53d8\u7248\uff0c\u7ed9\u8bd5\u6837\u65bd\u52a0\u6b63\u5f26\u65f6\u95f4\u51fd\u6570\u7684\u5f80\u590d\u5f62\u53d8\uff0c\u56e0\u6b64\u8fd9\u91cc\u9762\u624d\u6709\u4e2a\u201c\u632f\u5e45\u201d\u7684\u56e0\u7d20\u3002\u539f\u672c\u6309\u7167\u6211\u7684\u7406\u89e3\u7a0b\u5ea6\uff0c\u5927\u5bb6\u5173\u5fc3\u201c\u5927\u5e45\u201d\u7684\u632f\u8361\u526a\u5207\uff0c\u5b9e\u9645\u4e0a\u662f\u5728\u5173\u5fc3\u975e\u7ebf\u6027\u7c98\u5f39\u6027\u3002\u56e0\u4e3a\u8bb8\u591a\u7c98\u5f39\u6027\u8bd5\u6837\u90fd\u662f\u5728\u5927\u5e45\u5ea6\u5e94\u53d8\u4e0b\u8868\u73b0\u51fa\u660e\u663e\u7684\u975e\u7ebf\u6027\u884c\u4e3a\u7684\u3002\u7167\u6211\u7406\u89e3\u6240\u6709\u7c98\u5f39\u6027\u6837\u54c1\u90fd\u662f\u975e\u7ebf\u6027\u7c98\u5f39\u6027\u7684\u3002\u5728\u5b66\u754c\u8ba4\u8bc6\u4e86\u975e\u7ebf\u6027\u7c98\u5f39\u6027\u4e4b\u540e\uff0c\u7ebf\u6027\u7c98\u5f39\u6027\u7684\u90a3\u4e00\u5957\u5b9a\u5f8b\u53ea\u80fd\u8bf4\u662f\u5728\u5c0f\u5e45\u5f62\u53d8\u4e0b\u7684\u7b80\u5316\u8fd1\u4f3c\uff0c\u5c31\u597d\u50cf\u725b\u987f\u529b\u5b66\u5b9a\u5f8b\u662f\u76f8\u5bf9\u8bba\u5728\u4f4e\u901f\u6761\u4ef6\u4e0b\u7684\u7b80\u5316\u8fd1\u4f3c\u4e00\u6837\u3002\u81f3\u5e95\u4ec0\u4e48\u65f6\u5019\u7b97\u201c\u5927\u5e45\u201d\uff0c\u4ec0\u4e48\u65f6\u5019\u4e0d\u80fd\u5ffd\u7565\u975e\u7ebf\u6027\u7c98\u5f39\u6027\u7684\u95ee\u9898\uff0c\u4e5f\u5c31\u8ddf\u5230\u5e95\u4ec0\u4e48\u65f6\u5019\u662f\u9ad8\u901f\uff0c\u4ec0\u4e48\u65f6\u5019\u8981\u8003\u8651\u76f8\u5bf9\u8bba\u7684\u95ee\u9898\u4e00\u4e2a\u6027\u8d28\u3002\u5927\u5e45\u548c\u5c0f\u5e45\u4e4b\u95f4\u6ca1\u6709\u660e\u786e\u7684\u754c\u9650\u3002\u8fd9\u79cd\u7406\u89e3\u53ef\u80fd\u8981\u53d8\u4e00\u4e0b\u4e86\u30022005\u5e74Nature\u4e0a\u7684\u4e00\u7bc7\u6587\u7ae0\uff08Nature 2005, 438, 997-1100\uff09\u8003\u5bdf\u4e86\u60ac\u6d6e\u6db2\u5728\u632f\u8361\u526a\u5207\u4e0b\u60ac\u6d6e\u7c92\u5b50\u7684\u884c\u8e2a\u95ee\u9898\u3002\u53d1\u73b0\u5982\u679c\u632f\u8361\u526a\u5207\u7684\u5e45\u5ea6\u8db3\u591f\u5c0f\uff0c\u60ac\u6d6e\u7c92\u5b50\u57fa\u672c\u4e0a\u539f\u5730\u4e0d\u52a8\uff1b\u5f53\u5e45\u5ea6\u5927\u4e8e\u4e00\u5b9a\u7a0b\u5ea6\uff0c\u7c92\u5b50\u5c31\u6df7\u8d77\u6765\u4e86\uff0c\u5177\u6709\u6269\u6563\u7684\u6027\u8d28\u3002\u8be5\u5c0f\u7ec4\u8fdb\u4e00\u6b65\uff08Nat. Phys. 2008, 4, 420-424\uff09\u901a\u8fc7\u5efa\u6a21\u5728\u4e8c\u7ef4\u7a7a\u95f4\u91cd\u73b0\u4e86\u8fd9\u4e00\u73b0\u8c61\uff0c\u8868\u660e\u8fd9\u662f\u4e00\u79cd\u76f8\u53d8\uff0c\u6709\u6e1d\u6e17\u9608\u503c\u3002\u8fd9\u51e0\u5929\u53c8\u770b\u5230Menon\u5bf9\u8fd9\u4e00\u73b0\u8c61\u8fdb\u884c\u540e\u7eed\u7814\u7a76\uff08Phys. Rev. E 2009, 79, 061108\uff09\uff0c\u8c8c\u4f3c\u60f3\u8ba8\u8bbauniversality\u7684\u95ee\u9898\uff0c\u4f46\u5177\u4f53\u6211\u8fd8\u6ca1\u770b\u61c2\u3002\u8fd9\u4e00\u7cfb\u5217\u7814\u7a76\u5df2\u7ecf\u662f\u5728\u8ba8\u8bba\u632f\u8361\u526a\u5207\u7684\u5e45\u5ea6\u95ee\u9898\u4e86\uff0c\u53ea\u662f\u6ca1\u6709\u8ddf\u975e\u7ebf\u6027\u7c98\u5f39\u6027\u8054\u7cfb\u8d77\u6765\u3002\u4f5c\u8005\u662f\u5177\u4f53\u5230\u60ac\u6d6e\u6db2\u8fd9\u4e00\u4f53\u7cfb\uff0c\u4ececreep flow\u7684\u65b9\u7a0b\u51fa\u53d1\u8003\u8651\u95ee\u9898\uff0c\u76f8\u53d8\u539f\u56e0\u89e3\u91ca\u4e3a\u7c92\u5b50\u4e4b\u95f4\u7684\u76f8\u4e92\u4f5c\u7528\u5bfc\u81f4\u7684\u975e\u5e73\u8861\u6001\u3002\u800c\u5728\u6d41\u53d8\u5b66\u4e2d\uff0c\u5927\u5e45\u5f62\u53d8\u4e0b\u8bd5\u6837\u51fa\u73b0\u975e\u7ebf\u6027\u7c98\u5f39\u6027\u7684\u89e3\u91ca\u4e5f\u662f\u67d0\u79cd\u5e73\u8861\u7684\u7834\u574f\u3002\u6211\u731c\u6d4b\u8fd9\u4e24\u8005\u662f\u540c\u4e00\u4ef6\u4e8b\uff0c\u51fa\u73b0\u6df7\u6c8c\u7684\u90a3\u4e2a\u76f8\u53d8\u9608\u632f\u5e45\u5c31\u5bf9\u5e94\u7740\u975e\u7ebf\u6027\u7c98\u5f39\u6027\u4e0d\u53ef\u5ffd\u7565\u7684\u90a3\u4e2a\u632f\u5e45\u3002Nat. Phys.\u90a3\u7bc7\u6587\u7ae0\u8fd8\u8bf4\u76f8\u53d8\u4e4b\u540e\u6709\u81ea\u7ec4\u7ec7\u884c\u4e3a\uff0c\u800c\u8bb8\u591a\u8bd5\u6837\u5728\u5927\u5e45\u526a\u5207\u4e0b\u4e5f\u7684\u786e\u51fa\u73b0\u8bf8\u5982shear banding\u3001shear-induced ordering\u7684\u73b0\u8c61\uff0c\u6211\u731c\u6d4b\u4e8c\u8005\u4e5f\u662f\u5bf9\u5e94\u7684\u3002\u4e0d\u8fc7\uff0c\u5176\u4ed6\u8bd5\u6837\u60ac\u6d6e\u4f53\u7cfb\uff0c\u5982\u679c\u8981\u8bc1\u660e\u8fd9\u4e9b\u90fd\u662f\u540c\u4e00\u7c7b\u76f8\u53d8\u7684universality\uff0c\u4f3c\u4e4e\u8981\u5728creep flow\u65b9\u7a0b\u7684\u57fa\u7840\u4e0a\u8fdb\u4e00\u6b65\u62bd\u8c61\u7684\u7406\u8bba\u624d\u884c\u3002\u6211\u662f\u505a\u5b9e\u9a8c\u7684\u4e0d\u662f\u505a\u7406\u8bba\u7684\uff0c\u6211\u7422\u78e8\u7740\u8fd9\u4e00\u76f8\u53d8\u5728\u6d41\u53d8\u5b66\u51fd\u6570\u4e2d\u80fd\u4e0d\u80fd\u4f53\u73b0\u51fa\u6765\uff0c\u80fd\u4e0d\u80fd\u628a\u5b83\u4ece\u5b9e\u9a8c\u4e0a\u505a\u51fa\u6765\u3002Menon, G., & Ramaswamy, S. (2009). Universality class of the reversible-irreversible transition in sheared suspensions Physical Review E, 79 (6) DOI: 10.1103\/PhysRevE.79.061108","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":1742,"url":"https:\/\/www.andrewsun.net\/panta_rhei\/archives\/1742","url_meta":{"origin":646,"position":4},"title":"\u6d41\u53d8\u5b66\u4e09\u7ae0","author":"Andrew","date":"2010\u5e7411\u670812\u65e5","format":false,"excerpt":"\u6d41\u53d8\u5b66\u4e4b\u4e00\u2014\u2014Pardon me? 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