{"id":6670,"date":"2015-09-27T00:48:29","date_gmt":"2015-09-26T16:48:29","guid":{"rendered":"http:\/\/www.andrewsun.net\/panta_rhei\/?p=6670"},"modified":"2020-02-04T23:39:31","modified_gmt":"2020-02-04T15:39:31","slug":"plastic-number","status":"publish","type":"post","link":"https:\/\/www.andrewsun.net\/panta_rhei\/archives\/6670","title":{"rendered":"Plastic Number"},"content":{"rendered":"<div class=\"kcite-section\" kcite-section-id=\"6670\">\n<p>\u9ec4\u91d1\u6bd4\u4f8b\u6570\u5927\u5bb6\u90fd\u77e5\u9053\uff0c\u662f\u4e00\u4e2a\u65e0\u7406\u6570$\\phi=1.618\\cdots$\u3002\u8bb8\u591a\u7406\u8bba\u8bba\u8bc1\u5927\u81ea\u7136\u5f88\u591a\u81ea\u53d1\u6216\u6700\u4f18\u7684\u7ed3\u679c\u9075\u5faa\u8fd9\u4e2a\u6bd4\u4f8b\uff0c\u7f8e\u672f\u3001\u5efa\u7b51\u548c\u97f3\u4e50\u4e0a\u8fd9\u4e2a\u6bd4\u4f8b\u4e5f\u4ea7\u751f\u4e86\u795e\u5947\u7684\u548c\u8c10\u3002\u5229\u7528\u8fd9\u4e2a\u6bd4\u4f8b\u53ef\u4f5c\u51fa\u9ec4\u91d1\u87ba\u7ebf\u3002<\/p>\n<p><a title=\"By FakeRealLogSpiral.png: Pau derivative work: silverhammermba (FakeRealLogSpiral.png) [CC-BY-SA-3.0 (http:\/\/creativecommons.org\/licenses\/by-sa\/3.0\/) or GFDL (http:\/\/www.gnu.org\/copyleft\/fdl.html)], via Wikimedia Commons\" href=\"https:\/\/commons.wikimedia.org\/wiki\/File%3AFakeRealLogSpiral.svg\"><img decoding=\"async\" width=\"512\" alt=\"FakeRealLogSpiral\" src=\"https:\/\/upload.wikimedia.org\/wikipedia\/commons\/thumb\/a\/a5\/FakeRealLogSpiral.svg\/512px-FakeRealLogSpiral.svg.png\"\/><\/a><\/p>\n<p>\u4e0a\u56fe\u662f\u4e09\u79cd\u5f62\u72b6\u5341\u5206\u63a5\u8fd1\u9ec4\u91d1\u87ba\u7ebf\u7684\u87ba\u7ebf\u3002<\/p>\n<p>\u6700\u8fd1\u5728\u7f51\u4e0a\u770b\u5230\u53e6\u4e00\u4e2a\u7c7b\u4f3c\u7684\u65e0\u7406\u6570\uff0c\u53eb\u201c\u5851\u6599\u6570\u201d\uff08<a href=\"https:\/\/en.wikipedia.org\/wiki\/Plastic_number\" target=\"_blank\" rel=\"noopener noreferrer\">plastic number<\/a>\uff09\u3002\u6211\u89c9\u5f97\u6bd4\u8f83\u6709\u8da3\u7684\u662f\uff0c\u628a\u97f3\u7b26\u6309\u6309\u4f3c\u9ec4\u91d1\u6bd4\u4f8b\u7684Fibonacci\u6570\u5217\u6392\u5217\uff0c\u53d1\u73b0\u662f\u7ecf\u5e38\u88ab\u4f7f\u7528\u7684\u65cb\u5f8b1,2,3,5\uff0c\u8fd9\u4e2a\u6897\u5df2\u7ecf\u5e7f\u4e3a\u4eba\u6240\u77e5\u3002\u90a3\u4e48\u7528plastic number\u4f5c\u6bd4\u4f8b\u7684Padovan\u6570\u5217\u5f97\u51fa\u7684\u65cb\u5f8b\u662f\u600e\u4e48\u6837\u7684\u5462\uff1f<a href=\"https:\/\/bib.irb.hr\/datoteka\/628836.Plastic_Number_-_Construct.pdf\" target=\"_blank\" rel=\"noopener noreferrer\">\u8fd9\u7bc7\u6587\u7ae0<\/a>\u63a2\u8ba8\u4e86\u8fd9\u4e2a\u95ee\u9898\u3002<\/p>\n<p>\u8ddfFibonacci\u6570\u5217\u4e0d\u540c\uff0cPadovan\u6570\u5217\u5f97\u5230\u7684\u87ba\u7ebf\uff0c\u662f\u4f1a\u5206\u53c9\u7684\uff0c\u4e8e\u662f\u80fd\u591f\u5f62\u6210\u5341\u5206\u7f8e\u4e3d\u7684\u82b1\u7eb9\u3002\u8fd9\u662f\u7531\u4e00\u4e2a\u70ed\u7231\u87ba\u7ebf\u7684\u6570\u5b66\u5bb6\u53d1\u73b0\u7684\u3002\u82f1\u56fd\u300a\u536b\u62a5\u300b<a href=\"http:\/\/www.theguardian.com\/science\/alexs-adventures-in-numberland\/2015\/jan\/13\/golden-ratio-beautiful-new-curve-harriss-spiral\" target=\"_blank\" rel=\"noopener noreferrer\">\u62a5\u9053\u8fc7\u4ed6\u7684\u53d1\u73b0<\/a>\u3002\u6587\u672b\u4ed6\u8bf4\uff0c\u4ed6\u8fd8\u8003\u5bdf\u8fc7\u5176\u4ed6\u7279\u6b8a\u6bd4\u4f8b\u6570\uff0c\u4f46\u6ca1\u6709\u5f97\u5230\u50cfplastic number\u8fd9\u6837\u7f8e\u4e3d\u7684\u56fe\u6848\u3002<\/p>\n<div style=\"width: 630px\" class=\"wp-caption alignnone\"><a href=\"http:\/\/community.wolfram.com\/groups\/-\/m\/t\/430342\"><img loading=\"lazy\" decoding=\"async\" src=\"http:\/\/community.wolfram.com\/c\/portal\/getImageAttachment?filename=000cf828-22d6-4992-94d0-25e5cb156e9f-620x467.png&amp;userId=11733\" width=\"620\" height=\"467\" class=\"\"\/><\/a><p class=\"wp-caption-text\">\u6e90\uff1ahttp:\/\/community.wolfram.com\/groups\/-\/m\/t\/430342<\/p><\/div>\n<p>\u8fd9\u79cd\u82b1\u7eb9\u4e4d\u4e00\u770b\u4f1a\u611f\u89c9\u50cf\u67d0\u68f5\u690d\u7269\u3002\u690d\u7269\u4e2d\u51fa\u7ebf\u87ba\u7ebf\u7684\u60c5\u51b5\u786e\u5b9e\u5f88\u591a\uff0c\u8fd8\u6709\u4e2a\u672f\u8bed\u53eb\u201c\u53f6\u5e8f\u201d\uff08Phyllotaxis\uff09\u3002\u4e00\u5b9a\u53f6\u5e8f\u7684\u5f62\u6210\u662f\u6709\u673a\u5236\u7684\u3002\u4e00\u5b9a\u673a\u5236\u4ea7\u751f\u87ba\u65cb\u7684\u60c5\u51b5\u5728\u5927\u81ea\u7136\u4e2d\u5f88\u5e38\u89c1\uff0c<a href=\"https:\/\/originalbeauty.wordpress.com\/2009\/06\/27\/spirals-in-nature\/\" target=\"_blank\" rel=\"noopener noreferrer\">\u8fd9\u7bc7\u535a\u5ba2<\/a>\u8fd8\u6709\u66f4\u591a\u7684\u4f8b\u5b50\u3002<\/p>\n<p>\u5728Wikipedia\u4e0a\u80fd\u591f\u627e\u5230\u5f88\u591a\u79cd\u6570\u5b66\u4e0a\u7684\u87ba\u7ebf\u3002<\/p>\n<ul>\n<li><a href=\"https:\/\/en.wikipedia.org\/wiki\/Golden_spiral\" target=\"_blank\" rel=\"noopener noreferrer\">Golden spiral<\/a><\/li>\n<li><a href=\"https:\/\/en.wikipedia.org\/wiki\/Logarithmic_spiral\" target=\"_blank\" rel=\"noopener noreferrer\">Logarithmic spiral<\/a><\/li>\n<li><a href=\"https:\/\/en.wikipedia.org\/wiki\/Archimedean_spiral\" target=\"_blank\" rel=\"noopener noreferrer\">Archimedean spiral<\/a><\/li>\n<li><a href=\"https:\/\/en.wikipedia.org\/wiki\/Hyperbolic_spiral\" target=\"_blank\" rel=\"noopener noreferrer\">Hyperbolic spiral<\/a><\/li>\n<li><a href=\"https:\/\/en.wikipedia.org\/wiki\/Rose_(mathematics)\" target=\"_blank\" rel=\"noopener noreferrer\">Rose<\/a><\/li>\n<li><a href=\"https:\/\/en.wikipedia.org\/wiki\/Fermat%27s_spiral\" target=\"_blank\" rel=\"noopener noreferrer\">Fermat&#8217;s spiral<\/a><\/li>\n<li>Spiral of Theodorus<\/li>\n<\/ul>\n<p>\u73b0\u5728\uff0c\u7531plastic number\u4ea7\u751f\u7684\u87ba\u7ebf\uff0c\u4ee5\u53d1\u73b0\u4ed6\u7684\u6570\u5b66\u5bb6Edmund Harriss\u547d\u540d\u4e3aHarris spiral\uff0c\u8fd9\u4e2aspiral\u662f\u5206\u53c9\u7684\u3002\u6309\u7167plastic number\u8fd8\u80fd\u6784\u5efa\u4e09\u7ef4\u7684\u87ba\u7ebf\u3002<\/p>\n<p><a title=\"By The original uploader was Jtlien at English Wikipedia (Transferred from&nbsp;en.wikipedia&nbsp;to Commons.) [Copyrighted free use], via Wikimedia Commons\" href=\"https:\/\/commons.wikimedia.org\/wiki\/File%3APad4.gif\"><img decoding=\"async\" width=\"256\" alt=\"Pad4\" src=\"https:\/\/upload.wikimedia.org\/wikipedia\/commons\/3\/3f\/Pad4.gif\"\/><\/a><\/p>\n<!-- kcite active, but no citations found -->\n<\/div> <!-- kcite-section 6670 -->","protected":false},"excerpt":{"rendered":"<p>\u9ec4\u91d1\u6bd4\u4f8b\u6570\u5927\u5bb6\u90fd\u77e5\u9053\uff0c\u662f\u4e00\u4e2a\u65e0\u7406\u6570$\\phi=1.618\\cdots$\u3002\u8bb8\u591a\u7406\u8bba\u8bba\u8bc1\u5927\u81ea\u7136\u5f88\u591a\u81ea\u53d1\u6216\u6700\u4f18\u7684\u7ed3\u679c\u9075\u5faa\u8fd9\u4e2a\u6bd4\u4f8b\uff0c\u7f8e\u672f\u3001\u5efa\u7b51\u548c\u97f3\u4e50\u4e0a\u8fd9\u4e2a\u6bd4\u4f8b\u4e5f\u4ea7\u751f\u4e86\u795e\u5947\u7684\u548c\u8c10\u3002\u5229\u7528\u8fd9\u4e2a\u6bd4\u4f8b\u53ef\u4f5c\u51fa\u9ec4\u91d1\u87ba\u7ebf\u3002 \u4e0a\u56fe\u662f\u4e09\u79cd\u5f62\u72b6\u5341\u5206\u63a5\u8fd1\u9ec4\u91d1\u87ba\u7ebf\u7684\u87ba\u7ebf\u3002 \u6700\u8fd1\u5728\u7f51\u4e0a\u770b\u5230\u53e6\u4e00\u4e2a\u7c7b\u4f3c\u7684\u65e0\u7406\u6570\uff0c\u53eb\u201c\u5851\u6599\u6570\u201d\uff08plastic number\uff09\u3002\u6211\u89c9\u5f97\u6bd4\u8f83\u6709\u8da3\u7684\u662f\uff0c\u628a\u97f3\u7b26\u6309\u6309\u4f3c\u9ec4\u91d1\u6bd4\u4f8b\u7684Fibonacci\u6570\u5217\u6392\u5217\uff0c\u53d1\u73b0\u662f\u7ecf\u5e38\u88ab\u4f7f\u7528\u7684\u65cb\u5f8b1,2,3,5\uff0c\u8fd9\u4e2a\u6897\u5df2\u7ecf\u5e7f\u4e3a\u4eba\u6240\u77e5\u3002\u90a3\u4e48\u7528plastic number\u4f5c\u6bd4\u4f8b\u7684Padovan\u6570\u5217\u5f97\u51fa\u7684\u65cb\u5f8b\u662f\u600e\u4e48\u6837\u7684\u5462\uff1f\u8fd9\u7bc7\u6587\u7ae0\u63a2\u8ba8\u4e86\u8fd9\u4e2a\u95ee\u9898\u3002 \u8ddfFibonacci\u6570\u5217\u4e0d\u540c\uff0cPadovan\u6570\u5217\u5f97\u5230\u7684\u87ba\u7ebf\uff0c\u662f\u4f1a\u5206\u53c9\u7684\uff0c\u4e8e\u662f\u80fd\u591f\u5f62\u6210\u5341\u5206\u7f8e\u4e3d\u7684\u82b1\u7eb9\u3002\u8fd9\u662f\u7531\u4e00\u4e2a\u70ed\u7231\u87ba\u7ebf\u7684\u6570\u5b66\u5bb6\u53d1\u73b0\u7684\u3002\u82f1\u56fd\u300a\u536b\u62a5\u300b\u62a5\u9053\u8fc7\u4ed6\u7684\u53d1\u73b0\u3002\u6587\u672b\u4ed6\u8bf4\uff0c\u4ed6\u8fd8\u8003\u5bdf\u8fc7\u5176\u4ed6\u7279\u6b8a\u6bd4\u4f8b\u6570\uff0c\u4f46\u6ca1\u6709\u5f97\u5230\u50cfplastic number\u8fd9\u6837\u7f8e\u4e3d\u7684\u56fe\u6848\u3002 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Phys. 1982, 77, 4270\uff09\u7ed9\u51fa\u4e86\u7ed9\u5b9a\u5c3a\u5bf8\u5206\u5e03\u7684\u7c92\u5b50\u4f53\u7cfb\u7684\u5e73\u5747\u6269\u6563\u7cfb\u6570\u8868\u8fbe\u5f0f\uff1a\u5176\u4e2d\u4e0b\u6807p\u662f\u6307\u7b2cp\u79cd\u5c3a\u5bf8\u3002N\u662f\u4e2a\u6570\uff0cf\u662f\u6563\u5c04\u5f3a\u5ea6\u3002\u5bf9\u4e8e\u5c3a\u5bf8\u5206\u5e03\u672c\u6765\u662f\u5355\u5206\u6563\u7684\u7c92\u5b50\uff0c\u5728\u805a\u96c6\u8fc7\u7a0b\u4e2d\u5c31\u4f1a\u6709\u4e8c\u805a\u4f53\u3001\u4e09\u805a\u4f53\u5230p\u805a\u4f53\u7b49\u5927\u5c0f\u4e0d\u4e00\u7684\u5355\u5143\u5b58\u5728\uff0c\u56e0\u6b64\u662f\u4e00\u4e2a\u591a\u5206\u6563\u4f53\u7cfb\uff0c\u9002\u7528Pusey\u7684\u5f0f\u5b50\u3002\u800c\u4e14\u5404p\u805a\u4f53\u7684\u6570\u91cf\u90fd\u968f\u65f6\u95f4\u53d8\u5316\uff0c\u5373\u6574\u4e2a\u5c3a\u5bf8\u5206\u5e03\u5728\u968f\u65f6\u95f4\u53d8\u5316\u3002\u56e0\u6b64Pusey\u7684\u90a3\u6761\u5f0f\u5b50\u5c31\u8981\u52a0\u4e0a\u65f6\u95f4\u4f9d\u8d56\u6027\uff0c\u53d8\u6210\u4e86\uff1aVersmold & H\u00e4rtl\uff08J. Chem. Phys. 1983, 79, 4006\uff09\u901a\u8fc7\u7b80\u5355\u5047\u8bbe\u5404p\u805a\u4f53\u90fd\u662f\u7403\u4f53\uff0c\u4ee5\u4fbf\u90a3\u4e2a\u6269\u6563\u7cfb\u6570\u4e0e\u5c3a\u5bf8\u7684\u5173\u7cfb\u5f0f\u80fd\u5e94\u7528\u5728\u5404\u4e2ap\u805a\u4f53\u4e0a\uff1b\u53e6\u6839\u636e\u5149\u6563\u5c04\u539f\u7406\uff0c\u6563\u5c04\u5f3a\u5ea6f\u8ddf\u7c92\u5b50\u4f53\u79ef\uff08\u534a\u5f84\u7684\u7acb\u65b9\uff09\u6709\u5173\u3002\u8fd9\u6837\u5c31\u628aPusey\u7684\u5f0f\u5b50\u4e2dfp\u548cD0,p\u76f4\u63a5\u7528ap\u4ee3\u66ff\u4e86\uff0c\u53d8\u6210\uff1aSmoluchowski\u65b9\u7a0bNp(t\/t1\/2)=...\u7684\u7528\u5904\u5c31\u662f\u7528\u6765\u7b97\u4e0a\u5f0f\u90a3\u4e24\u4e2ap\u7684\u77e9\u3002\u636eVersmold & H\u00e4rtl\u7684\u6587\u7ae0\u6240\u5f15\u8ff0\uff0cp\u7684\u5747\u65b9\u503c\uff086\/3\uff09\u4e4b\u524d\u6709\u4eba\u7ed9\u51fa\u89e3\u6790\u89e3\u4e86\u3002\u53ef\u8fd95\/3\u9636\u77e9\u53ef\u600e\u4e48\u529e\u5462\uff1fVersmold & H\u00e4rtl\u53ea\u80fd\u5728\u65f6\u95f4t\/t1\/2\u5f88\u5c0f\u7684\u6761\u4ef6\u4e0b\uff08\u5373aggregation\u521a\u53d1\u751f\u6ca1\u591a\u4e45\uff09\u628aSmoluchowski\u65b9\u7a0b\u7ed9\u5c55\u5f00\u4e86\u53d6\u8fd1\u4f3c\uff0c\u8fd9\u6837\u7684\u8bddp\u7684n\/3\u9636\u77e9\u968ft\/t1\/2\u7684\u53d8\u5316\u5c31\u90fd\u80fd\u8ba1\u7b97\u3002\u4e0d\u8fc7\u8fd9\u6837\u7ed9\u51fa\u7684\u8868\u8fbe\u5f0f\u662f\u4e2a\u7ebf\u6027\u5f0f\uff0c\u53ea\u9002\u7528\u4e8e\u805a\u96c6\u53cd\u5e94\u7684\u521d\u671f\u3002\u81f3\u4e8e\u9002\u7528\u4e8e\u6574\u4e2a\u65f6\u95f4\u57df\u7684\u8868\u8fbe\u5f0f\uff0c\u53ef\u4ee5\u7528\u8ba1\u7b97\u673a\u7ed9\u51fa\u6570\u503c\u89e3\u3002\u4ee5\u4e0a\u7684\u5de5\u4f5c\uff0c\u901a\u8fc7Smoluchowski\u65b9\u7a0b\uff0c\u7ed9\u51fa\u4e86\u7c92\u5b50\u4f53\u7cfb\u5728\u805a\u96c6\u8fc7\u7a0b\u4e2d\u6269\u6563\u7cfb\u6570\u7684\u65f6\u95f4\u4f9d\u901f\u5173\u7cfbD(t)\u7684\u8868\u8fbe\u5f0f\uff0c\u5f0f\u4e2d\u552f\u4e00\u7684\u53c2\u6570\u662f\u90a3\u4e2at1\/2\uff0c\u6240\u4ee5\uff0c\u62ff\u8fd9\u4e2a\u8868\u8fbe\u5f0f\u53bb\u62df\u5408\u5b9e\u6d4b\u6570\u636e\uff0c\u5c31\u80fd\u5f97\u5230\u8fd9\u4e2at1\/2\u4e86\u3002\u8fd9\u4e2at1\/2\u8ddf\u805a\u96c6\u53cd\u5e94\u7684\u901f\u7387\u5e38\u6570k\u76f4\u63a5\u6709\u5173\uff1ak=1\/(t1\/2N0)\uff0c\u5176\u4e2dN0\u662f\u6700\u521d\u7684\u7c92\u5b50\u5bc6\u5ea6\uff08\u4e2a\u6570\u6bd4\u4f53\u79ef\uff09\u3002\u6240\u4ee5\uff0c\u7528\u52a8\u6001\u5149\u6563\u5c04\u53ef\u4ee5\u6d4b\u51fak\u3002k\u53c8\u8ddf\u7c92\u5b50\u95f4\u7684pair potential\u6709\u4ec0\u4e48\u5173\u7cfb\u5462\uff1f\u9996\u5148\uff0c\u8fd9\u4e2a\u901f\u7387\u5e38\u6570\u662f\u805a\u96c6\u53cd\u5e94\u7684\u6570\u7387\u5e38\u6570\uff0c\u4e24\u4e2a\u7c92\u5b50\u78b0\u649e\u540e\u8981\u53d1\u751f\u805a\u96c6\uff0c\u5b83\u4eec\u5f53\u7136\u8981\u514b\u670d\u6389\u4e24\u8005\u95f4\u7684potential barrier\u3002\u56e0\u6b64\u7c92\u5b50\u95f4\u7684potential barrier\u5c31\u51b3\u5b9a\u4e86\u6709\u6548\u78b0\u649e\u5360\u603b\u78b0\u649e\u6570\u4e4b\u6bd4\u4f8b\u3002\u603b\u78b0\u649e\u6570\u65e0\u975e\u5c31\u662f\u5e03\u6717\u8fd0\u52a8\u51b3\u5b9a\uff08\u7c98\u5ea6\u3001\u5c3a\u5bf8\u90fd\u5b9a\u4e86\u8fd9\u4e2a\u5c31\u662f\u5b9a\u7684\uff09\u3002\u56e0\u6b64\uff0c\u90a3\u4e2a\u6bd4\u4f8b\u2014\u2014\u79f0\u4e3astability ratio\uff0cW\u2014\u2014\u5c31\u8ddfpotential barrier\u76f4\u63a5\u6709\u5173\u4e86\uff1a\u636e\u4f20\u4e0a\u5f0f\u662fN. Fuch\u7ed9\u7684\uff0c\u4e4b\u6240\u4ee5\u8bf4\u201c\u636e\u4f20\u201d\uff0c\u662f\u56e0\u4e3a\u6211\u81ea\u5df1\u6ca1\u6709\u770b\u8fc7N. Fuch\u7684\u8bba\u6587\uff08\uff09\u2014\u2014\u5fb7\u8bed\u7684\uff0c\u770b\u4e0d\u61c2\u3002\u6211\u53ea\u77e5\u9053\u5f88\u591a\u4eba\u4e00\u63d0\u5230stability ratio\uff0c\u5c31\u5f15N. Fuch\u8fd9\u7bc7\u4e1c\u897f\u3002\u79ef\u5206\u5f0f\u4e2d\u7684U(r)\u5f62\u5f0f\u4e94\u82b1\u516b\u95e8\uff0c\u4e5f\u5f88\u590d\u6742\uff0c\u4ec0\u4e48van der Waals\u4f5c\u7528\u3001\u9759\u7535\u4f5c\u7528\u3001\u4f4d\u963b\u4f5c\u7528\u7b49\u7b49\u7406\u8bba\u6a21\u578b\u4e00\u5927\u5806\uff0c\u6240\u4ee5\u591a\u6570\u60c5\u51b5\u4e0bW\u7684\u76f4\u63a5\u8868\u8fbe\u5f0f\u90fd\u662f\u627e\u4e2a\u8fd1\u4f3c\u5f0f\u51d1\u5408\u7528\u7684\u3002Prieve and Ruckenstein\uff08J. Colloid Interf. Sci. 1980, 73, 539\uff09\u4e3a\u7403\u5f62\u7c92\u5b50\u5bfc\u51fa\u7684\u8fd1\u4f3c\u8868\u8fbe\u5f0f\uff1a\u8fd9\u6837\u4e00\u6765\uff0cW\u5c31\u8ddfpotential barrier\u6709\u5173\u4e86\u3002Smoluchowski\u7684\u8bba\u6587\u5f88\u591a\u6587\u7ae0\u4e00\u8bb2\u5230Smoluchowski\u7684\u8bba\u6587\uff0c\u5c31\u4e00\u5b9a\u662f\u5f15\u7528\u4ed6\u57281916\u548c1917\u5e74\u53d1\u8868\u7684\u4e24\u7bc7\u6587\u7ae0\u3002\u6211\u53d1\u73b0\u6709\u5f88\u5927\u4e00\u90e8\u5206\u5f15\u7528\u662f\u9519\u8bef\u7684\uff1aZ. Phys. 1916, 17, 557; ibid. 1916, 17,\u2026","rel":"","context":"In &quot;\u4e2a\u4eba\u6587\u96c6&quot;","block_context":{"text":"\u4e2a\u4eba\u6587\u96c6","link":"https:\/\/www.andrewsun.net\/panta_rhei\/archives\/category\/featured"},"img":{"alt_text":"M. Smoluchowski","src":"https:\/\/i0.wp.com\/www.andrewsun.net\/panta_rhei\/wp-content\/uploads\/2011\/03\/Smoluchowski_2-300x278.jpg?resize=350%2C200","width":350,"height":200},"classes":[]},{"id":6205,"url":"https:\/\/www.andrewsun.net\/panta_rhei\/archives\/6205","url_meta":{"origin":6670,"position":2},"title":"\u65b0\u53d1\u8868\u6587\u7ae0\u7684\u81f4\u8c22","author":"Andrew","date":"2015\u5e741\u670817\u65e5","format":"aside","excerpt":"[latexpage] \u6211\u7684\u4e00\u7bc7\u6587\u7ae0\u5728Journal of Colloid and Interface Science\u4e0a\u53d1\u8868\u4e86\u3002\u7b2c\u4e00\u4f5c\u8005\u662f\u5b9e\u9a8c\u7684\u5b8c\u6210\u4eba\uff0c\u6211\u5bf9\u5b9e\u9a8c\u7ed3\u679c\u8fdb\u884c\u4e86\u7406\u8bba\u5206\u6790\u3002\u5177\u4f53\u5185\u5bb9\u53ef\u4ee5\u76f4\u63a5\u53bb\u4e0b\u8f7d\u8bba\u6587\u770b\u3002 \u8fd9\u4e2a\u5de5\u4f5c\u4ece\u5b9e\u9a8c\u5b8c\u6210\u5230\u53d1\u8868\u62d6\u4e86\u5f88\u957f\uff0c\u4e3b\u8981\u65f6\u95f4\u82b1\u5728\u7406\u8bba\u5206\u6790\u90e8\u5206\u3002\u4e00\u5f00\u59cb\u6211\u5e76\u4e0d\u6e05\u695a\u53cd\u79bb\u5b50\u51dd\u805a\uff0c\u53ea\u662f\u53d1\u73b0\u7c98\u571f\u8868\u9762\u7535\u8377\u5bc6\u5ea6\u592a\u5927\uff0c\u800c\u4e14\u5904\u4e8e\u975e\u5bf9\u79f0\uff08asymmetric\uff09\u7684\u7535\u89e3\u8d28\u73af\u5883\uff0c\u56e0\u6b64\u7c92\u5b50\u95f4\u7684\u53cc\u7535\u5c42\u4f5c\u7528\u4e0d\u80fd\u91c7\u7528Debye-H\u00fcckel\u8fd1\u4f3c\uff0c\u4e8e\u662f\u67e5\u5230\u4e86Ohshima\u63a8\u5bfc\u7684\u4e00\u4e2aPoisson-Boltzmann\u7684\u7cbe\u786e\u89e3\u3002\u53ef\u662f\u7528\u8fd9\u4e2a\u89e3\u6765\u8ba1\u7b97\u76f8\u4e92\u4f5c\u7528\u7684\u65f6\u5019\u603b\u662f\u5f97\u51fanonphysical\u7684\u7ed3\u679c\u3002\u6709\u6000\u7591\u8fc7\u81ea\u5df1\u6570\u503c\u8ba1\u7b97\u7684\u4ee3\u7801\u6709\u95ee\u9898\uff0c\u518d\u4e09\u68c0\u9a8c\u548c\u8bf7\u6559\u8fc7\u6bd4\u8f83\u719f\u7684\u4eba\u4e4b\u540e\u4e5f\u6392\u9664\u4e86\u3002\u8fd9\u671f\u95f4\u8001\u677f\u4e5f\u50ac\u8fc7\uff0c\u4ed6\u4e0d\u77e5\u9053\u8fd9\u4e9b\u5177\u4f53\u7684\u7ec6\u8282\uff0c\u5c31\u53ea\u89c9\u5f97\u6ca1\u5fc5\u8981\u62d6\u8fd9\u4e48\u4e45\uff0c\u6211\u4e0d\u5f97\u4e0d\u76f4\u63a5\u8bf4\u6211\u8fd9\u4e2a\u53ef\u80fd\u4f1a\u62d6\u5f88\u4e45\uff0c\u56e0\u4e3a\u6211\u8981\u8ba4\u771f\u641e\u61c2\u8fd9\u4e2a\u95ee\u9898\u3002\u7b2c\u4e00\u4f5c\u8005\u7684\u5b66\u751f\u5bf9\u6211\u5c31\u66f4\u6ca1\u64a4\u4e86\u3002\u73b0\u5728\u6211\u8fd8\u5f97\u8c22\u8c22\u4ed6\u5e2e\u6211\u505a\u4e86\u8fd9\u4e48\u591a\u5b9e\u9a8c\uff0c\u8fd8\u5f97\u88ab\u6211\u538b\u7740\u4e0d\u53d1\u8868\u3002\u8981\u4e0d\u662f\u4ed6\u62fc\u547d\u505a\u5b9e\u9a8c\uff0c\u6211\u521a\u5de5\u4f5c\u7684\u8fd9\u4e24\u5e74\u53ef\u80fd\u90fd\u6ca1\u529e\u6cd5\u6709\u8fd9\u4e48\u51e0\u7bc7\u6587\u7ae0\u5411\u5916\u754c\u4ea4\u5dee\u3002\u8bf4\u56de\u5230\u8ba1\u7b97\u7684\u95ee\u9898\uff0c\u540e\u6765\u6211\u5b9e\u5728\u6ca1\u529e\u6cd5\uff0c\u60f3\u627eOhshima\u672c\u4eba\u95ee\u4e00\u4e0b\u3002\u5176\u5b9e\u4e4b\u524d\u4e00\u76f4\u4ee5\u4e3aOhshima\u662f\u4e00\u4e2a\u8fc7\u4e16\u4e86\u7684\u4eba\uff0c\u6240\u4ee5\u9047\u5230\u95ee\u9898\u4e00\u76f4\u90fd\u6ca1\u60f3\u8fc7\u53bb\u95ee\u672c\u4eba\u3002\u76f4\u5230\u6700\u540e\u6211\u60f3\u67e5\u4ed6\u7684\u5de5\u4f5c\u7684\u540e\u7eed\u5f15\u7528\u60c5\u51b5\uff0c\u770b\u770b\u522b\u4eba\u662f\u600e\u4e48\u4f7f\u7528\u4ed6\u7684\u7ed3\u679c\u7684\uff0c\u53d1\u73b0\u4f7f\u7528\u4ed6\u7ed3\u679c\u7684\u4eba\u51e0\u4e4e\u6ca1\u6709\uff0c\u4f46\u4ed6\u81ea\u5df1\u6709\u53d1\u8868\u65b0\u7684\u6587\u7ae0\uff0c\u6700\u65b0\u7684\u6709\u5230200X\u5e74\uff0c\u4e8e\u662f\u624d\u611f\u89c9\u8fd9\u4e2a\u4eba\u53ef\u80fd\u662f\u8fd8\u5728\u751f\u7684\u4eba\u3002\u7ecf\u8fc7\u4e00\u756a\u641c\u7d22\uff0c\u624d\u627e\u5230\u4ed6\u7684\u9875\u9762\u4ee5\u53caemail\uff0c\u539f\u6765\u662f\u4e2a\u521a\u9000\u4f11\u7684\u7814\u7a76\u6240\u6240\u957f\u3002\u5f88\u5feb\u5c31\u6536\u5230\u4e86\u4ed6\u7684\u56de\u4fe1\uff0c\u591a\u6b21\u6765\u5f80\u4e4b\u540e\uff0c\u6211\u624d\u77e5\u9053\uff0c\u6211\u7684\u4f53\u7cfb\u5c5e\u4e8esalt-free systems\u6216\u8005counterions only system\uff0c\u6240\u4ee5\u53cd\u79bb\u5b50\u6d53\u5ea6\u662f\u4e0d\u53ef\u5ffd\u7565\u7684\uff0c\u9ad8\u7535\u8377\u5bc6\u5ea6\u65f6\u4f1a\u53d1\u751f\u53cd\u79bb\u5b50\u51dd\u805a\u3002\u8fd9\u5e94\u8be5\u662f\u4e2a\u5e38\u8bc6\u4e86\uff0c\u65e0\u5948\u6211\u77e5\u8bc6\u8fd8\u662f\u6b20\u7f3a\uff0c\u5168\u8d56\u4ed6\u7684\u6307\u70b9\u3002\u4e8e\u662f\u6211\u624d\u91cd\u65b0\u6309\u7167\u53cd\u79bb\u5b50\u51dd\u805a\u7684\u89d2\u5ea6\u6765\u601d\u8003\u6211\u7684\u4f53\u7cfb\u3002 \u5728\u53cd\u79bb\u5b50\u51dd\u805a\u7684\u7814\u7a76\u4e2d\uff0c\u5927\u90e8\u5206\u662f\u8003\u8651\u67f1\u72b6\u7684\u5e26\u7535\u8868\u9762\u7684\uff0c\u4e3b\u8981\u9762\u5411\u7684\u5b9e\u9645\u4f53\u7cfb\u662f\u805a\u7535\u89e3\u8d28\uff08\u5305\u62ecDNA\uff09\u6eb6\u6db2\uff0c\u53c8\u53ebManning condensation\u3002\u7403\u72b6\u7684\u7814\u7a76\u6bd4\u8f83\u5c11\uff0c\u7ecf\u5e38\u53eb\u6210charge renormalization\u3002Manning\u81ea\u5df1\u4e5f\u8003\u8651\u8fc7\u7403\u72b6\u7684\u4f53\u7cfb\uff0c\u4ed6\u7684two-state model\u662f\u4ece\u8003\u8651\u81ea\u7531\u80fd\u51fa\u53d1\uff0c\u8ba4\u4e3a\u7cbe\u786e\u7684\u7ed3\u679c\u8ddfDH\u8fd1\u4f3c\u4e4b\u95f4\u5c31\u662f\u5dee\u4e00\u4e2a\u7cfb\u6570\uff0c\u8fd9\u4e2a\u7cfb\u6570\u7b80\u5355\u5730\u8ba4\u4e3a\u662f\u4e2a\u975e\u51dd\u805a\u79bb\u5b50\u7684\u6bd4\u4f8b\u7cfb\u6570$(1-z\\theta)$\uff0c\u5176\u4e2d$\\theta$\u662f\u51dd\u805a\u79bb\u5b50\u6240\u5360\u6bd4\u4f8b\u3002\u4ed6\u7684\u903b\u8f91\u5176\u5b9e\u662f\u975e\u5e38\u7b03\u5b9a\u201c\u53cd\u79bb\u5b50\u51dd\u805a\u201d\u7684\u56fe\u50cf\uff0c\u8ba4\u4e3a\u6709\u975e\u5e38\u786e\u5b9a\u6570\u91cf\u7684\u53cd\u79bb\u5b50\u53d1\u751f\u4e86\u201c\u51dd\u805a\u201d\u3002\u7136\u540e\uff0c\u901a\u8fc7\u81ea\u7531\u80fd\u6700\u5c0f\u5316\u6765\u6c42\u5f97$\\theta$\u7684\u8868\u8fbe\u5f0f\u3002\u800c\u5219\u662f\u7528cell model\u6765\u6c42\u89e3Poisson-Boltzmann\u65b9\u7a0b\uff0c\u8bc1\u5b9e\u4e86\u7684\u786e\u53ef\u4ee5\u8fdb\u884c\u8868\u9762\u7535\u8377\uff08\u52bf\uff09\u7684\u7b49\u6548\u3002\u7684\u5de5\u4f5c\u867d\u7136\u88ab\u591a\u6b21\u5f15\u7528\uff0c\u4f46\u5c40\u9650\u4e8e\u7406\u8bba\u7814\u7a76\u7684\u5708\u5b50\u4e4b\u5185\u3002\u5f88\u5c11\u6709\u7528\u4ed6\u7684\u7ed3\u679c\u89e3\u91ca\u5b9e\u9a8c\u7684\u5de5\u4f5c\u3002\u505a\u4e86\u4e00\u4e2asalt-free\u4f53\u7cfb\u7684\u7535\u6cf3\u5b9e\u9a8c\u5e76\u4e14\u8fdb\u884c\u4e86\u7406\u8bba\u63cf\u8ff0\uff0c\u4f7f\u7528\u4e86\u4e00\u4e2a\u4e0e\u7c7b\u4f3c\u7684approach\u3002\u6211\u7684\u8bba\u6587\u76f4\u63a5\u7528\u4e86\u7684\u7ed3\u679c\u6765\u8ba1\u7b97\u76f8\u4e92\u4f5c\u7528\u52bf\u80fd$U\\left(h\\right)$\uff0c\u7136\u540e\u8fdb\u4e00\u6b65\u8ba1\u7b97RLCA\u7684stability ratio\uff0c\u5f97\u51fa\u4e0e\u5b9e\u9a8c\u6bd4\u8f83\u543b\u5408\u7684\u7ed3\u679c\uff0c\u5e94\u8be5\u662f\u7b2c\u4e00\u4e2a\u3002 \u6211\u7684\u6587\u7ae0\u53d1\u8868\u65f6\uff0c\u5ba1\u7a3f\u4eba\u4e5f\u663e\u793a\u51fa\u6bd4\u8f83\u9ad8\u7684\u5174\u8da3\uff0c\u8bf4\u6211\u8fd9\u662f\u4e00\u7bc7excellent paper\uff0c\u6709\u4e00\u6761\u4fee\u6539\u610f\u89c1\u8fd8\u662f\u201cThis is an interesting point that should be explored and highlighted further.\u201d \u867d\u7136\u6211\u6587\u7ae0\u7684\u81f4\u8c22\u91cc\u5df2\u7ecf\u611f\u8c22\u4e86Ohshima\uff0c\u4f46\u603b\u89c9\u5f97\u8fd8\u662f\u8981\u4eb2\u81ea\u611f\u8c22\u4ed6\u3002\u6587\u7ae0\u53d1\u8868\u540e\uff0c\u6211\u7ed9Ohshima\u56de\u4fe1\u611f\u8c22\u4ed6\uff0c\u628a\u6587\u7ae0\u7684PDF\u7ed9\u4ed6\u770b\u4e86\u3002\u4ed6\u4e5f\u56de\u4fe1\u5bf9\u6211\u8fdb\u884c\u4e86\u9f13\u52b1\uff1a Dear Dr. Weixiang Sun Thank you very much for sending me your excellent work. Congratulations! I have read your\u2026","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":6062,"url":"https:\/\/www.andrewsun.net\/panta_rhei\/archives\/6062","url_meta":{"origin":6670,"position":3},"title":"\u8f6f\u8fb9\u754c\u5bf9\u80f6\u4f53\u73bb\u7483dynamics\u7684\u5f71\u54cd\uff0cetc.","author":"Andrew","date":"2014\u5e749\u67081\u65e5","format":false,"excerpt":"\u6e05\u626b\u6211\u7684RSS\u8ba2\u9605\u770b\u5230\u4e00\u4e9b\u6709\u8da3\u7684\u4e1c\u897f\u4e00\u5e76\u8bb0\u5f55\u4e00\u4e0b\u3002 Phys. Rev. Lett. 112, 218302\uff0c\u628aPMMA\u80f6\u4f53\u7c92\u5b50\u4f5c\u4e3a\u6cb9\u76f8\u5236\u6210\u6c34\u5305\u6cb9\u4e73\u6db2\uff0c\u6c34\u76f8\u662f\u6c34\u548c\u7518\u6cb9\u6df7\u5408\u7269\u8c03\u8282\u7c98\u5ea6\u3002\u901a\u8fc7particle tracking\u89c2\u5bdf\u6cb9\u6ef4\u4e2d\u7c92\u5b50\u7684\u52a8\u6001\u5982\u4f55\u968f\u6c34\u76f8\u7c98\u5ea6\u7684\u53d8\u5316\u800c\u53d8\u5316\u3002\u6211\u770b\u8fd9\u6587\u7ae0\u7684\u51e0\u4e2a\u60f3\u6cd5\uff08\u6587\u7ae0\u672a\u6d89\u53ca\u7684\uff09\uff1a 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