{"id":1031,"date":"2010-05-25T18:18:20","date_gmt":"2010-05-25T10:18:20","guid":{"rendered":"http:\/\/xiangge.andrewsun.net\/?p=1031"},"modified":"2010-05-25T18:18:20","modified_gmt":"2010-05-25T10:18:20","slug":"%e4%b8%ba%e4%bb%80%e4%b9%88g%e6%98%af%e8%b4%9f%e5%80%bc%ef%bc%9f","status":"publish","type":"post","link":"https:\/\/www.andrewsun.net\/panta_rhei\/archives\/1031","title":{"rendered":"\u4e3a\u4ec0\u4e48G&#039;&#039;\u662f\u8d1f\u503c\uff1f"},"content":{"rendered":"<div class=\"kcite-section\" kcite-section-id=\"1031\">\n<p>\u4e3b\u9898\u56de\u5f52\u5230\u6d41\u53d8\u5b66\u4e00\u4e0b\u3002<\/p>\n<p>\u4f17\u6240\u5468\u77e5\uff08\u7ebf\u6027\uff09\u7c98\u5f39\u6027\u662f\u5904\u4e8eHookian\u5f39\u6027\u548cNewtonian\u7c98\u6027\u8fd9\u4e24\u4e2a\u6781\u7aef\u4e4b\u95f4\u7684\u6027\u8d28\u3002\u5bf9Hookian\u5f39\u6027\u4f53\uff08Hookian\u5f39\u7c27\u6a21\u578b\uff09\u65bd\u52a0\u6b63\u5f26\u5f62\u53d8\uff0c\u6d4b\u5230\u7684\u662f\u540c\u76f8\u7684\u6b63\u5f26\u5e94\u529b\uff1b\u5411Newtonian\u7c98\u6d41\u4f53\uff08Newtonian\u7c98\u58f6\uff09\u65bd\u52a0\u6b63\u5f26\u5f62\u53d8\u901f\u7387\uff0c\u6d4b\u5230\u7684\u662f\u540c\u76f8\u7684\u6b63\u5f26\u5e94\u529b\u3002\u5411\u4e00\u4e2a\u7ebf\u6027\u7c98\u5f39\u6027\u6837\u54c1\u65bd\u52a0\u6b63\u5f26\u5f62\u53d8\uff0c\u6d4b\u5230\u7684\u662f\u76f8\u4f4d\u89d2\u4e3a[eq]\\delta[\/eq]\u7684\u6b63\u5f26\u5e94\u529b\uff1a[eq]\\gamma_0 \\sin \\left ( \\omega t+\\delta \\right )[\/eq]\u3002<\/p>\n<div id=\"attachment_1043\" style=\"width: 310px\" class=\"wp-caption alignnone\"><a href=\"http:\/\/www.andrewsun.net\/panta_rhei\/wp-content\/uploads\/2010\/05\/11.png\"><img loading=\"lazy\" decoding=\"async\" aria-describedby=\"caption-attachment-1043\" data-attachment-id=\"1043\" data-permalink=\"https:\/\/www.andrewsun.net\/panta_rhei\/archives\/1031\/1-2\" data-orig-file=\"https:\/\/www.andrewsun.net\/panta_rhei\/wp-content\/uploads\/2010\/05\/11.png\" data-orig-size=\"1000,628\" 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=\"\u5c0f\u5e45\u632f\u8361\u529b\u5b66\u54cd\u5e94\" data-image-description=\"\" data-image-caption=\"&lt;p&gt;\u5c0f\u5e45\u632f\u8361\u529b\u5b66\u54cd\u5e94&lt;\/p&gt;\n\" data-large-file=\"https:\/\/www.andrewsun.net\/panta_rhei\/wp-content\/uploads\/2010\/05\/11.png\" src=\"http:\/\/www.andrewsun.net\/xiangge\/wp-content\/uploads\/2010\/05\/11-300x188.png\" alt=\"\u5c0f\u5e45\u632f\u8361\u529b\u5b66\u54cd\u5e94\" title=\"\u5c0f\u5e45\u632f\u8361\u529b\u5b66\u54cd\u5e94\" width=\"300\" height=\"188\" class=\"size-medium wp-image-1043\" srcset=\"https:\/\/www.andrewsun.net\/panta_rhei\/wp-content\/uploads\/2010\/05\/11-300x188.png 300w, https:\/\/www.andrewsun.net\/panta_rhei\/wp-content\/uploads\/2010\/05\/11.png 1000w\" sizes=\"auto, (max-width: 300px) 100vw, 300px\" \/><\/a><p id=\"caption-attachment-1043\" class=\"wp-caption-text\">\u5c0f\u5e45\u632f\u8361\u529b\u5b66\u54cd\u5e94<\/p><\/div>\n<p>\u6700\u4e3a\u4eba\u719f\u6089\u7684\u6d41\u53d8\u5b66\u6d4b\u8bd5\uff08\u4e5f\u662f\u6700\u591a\u4e0d\u61c2\u6d41\u53d8\u7684\u4eba\u77e5\u9053\u8981\u505a\u7684\u6d4b\u8bd5\uff09\u5c31\u662f[eq]G'[\/eq]\u3001[eq]G&#8221;[\/eq]~[eq]\\omega[\/eq]\u66f2\u7ebf\uff0c\u8fd9\u4e2a\u4e5f\u53eb\u505a\u201c\u7c98\u5f39\u8c31\u201d\u3002\u6211\u66fe\u7ecf\u8be6\u7ec6<a href=\"http:\/\/www.andrewsun.net\/xiangge\/?p=807\">\u89e3\u91ca\u8fc7<\/a>[eq]G'[\/eq]\u548c[eq]G&#8221;[\/eq]\u5230\u5e95\u662f\u600e\u4e48\u6765\u7684\u3002\u5178\u578b\u7ebf\u578b\u805a\u5408\u7269\u7c98\u5f39\u8c31\u5982\u4e0b\u56fe\uff1a<\/p>\n<div style=\"width: 314px\" class=\"wp-caption alignnone\"><a href=\"http:\/\/www.mpip-mainz.mpg.de\/documents\/akbu\/media\/mech1.jpg\"><img decoding=\"async\" alt=\"\u7ebf\u578b\u805a\u5408\u7269\u7c98\u5f39\u8c31\" src=\"http:\/\/www.mpip-mainz.mpg.de\/documents\/akbu\/media\/mech1.jpg\" title=\"\u7ebf\u578b\u805a\u5408\u7269\u7c98\u5f39\u8c31\" width=\"304\"  \/><\/a><p class=\"wp-caption-text\">\u7ebf\u578b\u805a\u5408\u7269\u7c98\u5f39\u8c31<\/p><\/div>\n<p>\u4e0b\u56fe\u662f\u6211\u914d\u5236\u7684\u5408\u6210\u9502\u85fb\u571fLaponite\u51dd\u80f6\u7684\u7c98\u5f39\u8c31\uff0c\u53d1\u73b0[eq]G&#8221;[\/eq]\u5728\u9ad8\u9891\u5904\u51fa\u73b0\u8d1f\u503c\u3002\u4e0b\u9762\u662f\u5bf9\u8fd9\u4e2a\u4e0d\u6b63\u5e38\u73b0\u8c61\u7684\u89e3\u91ca\u3002<\/p>\n<div id=\"attachment_1045\" style=\"width: 310px\" class=\"wp-caption alignnone\"><a href=\"http:\/\/www.andrewsun.net\/panta_rhei\/wp-content\/uploads\/2010\/05\/Graph16.png\"><img loading=\"lazy\" decoding=\"async\" aria-describedby=\"caption-attachment-1045\" data-attachment-id=\"1045\" data-permalink=\"https:\/\/www.andrewsun.net\/panta_rhei\/archives\/1031\/graph16\" data-orig-file=\"https:\/\/www.andrewsun.net\/panta_rhei\/wp-content\/uploads\/2010\/05\/Graph16.png\" data-orig-size=\"3300,2550\" 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=\"Laponite\u51dd\u80f6\u7c98\u5f39\u8c31\" data-image-description=\"\" data-image-caption=\"&lt;p&gt;Laponite\u51dd\u80f6\u7c98\u5f39\u8c31&lt;\/p&gt;\n\" data-large-file=\"https:\/\/www.andrewsun.net\/panta_rhei\/wp-content\/uploads\/2010\/05\/Graph16-1024x791.png\" src=\"http:\/\/www.andrewsun.net\/xiangge\/wp-content\/uploads\/2010\/05\/Graph16-300x231.png\" alt=\"Laponite\u51dd\u80f6\u7c98\u5f39\u8c31\" title=\"Laponite\u51dd\u80f6\u7c98\u5f39\u8c31\" width=\"300\" height=\"231\" class=\"size-medium wp-image-1045\" srcset=\"https:\/\/www.andrewsun.net\/panta_rhei\/wp-content\/uploads\/2010\/05\/Graph16-300x231.png 300w, https:\/\/www.andrewsun.net\/panta_rhei\/wp-content\/uploads\/2010\/05\/Graph16-1024x791.png 1024w\" sizes=\"auto, (max-width: 300px) 100vw, 300px\" \/><\/a><p id=\"caption-attachment-1045\" class=\"wp-caption-text\">Laponite\u51dd\u80f6\u7c98\u5f39\u8c31<\/p><\/div>\n<p>\u4e00\u53f0\u5e94\u53d8\u63a7\u5236\u578b\u6d41\u53d8\u4eea\u82e5\u8981\u7ed9\u51fa\u8fd9\u6837\u7684\u56fe\uff0c\u5c31\u8981\u7ed9\u6837\u54c1\u65bd\u52a0\u4e00\u5b9a\u9891\u7387[eq]\\omega[\/eq]\u548c\u5e45\u5ea6[eq]\\gamma[\/eq]\u7684\u6b63\u5f26\u5e94\u53d8[eq]\\gamma \\left ( t \\right ) = \\gamma_0 \\sin \\left ( \\omega t \\right)[\/eq]\uff0c\u7136\u540e\u5939\u5177\u6240\u8fde\u63a5\u7684\u529b\u5b66\u4f20\u611f\u5668\u8bb0\u5f55\u6837\u54c1\u5411\u5939\u5177\u65bd\u52a0\u7684\u8f6c\u77e9\uff0c\u5e76\u6839\u636e\u5939\u5177\u5f62\u72b6\u548cGap\u503c\u6362\u7b97\u6210\u5e94\u53d8[eq]\\sigma \\left ( t \\right )[\/eq]\uff0c\u5728\u7ebf\u6027\u7c98\u5f39\u6027\u6761\u4ef6\u4e0b[eq]\\sigma \\left ( t \\right )=\\sigma_0 \\sin \\left ( \\omega t + \\delta \\right )[\/eq]\u3002\u4eea\u54c1\u4ec5\u9700\u4e14\u5fc5\u987b\u51c6\u786e\u6d4b\u91cf\u51fa\u4e24\u4e2a\u503c\uff1a[eq]\\sigma_0[\/eq]\uff08\u4ece\u5728\u8f6c\u77e9\u6570\u636e\u4e2d\u627e\u5230\u7684\u6700\u503c\u6362\u7b97\uff09\u548c[eq]\\delta[\/eq]\uff08\u901a\u8fc7\u6bd4\u8f83\u8f6c\u77e9\u6570\u636e\u548c\u5e94\u53d8\u6570\u636e\u7684\u76f8\u4f4d\u5dee[eq]\\Delta t[\/eq]\u6362\u7b97\uff0c\u89c1\u7b2c1\u5e45\u56fe\uff09\u3002\u5176\u4e2d\uff0c[eq]\\Delta t=\\frac{\\delta}{\\omega}[\/eq]\u3002\u5176\u4ed6\u8bf8\u5982[eq]G'[\/eq]\u3001[eq]\\eta'[\/eq]\u4e4b\u7c7b\u7684\uff0c\u90fd\u662f\u4ece\u8fd9\u4e24\u4e2a\u6570\u636e\u7b97\u51fa\u6765\u7684\u3002\u4f8b\u5982[eq]G&#8221;=\\frac {\\sigma_0}{\\gamma_0} \\sin \\left( \\omega \\right )[\/eq]\u3002<\/p>\n<p>\u5982\u679c\u6837\u54c1\u975e\u5e38\u63a5\u8fd1Hookian\u5f39\u6027\u4f53\uff0c\u5e94\u529b\u548c\u5e94\u53d8\u7684\u65f6\u95f4\u66f2\u7ebf\u63a5\u8fd1\u540c\u76f8\uff0c\u76f8\u4f4d\u89d2[eq]\\delta[\/eq]\u7684\u503c\u662f\u975e\u5e38\u5c0f\u7684\uff0c\u5982\u679c\u540c\u65f6\u9891\u7387[eq]\\omega[\/eq]\u7684\u503c\u5f88\u5927\uff0c\u90a3\u4e48\u76f8\u4f4d\u5dee[eq]\\Delta t[\/eq]\u7684\u503c\u5c31\u4f1a\u975e\u5e38\u5c0f\u3002\u6309\u7167\u7b2c\u4e00\u5e45\u56fe\u7684\u60c5\u51b5\uff0c<img decoding=\"async\" src=\"http:\/\/latex.codecogs.com\/gif.latex?\\inline \\Delta t=\\frac{\\delta}{\\omega}=52.36 \\textup{(s)}\" title=\"\\inline \\Delta t=\\frac{\\delta}{\\omega}=52.36 \\textup{(s)}\" align=\"absmiddle\"\/>\uff0c\u8fd9\u4e48\u5927\u7684\u65f6\u95f4\u5dee\u5c31\u7b97\u4eba\u4e5f\u80fd\u6d4b\u5f97\u5f88\u51c6\u3002\u4f46\u662f\uff0c\u5728Laponite\u51dd\u80f6\u7c98\u5f39\u8c31\u4e2d\uff0c\u6837\u54c1\u5728\u9ad8\u9891\u533a\u975e\u5e38\u63a5\u8fd1Hookian\u884c\u4e3a\uff0c[eq]\\delta[\/eq]\u5c0f\u4e8e2&deg;\uff0c\u8fd9\u65f6\uff0c\u5982\u679c\u8981\u6c42\u4eea\u5668\u4ecd\u7136\u628a[eq]\\delta[\/eq]\u6d4b\u51c6\uff0c\u5c31\u7b49\u4e8e\u8981\u6c42\u51c6\u786e\u5206\u8fa8\u5c0f\u4e8e\u4e07\u5206\u4e4b\u51e0\u79d2\u7684\u65f6\u95f4\u5dee\u3002\u4ee5<img decoding=\"async\" src=\"http:\/\/latex.codecogs.com\/gif.latex?\\inline \\delta=30^{\\circ}, \\omega=0.01 \\textup{rad\/s}\" title=\"\\inline \\delta=1^{\\circ}, \\omega=100 \\textup{rad\/s}\" align=\"absmiddle\"\/>\u4e3a\u4f8b\uff1a<a href=\"http:\/\/www.codecogs.com\/eqnedit.php?latex=\\inline \\Delta t=\\frac{\\delta}{\\omega}=\\frac {\\pi}{180\\times 100}=1.74\\times 10^{-4}\\textup{(s)}\" target=\"_blank\"><img decoding=\"async\" src=\"http:\/\/latex.codecogs.com\/gif.latex?\\inline \\Delta t=\\frac{\\delta}{\\omega}=\\frac {\\pi}{180\\times 100}=1.74\\times 10^{-4}\\textup{(s)}\" title=\"\\inline \\Delta t=\\frac{\\delta}{\\omega}=\\frac {\\pi}{180\\times 100}=1.74\\times 10^{-4}\\textup{(s)}\" align=\"absmiddle\"\/><\/a>\uff01<\/p>\n<p>\u4eea\u5668\u662f\u901a\u8fc7\u6bd4\u8f83\u5e94\u529b\u548c\u5e94\u53d8\u4e24\u6761\u66f2\u7ebf\u5728\u6a2a\u8f74\u4e0a\u7684\u4f4d\u503c\u5dee\u6765\u83b7\u5f97[eq]\\Delta t[\/eq]\u7684\u3002\u7406\u8bba\u4e0a[eq]\\Delta t[\/eq]\u518d\u5c0f\u4e5f\u603b\u5927\u4e8e0\u3002\u4f46\u5982\u679c\u5f85\u6d4b\u503c\u5c0f\u4e8e\u4eea\u5668\u8bef\u5dee\uff0c\u4eea\u5668\u53ef\u80fd\u5c31\u641e\u4e0d\u6e05\u4e24\u6761\u66f2\u7ebf\u8c01\u524d\u8c01\u540e\u4e86\uff0c\u5c31\u4f1a\u51fa\u73b0\u8d1f\u503c\u7684[eq]\\Delta t[\/eq]\uff0c\u4ece\u800c\u51fa\u73b0\u8d1f\u503c\u7684[eq]\\delta[\/eq]\u3002\u867d\u7136[eq]\\delta[\/eq]\u51fa\u73b0\u8d1f\u503c\uff0c\u4f46\u7edd\u5bf9\u503c\u603b\u4e4b\u5e76\u4e0d\u4f1a\u592a\u5927\uff0c\u6240\u4ee5[eq]\\delta[\/eq]\u5728\u7b2c\u56db\u8c61\u9650\uff0c[eq]\\cos\\left(\\delta\\right)\\gg 0,\\sin\\left(\\delta\\right)<0[\/eq]\uff0c\u6240\u4ee5\u201c\u906d\u6b83\u201d\u7684\u5c31\u4f1a\u662f[eq]G''[\/eq]\u3002<\/p>\n<p>\u603b\u4e4b\uff0c[eq]G&#8221;<0[\/eq]\u7684\u5b9e\u8d28\u662f\uff0cHookian\u6837\u54c1\u635f\u8017\u89d2[eq]\\delta[\/eq]\u7684\u9ad8\u9891\u503c\u5df2\u8d85\u8fc7\u4eea\u5668\u7684\u6d4b\u91cf\u80fd\u529b\uff0c\u6d4b\u51fa\u6765\u7684\u503c\u4e0d\u7ba1\u662f\u6b63\u662f\u8d1f\uff0c\u90fd\u5728\u8bef\u5dee\u8303\u56f4\u5185\uff0c\u5df2\u7ecf\u4e0d\u53ef\u9760\u4e86\u3002<\/p>\n<!-- kcite active, but no citations found -->\n<\/div> <!-- kcite-section 1031 -->","protected":false},"excerpt":{"rendered":"<p>\u4e3b\u9898\u56de\u5f52\u5230\u6d41\u53d8\u5b66\u4e00\u4e0b\u3002 \u4f17\u6240\u5468\u77e5\uff08\u7ebf\u6027\uff09\u7c98\u5f39\u6027\u662f\u5904\u4e8eHookian\u5f39\u6027\u548cNewtonian\u7c98\u6027\u8fd9\u4e24\u4e2a\u6781\u7aef\u4e4b\u95f4\u7684\u6027\u8d28\u3002\u5bf9Hookian\u5f39\u6027\u4f53\uff08Hookian\u5f39\u7c27\u6a21\u578b\uff09\u65bd\u52a0\u6b63\u5f26\u5f62\u53d8\uff0c\u6d4b\u5230\u7684\u662f\u540c\u76f8\u7684\u6b63\u5f26\u5e94\u529b\uff1b\u5411Newtonian\u7c98\u6d41\u4f53\uff08Newtonian\u7c98\u58f6\uff09\u65bd\u52a0\u6b63\u5f26\u5f62\u53d8\u901f\u7387\uff0c\u6d4b\u5230\u7684\u662f\u540c\u76f8\u7684\u6b63\u5f26\u5e94\u529b\u3002\u5411\u4e00\u4e2a\u7ebf\u6027\u7c98\u5f39\u6027\u6837\u54c1\u65bd\u52a0\u6b63\u5f26\u5f62\u53d8\uff0c\u6d4b\u5230\u7684\u662f\u76f8\u4f4d\u89d2\u4e3a[eq]\\delta[\/eq]\u7684\u6b63\u5f26\u5e94\u529b\uff1a[eq]\\gamma_0 \\sin \\left ( \\omega t+\\delta \\right )[\/eq]\u3002 \u6700\u4e3a\u4eba\u719f\u6089\u7684\u6d41\u53d8\u5b66\u6d4b\u8bd5\uff08\u4e5f\u662f\u6700\u591a\u4e0d\u61c2\u6d41\u53d8\u7684\u4eba\u77e5\u9053\u8981\u505a\u7684\u6d4b\u8bd5\uff09\u5c31\u662f[eq]G'[\/eq]\u3001[eq]G&#8221;[\/eq]~[eq]\\omega[\/eq]\u66f2\u7ebf\uff0c\u8fd9\u4e2a\u4e5f\u53eb\u505a\u201c\u7c98\u5f39\u8c31\u201d\u3002\u6211\u66fe\u7ecf\u8be6\u7ec6\u89e3\u91ca\u8fc7[eq]G'[\/eq]\u548c[eq]G&#8221;[\/eq]\u5230\u5e95\u662f\u600e\u4e48\u6765\u7684\u3002\u5178\u578b\u7ebf\u578b\u805a\u5408\u7269\u7c98\u5f39\u8c31\u5982\u4e0b\u56fe\uff1a \u4e0b\u56fe\u662f\u6211\u914d\u5236\u7684\u5408\u6210\u9502\u85fb\u571fLaponite\u51dd\u80f6\u7684\u7c98\u5f39\u8c31\uff0c\u53d1\u73b0[eq]G&#8221;[\/eq]\u5728\u9ad8\u9891\u5904\u51fa\u73b0\u8d1f\u503c\u3002\u4e0b\u9762\u662f\u5bf9\u8fd9\u4e2a\u4e0d\u6b63\u5e38\u73b0\u8c61\u7684\u89e3\u91ca\u3002 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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":6627,"url":"https:\/\/www.andrewsun.net\/panta_rhei\/archives\/6627","url_meta":{"origin":1031,"position":2},"title":"\u6d41\u53d8\u5b66\u7814\u7a76\u4ec0\u4e48","author":"Andrew","date":"2015\u5e746\u670827\u65e5","format":"aside","excerpt":"\u4eca\u5929\u53bb\u9762\u7b7e\uff0c\u9762\u8bd5\u5b98\u95ee\u6211What is rheology\uff0c\u6211\u629b\u51fa\u5b98\u8bdd\uff1athe study of the deformation and flow of 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Philippoff\u7684\u535a\u58eb\u5b66\u4f4d\u8bba\u6587\uff0c\u5df2\u7ecf\u5341\u5206\u4e25\u8083\u5730\u63d0\u51fa\u5bf9\u6d41\u4f53\u8fdb\u884c\u632f\u8361\u5f62\u53d8\u7684\u4e00\u6574\u5957\u65b9\u6cd5\uff0c\u7279\u522b\u662f\u4ed6\u642d\u5efa\u4e86\u7535\u5668\u5316\u7684\u4eea\u5668\uff08\u6d4b\u91cf\u7684\u539f\u59cb\u4fe1\u53f7\u662f\u7535\u4fe1\u53f7\uff09\u2014\u2014\u800c\u975e\u626d\u6446\uff08\u79e4\uff09\u8fd9\u79cd19\u4e16\u7eaa\u4ee5\u524d\u7684\u7eaf\u529b\u5b66\u4eea\u5668\uff08\u6d4b\u91cf\u7684\u539f\u59cb\u4fe1\u53f7\u662f\u4f4d\u79fb\uff09\u2014\u2014\u6765\u5b9e\u73b0\u8fd9\u79cd\u6d4b\u91cf\u3002A. Gemant\u7814\u7a76\u5174\u8da3\u5c31\u662f\u7c98\u5f39\u6027\u3002\u4ed6\u80fd\u63d0\u51fa\u201c\u590d\u6570\u7c98\u5ea6\u201d\u8fd9\u79cd\u6982\u5ff5\uff0cW. Philippoff\u2014\u2014\u4ee5\u53ca\u540c\u65f6\u4ee3\u7684\u5176\u4ed6\u5de5\u7a0b\u5e08\u4eec\u2014\u2014\u672a\u5fc5\u5c31\u63d0\u4e0d\u51fa\u3002\u518d\u52a0\u4e0aA. Gemant\u63d0\u51fa\u590d\u6570\u7c98\u5ea6\u7684\u8bba\u6587\u662f1935\u5e74\uff0c\u800cW. Philippoff\u60f3\u5230\u7528\u632f\u8361\u5f62\u53d8\u53bb\u6d4b\u91cf\u6d41\u4f53\u662f\u57281933\u5e74\u4ee5\u524d\u3002\u56e0\u6b64\u516c\u5e73\u8d77\u89c1\uff0c\u66f4\u5e94\u8be5\u8fd9\u4e48\u8bf4\uff1aW. Philippoff\u3001A. Gemant\u662f\u6700\u65e9\uff081930\u5e74\u4ee3\uff09\u4e3b\u7c98\u5f39\u6027\u73b0\u8c61\u7684\u632f\u8361\u6d4b\u8bd5\u53ca\u590d\u6570\u63cf\u8ff0\u7684\u4e24\u4f4d\u79d1\u5b66\u5bb6\u3002\u8c01\u5148\u675c\u64b0\u201c\u590d\u6570\u7c98\u5ea6\u201d\u8fd9\u4e2a\u8bcd\uff0c\u663e\u5f97\u6bd4\u8f83\u6b21\u8981\u3002 \u6240\u4ee5\uff0c\u6211\u4ecd\u7136\u53ef\u4ee5\u8bf4\uff0c\u6211\u57282009\u5e74\u7684\u6587\u7ae0\u6807\u9898\uff0c\u4e0d\u4ec5\u4ecd\u7136\u6210\u7acb\uff0c\u800c\u4e14\u662f\u6bd4A. 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":5297,"url":"https:\/\/www.andrewsun.net\/panta_rhei\/archives\/5297","url_meta":{"origin":1031,"position":5},"title":"Fourier\u53d8\u6362\uff08\u4e8c\uff09","author":"Andrew","date":"2013\u5e744\u670823\u65e5","format":false,"excerpt":"[mathjax] \u4e0a\u4e00\u7bc7\u4ecb\u7ecd\u4e86\u7528Fourier\u53d8\u6362\u6765\u91cd\u6784\u4e00\u4e2a\u672a\u77e5\u6b63\u5f26\u4fe1\u53f7\u7684\u65b9\u6cd5\u3002\u672c\u7bc7\u4ecb\u7ecd\u5bf9\u4e8e\u672a\u77e5\u975e\u6b63\u5f26\u4fe1\u53f7\u7684\u60c5\u51b5\u3002 \u5927\u5e45\u632f\u8361\u526a\u5207\u7684\u53c2\u6570 \u5927\u5e45\u632f\u8361\u526a\u5207\u5b9e\u9a8c\u4ea7\u751f\u7684\u6ce2\u5f62\u662f\u975e\u6b63\u5f26\u4fe1\u53f7\uff0c\u975e\u6b63\u5f26\u662f\u975e\u7ebf\u6027\u7c98\u5f39\u6027\u7684\u7279\u70b9\u3002\u6240\u4ee5\u5bf9\u975e\u7ebf\u6027\u7c98\u5f39\u6027\u7a0b\u5ea6\u7684\u8868\u5f81\uff0c\u5c31\u662f\u5bf9\u6ce2\u5f62\u6b63\u5f26\u5f62\u72b6\u504f\u79bb\u7a0b\u5ea6\u7684\u8868\u5f81\u3002\u5173\u4e8e\u5927\u5e45\u632f\u8361\u526a\u5207\u548c\u975e\u7ebf\u6027\u7c98\u5f39\u6027\u7684\u539f\u7406\u4e0e\u5b9e\u8df5\uff0c\u53ef\u89c1Hyhn\u7b49\u7684\u7efc\u8ff0\uff0c\u6216\u8005\u53c2\u9605\u6211\u7684\u535a\u58eb\u5b66\u4f4d\u8bba\u6587\u7b2c1.2.1\u8282\u3001\u7b2c1.3\u8282\u548c\u7b2c2\u7ae0\u3002\u672c\u6587\u53ea\u89e3\u51b3MATLAB\u7f16\u7a0b\u5b9e\u73b0\u95ee\u9898\u3002 \u5927\u5e45\u632f\u8361\u526a\u5207\uff08LAOS\uff09\u5b9e\u9a8c\u4e2d\uff0c\u6211\u4eec\u4ece\u6d41\u53d8\u4eea\u540c\u65f6\u83b7\u53d6\u4e24\u4e2a\u4fe1\u53f7\u3002\u4e00\u4e2a\u662f\u5e94\u53d8\u7684\u4fe1\u53f7\uff0c\u4e00\u4e2a\u662f\u5e94\u529b\u7684\u4fe1\u53f7\uff08\u4e8b\u5b9e\u4e0a\uff0c\u4e00\u4e2a\u662f\u9a6c\u8fbe\u4f4d\u79fb\u4fe1\u53f7\uff0c\u53e6\u4e00\u4e2a\u662f\u529b\u77e9\u4fe1\u53f7\uff0c\u5b83\u4eec\u90fd\u8981\u4e58\u4ee5\u4e00\u4e2a\u7cfb\u6570\uff0c\u624d\u662f\u5e94\u53d8\u548c\u5e94\u529b\u3002\u6b64\u6587\u5148\u7565\u53bb\u8fd9\u4e00\u4e8b\u5b9e\u4e86\uff09\u3002\u5728\u5e94\u53d8\u63a7\u5236\u7684\u5b9e\u9a8c\u4e2d\uff0c\u6211\u4eec\u65bd\u52a0\u4e00\u4e2a\u6b63\u5f26\u7684\u5e94\u53d8\uff0c\u6d4b\u91cf\u5e94\u529b\u7684\u54cd\u5e94\uff0c\u5373 $$\\begin{cases}\\gamma\\left(t\\right)=\\sin\\omega t\\\\ \\sigma\\left(t\\right)=\\sum_{n=0:\\text{odd}}^\\infty\\sigma_n\\sin\\left(\\omega t+\\delta_n\\right)\\end{cases}$$\u7531\u6b64\u5f0f\u53ef\u5b9a\u4e49LAOS\u5b9e\u9a8c\u7ed3\u679c\u7684\u8868\u5f81\u53c2\u6570\uff0c\u4ee5\u53ca\uff0c\u6765\u8868\u5f81\u975e\u7ebf\u6027\u7c98\u5f39\u6027\u7684\u7a0b\u5ea6\uff08\u5373\u504f\u79bb\u6b63\u5f26\u51fd\u6570\u7684\u7a0b\u5ea6\u3002\u6b64\u5916\uff0c\u6211\u4eec\u8fd8\u4f1a\u4ee5\u5bf9\u4f5c\u56fe\uff08\u53c2\u6570\u65b9\u7a0b\u4f5c\u56fe\uff09\uff0c\u5f97\u5230Lissajous\u66f2\u7ebf\u3002\u7136\u540e\u7528\u66f2\u7ebf\u7684\u5f62\u72b6\u7279\u5f81\u6765\u8868\u5f81\u975e\u7ebf\u6027\u7c98\u5f39\u6027\u7684\u7a0b\u5ea6\uff08\u5373\u66f2\u7ebf\u504f\u79bb\u692d\u5706\u7684\u7a0b\u5ea6\uff09\u3002\u63cf\u8ff0\u66f2\u7ebf\u5f62\u72b6\u7279\u5f81\uff0c\u5f80\u5f80\u5c31\u662f\u5404\u79cd\u5404\u6837\u7684\u5207\u7ebf\u659c\u7387\uff08\u53ef\u81ea\u884c\u4e0a\u7f51\u641c\u7d22\u590d\u4e60\u53c2\u6570\u65b9\u7a0b\u6c42\u5bfc\uff09\u3002\u5728LAOS\u4e2d\u5e38\u7528\uff1a$$G_\\text{M}=\\left.\\frac{d\\sigma}{d\\gamma}\\right|_{\\gamma=0}$$$$G_\\text{L}=\\frac{\\sigma{\\gamma_0}}{\\gamma_0}$$$$G_\\text{k}=\\left.\\frac{d\\sigma}{d\\gamma}\\right|_{\\sigma=0}$$ MATLAB\u7f16\u7a0b\u6b65\u9aa4 \u5728\u8be6\u7ec6\u4ecb\u7ecdMATLAB\u4ee3\u7801\u4e4b\u524d\uff0c\u5148\u603b\u7ed3\u4e00\u4e0b\u6211\u4eec\u8981\u5b8c\u6210\u4ec0\u4e48\u4efb\u52a1\uff0c\u8ddf\u4ece\u54ea\u4e9b\u6b65\u9aa4\u3002\u6211\u4eec\u7684\u4efb\u52a1\u5c31\u662f\u8981\u4ece\u5e94\u529b\u548c\u5e94\u53d8\u7684\u4fe1\u53f7\u8ba1\u7b97\u51fa\u4e0a\u8ff0\u7684\u8fd9\u4e48\u591a\u53c2\u6570\u3002\u5b9e\u9a8c\u65f6\uff0c\u6211\u4eec\u4f1a\u89c4\u5b9a\u5e94\u53d8\u7684\u5e45\u5ea6\u548c\u9891\u7387\uff0c\u4f46\u662f\uff0c\u7531\u4e8e\u4eea\u5668\u8bef\u5dee\uff0c\u5b9e\u9645\u65bd\u52a0\u5728\u6837\u54c1\u4e0a\u7684\u5e94\u53d8\u5e45\u5ea6\u548c\u9891\u7387\uff0c\u672a\u5fc5\u5b8c\u5168\u7b49\u4e8e\u7684\u547d\u4ee4\u503c\u3002\u5c3d\u7ba1\u8fd9\u4e00\u8bef\u5dee\u975e\u5e38\u5c0f\uff0c\u4f46\u4ece\u505a\u6cd5\u4e0a\u6211\u4eec\u8fd8\u662f\u8981\u4ee5\u5b9e\u9645\u5e94\u53d8\u4fe1\u53f7\u4e3a\u51c6\u3002\u6240\u4ee5\uff0c\u6211\u4eec\u9996\u5148\u8981\u5bf9\u5b9e\u9645\u5e94\u53d8\u4fe1\u53f7\u8fdb\u884c\u5224\u65ad\uff0c\u83b7\u5f97\u5b9e\u9645\u7684\u5e94\u53d8\u5e45\u5ea6\u548c\u9891\u7387\u3002\u5982\u4f55\u5224\u65ad\u4e00\u4e2a\u672a\u77e5\u6b63\u5f26\u4fe1\u53f7\u7684\u632f\u5e45\u3001\u9891\u7387\u548c\u76f8\u4f4d\u7684\u65b9\u6cd5\u5df2\u7ecf\u5728\u4e0a\u4e00\u7bc7\u6587\u7ae0\u4e2d\u4ecb\u7ecd\u4e86\u3002 \u7136\u540e\uff0c\u5c31\u8981\u5904\u7406\u5e94\u529b\u7684\u4fe1\u53f7\u3002\u4e3a\u4e86\u83b7\u5f97\u548c\u540c\u6837\u9700\u8981\u5bf9\u8fdb\u884cfft\u5904\u7406\uff0c\u65b9\u6cd5\u8ddf\u4e0a\u4e00\u7bc7\u6587\u7ae0\u4ecb\u7ecd\u7684\u7c7b\u4f3c\uff0c\u533a\u522b\u53ea\u5728\u4e8e\u6211\u4eec\u9664\u4e86\u8981\u83b7\u5f97\u57fa\u9891\u7684\u5e45\u503c\u548c\u76f8\u4f4d\u4e4b\u5916\uff0c\u8fd8\u8981\u83b7\u5f97\u9ad8\u6b21\u8c10\u6ce2\u7684\u5e45\u503c\u548c\u76f8\u4f4d\u3002\u7406\u8bba\u4e0a\u6765\u8bf4\uff0c\u4f46\u662f\u5b9e\u9645\u4e0a\u6211\u4eec\u6839\u636e\u9700\u8981\u53d6\u6709\u9650\u7684n\u4e2a\u9ad8\u6b21\u8c10\u6ce2\uff0c\u5c31\u53ef\u4ee5\u6bd4\u8f83\u51c6\u786e\u5730\u91cd\u6784\u51fa\u7684\u6ce2\u5f62\u4e86\u3002\u63d0\u9192\u4e00\u4e0b\uff0c\u5b9a\u4e49\u5f0f\u91cc\u5e94\u53d8\u662f\u4e00\u4e2a\u96f6\u76f8\u4f4d\u7684\u6807\u51c6\u6b63\u5f26\u51fd\u6570\uff0c\u4f46\u5b9e\u9645\u91cd\u6784\u7684\u5e94\u53d8\u6ce2\u5f62\u53ef\u80fd\u4f1a\u6709\u975e\u96f6\u7684\u76f8\u4f4d\uff0c\u8fd9\u65f6\uff0c\u5e94\u529b\u7684\u5404\u4e2a\u8c10\u6ce2\u7684\u76f8\u4f4d\u8981\u90fd\u51cf\u53bb\u5e94\u53d8\u7684\u76f8\u4f4d\uff0c\u624d\u662f\u6211\u4eec\u8981\u6c42\u7684\u3002 Lissajous\u66f2\u7ebf\u7684\u5404\u79cd\u5bfc\u6570\uff0c\u8981\u540c\u65f6\u5728\u548c\u90fd\u91cd\u6784\u4e86\u4e4b\u540e\uff0c\u518d\u8fdb\u884c\u6c42\u5bfc\u8ba1\u7b97\u5f97\u5230\u3002\u603b\u800c\u8a00\u4e4b\uff0c\u8981\u5b8c\u6210\u4ee5\u4e0b\u4e09\u4e2a\u6b65\u9aa4\uff1a \u91cd\u6784\u5e94\u53d8\uff0c\u83b7\u5f97\u3001\u548c\u76f8\u4f4d \u91cd\u6784\uff0c\u83b7\u5f97\u548c\uff0c\u8ba1\u7b97 \u7528\u91cd\u6784\u7684\u548c\u4f5cLissajous\u66f2\u7ebf\uff0c\u4ee5\u53ca\u8ba1\u7b97\u3001\u548c \u91cd\u6784\u548c MATLAB\u5e2e\u52a9\u6587\u4ef6\u91ccfft\u547d\u4ee4\u7684\u6761\u76ee\u6709\u4e00\u4e2a\u8303\u4f8b\uff0c\u5e94\u8be5\u80fd\u89e3\u51b3\u5927\u90e8\u5206\u95ee\u9898\u4e86\u3002\u5176\u4e2d\u5728coherent sampling\uff08\u89c1\u4e0a\u7bc7\u6587\u7ae0\uff09\u5904\uff0c\u8303\u4f8b\u7528next power of 2\uff0c\u5176\u5b9e\u6ca1\u6709\u5fc5\u8981\u3002\u4e0b\u9762\u7684\u4ee3\u7801\uff0c\u6211\u5c31\u4e0d\u591a\u4f5c\u89e3\u91ca\u4e86\u3002 clear all clc % the strain signal fs=1000; % sampling frequency t=0:1\/fs:30.2; % the time series of the strain signal t=t(:); % convert to colume vector w=5; %\u2026","rel":"","context":"In &quot;\u5de5\u4f5c\u7b14\u8bb0&quot;","block_context":{"text":"\u5de5\u4f5c\u7b14\u8bb0","link":"https:\/\/www.andrewsun.net\/panta_rhei\/archives\/category\/personal\/%e5%b7%a5%e4%bd%9c%e7%ac%94%e8%ae%b0"},"img":{"alt_text":"Figure 1 Parts of the strain and the stress signals","src":"https:\/\/i0.wp.com\/www.andrewsun.net\/panta_rhei\/wp-content\/uploads\/2013\/04\/fig1.png?resize=350%2C200","width":350,"height":200,"srcset":"https:\/\/i0.wp.com\/www.andrewsun.net\/panta_rhei\/wp-content\/uploads\/2013\/04\/fig1.png?resize=350%2C200 1x, https:\/\/i0.wp.com\/www.andrewsun.net\/panta_rhei\/wp-content\/uploads\/2013\/04\/fig1.png?resize=525%2C300 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