{"id":29349,"date":"2024-03-12T04:59:59","date_gmt":"2024-03-12T05:59:59","guid":{"rendered":"https:\/\/express24.ir\/d\/product\/%d9%85%d9%82%d8%a7%d9%84%d9%87-%d8%b4%d8%a8%db%8c%d9%87-%d8%b3%d8%a7%d8%b2%db%8c-%da%af%d8%b1%d9%85%d8%a7%db%8c%d8%b4-%d8%b3%d9%87-%d8%a8%d8%af%d9%86%d9%87-%da%a9%d9%84%d8%a7%d8%b3%db%8c%da%a9-%d8%af\/"},"modified":"2024-03-12T05:00:00","modified_gmt":"2024-03-12T06:00:00","slug":"%d9%85%d9%82%d8%a7%d9%84%d9%87-%d8%b4%d8%a8%db%8c%d9%87-%d8%b3%d8%a7%d8%b2%db%8c-%da%af%d8%b1%d9%85%d8%a7%db%8c%d8%b4-%d8%b3%d9%87-%d8%a8%d8%af%d9%86%d9%87-%da%a9%d9%84%d8%a7%d8%b3%db%8c%da%a9-%d8%af","status":"publish","type":"product","link":"https:\/\/express24.ir\/d\/product\/%d9%85%d9%82%d8%a7%d9%84%d9%87-%d8%b4%d8%a8%db%8c%d9%87-%d8%b3%d8%a7%d8%b2%db%8c-%da%af%d8%b1%d9%85%d8%a7%db%8c%d8%b4-%d8%b3%d9%87-%d8%a8%d8%af%d9%86%d9%87-%da%a9%d9%84%d8%a7%d8%b3%db%8c%da%a9-%d8%af\/","title":{"rendered":"\u0645\u0642\u0627\u0644\u0647 \u0634\u0628\u06cc\u0647 \u0633\u0627\u0632\u06cc \u06af\u0631\u0645\u0627\u06cc\u0634 \u0633\u0647 \u0628\u062f\u0646\u0647 \u06a9\u0644\u0627\u0633\u06cc\u06a9 \u062f\u0631 \u06cc\u06a9 \u0628\u0639\u062f"},"content":{"rendered":"<table class=\"table table-striped table-hover\">\n<tbody>\n<tr>\n<td>\u0639\u0646\u0648\u0627\u0646 \u0645\u0642\u0627\u0644\u0647 \u0628\u0647 \u0627\u0646\u06af\u0644\u06cc\u0633\u06cc <\/td>\n<td>Simulations of Classical Three-Body Thermalization in One Dimension<\/td>\n<\/tr>\n<tr>\n<td>\u0639\u0646\u0648\u0627\u0646 \u0645\u0642\u0627\u0644\u0647 \u0628\u0647 \u0641\u0627\u0631\u0633\u06cc <\/td>\n<td>\u0645\u0642\u0627\u0644\u0647 \u0634\u0628\u06cc\u0647 \u0633\u0627\u0632\u06cc \u06af\u0631\u0645\u0627\u06cc\u0634 \u0633\u0647 \u0628\u062f\u0646\u0647 \u06a9\u0644\u0627\u0633\u06cc\u06a9 \u062f\u0631 \u06cc\u06a9 \u0628\u0639\u062f<\/td>\n<\/tr>\n<tr>\n<td>\u0646\u0648\u06cc\u0633\u0646\u062f\u06af\u0627\u0646 <\/td>\n<td>M. Eltohfa, Xinghan Wang, Colton M. Griffin, F. Robicheaux<\/td>\n<\/tr>\n<tr>\n<td>\u0632\u0628\u0627\u0646 \u0645\u0642\u0627\u0644\u0647 <\/td>\n<td>\u0627\u0646\u06af\u0644\u06cc\u0633\u06cc<\/td>\n<\/tr>\n<tr>\n<td>\u0641\u0631\u0645\u062a \u0645\u0642\u0627\u0644\u0647: <\/td>\n<td>PDF<\/td>\n<\/tr>\n<tr>\n<td>\u062a\u0639\u062f\u0627\u062f \u0635\u0641\u062d\u0627\u062a<\/td>\n<td>13<\/td>\n<\/tr>\n<tr>\n<td>\u062f\u0633\u062a\u0647 \u0628\u0646\u062f\u06cc \u0645\u0648\u0636\u0648\u0639\u0627\u062a  <\/td>\n<td>Atomic Physics,Statistical Mechanics,Classical Physics,\u0641\u06cc\u0632\u06cc\u06a9 \u0627\u062a\u0645\u06cc , \u0645\u06a9\u0627\u0646\u06cc\u06a9 \u0622\u0645\u0627\u0631\u06cc , \u0641\u06cc\u0632\u06cc\u06a9 \u06a9\u0644\u0627\u0633\u06cc\u06a9 ,<\/td>\n<\/tr>\n<tr>\n<td>\u062a\u0648\u0636\u06cc\u062d\u0627\u062a    <\/td>\n<td>Submitted 29 February, 2024; originally announced March 2024. , Comments: 13 pages, 12 figures<\/td>\n<\/tr>\n<tr>\n<td>\u062a\u0648\u0636\u06cc\u062d\u0627\u062a \u0628\u0647 \u0641\u0627\u0631\u0633\u06cc    <\/td>\n<td>\u0627\u0631\u0633\u0627\u0644 \u0634\u062f\u0647 29 \u0641\u0648\u0631\u06cc\u0647 2024 \u061b\u062f\u0631 \u0627\u0628\u062a\u062f\u0627 \u0645\u0627\u0631\u0633 2024 \u0627\u0639\u0644\u0627\u0645 \u0634\u062f \u060c \u0646\u0638\u0631\u0627\u062a: 13 \u0635\u0641\u062d\u0647 \u060c 12 \u0631\u0642\u0645<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<h2>\u0686\u06a9\u06cc\u062f\u0647<\/h2>\n<p style=\"direction:ltr;\">One-dimensional systems, such as nanowires or electrons moving along strong magnetic field lines, have peculiar thermalization physics. The binary collision of point-like particles, typically the dominant process for reaching thermal equilibrium in higher dimensional systems, cannot thermalize a 1D system. We study how dilute classical 1D gases thermalize through three-body collisions. We consider a system of identical classical point particles with pairwise repulsive inverse power-law potential $V_{ij} \\propto 1\/|x_i-x_j|^n$ or the pairwise Lennard-Jones potential. Using Monte Carlo methods, we compute a collision kernel and use it in the Boltzmann equation to evolve a perturbed thermal state with temperature $T$ toward equilibrium. We explain the shape of the kernel and its dependence on the system parameters. Additionally, we implement molecular dynamics simulations of a many-body gas and show agreement with the Boltzmann evolution in the low density limit. For the inverse power-law potential, the rate of thermalization is proportional to $\u03c1^2 T^{\\frac{1}{2}-\\frac{1}{n}}$ where $\u03c1$ is the number density. The corresponding proportionality constant decreases with increasing $n$.<\/p>\n<h2>\u0686\u06a9\u06cc\u062f\u0647 \u0628\u0647 \u0641\u0627\u0631\u0633\u06cc (\u062a\u0631\u062c\u0645\u0647 \u0645\u0627\u0634\u06cc\u0646\u06cc)<\/h2>\n<p>\u0633\u06cc\u0633\u062a\u0645 \u0647\u0627\u06cc \u06cc\u06a9 \u0628\u0639\u062f\u06cc \u060c \u0645\u0627\u0646\u0646\u062f \u0646\u0627\u0646\u0648\u0633\u06cc\u0645 \u0647\u0627 \u06cc\u0627 \u0627\u0644\u06a9\u062a\u0631\u0648\u0646 \u0647\u0627\u06cc\u06cc \u06a9\u0647 \u062f\u0631 \u0627\u0645\u062a\u062f\u0627\u062f \u062e\u0637\u0648\u0637 \u0645\u06cc\u062f\u0627\u0646 \u0645\u063a\u0646\u0627\u0637\u06cc\u0633\u06cc \u0642\u0648\u06cc \u062d\u0631\u06a9\u062a \u0645\u06cc \u06a9\u0646\u0646\u062f \u060c \u062f\u0627\u0631\u0627\u06cc \u0641\u06cc\u0632\u06cc\u06a9 \u062d\u0631\u0627\u0631\u062a\u06cc \u0639\u062c\u06cc\u0628 \u0648 \u063a\u0631\u06cc\u0628 \u0647\u0633\u062a\u0646\u062f.\u0628\u0631\u062e\u0648\u0631\u062f 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\u0627\u0633\u062a.\u062b\u0627\u0628\u062a \u0645\u062a\u0646\u0627\u0633\u0628 \u0628\u0627 \u0627\u0641\u0632\u0627\u06cc\u0634 $ N $ \u06a9\u0627\u0647\u0634 \u0645\u06cc \u06cc\u0627\u0628\u062f.<\/p>\n<table class=\"table table-bordered table-primary\">\r\n<tr>\r\n\t<td>\r\n\t\u062a\u0648\u062c\u0647 \u06a9\u0646\u06cc\u062f \u0627\u06cc\u0646 \u0645\u0642\u0627\u0644\u0647 \u0628\u0647 \u0632\u0628\u0627\u0646 \u0627\u0646\u06af\u0644\u06cc\u0633\u06cc \u0627\u0633\u062a.\r\n\t<\/td>\r\n<\/tr>\r\n\t\r\n<tr>\r\n\t<td>\r\n     \u0628\u0631\u0627\u06cc \u0633\u0641\u0627\u0631\u0634 \u062a\u0631\u062c\u0645\u0647 \u0627\u06cc\u0646 \u0645\u0642\u0627\u0644\u0647 \u0645\u06cc \u062a\u0648\u0627\u0646\u06cc\u062f \u0628\u0647 \u06cc\u06a9\u06cc \u0627\u0632 \u0631\u0648\u0634 \u0647\u0627\u06cc \u062a\u0645\u0627\u0633\u060c \u067e\u06cc\u0627\u0645\u06a9\u060c \u062a\u0644\u06af\u0631\u0627\u0645 \u0648 \u06cc\u0627 \u0648\u0627\u062a\u0633 \u0627\u067e \u0628\u0627 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\u0628\u0627\u0634\u062f.\r\n\t\t<\/li>\r\n\t\t<li>\r\n\t\t\u0632\u0645\u0627\u0646 \u062a\u062d\u0648\u06cc\u0644 \u062a\u0631\u062c\u0645\u0647 \u0645\u0642\u0627\u0644\u0647 \u062f\u0631 \u0635\u0648\u0631\u062a \u062f\u0627\u0634\u062a\u0646 \u062a\u0639\u062f\u0627\u062f \u0635\u0641\u062d\u0627\u062a \u0639\u0627\u062f\u06cc \u0628\u06cc\u0646 3 \u062a\u0627 5 \u0631\u0648\u0632 \u062e\u0648\u0627\u0647\u062f \u0628\u0648\u062f.\r\n\t\t<\/li>\r\n\t\t\r\n\t\t<li>\r\n\t\t\u06a9\u06cc\u0641\u06cc\u062a \u062a\u0631\u062c\u0645\u0647 \u0628\u0633\u06cc\u0627\u0631 \u0628\u0627\u0644\u0627 \u0645\u06cc \u0628\u0627\u0634\u062f. \u0645\u0642\u0627\u0644\u0647 \u0641\u0642\u0637 \u062a\u0648\u0633\u0637 \u0645\u062a\u0631\u062c\u0645\u06cc\u0646 \u0628\u0627 \u0645\u062f\u0631\u06a9 \u062f\u0627\u0646\u0634\u06af\u0627\u0647\u06cc \u0645\u062a\u0631\u062c\u0645\u06cc \u062a\u0631\u062c\u0645\u0647 \u0645\u06cc\u200c\u0634\u0648\u062f.\r\n\t\t<\/li>\r\n\t\t<li>\r\n\t\t\u06a9\u0644\u06cc\u0647 \u062c\u062f\u0627\u0648\u0644 \u0648 \u0641\u0631\u0645\u0648\u0644 \u0647\u0627 \u0646\u06cc\u0632 \u062f\u0631 \u0641\u0627\u06cc\u0644 \u062a\u062d\u0648\u06cc\u0644\u06cc \u0648\u0631\u062f \u062f\u0631\u062c \u0645\u06cc\u200c\u0634\u0648\u0646\u062f.\r\n\t\t<\/li>\r\n\t<\/td>\r\n\t\r\n\t\r\n<\/tr>\r\n<\/table>\r\n\r\n\r\n\n","protected":false},"excerpt":{"rendered":"<p>\u0639\u0646\u0648\u0627\u0646 \u0645\u0642\u0627\u0644\u0647 \u0628\u0647 \u0627\u0646\u06af\u0644\u06cc\u0633\u06cc Simulations of Classical Three-Body Thermalization in One Dimension \u0639\u0646\u0648\u0627\u0646 \u0645\u0642\u0627\u0644\u0647 \u0628\u0647 \u0641\u0627\u0631\u0633\u06cc \u0645\u0642\u0627\u0644\u0647 \u0634\u0628\u06cc\u0647 \u0633\u0627\u0632\u06cc \u06af\u0631\u0645\u0627\u06cc\u0634 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