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翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Brownian dynamics ： ウィキペディア英語版 Brownian dynamics Brownian dynamics (BD) can be used to describe the motion of molecules for example in molecular simulations or in reality. It is a simplified version of Langevin dynamics and corresponds to the limit where no average acceleration takes place. This approximation can also be described as 'overdamped' Langevin dynamics, or as Langevin dynamics without inertia. In Langevin dynamics, the equation of motion is :$M\backslash ddot\; =\; -\; \backslash nabla\; U(X)\; -\; \backslash gamma\; \backslash dot\; +\; \backslash sqrt\; R(t)$ where $\backslash gamma$ is a friction coefficient, $U(X)$ is the particle interaction potential; $\backslash nabla$ is the gradient operator such that $-\; \backslash nabla\; U(X)$ is the force calculated from the particle interaction potentials; the dot is a time derivative such that $\backslash dot$ is the velocity and $\backslash ddot$ is the acceleration; T is the temperature, kB is Boltzmann's constant; and $R(t)$ is a delta-correlated stationary Gaussian process with zero-mean, satisfying :$\backslash left\backslash langle\; R(t)\; \backslash right\backslash rangle\; =0$ :$\backslash left\backslash langle\; R(t)R(t\text{'})\; \backslash right\backslash rangle\; =\; \backslash delta(t-t\text{'}).$ In Brownian dynamics, it is assumed that the mass $M$ goes to zero. Thus, the $M\backslash ddot(t)$ term is neglected, and the sum of these terms is zero. :$0\; =\; -\; \backslash nabla\; U(X)\; -\; \backslash gamma\; \backslash dot+\; \backslash sqrt\; R(t)$ Using the Einstein relation, $D\; =\; k\_B\; T/\backslash gamma$, it is often convenient to write the equation as, :$\backslash dot(t)\; =\; -\; \backslash nabla\; U(X)/\backslash gamma\; +\; \backslash sqrt\; R(t).$ ==See also== * Brownian motion * Immersed boundary method 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Brownian dynamics」の詳細全文を読む スポンサード リンク 翻訳と辞書 : 翻訳のためのインターネットリソース Copyright(C) kotoba.ne.jp 1997-2016. All Rights Reserved.