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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 Langevin dynamics ： ウィキペディア英語版 Langevin dynamics In physics, Langevin dynamics is an approach to the mathematical modeling of the dynamics of molecular systems, originally developed by the French physicist Paul Langevin. The approach is characterized by the use of simplified models while accounting for omitted degrees of freedom by the use of stochastic differential equations. A molecular system in the real world is unlikely to be present in vacuum. Jostling of solvent or air molecules causes friction, and the occasional high velocity collision will perturb the system. Langevin dynamics attempts to extend molecular dynamics to allow for these effects. Also, Langevin dynamics allows controlling the temperature like a thermostat, thus approximating the canonical ensemble. Langevin dynamics mimics the viscous aspect of a solvent. It does not fully model an implicit solvent; specifically, the model does not account for the electrostatic screening and also not for the hydrophobic effect. It should also be noted that for denser solvents, hydrodynamic interactions are not captured via Langevin dynamics. For a system of $N$ particles with masses $M$, with coordinates $X=X(t)$ that constitute a time-dependent random variable, the resulting Langevin equation is :$M\backslash ddot\; =\; -\; \backslash nabla\; U(X)\; -\; \backslash gamma\; M\; \backslash dot\; +\; \backslash sqrt\; R(t)\backslash ,,$ where $U(X)$ 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 :$\backslash left\backslash langle\; R(t)\; \backslash right\backslash rangle\; =0$ :$\backslash left\backslash langle\; R(t)R(t\text{'})\; \backslash right\backslash rangle\; =\; \backslash delta(t-t\text{'})$ Here, $\backslash delta$ is the Dirac delta. If the main objective is to control temperature, care should be exercised to use a small damping constant $\backslash gamma$. As $\backslash gamma$ grows, it spans the inertial all the way to the diffusive (Brownian) regime. The Langevin dynamics limit of non-inertia is commonly described as Brownian dynamics. Brownian dynamics can be considered as overdamped Langevin dynamics, i.e. Langevin dynamics where no average acceleration takes place. The Langevin equation can be reformulated as a Fokker–Planck equation that governs the probability distribution of the random variable ''X''. ==See also== * Hamiltonian mechanics * Statistical mechanics * Implicit solvation * Stochastic differential equations * Langevin equation 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「Langevin 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.