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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 Percus-Yevick approximation ： ウィキペディア英語版 Percus–Yevick approximation In statistical mechanics the Percus–Yevick approximation〔Percus, Jerome K. and Yevick, George J. Analysis of Classical Statistical Mechanics by Means of Collective Coordinates. Phys. Rev. 1958, 110, 1, DOI: (10.1103/PhysRev.110.1 )〕 is a closure relation to solve the Ornstein–Zernike equation. It is also referred to as the Percus–Yevick equation. It is commonly used in fluid theory to obtain e.g. expressions for the radial distribution function. ==Derivation== The direct correlation function represents the direct correlation between two particles in a system containing ''N'' − 2 other particles. It can be represented by : $c(r)=g\_(r)\; -\; g\_(r)\; \backslash ,$ where $g\_(r)$ is the radial distribution function, i.e. $g(r)=\backslash exp(w(r))$ (with ''w''(''r'') the potential of mean force) and $g\_(r)$ is the radial distribution function without the direct interaction between pairs $u(r)$ included; i.e. we write $g\_(r)=\backslash exp^$. Thus we ''approximate'' ''c''(''r'') by : $c(r)=e^-\; e^.\; \backslash ,$ If we introduce the function $y(r)=e^g(r)$ into the approximation for ''c''(''r'') one obtains : $c(r)=g(r)-y(r)=e^y(r)-y(r)=f(r)y(r).\; \backslash ,$ This is the essence of the Percus–Yevick approximation for if we substitute this result in the Ornstein–Zernike equation, one obtains the Percus–Yevick equation: : $y(r\_)=1+\backslash rho\; \backslash int\; f(r\_)y(r\_)h(r\_)\; d\; \backslash mathbf\{r\_\{3\}\}.\; \backslash ,$ The approximation was defined by Percus and Yevick in 1958. For hard spheres, the equation has an analytical solution.〔Wertheim, M. S. Exact Solution of the Percus-Yevick Integral Equation for Hard Spheres. Phys. Rev. Lett. 1963, 10, 321-323, DOI: (10.1103/PhysRevLett.10.321 )〕 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「Percus–Yevick approximation」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.