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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 Hypernetted-chain equation ： ウィキペディア英語版 Hypernetted-chain equation In statistical mechanics the hypernetted-chain equation is a closure relation to solve the Ornstein–Zernike equation which relates the direct correlation function to the total correlation function. It is commonly used in fluid theory to obtain e.g. expressions for the radial distribution function. It is given by: : $$ \ln y(r_) =\ln g(r_) + \beta u(r_) =\rho \int \left(- \ln g(r_) - \beta u(r_)\right ) h(r_) \, d \mathbf is the number density of molecules, $h(r)\; =\; g(r)-1$, $g(r)$ is the radial distribution function, $u(r)$ is the direct interaction between pairs. $\backslash beta\; =\; \backslash frac$ with $T$ being the Thermodynamic temperature and $k\_$ the Boltzmann constant. ==Derivation== The direct correlation function represents the direct correlation between two particles in a system containing ''N'' − 2 other particles. It can be represented by : $c(r)=g\_(r)\; -\; g\_(r)\; \backslash ,$ where $g\_(r)=g(r)\; =\; \backslash exp(w(r))$ (with $w(r)$ the potential of mean force) and $g\_(r)$ is the radial distribution function without the direct interaction between pairs $u(r)$ included; i.e. we write $g\_(r)=\backslash exp\backslash$. Thus we ''approximate'' $c(r)$ by : $c(r)=e^-\; e^.\; \backslash ,$ By expanding the indirect part of $g(r)$ in the above equation and introducing the function $y(r)=e^g(r)\; (=\; g\_(r)\; )$ we can approximate $c(r)$ by writing: : $c(r)=e^-1+\backslash beta()\; \backslash ,$ = g(r)-1-\ln y(r) \, = f(r)y(r)+(y(r) ) \,\, (\text), with $f(r)\; =\; e^-1$. This equation is the essence of the hypernetted chain equation. We can equivalently write : $$ h(r) - c(r) = g(r) - 1 -c(r) = \ln y(r). If we substitute this result in the Ornstein–Zernike equation :$$ h(r_)- c(r_) = \rho \int c(r_)h(r_)d \mathbf_, one obtains the hypernetted-chain equation: : $$ \ln y(r_) =\ln g(r_) + \beta u(r_) =\rho \int \left(-\ln g(r_) - \beta u(r_)\right ) h(r_) \, d \mathbf{r_{3}}. \, 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「Hypernetted-chain equation」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.