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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 Widom insertion method ： ウィキペディア英語版 Widom insertion method The Widom Insertion Method is a statistical thermodynamic approach to the calculation of material and mixture properties. It is named for Benjamin Widom, who derived it in 1963.〔Widom, B, "Some Topics in the Theory of Fluids", ''J. Chem. Phys.'', 1963, 39(11), 2808-2812.〕 In general, there are two theoretical approaches to determining the statistical mechanical properties of materials. The first is the direct calculation of the overall Partition Function of the system, which directly yields the system free energy. The second approach, known as the Widom Insertion method, instead derives from calculations centering on one molecule. The Widom Insertion method directly yields the chemical potential of one component rather than the system free energy. This approach is most widely applied in molecular computer simulations〔Binder, K. "Applications of Monte Carlo Methods to Statistical Physics," ''Rep. Prog. Phys.'', 1997,60,487-559.〕〔Dullens, RPA, et al., (), ''Mol. Phys.'', 2005, 103, 3195-3200.〕 but has also been applied in the development of analytical statistical mechanical models. ==Overview== As originally formulated by Benjamin Widom in 1963,〔 the approach can be summarized by the equation: $\backslash mathbf\_i=\backslash frac=\backslash left\; \backslash langle\; \backslash exp\; \backslash left\; (\; -\backslash frac\; \backslash right\; )\; \backslash right\; \backslash rangle$ where $\backslash mathbf\_i$ is called the 'insertion parameter', $\backslash rho\_i$ is the number density of species $i$, $a\_i$ is the activity of species $i$, $k\_B$ is the Boltzmann constant, and $T$ is temperature, and $\backslash psi$ is the interaction energy of an inserted particle with all other particles in the system. The average is over all possible insertions. This can be understood conceptually as fixing the location of all molecules in the system and then inserting a particle of species $i$ at all locations through the system, averaging over a Boltzmann factor in its interaction energy over all of those locations. 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「Widom insertion method」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.