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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 Smoluchowski coagulation equation ： ウィキペディア英語版 Smoluchowski coagulation equation In statistical physics, the Smoluchowski coagulation equation is a population balance equation introduced by Marian Smoluchowski in a seminal 1916 publication, describing the time evolution of the number density of particles as they coagulate (in this context "clumping together") to size ''x'' at time ''t''. Simultaneous coagulation (or aggregation) encountered in processes involving polymerization, coalescence of aerosols, emulsication, flocculation. ==Equation== The distribution of particle size change in time according to the interrelation of all particles of the system. Therefore, the Smoluchowski coagulation equation is an integrodifferential equation of the particle-size distribution. In the case when the sizes of the coagulated particles are continuous variables, the equation involves an integral: : $\backslash frac=\backslash frac\backslash int^x\_0K(x-y,y)n(x-y,t)n(y,t)\backslash ,dy\; -\; \backslash int^\backslash infty\_0K(x,y)n(x,t)n(y,t)\backslash ,dy.$ If ''dy'' is interpreted as a discrete measure, i.e. when particles join in discrete sizes, then the discrete form of the equation is a summation: : $\backslash frac=\backslash frac\backslash sum^\_$ K(x_i-x_j,x_j)n(x_i-x_j,t)n(x_j,t) - \sum^\infty_K(x_i,x_j)n(x_i,t)n(x_j,t). There exist a unique solution for a chosen kernel function. 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「Smoluchowski coagulation 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.