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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 Scale-free ideal gas ： ウィキペディア英語版 Scale-free ideal gas The scale-free ideal gas (SFIG) is a physical model assuming a collection of non-interacting elements with an stochastic proportional growth. It is the scale-invariant version of an ideal gas. Some cases of city-population, electoral results and cites to scientific journals can be approximately considered scale-free ideal gases. In a one-dimensional discrete model with size-parameter ''k'', where ''k''1 and ''k''''M'' are the minimum and maximum allowed sizes respectively, and ''v'' = ''dk''/''dt'' is the growth, the bulk probability density function ''F''(''k'', ''v'') of a scale-free ideal gas follows : $$ F(k,v)=\frac\frac)^2/2\sigma_w^2\right">)}, where ''N'' is the total number of elements, Ω = ln ''k''1/''k''''M'' is the logaritmic "volume" of the system, $\backslash overline=\backslash langle\; v/k\; \backslash rangle$ is the mean relative growth and $\backslash sigma\_w$ is the standard deviation of the relative growth. The entropy equation of state is : $S=N\backslash kappa\backslash left\backslash \backslash frac+\backslash frac\backslash right\backslash \},$ where $\backslash kappa$ is a constant that accounts for dimensionality and $H\text{'}=1/M\backslash Delta\backslash tau$ is the elementary volume in phase space, with $\backslash Delta\backslash tau$ the elementary time and ''M'' the total number of allowed discrete sizes. This expression has the same form as the one-dimensional ideal gas, changing the thermodynamical variables (''N'', ''V'', ''T'') by (''N'', Ω,''σ''''w''). Zipf's law may emerge in the external limits of the density since it is a special regime of scale-free ideal gases. == References == 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「Scale-free ideal gas」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.