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Titlebook: Non-Linear Dynamics Near and Far from Equilibrium; J.K. Bhattacharjee,S. Bhattacharyya Book 2007 Springer Science+Business Media B.V. 2007

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發(fā)表于 2025-3-21 19:26:16 | 只看該作者 |倒序?yàn)g覽 |閱讀模式
書(shū)目名稱Non-Linear Dynamics Near and Far from Equilibrium
編輯J.K. Bhattacharjee,S. Bhattacharyya
視頻videohttp://file.papertrans.cn/667/666943/666943.mp4
概述A detailed description of perturbation theory for nonlinear continuous systems.Focus on techniques which can be applied to problems ranging from near equilibrium dynamics to fully developed turbulence
圖書(shū)封面Titlebook: Non-Linear Dynamics Near and Far from Equilibrium;  J.K. Bhattacharjee,S. Bhattacharyya Book 2007 Springer Science+Business Media B.V. 2007
描述We will be concerned mainly with systems with in?nite degrees of freedom which can however, be described by a few variables. These variables must necessarily be ?elds i. e. functions of space and time. A typical example would be to try to describethe?owofairaroundus. Thevariablesthatwouldbenecessarytodescribe the state of air would certainly be its density, its temperature and its velocity. All these variables (density, temperature and velocity) are, in general, functions of space and time. They are mesoscopic variables. They do not re?ect the variations occurring at the molecular level. To de?ne a density, it should be recalled, we take a small volume (small compared to the total system size, yet large compared to atomic dimensions) and consider the mass of this small volume. The ratio of mass tovolumeremainsconstantforareasonablylargevariationinthesizeofthevolume chosen and de?nes the density of the system. It fails to be a constant if the volume becomessosmallthatitcontainsonlyafewmolecules. Inthatcaseourdescription in terms of a density fails. All the systems that we will talk about can be described in terms of a coarse grained ?eld like the density. Because of the smallness (a
出版日期Book 2007
關(guān)鍵詞Renormalization group; critical phenomena; growth models; perturbation theory; phase ordering; phase tran
版次1
doihttps://doi.org/10.1007/978-1-4020-5388-7
isbn_ebook978-1-4020-5388-7
copyrightSpringer Science+Business Media B.V. 2007
The information of publication is updating

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https://doi.org/10.1007/978-1-4020-5388-7Renormalization group; critical phenomena; growth models; perturbation theory; phase ordering; phase tran
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The Renormalization Group,s did not work. The difficulty is enshrined in the infinite correlation length at the critical point. The renormalization group (RG) is a technique that is specifically designed to lead to an infinite correlation length. The idea is best set out using the Kadanoff construction in the two dimensional Ising model shown in
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Introduction,essarily be fields i.e. functions of space and time. A typical example would be to try to describe the flow of air around us. The variables that would be necessary to describe the state of air would certainly be its density, its temperature and its velocity. All these variables (density, temperature
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Models of Dynamics,) than atomic scales but still small compared to macroscopic scales (system size etc.). A typical example is provided by a system near a second order phase transition point, e.g. a magnet being cooled towards the Curie point. For temperatures far above the Curie point the individual magnetic moments
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