| 書目名稱 | Stochastic Ordinary and Stochastic Partial Differential Equations | | 副標(biāo)題 | Transition from Micr | | 編輯 | Peter Kotelenez | | 視頻video | http://file.papertrans.cn/879/878072/878072.mp4 | | 概述 | Includes supplementary material: | | 叢書名稱 | Stochastic Modelling and Applied Probability | | 圖書封面 |  | | 描述 | The present volume analyzes mathematical models of time-dependent physical p- nomena on three levels: microscopic, mesoscopic, and macroscopic. We provide a rigorous derivation of each level from the preceding level and the resulting me- scopic equations are analyzed in detail. Following Haken (1983, Sect. 1. 11. 6) we deal, “at the microscopic level, with individual atoms or molecules, described by their positions, velocities, and mutual interactions. At the mesoscopic level, we describe the liquid by means of ensembles of many atoms or molecules. The - tension of such an ensemble is assumed large compared to interatomic distances but small compared to the evolving macroscopic pattern. . . . At the macroscopic level we wish to study the corresponding spatial patterns. ” Typically, at the mac- scopic level, the systems under consideration are treated as spatially continuous systems such as ?uids or a continuous distribution of some chemical reactants, etc. Incontrast,onthemicroscopiclevel,Newtonianmechanicsgovernstheequationsof 1 motion of the individual atoms or molecules. These equations are cast in the form 2 of systems of deterministic coupled nonlinear oscillators. The mesosco | | 出版日期 | Book 2008 | | 關(guān)鍵詞 | Kotelenez; Macroscopic; Microscopic; Ordinary; Partial Differential Equations; Stochastic; Variance; partia | | 版次 | 1 | | doi | https://doi.org/10.1007/978-0-387-74317-2 | | isbn_softcover | 978-1-4899-8658-0 | | isbn_ebook | 978-0-387-74317-2Series ISSN 0172-4568 Series E-ISSN 2197-439X | | issn_series | 0172-4568 | | copyright | Springer-Verlag New York 2008 |
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