| 書目名稱 | Fundamentals of Stochastic Nature Sciences | | 編輯 | Valery I. Klyatskin | | 視頻video | http://file.papertrans.cn/351/350577/350577.mp4 | | 概述 | Deals with three types of the simplest dynamic systems: systems related to Gaussian random fields, to stochastic parametric excitation, and to stochastic parametric excitation fed by Gaussian pumping. | | 叢書名稱 | Understanding Complex Systems | | 圖書封面 |  | | 描述 | .This book addresses the processes of stochastic structure formation in two-dimensional geophysical fluid dynamics based on statistical analysis of Gaussian random fields, as well as stochastic structure formation in dynamic systems with parametric excitation of positive random fields f(r,t) described by partial differential equations. Further, the book considers two examples of stochastic structure formation in dynamic systems with parametric excitation in the presence of Gaussian pumping. In dynamic systems with parametric excitation in space and time, this type of structure formation either happens – or doesn’t! However, if it occurs in space, then this almost always happens (exponentially quickly) in individual realizations with a unit probability..In the case considered, clustering of the field f(r,t) of any nature is a general feature of dynamic fields, and one may claim that structure formation is the Law of Nature for arbitrary random fields of such type. The study clarifies the conditions under which such structure formation takes place. To make the content more accessible, these conditions are described at a comparatively elementary mathematical level by employing ideas f | | 出版日期 | Book 2017 | | 關(guān)鍵詞 | Stochastic Dynamic Systems; Parametrically Excited Dynamic Systems; Two-dimensional Geophysical Fluid | | 版次 | 1 | | doi | https://doi.org/10.1007/978-3-319-56922-2 | | isbn_softcover | 978-3-319-86036-7 | | isbn_ebook | 978-3-319-56922-2Series ISSN 1860-0832 Series E-ISSN 1860-0840 | | issn_series | 1860-0832 | | copyright | Springer International Publishing AG 2017 |
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