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Fundamentals of stochastic nature sc...

Klyatskin, Valery I.

Fundamentals of stochastic nature sciences

紀錄類型:	書目-電子資源 : Monograph/item
正題名/作者:	Fundamentals of stochastic nature sciencesby Valery I. Klyatskin.
作者:	Klyatskin, Valery I.
出版者:	Cham :Springer International Publishing :2017.
面頁冊數:	xii, 190 p. :ill. (some col.), digital ;24 cm.
Contained By:	Springer eBooks
標題:	Stochastic systems.
電子資源:	http://dx.doi.org/10.1007/978-3-319-56922-2
ISBN:	9783319569222$q(electronic bk.)

Fundamentals of stochastic nature sciences
Klyatskin, Valery I.

Fundamentals of stochastic nature sciences[electronic resource] /by Valery I. Klyatskin. - Cham :Springer International Publishing :2017. - xii, 190 p. :ill. (some col.), digital ;24 cm. - Understanding complex systems,1860-0832. - Understanding complex systems..

Two-dimensional geophysical ﬂuid dynamics -- Parametrically excited dynamic systems -- Examples of stochastic dynamic systems -- Statistical characteristics of a random velocity ﬁeld u(r, t) -- Lognormal processes, intermittency, and dynamic localization -- Stochastic parametric resonance -- Wave localization in randomly layered media -- Lognormal ﬁelds, statistical topography, and clustering -- Stochastic transport phenomena in a random velocity ﬁeld -- Parametrically excited dynamic systems with Gaussian pumping -- Conclusion.

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 from statistical topography.

ISBN: 9783319569222$q(electronic bk.)

Standard No.: 10.1007/978-3-319-56922-2doiSubjects--Topical Terms:

240201
Stochastic systems.

LC Class. No.: QA402

Dewey Class. No.: 003.76

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520 $a 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 from statistical topography.
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