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portada Fundamentals of Stochastic Nature Sciences
Type
Physical Book
Publisher
Author
Language
English
Pages
190
Format
Hardcover
ISBN13
9783319569215

Fundamentals of Stochastic Nature Sciences

Klyatskin, Valery I.: (Author) · Springer Verlag Gmbh · Hardcover

Fundamentals of Stochastic Nature Sciences - Klyatskin, Valery I.:

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Synopsis "Fundamentals of Stochastic Nature Sciences "

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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