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Fundamentals of Stochastic Nature Sciences [electronic resource] / by Valery I. Klyatskin.

By: Klyatskin, Valery I [author.].
Contributor(s): SpringerLink (Online service).
Material type: materialTypeLabelBookSeries: Understanding Complex Systems: Publisher: Cham : Springer International Publishing : Imprint: Springer, 2017Edition: 1st ed. 2017.Description: XII, 190 p. 62 illus., 11 illus. in color. online resource.Content type: text Media type: computer Carrier type: online resourceISBN: 9783319569222.Subject(s): Dynamics | Nonlinear theories | System theory | Geotechnical engineering | Applied Dynamical Systems | Complex Systems | Geotechnical Engineering and Applied Earth SciencesAdditional physical formats: Printed edition:: No title; Printed edition:: No title; Printed edition:: No titleDDC classification: 515.39 Online resources: Click here to access online
Contents:
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.
In: Springer Nature eBookSummary: 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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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.

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