04026nam 22006375 450 991025432640332120200703125558.03-319-56922-810.1007/978-3-319-56922-2(CKB)3850000000027394(DE-He213)978-3-319-56922-2(MiAaPQ)EBC6298228(MiAaPQ)EBC5595474(Au-PeEL)EBL5595474(OCoLC)985437072(PPN)200513001(EXLCZ)99385000000002739420170428d2017 u| 0engurnn#008mamaatxtrdacontentcrdamediacrrdacarrierFundamentals of Stochastic Nature Sciences /by Valery I. Klyatskin1st ed. 2017.Cham :Springer International Publishing :Imprint: Springer,2017.1 online resource (XII, 190 p. 62 illus., 11 illus. in color.)Understanding Complex Systems,1860-08323-319-56921-X Includes bibliographical references.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.Understanding Complex Systems,1860-0832Computational complexityStatistical physicsDynamicsGeotechnical engineeringComplexityhttps://scigraph.springernature.com/ontologies/product-market-codes/T11022Complex Systemshttps://scigraph.springernature.com/ontologies/product-market-codes/P33000Geotechnical Engineering & Applied Earth Scienceshttps://scigraph.springernature.com/ontologies/product-market-codes/G37010Computational complexity.Statistical physics.Dynamics.Geotechnical engineering.Complexity.Complex Systems.Geotechnical Engineering & Applied Earth Sciences.003.76Klyatskin Valery Iauthttp://id.loc.gov/vocabulary/relators/aut934990MiAaPQMiAaPQMiAaPQBOOK9910254326403321Fundamentals of Stochastic Nature Sciences2105546UNINA