Fundamentals of stochastic nature sciences / Valery I. Klyatskin.
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) describ...
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| Format: | eBook |
| Language: | English Russian |
| Published: |
Cham, Switzerland :
Springer,
2017.
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| Series: | Understanding complex systems.
Springer complexity. |
| Subjects: |
MARC
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| 100 | 1 | |a Kli︠a︡t︠s︡kin, V. I. |q (Valeriĭ Isaakovich), |e author. |0 http://id.loc.gov/authorities/names/n80124837 |1 http://isni.org/isni/0000000116210676. | |
| 245 | 1 | 0 | |a Fundamentals of stochastic nature sciences / |c Valery I. Klyatskin. |
| 264 | 1 | |a Cham, Switzerland : |b Springer, |c 2017. | |
| 300 | |a 1 online resource (xii, 190 pages) : |b illustrations (some color) | ||
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| 490 | 1 | |a Understanding complex systems, |x 1860-0832. | |
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| 504 | |a Includes bibliographical references. | ||
| 505 | 0 | |a 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. | |
| 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. | ||
| 588 | 0 | |a Online resource; title from PDF title page (SpringerLink, viewed May 4, 2017) | |
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| 700 | 1 | |a Vinogradov, A., |e translator. | |
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| 880 | 8 | |6 505-00/(S |a 8.2 Statistical Topography of Random Fields8.2.1 Conditions of Cluster Structure Formation; 8.2.2 Statistical Topography of Lognormal Random Fields; 9 Stochastic Transport Phenomena in a Random Velocity Field; 9.1 Clustering of the Density Field in a Random Velocity Field; 9.2 Probabilistic Description of a Magnetic Field and Its Energy in a Random #x83;; 9.2.1 Probabilistic Description of a Magnetic Field; 9.2.2 Probabilistic Description of Magnetic Field Energy; 9.2.3 The Critical Case of α=0 (DP=Ds); 10 Parametrically Excited Dynamic Systems with Gaussian Pumping. | |
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