Fundamentals of Stochastic Nature Sciences

  • Valery I. Klyatskin

Part of the Understanding Complex Systems book series (UCS)

Table of contents

  1. Front Matter
    Pages i-xii
  2. Valery I. Klyatskin
    Pages 1-14
  3. Valery I. Klyatskin
    Pages 15-19
  4. Valery I. Klyatskin
    Pages 21-44
  5. Valery I. Klyatskin
    Pages 55-57
  6. Valery I. Klyatskin
    Pages 59-93
  7. Back Matter
    Pages 143-190

About this book


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.


Stochastic Dynamic Systems Parametrically Excited Dynamic Systems Two-dimensional Geophysical Fluid Dynamics Stochastic Parametric Resonance Stochastic Transport Phenomena Partial Differential Equations

Authors and affiliations

  • Valery I. Klyatskin
    • 1
  1. 1.Russian Academy of Sciences (RAS)A.M. Obukhov Institute of Atmospheric PhysicsMoscowRussia

Bibliographic information

  • DOI
  • Copyright Information Springer International Publishing AG 2017
  • Publisher Name Springer, Cham
  • eBook Packages Engineering Engineering (R0)
  • Print ISBN 978-3-319-56921-5
  • Online ISBN 978-3-319-56922-2
  • Series Print ISSN 1860-0832
  • Series Online ISSN 1860-0840
  • Buy this book on publisher's site