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Discontinuity, Nonlinearity, and Complexity

Dimitry Volchenkov (editor), Dumitru Baleanu (editor)

Dimitry Volchenkov(editor)

Mathematics & Statistics, Texas Tech University, 1108 Memorial Circle, Lubbock, TX 79409, USA

Email: dr.volchenkov@gmail.com

Dumitru Baleanu (editor)

Cankaya University, Ankara, Turkey; Institute of Space Sciences, Magurele-Bucharest, Romania

Email: dumitru.baleanu@gmail.com


Clustering of a Positive Random Field –What is This?

Discontinuity, Nonlinearity, and Complexity 4(3) (2016) 225--242 | DOI:10.5890/DNC.2016.09.002

V.I. Klyatskin

A. M. Obukhov Institute of Atmospheric Physics RAS, Moscow, Pyzhevsky per. 3, 119017, Russia

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Abstract

It is shown that, in parametrically excited stochastic dynamic systems described by partial differential equations, spatial structures (clusters) can appear with probability one, i.e., almost in every system realization, due to rare events happened with probability approaching to zero. The problems of such type arise in hydrodynamics, magnetohydrodynamics, physics of plasma, astrophysics, and radiophysics.

Acknowledgments

This work was supported by the RSF 14-27-00134.

References

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