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On the statistical theory of spatial structure formation in random media

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Abstract

It is shown that, in parametrically excited stochastic dynamic systems described by partial differential equations, space structures (clustering) can be formed with probability 1 due to rare events occurring with probability tending to zero. Such problems arise in hydrodynamics, magnetohydrodynamics, plasma physics, astrophysics, and radiophysics.

… Chaos is the place which serves to contain all things; for if this had not subsisted neither earth nor water nor the rest of the elements, nor the Universe a whole, could have been constructed… Sextus Empiricus, Against the Physics, against the Ethicists, R. G. Bury, p. 217, Harvard University Press, 1997.

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  1. A. M. Obukhov Institute of the Physics of the Atmosphere, Russian Academy of Sciences, Pyzhevskii per., 3, 119017, Moscow, Russian Federation

    V. I. Klyatskin

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Klyatskin, V.I. On the statistical theory of spatial structure formation in random media. Russ. J. Math. Phys. 20, 295–314 (2013). https://doi.org/10.1134/S1061920813030059

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  • DOI: https://doi.org/10.1134/S1061920813030059

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