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On the statistical theory of spatial structure formation in random media
Authors:V. I. Klyatskin
Affiliation:1. A. M. Obukhov Institute of the Physics of the Atmosphere, Russian Academy of Sciences, Pyzhevskii per., 3, 119017, Moscow, Russian Federation
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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