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arXiv · 1305.4135

A new stochastic mode reduction strategy for dissipative systems

M. Schmuck·M. Pradas·S. Kalliadasis·G. A. Pavliotis
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Abstract

We present a new methodology for studying non-Hamiltonian nonlinear systems based on an information theoretic extension of a renormalization group technique using a modified maximum entropy principle. We obtain a rigorous dimensionally reduced description for such systems. The neglected degrees of freedom by this reduction are replaced by a systematically deefined stochastic process under a constraint on the second moment. This then forms the basis of a computationally efficient method. Numerical computations for the generalized Kuramoto-Sivashinsky equation sup- port our method and reveal that the long-time underlying stochastic process of the fast (unresolved) modes obeys a universal distribution which does not depend on the initial conditions and which we rigorously derive by the maximum entropy principle.

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M. Schmuck, M. Pradas, S. Kalliadasis, G. A. Pavliotis. 2013-05-17. A new stochastic mode reduction strategy for dissipative systems. https://doi.org/10.1103/physrevlett.110.244101

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