New stochastic mode reduction strategy for dissipative systems

Schmuck, M.; Pradas, M.; Kalliadasis, S. and Pavliotis, G. A. (2013). New stochastic mode reduction strategy for dissipative systems. Physical Review Letters, 110(24), article no. 244101.

DOI: https://doi.org/10.1103/PhysRevLett.110.244101

Abstract

We present a new methodology for studying non-Hamiltonian nonlinear systems based on an information theoretical 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 defined 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 support our method and reveal that the long-time underlying stochastic process of the fast (unresolved) modes obeys a universal distribution that does not depend on the initial conditions and which we rigorously derive by the maximum entropy principle.

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