title: New stochastic mode reduction strategy for dissipative systems.
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.
authors.affiliation: Department of Chemical Engineering, Imperial College London, London SW7 2AZ, United Kingdom and Department of Mathematics, Imperial College London, London SW7 2AZ, United Kingdom.
authors.forename: M
authors.initials: M
authors.lastname: Schmuck
authors.affiliation: Department of Chemical Engineering, Imperial College London, London SW7 2AZ, United Kingdom.
authors.forename: M
authors.initials: M
authors.lastname: Pradas
authors.affiliation: Department of Chemical Engineering, Imperial College London, London SW7 2AZ, United Kingdom.
authors.forename: S
authors.initials: S
authors.lastname: Kalliadasis
authors.affiliation: Department of Mathematics, Imperial College London, London SW7 2AZ, United Kingdom.
authors.forename: G A
authors.initials: GA
authors.lastname: Pavliotis