Authors

M. Schmuck, M. Pradas, S. Kalliadasis, G. A. Pavliotis

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.

Citation

  • Journal: Physical Review Letters
  • Year: 2013
  • Volume: 110
  • Issue: 24
  • Pages:
  • Publisher: American Physical Society (APS)
  • DOI: 10.1103/physrevlett.110.244101

BibTeX

@article{Schmuck_2013,
  title={{New Stochastic Mode Reduction Strategy for Dissipative Systems}},
  volume={110},
  ISSN={1079-7114},
  DOI={10.1103/physrevlett.110.244101},
  number={24},
  journal={Physical Review Letters},
  publisher={American Physical Society (APS)},
  author={Schmuck, M. and Pradas, M. and Kalliadasis, S. and Pavliotis, G. A.},
  year={2013}
}

Download the bib file

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