Remarkable statistical behavior for truncated Burgers-Hopf dynamics

A. J. Maida, I. Timofeyev

Research output: Contribution to journalArticle

Abstract

A simplified one-dimensional model system is introduced and studied here that exhibits intrinsic chaos with many degrees of freedom as well as increased predictability and slower decay of correlations for the large-scale features of the system. These are important features in common with vastly more complex problems involving climate modeling or molecular biological systems. This model is a suitable approximation of the Burgers-Hopf equation involving Galerkin projection on Fourier modes. The model has a detailed mathematical structure that leads to a well-defined equilibrium statistical theory as well as a simple scaling theory for correlations. The numerical evidence presented here strongly supports the behavior predicted from these statistical theories. Unlike the celebrated dissipative and dispersive approximations of the Burgers-Hopf equation, which exhibit exactly solvable and/or completely integrable behavior, these model approximations have strong intrinsic chaos with ergodic behavior.

Original languageEnglish (US)
Pages (from-to)12413-12417
Number of pages5
JournalProceedings of the National Academy of Sciences of the United States of America
Volume97
Issue number23
DOIs
StatePublished - 2000

ASJC Scopus subject areas

  • General

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