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

Fingerprint

Climate

ASJC Scopus subject areas

  • General
  • Genetics

Cite this

Remarkable statistical behavior for truncated Burgers-Hopf dynamics. / Maida, A. J.; Timofeyev, I.

In: Proceedings of the National Academy of Sciences of the United States of America, Vol. 97, No. 23, 2000, p. 12413-12417.

Research output: Contribution to journalArticle

@article{6a668a435a8248d887329c39b17c368d,
title = "Remarkable statistical behavior for truncated Burgers-Hopf dynamics",
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.",
author = "Maida, {A. J.} and I. Timofeyev",
year = "2000",
doi = "10.1073/pnas.230433997",
language = "English (US)",
volume = "97",
pages = "12413--12417",
journal = "Proceedings of the National Academy of Sciences of the United States of America",
issn = "0027-8424",
number = "23",

}

TY - JOUR

T1 - Remarkable statistical behavior for truncated Burgers-Hopf dynamics

AU - Maida, A. J.

AU - Timofeyev, I.

PY - 2000

Y1 - 2000

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=0033751055&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0033751055&partnerID=8YFLogxK

U2 - 10.1073/pnas.230433997

DO - 10.1073/pnas.230433997

M3 - Article

VL - 97

SP - 12413

EP - 12417

JO - Proceedings of the National Academy of Sciences of the United States of America

JF - Proceedings of the National Academy of Sciences of the United States of America

SN - 0027-8424

IS - 23

ER -