Statistical Mechanics for Truncations of the Burgers-Hopf Equation: A Model for Intrinsic Stochastic Behavior with Scaling

@article{Majda2002StatisticalMF,
  title={Statistical Mechanics for Truncations of the Burgers-Hopf Equation: A Model for Intrinsic Stochastic Behavior with Scaling
},
  author={Andrew Majda and I. Tomofeyev},
  journal={Milan Journal of Mathematics},
  year={2002},
  volume={70},
  pages={39-96}
}
In this paper we consider both analytically and numerically several finite-dimensional approximations for the inviscid Burgers-Hopf equation. Fourier Galerkin truncation is introduced and studied as a simple one-dimensional model with intrinsic chaos and a well-defined mathematical structure allowing for an equilibrium statistical mechan- ics formalism. A simple scaling theory for correlations is developed that is supported strongly by the numerical evidence. Several semi-discrete difference… CONTINUE READING

Citations

Publications citing this paper.
SHOWING 1-10 OF 37 CITATIONS

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  • J. Comput. Physics
  • 2013
VIEW 4 EXCERPTS
CITES BACKGROUND & METHODS
HIGHLY INFLUENCED

References

Publications referenced by this paper.
SHOWING 1-10 OF 22 REFERENCES

Phys

C. S. Gardner, J. M. Greene, M. D. Kruskal, R. M. Miura
  • Rev. Lett. 19
  • 1967
VIEW 9 EXCERPTS
HIGHLY INFLUENTIAL

Comm

E. Hopf
  • Pure Appl. Math. 3
  • 1950
VIEW 12 EXCERPTS
HIGHLY INFLUENTIAL

Remarkable statistical behavior for truncated Burgers-Hopf dynamics.

  • Proceedings of the National Academy of Sciences of the United States of America
  • 2000
VIEW 10 EXCERPTS
HIGHLY INFLUENTIAL

Phys

G. Carnevale, M. Falcioni, S. Isola, R. Purini, A. Vulpiani
  • Fluids A 3 (1991), 2247–2254. 96 A. Majda and I. Timofeyev Vol. 70
  • 2002

Stochastic modeling of nonlinear dynamics with intrinsic stochasticity and scaling behavior

D. Cai, A. Majda, E. Vanden Eijnden
  • 2000
VIEW 1 EXCERPT

Proc

A. Majda, I. Timofeyev, E. Vanden Eijnden
  • Nat. Acad. Sci. 96
  • 1999
VIEW 2 EXCERPTS

J

R. Saravanan, J. McWilliams
  • Climate 10
  • 1997

Sci

R. Kleeman, A. Moore, J. Atmos
  • 54
  • 1997