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
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