DIFFUSIVE PROPAGATION OF ENERGY IN A NON-ACOUSTIC CHAINReport as inadecuate




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1 PAN - Institut of Mathematics - Polish Academy of Sciences 2 CEREMADE - CEntre de REcherches en MAthématiques de la DEcision

Abstract : We consider a non acoustic chain of harmonic oscil-lators with the dynamics perturbed by a random local exchange of momentum, such that energy and momentum are conserved. The macroscopic limits of the energy density, momentum and the curvature or bending of the chain satisfy a system of evolution equations. We prove that, in a diffusive space-time scaling, the curvature and momentum evolve following a linear system that corresponds to a damped Euler-Bernoulli beam equation. The macro-scopic energy density evolves following a non linear diffusive equation. In particular the energy transfer is diffusive in this dynamics. This provides a first rigorous example of a normal diffusion of energy in a one dimensional dynamics that conserves the momentum.

Keywords : beam equation Non-acoustic chain thermal conductivity Wigner distributions





Author: Tomasz Komorowski - Stefano Olla -

Source: https://hal.archives-ouvertes.fr/



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