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Article Dans Une Revue Archive for Rational Mechanics and Analysis Année : 2017

DIFFUSIVE PROPAGATION OF ENERGY IN A NON-ACOUSTIC CHAIN

Résumé

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.
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Dates et versions

hal-01253315 , version 1 (09-01-2016)

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Tomasz Komorowski, Stefano Olla. DIFFUSIVE PROPAGATION OF ENERGY IN A NON-ACOUSTIC CHAIN. Archive for Rational Mechanics and Analysis, 2017, 223 (1), pp.95-139. ⟨10.1007/s00205-016-1032-9⟩. ⟨hal-01253315⟩
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