Diffusive Propagation of Energy in a Non-acoustic Chain
Komorowski, Tomasz; Olla, Stefano (2017), Diffusive Propagation of Energy in a Non-acoustic Chain, Archive for Rational Mechanics and Analysis, 223, 1, p. 95-139. 10.1007/s00205-016-1032-9
TypeArticle accepté pour publication ou publié
Journal nameArchive for Rational Mechanics and Analysis
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Abstract (EN)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.
Subjects / Keywordsbeam equation; Non-acoustic chain; thermal conductivity; Wigner distributions
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Macroscopic evolution of mechanical and thermal energy in a harmonic chain with random flip of velocities Olla, Stefano; Simon, Marielle; Komorowski, Tomasz (2018) Article accepté pour publication ou publié