Macroscopic evolution of mechanical and thermal energy in a harmonic chain with random flip of velocities

Abstract : We consider an unpinned chain of harmonic oscillators with periodic boundary conditions, whose dynamics is perturbed by a random flip of the sign of the velocities. The dynamics conserves the total volume (or elongation) and the total energy of the system. We prove that in a diffusive space-time scaling limit the profiles corresponding to the two conserved quantities converge to the solution of a diffusive system of differential equations. While the elongation follows a simple autonomous linear diffusive equation, the evolution of the energy depends on the gradient of the square of the elongation.
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Submitted on : Wednesday, September 20, 2017 - 9:25:02 AM
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Tomasz Komorowski, Stefano Olla, Marielle Simon. Macroscopic evolution of mechanical and thermal energy in a harmonic chain with random flip of velocities. Kinetic and Related Models , AIMS, 2018, 11 (3), pp.615-645. ⟨hal-01358979v3⟩

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