Macroscopic evolution of mechanical and thermal energy in a harmonic chain with random flip of velocities - Archive ouverte HAL Access content directly
Journal Articles Kinetic and Related Models Year : 2018

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.
Fichier principal
Vignette du fichier
Komorowski-Olla-Simon-corrections-to-KRM.pdf (397.94 Ko) Télécharger le fichier
Origin : Files produced by the author(s)
Loading...

Dates and versions

hal-01358979 , version 1 (01-09-2016)
hal-01358979 , version 2 (29-03-2017)
hal-01358979 , version 3 (20-09-2017)

Identifiers

Cite

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 , 2018, 11 (3), pp.615-645. ⟨10.3934/krm.2018026⟩. ⟨hal-01358979v3⟩
542 View
178 Download

Altmetric

Share

Gmail Facebook X LinkedIn More