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

Olla, Stefano; Simon, Marielle; Komorowski, Tomasz

Olla, Stefano; Simon, Marielle; Komorowski, Tomasz (2018), Macroscopic evolution of mechanical and thermal energy in a harmonic chain with random flip of velocities, Kinetic & Related Models, 11, 3, p. 615-645. 10.3934/krm.2018026

Type

Article accepté pour publication ou publié

External document link

https://hal.archives-ouvertes.fr/hal-01358979

Date

2018

Journal name

Kinetic & Related Models

Volume

Number

Pages

615-645

Abstract (EN)

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.

Subjects / Keywords

mathématiques; physique; matière condensée; probabilités; mécanique statistique; physique mathématique