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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), 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
11
Number
3
Pages
615-645
Publication identifier
10.3934/krm.2018026
Metadata
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Author(s)
Olla, Stefano cc

Simon, Marielle

Komorowski, Tomasz
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

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