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- Title
MACROSCOPIC EVOLUTION OF MECHANICAL AND THERMAL ENERGY IN A HARMONIC CHAIN WITH RANDOM FLIP OF VELOCITIES.
- Authors
Komorowski, Tomasz; Olla, Stefano; Simon, Marielle
- 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.
- Subjects
HARMONIC oscillators; VELOCITY; MACROSCOPIC kinetics; MECHANICAL energy; HEAT; SPACETIME; BOUNDARY value problems
- Publication
Kinetic & Related Models, 2018, Vol 11, Issue 3, p615
- ISSN
1937-5093
- Publication type
Article
- DOI
10.3934/krm.2018026