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Thermo-mechanical transport in rotor chains

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2006.10431.pdf (2.193Mb)
Date
2020
Collection title
Cahier de recherche CEREMADE
Link to item file
https://hal.archives-ouvertes.fr/hal-02904454
Dewey
Sciences connexes (physique, astrophysique)
Sujet
Thermo-mechanical
URI
https://basepub.dauphine.fr/handle/123456789/21115
Collections
  • CEREMADE : Publications
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Author
Iacobucci, Alessandra
60 CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Olla, Stefano
60 CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Stoltz, Gabriel
2567 Centre d'Enseignement et de Recherche en Mathématiques, Informatique et Calcul Scientifique [CERMICS]
Type
Document de travail / Working paper
Item number of pages
32
Abstract (EN)
We study the macroscopic profiles of temperature and angular momentum in the stationary state of chains of rotors under a thermo-mechanical forcing applied at the boundaries. These profiles are solutions of a system of diffusive partial differential equations with boundary conditions determined by the thermo-mechanical forcing. Instead of expensive Monte Carlo simulations of the underlying microscopic dynamics, we perform extensive numerical simulations based on a finite difference method for the system of partial differential equations describing the macroscopic steady state. We first present a formal derivation of these stationary equations based on a linear response argument and local equilibrium assumptions. We then study various properties of the solutions to these equations. This allows to characterize the regime of parameters leading to uphill diffusion, a situation where the energy flows in the direction of the gradient of temperature; and to identify regions of parameters corresponding to a negative thermal conductivity (i.e. a positive linear response to a gradient of temperature). The agreement with previous results obtained by numerical simulation of the microscopic physical system confirms the validity of the macroscopic equations we derive.

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