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Thermo-mechanical Transport in Rotor Chains

Iacobucci, Alessandra; Olla, Stefano; Stoltz, Gabriel (2021), Thermo-mechanical Transport in Rotor Chains, Journal of Statistical Physics, 183, 2. 10.1007/s10955-021-02748-8

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Type
Article accepté pour publication ou publié
Date
2021
Journal name
Journal of Statistical Physics
Volume
183
Number
2
Publisher
Springer
Publication identifier
10.1007/s10955-021-02748-8
Metadata
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Author(s)
Iacobucci, Alessandra cc
CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Olla, Stefano cc
CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Stoltz, Gabriel
Centre d'Enseignement et de Recherche en Mathématiques et Calcul Scientifique [CERMICS]
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.
Subjects / Keywords
Thermal transport; Rotor chain; Thermo-mechanical response; Macroscopic diffusion equations; Uphill diffusion

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