Hydrodynamic limit for a chain with thermal and mechanical boundary\n forces

2020/04/18 by Tomasz Komorowski, Komorowski, Tomasz, Stefano Olla +3
Computer Science · Mathematics · #Advanced Mathematical Modeling in Engineering #FOS: Mathematics #FOS: Physical sciences #Markov Chains and Monte Carlo Methods #Mathematical Physics (math-ph) #Probability (math.PR) #Stochastic processes and statistical mechanics

paper · pdf · doi:10.48550/arxiv.2004.08623

openalex publication_date 2020/04/18 · openalex created_date 2022/07/26 · openalex updated_date 2026/07/28

Abstract

We prove the hydrodynamic limit for a one dimensional harmonic chain with a\nrandom flip of the momentum sign. The system is open and subject to two\nthermostats at the boundaries and to an external tension at one of the\nendpoints. Under a diffusive scaling of space-time, we prove that the empirical\nprofiles of the two locally conserved quantities, the volume stretch and the\nenergy, converge to the solution of a non-linear diffusive system of\nconservative partial differential equations.\n

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