Hydrodynamic limit for a chain with thermal and mechanical boundary forces
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arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2020
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| _version_ | 1866910475647713280 |
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| author | Komorowski, Tomasz Olla, Stefano Simon, Marielle |
| author_facet | Komorowski, Tomasz Olla, Stefano Simon, Marielle |
| contents | We prove the hydrodynamic limit for a one dimensional harmonic chain with a random flip of the momentum sign. The system is open and subject to two thermostats at the boundaries and to an external tension at one of the endpoints. Under a diffusive scaling of space-time, we prove that the empirical profiles of the two locally conserved quantities, the volume stretch and the energy, converge to the solution of a non-linear diffusive system of conservative partial differential equations. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2004_08623 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | Hydrodynamic limit for a chain with thermal and mechanical boundary forces Komorowski, Tomasz Olla, Stefano Simon, Marielle Probability Mathematical Physics We prove the hydrodynamic limit for a one dimensional harmonic chain with a random flip of the momentum sign. The system is open and subject to two thermostats at the boundaries and to an external tension at one of the endpoints. Under a diffusive scaling of space-time, we prove that the empirical profiles of the two locally conserved quantities, the volume stretch and the energy, converge to the solution of a non-linear diffusive system of conservative partial differential equations. |
| title | Hydrodynamic limit for a chain with thermal and mechanical boundary forces |
| topic | Probability Mathematical Physics |
| url | https://arxiv.org/abs/2004.08623 |