A gallery of maximum-entropy distributions: 14 and 21 moments
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866917601108557824 |
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| author | Boccelli, Stefano Giroux, Fabien McDonald, James G. |
| author_facet | Boccelli, Stefano Giroux, Fabien McDonald, James G. |
| contents | This work explores the different shapes that can be realized by the one-particle velocity distribution functions (VDFs) associated with the fourth-order maximum-entropy moment method. These distributions take the form of an exponential of a polynomial of the particle velocity, with terms up to the fourth-order. The 14- and 21-moment approximations are investigated. Various non-equilibrium gas states are probed throughout moment space. The resulting maximum-entropy distributions deviate strongly from the equilibrium VDF, and show a number of lobes and branches. The Maxwellian and the anisotropic Gaussian distributions are recovered as special cases. The eigenvalues associated with the maximum-entropy system of transport equations are also illustrated for some selected gas states. Anisotropic and/or asymmetric non-equilibrium states are seen to be associated with a non-uniform spacial propagation of perturbations. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_18453 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A gallery of maximum-entropy distributions: 14 and 21 moments Boccelli, Stefano Giroux, Fabien McDonald, James G. Statistical Mechanics Mathematical Physics This work explores the different shapes that can be realized by the one-particle velocity distribution functions (VDFs) associated with the fourth-order maximum-entropy moment method. These distributions take the form of an exponential of a polynomial of the particle velocity, with terms up to the fourth-order. The 14- and 21-moment approximations are investigated. Various non-equilibrium gas states are probed throughout moment space. The resulting maximum-entropy distributions deviate strongly from the equilibrium VDF, and show a number of lobes and branches. The Maxwellian and the anisotropic Gaussian distributions are recovered as special cases. The eigenvalues associated with the maximum-entropy system of transport equations are also illustrated for some selected gas states. Anisotropic and/or asymmetric non-equilibrium states are seen to be associated with a non-uniform spacial propagation of perturbations. |
| title | A gallery of maximum-entropy distributions: 14 and 21 moments |
| topic | Statistical Mechanics Mathematical Physics |
| url | https://arxiv.org/abs/2402.18453 |