Generalized flux-weighted boundary walls in kinetic models
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866911626711531520 |
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| author | Barbieri, Luca Di Cintio, Pierfrancesco |
| author_facet | Barbieri, Luca Di Cintio, Pierfrancesco |
| contents | We present a technique to investigate the stationary states of a system of a collisionless system confined by an external potential and coupled to boundary reservoirs through prescribed reinjection rules. We consider a family of boundary conditions parametrized by an integer $n$, corresponding to different velocity distributions imposed at the boundaries, generalizing the standard flux-weighted Maxwellian scheme. By combining Liouville's theorem with the boundary injection rule, we derive an explicit analytical expression for the stationary distribution function. This framework provides a direct link between microscopic boundary dynamics and macroscopic stationary profiles. We show that thermal equilibrium is recovered only for the standard flux-weighted injection method, while for all other cases the system relaxes to manifestly non-thermal stationary states. The resulting density and temperature profiles exhibit non-trivial spatial structures, including non-monotonic behaviour and temperature gradients induced by the boundary conditions alone. Analytical predictions for stationary moments are obtained in closed form for representative cases and are nicely reproduced by particle-based numerical simulations. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2604_24592 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Generalized flux-weighted boundary walls in kinetic models Barbieri, Luca Di Cintio, Pierfrancesco Statistical Mechanics Computational Physics Plasma Physics We present a technique to investigate the stationary states of a system of a collisionless system confined by an external potential and coupled to boundary reservoirs through prescribed reinjection rules. We consider a family of boundary conditions parametrized by an integer $n$, corresponding to different velocity distributions imposed at the boundaries, generalizing the standard flux-weighted Maxwellian scheme. By combining Liouville's theorem with the boundary injection rule, we derive an explicit analytical expression for the stationary distribution function. This framework provides a direct link between microscopic boundary dynamics and macroscopic stationary profiles. We show that thermal equilibrium is recovered only for the standard flux-weighted injection method, while for all other cases the system relaxes to manifestly non-thermal stationary states. The resulting density and temperature profiles exhibit non-trivial spatial structures, including non-monotonic behaviour and temperature gradients induced by the boundary conditions alone. Analytical predictions for stationary moments are obtained in closed form for representative cases and are nicely reproduced by particle-based numerical simulations. |
| title | Generalized flux-weighted boundary walls in kinetic models |
| topic | Statistical Mechanics Computational Physics Plasma Physics |
| url | https://arxiv.org/abs/2604.24592 |