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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| Online-Zugang: | https://arxiv.org/abs/2401.01726 |
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| _version_ | 1866911768196939776 |
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| author | Heizler, Shay I. Krief, Menahem Assaf, Michael |
| author_facet | Heizler, Shay I. Krief, Menahem Assaf, Michael |
| contents | We resolve a long standing question regarding the suitable effective diffusion coefficient of the spherically-symmetric transport equation, which is valid at long times. To that end, we generalize a transport solution in three dimensions for homogeneous media, to include general collisional properties, including birth-death events and linearly anisotropic scattering. This is done by introducing an exact scaling law relating the Green function of the pure-scattering case with the general collision case, which is verified using deterministic and Monte-Carlo simulations. Importantly, the effective diffusion coefficient is identified by inspecting the transport solution at long times. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_01726 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | An accurate reaction-diffusion limit to the spherical-symmetric Boltzmann equation Heizler, Shay I. Krief, Menahem Assaf, Michael Statistical Mechanics Instrumentation and Methods for Astrophysics Computational Physics We resolve a long standing question regarding the suitable effective diffusion coefficient of the spherically-symmetric transport equation, which is valid at long times. To that end, we generalize a transport solution in three dimensions for homogeneous media, to include general collisional properties, including birth-death events and linearly anisotropic scattering. This is done by introducing an exact scaling law relating the Green function of the pure-scattering case with the general collision case, which is verified using deterministic and Monte-Carlo simulations. Importantly, the effective diffusion coefficient is identified by inspecting the transport solution at long times. |
| title | An accurate reaction-diffusion limit to the spherical-symmetric Boltzmann equation |
| topic | Statistical Mechanics Instrumentation and Methods for Astrophysics Computational Physics |
| url | https://arxiv.org/abs/2401.01726 |