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arXiv · 2401.01726

An accurate reaction-diffusion limit to the spherical-symmetric Boltzmann equation

Shay I. Heizler·Menahem Krief·Michael Assaf
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Abstract

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.

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Shay I. Heizler, Menahem Krief, Michael Assaf. 2024-01-03. An accurate reaction-diffusion limit to the spherical-symmetric Boltzmann equation. https://doi.org/10.1103/physrevresearch.6.l012023

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