Accurate reaction-diffusion limit to the spherical-symmetric Boltzmann equation

Shay I. Heizler, Menahem Krief, Michael Assaf

Research output: Contribution to journalArticlepeer-review

Abstract

We resolve a long-standing question regarding the suitable effective diffusion coefficient of the spherical-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's 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.

Original languageAmerican English
Article numberL012023
JournalPhysical Review Research
Volume6
Issue number1
DOIs
StatePublished - Jan 2024

Bibliographical note

Publisher Copyright:
© 2024 authors. Published by the American Physical Society. Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

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