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

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.

9 pages, 4 figures

References in corpus (1)

• Collision densities and mean residence times for $d$-dimensional exponential flights

Cited by in corpus (1)

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