Revisiting Discrepancies in Diffusion Theory: The Solution to Milne’s Problem for B-particles by@extrapolate
Revisiting Discrepancies in Diffusion Theory: The Solution to Milne’s Problem for B-particles
by ExtrapolateSeptember 4th, 2024
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K. Razi Naqvi, Department of Physics, Norwegian University of Science and Technology (NTNU), 7094 Trondheim, Norway. Far from the wall the density increases linearly with distance, as one expects from the diffusion equation. The value we find for this “Milne extrapolation length” is, in the appropriate dimensionless units, approximately twice the value found in the radiative transfer problem.
Author:
(1) K. Razi Naqvi, Department of Physics, Norwegian University of Science and Technology (NTNU), 7094 Trondheim, Norway
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3 Comments elicited by the solution to Milne’s problem for B-particles
6 Concluding remarks and References
3 Comments elicited by the solution to Milne’s problem for B-particles
Far from the wall the density increases linearly with distance, as one expects from the diffusion equation. When this asymptotic solution is extrapolated across the boundary region it reaches zero not at the wall (as the solution of the diffusion equation with absorbing boundary would) but at some distance beyond it. The value we find for this “Milne extrapolation length” is, in the appropriate dimensionless units, approximately twice the value found in the radiative transfer problem. The density in the actual solution is everywhere lower than that of the extrapolated asymptotic solution, but of course it stays finite at the wall.
3.1 Length scales for Brownian moton and its inverse
3.2 Profiles of particle density
This paper is available on arxiv under CC BY 4.0 DEED license.
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