scholarly journals Parallel calculation of the stationary diffusion equation

2020 ◽  
Vol 1689 ◽  
pp. 012074
Author(s):  
E O Soldatov ◽  
Yu N Volkov ◽  
M N Zizin
Keyword(s):  
Diffusion Equation ◽  
Parallel Calculation ◽  
Stationary Diffusion ◽  
Stationary Diffusion Equation

scholarly journals On a pore-scale stationary diffusion equation: Scaling effects and correctors for the homogenization limit

2017 ◽  
Vol 22 (11) ◽  
pp. 0-0 ◽  
Author(s):  
Vo Anh Khoa ◽  
◽  
Thi Kim Thoa Thieu ◽  
Ekeoma Rowland Ijioma ◽  
◽  
...  
Keyword(s):  
Diffusion Equation ◽  
Pore Scale ◽  
Scaling Effects ◽  
Stationary Diffusion ◽  
Stationary Diffusion Equation

scholarly journals “CHAPTER 5” DIFFUSION THEORY

2021 ◽  
Vol 247 ◽  
pp. 14005
Author(s):  
B. Ganapol ◽  
P. Tsvetkov
Keyword(s):  
Diffusion Equation ◽  
Nuclear Reactor ◽  
Diffusion Theory ◽  
General Setting ◽  
Usual Method ◽  
Diffusion Equations ◽  
Basic Form ◽  
Reactor Physics ◽  
Stationary Diffusion ◽  
Stationary Diffusion Equation

In many nuclear reactor physics texts (excluding Elmer Lewis’s recent text however), “Chapter 5” is dedicated to diffusion theory; hence, the title of this submission. Here, we will investigate analytical solutions to the most basic form of the monoenergetic 1D stationary diffusion equation. The intuitive approach taken radically departs from the usual method of solving the diffusion equation. In particular, we consider a general setting such that the method accommodates all solutions to the monoenergetic diffusion equations in 1D plane and curvilinear geometries. This is not your father’s diffusion theory and, for this reason, we anticipate it will eventually become the classroom standard.

scholarly journals Reconstructing a point source from diffusion fluxes to narrow windows in three dimensions

2021 ◽  
Vol 477 (2253) ◽  
pp. 20210271
Author(s):  
U. Dobramysl ◽  
D. Holcman
Keyword(s):  
Point Source ◽  
Mixed Boundary ◽  
Three Dimensional ◽  
Three Dimensions ◽  
Infinite Domain ◽  
Uniform Distributions ◽  
Stationary Diffusion ◽  
Analytical Formulae ◽  
Stationary Diffusion Equation ◽  
Additive Fluctuations

We develop a computational approach to locate the source of a steady-state gradient of diffusing particles from the fluxes through narrow windows distributed either on the boundary of a three-dimensional half-space or on a sphere. This approach is based on solving the mixed boundary stationary diffusion equation with Neumann–Green’s function. The method of matched asymptotic expansions enables the computation of the probability fluxes. To explore the range of validity of this expansion, we develop a fast analytical-Brownian numerical scheme. This scheme accelerates the simulation time by avoiding the explicit computation of Brownian trajectories in the infinite domain. The results obtained from our derived analytical formulae and the fast numerical simulation scheme agree on a large range of parameters. Using the analytical representation of the particle fluxes, we show how to reconstruct the location of the point source. Furthermore, we investigate the uncertainty in the source reconstruction due to additive fluctuations present in the fluxes. We also study the influence of various window configurations: clustered versus uniform distributions on recovering the source position. Finally, we discuss possible applications for cell navigation in biology.

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