Paper Info
Title
Mixed analytical-stochastic simulation method for the recovery of a Brownian gradient source from probability fluxes to small windows.
Abstract
Is it possible to recover the position of a source from the steady-state fluxes of Brownian particles to small absorbing windows located on the boundary of a domain? To address this question, we develop a numerical procedure to avoid tracking Brownian trajectories in the entire infinite space. Instead, we generate particles near the absorbing windows, computed from the analytical expression of the exit probability. When the Brownian particles are generated by a steady-state gradient at a single point, we compute asymptotically the fluxes to small absorbing holes distributed on the boundary of half-space and on a disk in two dimensions, which agree with stochastic simulations. We also derive an expression for the splitting probability between small windows using the matched asymptotic method. Finally, when there are more than two small absorbing windows, we show how to reconstruct the position of the source from the diffusion fluxes. The present approach provides a computational first principle for the mechanism of sensing a gradient of diffusing particles, a ubiquitous problem in cell biology.
Year
DOI
Venue
2018
10.1016/j.jcp.2017.10.058
Journal of Computational Physics
Keywords
Field
DocType
PDEs,Asymptotics,Diffusion,Stochastic simulations
Stochastic simulation,First principle,Mathematical optimization,Flux (metallurgy),Mathematical analysis,Brownian motion,Mathematics
Journal
Volume
ISSN
Citations 
355
0021-9991
0
PageRank 
References 
Authors
0.34
4
2
Name
Order
Citations
PageRank
Ulrich Dobramysl120.77
David Holcman27614.22