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SUMMARY:Stationary diffusion among partially reactive sinks: from von Smol
uchowski to recent advances
DTSTART;VALUE=DATE-TIME:20170904T130000Z
DTEND;VALUE=DATE-TIME:20170904T132000Z
DTSTAMP;VALUE=DATE-TIME:20221203T112215Z
UID:indico-contribution-35@zakopane.if.uj.edu.pl
DESCRIPTION:Speakers: Denis Grebenkov (CNRS)\nIn 1917\, von Smoluchowski f
ounded the first mathematical theory of diffusion-limited reactions by com
puting the diffusive flux towards a perfect spherical sink. In spite of ma
ny advances over the past hundred years\, stationary diffusion in complex
media with numerous sinks of various shapes and reactivities remains poorl
y understood. After a brief overview\, we present a recently developed gen
eralized method of separation of variables (GMSV) to solve boundary value
problems for the Poisson equation in three-dimensional canonical domains (
e.g.\, parallelepipeds\, cylinders\, spheres\, spheroids\, ...\, \nand the
ir combinations). In particular\, we derive a semi-analytical representati
on of the Green function for an arbitrary configuration of non-overlapping
partially reactive spherical sinks. This is the key object to determine v
arious characteristics of stationary diffusion such as reaction rate\, esc
ape probability\, harmonic measure\, residence time\, and mean first passa
ge time\, to name but a few. Based on this solution\, we introduce and inv
estigate an effective reaction radius of individual sinks or their cluster
s that significantly generalizes the famous Smoluchowski formula by accoun
ting for diffusion interactions between sinks and their mutual screening.\
n\nhttps://zakopane.if.uj.edu.pl/event/4/contributions/35/
LOCATION: 56
URL:https://zakopane.if.uj.edu.pl/event/4/contributions/35/
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