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SUMMARY:Subdiffusion in the Presence of Reactive Boundaries: A Generalized
  Feynman-Kac Approach - Toby Kay (University of Bristol)
DTSTART:20231106T120000Z
DTEND:20231106T123000Z
UID:TALK203221@talks.cam.ac.uk
DESCRIPTION:We derive\, through subordination techniques\, a generalized F
 eynman&ndash\;Kac equation in theform of a time fractional Schr&ouml\;ding
 er equation. We relate such equation to a functional whichwe name the subo
 rdinated local time. We demonstrate through a stochastic treatment how thi
 sgeneralized Feynman&ndash\;Kac equation describes subdiffusive processes 
 with reactions. In thisinterpretation\, the subordinated local time repres
 ents the number of times a specific spatialpoint is reached\, with the amo
 unt of time spent there being immaterial. This distinctionprovides a pract
 ical advance due to the potential long waiting time nature of subdiffusive
 processes. The subordinated local time is used to formulate a probabilisti
 c understandingof subdiffusion with reactions\, leading to the well known 
 radiation boundary condition.We demonstrate the equivalence between the ge
 neralized Feynman&ndash\;Kac equation with areflecting boundary and the fr
 actional diffusion equation with a radiation boundary. Wesolve the former 
 and find the first-reaction probability density in analytic form in the ti
 medomain\, in terms of the Wright function. We are also able to find the s
 urvival probabilityand subordinated local time density analytically. These
  results are validated by stochasticsimulations that use the subordinated 
 local time description of subdiffusion in the presenceof reactions.
LOCATION:Seminar Room 1\, Newton Institute
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