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SUMMARY:Stochastic processes with resetting - Paul Bressloff (Imperial Col
 lege London)
DTSTART:20231124T133000Z
DTEND:20231124T143000Z
UID:TALK208444@talks.cam.ac.uk
DESCRIPTION:A topic of considerable interest within nonequilibrium statist
 ical physics is the study of stochastic search processes with resetting\, 
 whereby the current position of the particle or searcher is reset to a fix
 ed location over a random sequence of times. In many cases\, the mean firs
 t passage time (MFPT) for finding a target has a unique minimum as a funct
 ion of the resetting rate. In this talk we review the basic theory of rand
 om search processes with resetting\, and then consider two applications.&n
 bsp\;\n(A)&nbsp\;Cytoneme-mediated morphogenesis. Cytonemes are long\, thi
 n actin-rich cell protrusions varying in length from 10-200&nbsp\;mm. They
  allow for the active transport of morphogens or their cognate receptors b
 y establishing direct physical contacts between cells. Cytonemes are also 
 thought to play a role in cell-to-cell viral spread. We formulate the rapi
 d growth and shrinkage of cytonemes prior to finding a target cell as a FP
 T problem with resetting and determine the MFPT. We also indicate how queu
 ing theory can be used to determine the accumulation of resources across a
 n array of target cells.&nbsp\;\n(B)&nbsp\;Transition path theory (TPT). M
 any chemical reactions can be formulated in terms of particle diffusion in
  a complex energy landscape. TPT is a theoretical framework for describing
  the direct (reaction) pathways from reactant to product states within thi
 s energy landscape\, and calculating the effective reaction rate. It is no
 w the standard method for analyzing rare events between long lived states.
  We consider a completely different application of TPT\, namely\, a dual-a
 spect diffusive search process in which a particle alternates between coll
 ecting cargo from a source domain A and then delivering it to a target dom
 ain B. The rate of resource accumulation at the target\, kAB\, is determin
 ed by the statistics of direct paths from A to B. Stochastic resetting int
 roduces two non-trivial problems in the application of TPT. First\, the pr
 ocess is not time-reversal invariant. Second\, calculating kAB involves de
 termining the total probability flux of direct transport paths across a di
 viding surface&nbsp\;S&nbsp\;between A and B\, which includes discontinuou
 s jumps due to resetting.
LOCATION:Seminar Room 2\, Newton Institute
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