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SUMMARY:Correlated Motion in Bounded Domains: Revealing the First Passage 
 Dynamics - Daniel Marris (University of Bristol)
DTSTART:20231109T093000Z
DTEND:20231109T100000Z
UID:TALK203197@talks.cam.ac.uk
DESCRIPTION:We consider here the one step non-Markovian extension to the s
 imple lattice random walk\, theso called correlated or persistent random w
 alk\, which has been used extensively in models of bothphysical and social
  systems ranging from the movement of individual organisms such as e-coli 
 andinsects through to collective motion of animal flocking behaviour and t
 erritorial formation. However\,despite its ubiquity\, there has been littl
 e progress in the understanding of its transport properties\,especially in
  the more realistic scenario of bounded domains. In the discrete space-tim
 e formulation\,which has recently been shown to be highly effective in tac
 kling transport processes in boundedspace\, previous insights into the sea
 rch statistics of correlated motion in bounded domains haverelied\, mainly
 \, on the mean first-passage. Here\, by combining the representation of ra
 ndom walkswith internal states with recent theory of splitting probabiliti
 es to multiple targets\, we are ableto derive\, entirely analytically\, th
 e full first-passage\, or first-hitting\, probability&nbsp\; in bounded pe
 riodic and reflectivedomains. In doing so\, we uncover hidden properties o
 f the search process. With both reflecting andperiodic boundaries\, persis
 tence leads to a first-hitting time probability that is multi-modal. When 
 present\, this multimodality may lead to a mean first-passage time far awa
 y fromthe peaks\, which instead corresponds to a timestep with a negligibl
 e first-passage probability value.However\, with anti-persistence\, when t
 he walker is more likely to change direction\, one can find aninvariance b
 etween the boundary conditions for much of the first-passage probability. 
 Furthermore\,for reflective boundaries\, by using a simple iterative proce
 dure we also compare the first-passagedynamics based on whether reflecting
  boundaries reverse the direction of movement or not.\nCo-authored with Lu
 ca Giuggioli.&nbsp\;
LOCATION:Seminar Room 1\, Newton Institute
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