Correlated Motion in Bounded Domains: Revealing the First Passage Dynamics

Add to your list(s) Download to your calendar using vCal

• Daniel Marris (University of Bristol)
• Thursday 09 November 2023, 09:30-10:00
• Seminar Room 1, Newton Institute.

If you have a question about this talk, please contact nobody.

MMVW04 - Modelling non-Markov Movement Processes

We consider here the one step non-Markovian extension to the simple lattice random walk, theso called correlated or persistent random walk, 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 territorial formation. However,despite its ubiquity, there has been little progress in the understanding of its transport properties,especially in the more realistic scenario of bounded domains. In the discrete space-time formulation,which has recently been shown to be highly effective in tackling transport processes in boundedspace, previous insights into the search statistics of correlated motion in bounded domains haverelied, mainly, on the mean first-passage. Here, by combining the representation of random walkswith internal states with recent theory of splitting probabilities to multiple targets, we are ableto derive, entirely analytically, the full first-passage, or first-hitting, probability  in bounded periodic and reflectivedomains. In doing so, we uncover hidden properties of the search process. With both reflecting andperiodic boundaries, persistence leads to a first-hitting time probability that is multi-modal. When present, this multimodality may lead to a mean first-passage time far away fromthe peaks, which instead corresponds to a timestep with a negligible first-passage probability value.However, with anti-persistence, when the walker is more likely to change direction, one can find aninvariance between the boundary conditions for much of the first-passage probability. Furthermore,for reflective boundaries, by using a simple iterative procedure we also compare the first-passagedynamics based on whether reflecting boundaries reverse the direction of movement or not. Co-authored with Luca Giuggioli. 

This talk is part of the Isaac Newton Institute Seminar Series series.

This talk is included in these lists:

• All CMS events
• Featured lists
• INI info aggregator
• Isaac Newton Institute Seminar Series
• School of Physical Sciences
• Seminar Room 1, Newton Institute
• bld31

Note that ex-directory lists are not shown.