KEVIN PAINTER - HERIOT-WATT UNIVERSITY -INCORPORATING NONLOCALITY INTO MOVEMENT MODELS
A large literature has emerged on the modelling of cells or organism movement, due to its indisputable importance in a wide variety of processes. The velocity-jump random walk description has proven particularly popular, where individual particles are assumed to alternate between ballistic movements with fixed velocities and turning events where new orientations are selected. Standard assumptions typically result in local diffusion-advection models in a macroscopic limit. Yet, movement behaviour often incorporates various elements of nonlocality. Environmental sensing can be nonlocal, in that the particle detects an environmental cue over some spatially extended region. Movement can be nonlocal, in that a particle may range from short movements that restrict it locally to occasional long movements taking it to a distant location.
In this seminar Prof. Painter will show how considering nonlocality impacts on the macroscopic limiting equations. Along the way, he will discuss the relevance of the work within a number of biological applications, including population structuring according to topography and immunosurveillance of the central nervous system.
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