Numerical Analysis and Scientific Computing Seminar | Lennaert van Veen, A non-local PDE model for animal aggregation

MC 5417 (in person) and online talk (for Zoom Link please contact ddelreyfernandez@uwaterloo.ca)  

Speaker

Professor Lennaert van Veen, University of Ontario Institute of Technology Department of Mathematics

Title

A non-local PDE model for animal aggregation

Abstract

Organisms moving in groups can exhibit intricate pattern formation and dynamics. From bacteria in a petri dish to grazing caribou, forming groups and moving towards a common goal can be part of a survival strategy. Many types of models have been introduced to simulate and predict the aggregation of organisms, such as agent-based models, Boltzmann equations and active fluids. We study a kinetic model in two spatial dimensions with non-linear terms that correspond to the sensing of the environment by, for instance, vision, hearing or chemotaxis. The information thus gathered is passed through a sigmoidal function that models a sensing threshold and a saturation effect. I will explain the somewhat non-standard simulation scheme and explore the relative influence of the strength of alignment and attraction forces, as well as the sensing threshold and saturation, on the pattern formation.

Joint work with Luciano Buono and Andree Qi.