Green's functions in pattern formation and random search

Date: Thursday 18th April 2024

Abstract

We will discuss a method of employing Green's functions to solve two classes of problems involving small, spatially localized features. For the random search problem, we consider the example of comparing Brownian and Levy flight search strategies of a small stationary target. For pattern formation, we apply the method to a model of vegetation patterning in a semi-arid climate in which the vegetation organizes into small clusters amid an otherwise barren terrain. In the latter problem, we introduce an analytic-numerical method for computing Green's functions on a curved manifold - the curved terrain on which the vegetation patterns form. In both classes of problems, we show that effects of domain geometry are encoded in the regular part of the Green's function.