A numerical taxonomy of 2D spatial patterns from nonlocal advection-diffusion models maps interaction strengths to stripes, clusters, volcanos, and polygonal mosaics.
Aggregation-Diffusion Equations for Collective Behaviour in the Sciences
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abstract
This is a survey article based on the content of the plenary lecture given by Jos\'e A. Carrillo at the ICIAM23 conference in Tokyo. It is devoted to produce a snapshot of the state of the art in the analysis, numerical analysis, simulation, and applications of the vast area of aggregation-diffusion equations. We also discuss the implications in mathematical biology explaining cell sorting in tissue growth as an example of this modelling framework. This modelling strategy is quite successful in other timely applications such as global optimisation, parameter estimation and machine learning.
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A phylogeny of biological patterns formed by nonlocal advection
A numerical taxonomy of 2D spatial patterns from nonlocal advection-diffusion models maps interaction strengths to stripes, clusters, volcanos, and polygonal mosaics.