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From slow diffusion to a hard height constraint: a singular limit of Keller-Segel

Banff International Research Station for Mathematical Innovation and Discovery

For a range of physical and biological processes—from dynamics of granular media to biological swarming—the evolution of a large number of interacting agents is modeled according to the competing effects of pairwise attraction and (possibly degenerate) diffusion. We prove that, in the slow diffusion limit, the degenerate diffusion becomes a hard height constraint on the density of the population, as arises in models of pedestrian crown motion. We then apply this to develop numerical insight for open conjectures in geometric optimization.

Mathematics; Partial differential equations; Statistical mechanics, structure of matter

video/mp4

Author affiliation: University of California Santa Barbara

2018-10-13

Attribution-NonCommercial-NoDerivatives 4.0 International

http://hdl.handle.net/2429/67530

Unreviewed

http://creativecommons.org/licenses/by-nc-nd/4.0/