A `liquid-solid' phase transition in a simple model for swarming, based on the `no flat-spots' theorem for subharmonic functions
Analysis of PDEs
2017-06-21 v4 Mathematical Physics
math.MP
Abstract
We consider a non-local shape optimization problem, which is motivated by a simple model for swarming and other self-assembly/aggregation models, and prove the existence of different phases. A technical key ingredient, which we establish, is that a strictly subharmonic function cannot be constant on a set of positive measure.
Keywords
Cite
@article{arxiv.1607.07971,
title = {A `liquid-solid' phase transition in a simple model for swarming, based on the `no flat-spots' theorem for subharmonic functions},
author = {Rupert L. Frank and Elliott H. Lieb},
journal= {arXiv preprint arXiv:1607.07971},
year = {2017}
}
Comments
20 pages; result extended to more general interaction kernels