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A 'liquid-solid' phase transition in a simple model for swarming, based on the 'no flat-spots' theorem for subharmonic functions

Frank, Rupert L. and Lieb, Elliott H. (2016) A 'liquid-solid' phase transition in a simple model for swarming, based on the 'no flat-spots' theorem for subharmonic functions. . (Submitted) http://resolver.caltech.edu/CaltechAUTHORS:20170428-161302774

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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.


Item Type:Report or Paper (Discussion Paper)
Related URLs:
URLURL TypeDescription
https://arxiv.org/abs/1607.07971arXivDiscussion Paper
Record Number:CaltechAUTHORS:20170428-161302774
Persistent URL:http://resolver.caltech.edu/CaltechAUTHORS:20170428-161302774
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:77075
Collection:CaltechAUTHORS
Deposited By: Tony Diaz
Deposited On:28 Apr 2017 23:35
Last Modified:28 Apr 2017 23:35

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