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) https://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) | ||||||
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| Record Number: | CaltechAUTHORS:20170428-161302774 | ||||||
| Persistent URL: | https://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: | 09 Mar 2020 13:19 |
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