Published April 28, 2017
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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
- Creators
- Frank, Rupert L.
- Lieb, Elliott H.
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.
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Additional details
- Eprint ID
- 77075
- Resolver ID
- CaltechAUTHORS:20170428-161302774
- Created
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2017-04-28Created from EPrint's datestamp field
- Updated
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2023-06-02Created from EPrint's last_modified field