On global minimizers of repulsive–attractive power-law interaction energies

We consider the minimization of the attrarepulsive–ctive power-law interaction energies that occur in many biological and physical situations. We show the existence of global minimizers in the discrete setting and obtain bounds for their supports independently of the number of Dirac deltas in a cert...

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Bibliographic Details
Published in:Philosophical transactions of the Royal Society of London. Series A: Mathematical, physical, and engineering sciences physical, and engineering sciences, 2014-11, Vol.372 (2028), p.1-13
Main Authors: Carrillo, José Antonio, Chipot, Michel, Huang, Yanghong
Format: Article
Language:English
Subjects:
Aggregation
Center of mass
Convexity
Crystallization
Dirac delta function
Energy
Mathematical lattices
Social interaction
Uniqueness
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Summary:We consider the minimization of the attrarepulsive–ctive power-law interaction energies that occur in many biological and physical situations. We show the existence of global minimizers in the discrete setting and obtain bounds for their supports independently of the number of Dirac deltas in a certain range of exponents. These global discrete minimizers correspond to the stable spatial profiles of flock patterns in swarming models. Global minimizers of the continuum problem are obtained by compactness. We also illustrate our results through numerical simulations.
ISSN:1364-503X