On global minimizers of repulsive-attractive power-law interaction energies
Abstract
We consider the minimisation of power-law repulsive-attractive interaction energies which occur in many biological and physical situations. We show existence of global minimizers in the discrete setting and get bounds for their supports independently of the number of Dirac Deltas in 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.
- Publication:
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Philosophical Transactions of the Royal Society of London Series A
- Pub Date:
- October 2014
- DOI:
- 10.1098/rsta.2013.0399
- arXiv:
- arXiv:1403.7420
- Bibcode:
- 2014RSPTA.37230399C
- Keywords:
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- Mathematics - Classical Analysis and ODEs;
- Mathematics - Analysis of PDEs
- E-Print:
- 14 pages, 2 figures