Existence of Compactly Supported Global Minimisers for the Interaction Energy View Full Text


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Article Info

DATE

2015-09

AUTHORS

José A. Cañizo, José A. Carrillo, Francesco S. Patacchini

ABSTRACT

The existence of compactly supported global minimisers for continuum models of particles interacting through a potential is shown under almost optimal hypotheses. The main assumption on the potential is that it is catastrophic, or not H-stable, which is the complementary assumption to that in classical results on thermodynamic limits in statistical mechanics. The proof is based on a uniform control on the local mass around each point of the support of a global minimiser, together with an estimate on the size of the "gaps" it may have. The class of potentials for which we prove the existence of global minimisers includes power-law potentials and, for some range of parameters, Morse potentials, widely used in applications. We also show that the support of local minimisers is compact under suitable assumptions. More... »

PAGES

1197-1217

References to SciGraph publications

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  • 2012-05. Minimizing atomic configurations of short range pair potentials in two dimensions: crystallization in the Wulff shape in CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS
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  • 2009-03. On the Crystallization of 2D Hexagonal Lattices in COMMUNICATIONS IN MATHEMATICAL PHYSICS
  • 2004-05. Long-Time Asymptotics of Kinetic Models of Granular Flows in ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS
  • 2012-12. On Soccer Balls and Linearized Inverse Statistical Mechanics in JOURNAL OF NONLINEAR SCIENCE
  • 2013-09. Dimensionality of Local Minimizers of the Interaction Energy in ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS
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    http://scigraph.springernature.com/pub.10.1007/s00205-015-0852-3

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    http://dx.doi.org/10.1007/s00205-015-0852-3

    DIMENSIONS

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