期刊
JOURNAL OF STATISTICAL PHYSICS
卷 159, 期 4, 页码 972-986出版社
SPRINGER
DOI: 10.1007/s10955-015-1215-z
关键词
Ground states; Global minimizers; H-stability; Pair potentials; Self-assembly; Aggregation
资金
- Fundacao para a Ciencia e a Tecnologia (Portuguese Foundation for Science and Technology) through Carnegie Mellon Portugal Program [SFRH/BD/33778/2009]
- NSF [DMS-1211760]
- FCT [UTA CMU/MAT/0007/2009]
- Applied Mathematics Laboratory of the Centre de Recherches Mathematiques
- NSF PIRE [OISE-0967140]
- Division Of Mathematical Sciences
- Direct For Mathematical & Physical Scien [1211760] Funding Source: National Science Foundation
- Office Of The Director
- Office Of Internatl Science &Engineering [967140] Funding Source: National Science Foundation
- Fundação para a Ciência e a Tecnologia [SFRH/BD/33778/2009] Funding Source: FCT
We investigate which nonlocal-interaction energies have a ground state (global minimizer). We consider this question over the space of probability measures and establish a sharp condition for the existence of ground states. We show that this condition is closely related to the notion of stability (i.e. -stability) of pairwise interaction potentials. Our approach uses the direct method of the calculus of variations.
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