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• W2040416019 startingPage "1140002" @default.
• W2040416019 abstract "Large systems of particles interacting pairwise in d dimensions give rise to extraordinarily rich patterns. These patterns generally occur in two types. On one hand, the particles may concentrate on a co-dimension one manifold such as a sphere (in 3D) or a ring (in 2D). Localized, space-filling, co-dimension zero patterns can occur as well. In this paper, we utilize a dynamical systems approach to predict such behaviors in a given system of particles. More specifically, we develop a nonlocal linear stability analysis for particles uniformly distributed on a d - 1 sphere. Remarkably, the linear theory accurately characterizes the patterns in the ground states from the instabilities in the pairwise potential. This aspect of the theory then allows us to address the issue of inverse statistical mechanics in self-assembly: given a ground state exhibiting certain instabilities, we construct a potential that corresponds to such a pattern." @default.
• W2040416019 created "2016-06-24" @default.
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• W2040416019 date "2012-04-01" @default.
• W2040416019 modified "2023-09-23" @default.
• W2040416019 title "PREDICTING PATTERN FORMATION IN PARTICLE INTERACTIONS" @default.
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• W2040416019 doi "https://doi.org/10.1142/s0218202511400021" @default.
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