We show that minimizers of the Heitmann-Radin energy [6] are unique if and only if the particle number N belongs to an infinite sequence whose first thirty-five elements are 1, 2, 3, 4, 5, 7, 8, 10, 12, 14, 16, 19, 21, 24, 27, 30, 33, 37, 40, 44, 48, 52, 56, 61, 65, 70, 75, 80, 85, 91, 96, 102, 108, 114, 120 (see the paper for a closed-form description of this sequence). The proof relies on the discrete differential geometry techniques introduced in [3].
Classification of Particle Numbers with Unique Heitmann–Radin Minimizer / DE LUCA, Lucia; Friesecke, GERO HELMUTH. - In: JOURNAL OF STATISTICAL PHYSICS. - ISSN 0022-4715. - ELETTRONICO. - (2017), pp. ?-?. [10.1007/s10955-017-1781-3]
Classification of Particle Numbers with Unique Heitmann–Radin Minimizer
DE LUCA, LUCIA;FRIESECKE, GERO HELMUTH
2017
Abstract
We show that minimizers of the Heitmann-Radin energy [6] are unique if and only if the particle number N belongs to an infinite sequence whose first thirty-five elements are 1, 2, 3, 4, 5, 7, 8, 10, 12, 14, 16, 19, 21, 24, 27, 30, 33, 37, 40, 44, 48, 52, 56, 61, 65, 70, 75, 80, 85, 91, 96, 102, 108, 114, 120 (see the paper for a closed-form description of this sequence). The proof relies on the discrete differential geometry techniques introduced in [3].| File | Dimensione | Formato | |
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