| Modified Thomson problem. | |
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MedLine Citation:
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PMID: 19518357 Owner: NLM Status: PubMed-not-MEDLINE |
Abstract/OtherAbstract:
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The modified Thomson problem, which concerns an assembly of N particles mutually interacting through a Coulombic potential and subject to a Coulombic-harmonic confinement, is introduced. For sufficiently strong confinement strengths M, properties of its solutions (such as the energy and the particle positions at the minimum, and the corresponding zero-point vibrational energy) are accurately estimated by expressions dependent on only a few quantities pertaining to the original Thomson problem [such as the energy E_{Th}(N) ] and the reduced confinement strength xi=NM/E_{Th}(N). For N<or=12, this regime of the perturbed Thomson problem persists for all non-negative values of xi. On the other hand, the perturbed spherical Coulomb crystal regime emerges for xi<xi_{crit}(N) and larger numbers of particles. For 13<or=N<or=22, the transition that delineates these two regimes is due to the existence of two energy minima, the crystal-like one becoming global for sufficiently weak confinements. For N>or=23, the transition involves a catastrophe brought about by the vanishing of one of the Hessian matrix eigenvalues, the value of xi_{crit}(N) being related to the magnitude of radial instability in the corresponding solution of the original Thomson problem. |
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Authors:
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Jerzy Cioslowski |
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Publication Detail:
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Type: Journal Article Date: 2009-04-15 |
Journal Detail:
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Title: Physical review. E, Statistical, nonlinear, and soft matter physics Volume: 79 ISSN: 1539-3755 ISO Abbreviation: Phys Rev E Stat Nonlin Soft Matter Phys Publication Date: 2009 Apr |
Date Detail:
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Created Date: 2009-06-12 Completed Date: 2009-07-14 Revised Date: - |
Medline Journal Info:
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Nlm Unique ID: 101136452 Medline TA: Phys Rev E Stat Nonlin Soft Matter Phys Country: United States |
Other Details:
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Languages: eng Pagination: 046405 Citation Subset: - |
Affiliation:
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Institute of Physics, University of Szczecin, 70-451 Szczecin, Poland. |
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From MEDLINE®/PubMed®, a database of the U.S. National Library of Medicine
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