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Asymptotic analysis of the Ginzburg-Landau functional on point clouds

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Theil, Florian and Thorpe, Matthew (2019) Asymptotic analysis of the Ginzburg-Landau functional on point clouds. Proceedings of the Royal Society of Edinburgh Section A: Mathematics, 149 (2). pp. 387-427. doi:10.1017/prm.2018.32

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Official URL: https://doi.org/10.1017/prm.2018.32

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Abstract

The Ginzburg–Landau functional is a phase transition model which is suitable for classification type problems. We study the asymptotics of a sequence of Ginzburg–Landau functionals with anisotropic interaction potentials on point clouds Ψn where n denotes the number data points. In particular, we show the limiting problem, in the sense of Γ-convergence, is related to the total variation norm restricted to functions taking binary values, which can be understood as a surface energy. We generalize the result known for isotropic interaction potentials to the anisotropic case and add a result concerning the rate of convergence.

Item Type: Journal Article
Subjects: Q Science > QA Mathematics
Divisions: Faculty of Science > Mathematics
Library of Congress Subject Headings (LCSH): Functionals, Geometry, Analytic
Journal or Publication Title: Proceedings of the Royal Society of Edinburgh Section A: Mathematics
Publisher: Cambridge University Press
ISSN: 0308-2105
Official Date: April 2019
Dates:
DateEvent
April 2019Published
27 December 2018Available
31 December 2017Accepted
Volume: 149
Number: 2
Page Range: pp. 387-427
DOI: 10.1017/prm.2018.32
Status: Peer Reviewed
Publication Status: Published
Access rights to Published version: Restricted or Subscription Access
RIOXX Funder/Project Grant:
Project/Grant IDRIOXX Funder NameFunder ID
UNSPECIFIEDUniversity of Warwickhttp://dx.doi.org/10.13039/501100000741
UNSPECIFIED[EPSRC] Engineering and Physical Sciences Research Councilhttp://dx.doi.org/10.13039/501100000266
UNSPECIFIEDSelex ES LtdUNSPECIFIED
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