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Asymptotic analysis of the Ginzburg-Landau functional on point clouds
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Theil, Florian and Thorpe, Matthew (2018) Asymptotic analysis of the Ginzburg-Landau functional on point clouds. Proceedings of the Royal Society of Edinburgh Section A: Mathematics . doi:10.1017/prm.2018.32 (In Press)
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WRAP-asymptotic-analysis-functional-point-clouds-Theil-2018.pdf - Accepted Version - Requires a PDF viewer. Download (1011Kb) | Preview |
Official URL: https://doi.org/10.1017/prm.2018.32
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 | ||||||||||||
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| 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: | 27 December 2018 | ||||||||||||
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| Date of first compliant deposit: | 12 February 2018 | ||||||||||||
| DOI: | 10.1017/prm.2018.32 | ||||||||||||
| Status: | Peer Reviewed | ||||||||||||
| Publication Status: | In Press | ||||||||||||
| Access rights to Published version: | Restricted or Subscription Access | ||||||||||||
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