[Formula: see text] Law in the Cubic Lattice

We investigate the Edge-Isoperimetric Problem (EIP) for sets with n elements of the cubic lattice by emphasizing its relation with the emergence of the Wulff shape in the crystallization problem. Minimizers [Formula: see text] of the edge perimeter are shown to deviate from a corresponding cubic Wul...

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Detalles Bibliográficos
Autores principales: Mainini, Edoardo, Piovano, Paolo, Schmidt, Bernd, Stefanelli, Ulisse
Formato: Online Artículo Texto
Lenguaje:English
Publicado: Springer US 2019
Materias:
Article
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC6733839/
https://www.ncbi.nlm.nih.gov/pubmed/31555015
http://dx.doi.org/10.1007/s10955-019-02350-z
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author Mainini, Edoardo
Piovano, Paolo
Schmidt, Bernd
Stefanelli, Ulisse
author_facet Mainini, Edoardo
Piovano, Paolo
Schmidt, Bernd
Stefanelli, Ulisse
author_sort Mainini, Edoardo
collection PubMed
description We investigate the Edge-Isoperimetric Problem (EIP) for sets with n elements of the cubic lattice by emphasizing its relation with the emergence of the Wulff shape in the crystallization problem. Minimizers [Formula: see text] of the edge perimeter are shown to deviate from a corresponding cubic Wulff configuration with respect to their symmetric difference by at most [Formula: see text] elements. The exponent 3 / 4 is optimal. This extends to the cubic lattice analogous results that have already been established for the triangular, the hexagonal, and the square lattice in two space dimensions.
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spelling pubmed-67338392019-09-23 [Formula: see text] Law in the Cubic Lattice Mainini, Edoardo Piovano, Paolo Schmidt, Bernd Stefanelli, Ulisse J Stat Phys Article We investigate the Edge-Isoperimetric Problem (EIP) for sets with n elements of the cubic lattice by emphasizing its relation with the emergence of the Wulff shape in the crystallization problem. Minimizers [Formula: see text] of the edge perimeter are shown to deviate from a corresponding cubic Wulff configuration with respect to their symmetric difference by at most [Formula: see text] elements. The exponent 3 / 4 is optimal. This extends to the cubic lattice analogous results that have already been established for the triangular, the hexagonal, and the square lattice in two space dimensions. Springer US 2019-07-24 2019 /pmc/articles/PMC6733839/ /pubmed/31555015 http://dx.doi.org/10.1007/s10955-019-02350-z Text en © The Author(s) 2019 Open AccessThis article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.
spellingShingle Article
Mainini, Edoardo
Piovano, Paolo
Schmidt, Bernd
Stefanelli, Ulisse
[Formula: see text] Law in the Cubic Lattice
title [Formula: see text] Law in the Cubic Lattice
title_full [Formula: see text] Law in the Cubic Lattice
title_fullStr [Formula: see text] Law in the Cubic Lattice
title_full_unstemmed [Formula: see text] Law in the Cubic Lattice
title_short [Formula: see text] Law in the Cubic Lattice
title_sort [formula: see text] law in the cubic lattice
topic Article
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC6733839/
https://www.ncbi.nlm.nih.gov/pubmed/31555015
http://dx.doi.org/10.1007/s10955-019-02350-z
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