Two geometric lemmas for S^N-1-valued maps and an application to the homogenization of spin systems

2020/10/27 by Andrea Braides, Braides, Andrea, Valerio Vallocchia +1
Computer Science · Mathematics · #Advanced Mathematical Modeling in Engineering #math.AP #math.PR #msc:35B27 #msc:46E39 #msc:49J45

paper · pdf · doi:10.48550/arxiv.2010.14280

arxiv created 2020/10/27 · arxiv updated 2020/10/28

Abstract

We prove two geometric lemmas for S^N-1-valued functions that allow to modify sequences of lattice spin functions on a small percentage of nodes during a discrete-to-continuum process so as to have a fixed average. This is used to simplify known formulas for the homogenization of spin systems.

Citations

• The Physics of Liquid Crystals

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