Publication 23-CNA-001

Vector Field Models For Nematic Disclinations

Amit Acharya
Dept. of Civil & Environmental Engineering
Center for Nonlinear Analysis
Carnegie Mellon University
Pittsburgh, PA 15213
acharyaamit@cmu.edu

Irene Fonseca
Department of Mathematical Sciences
Carnegie Mellon University
Pittsburgh, PA 15213
fonseca@andrew.cmu.edu

Likhit Ganedi
Institut für Mathematik
RWTH Aachen University
Aachen, Germany

Kerrek Stinson
University of Bonn
Bonn, Germany

Abstract: In this paper, a model for defects that was introduced in [ZANV21] is studied. In the literature, the setting of most models for defects is the function space SBV (special bounded variation functions) (see, e.g., [ CGO15, GMPS21]). However, this model regularizes the director field to be in a Sobolev space by adding a second field to incorporate the defect. A relaxation result in the case of fixed parameters is proven along with some partial compactness results.

Get the paper in its entirety as  23-CNA-001.pdf

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