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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

Irene Fonseca
Department of Mathematical Sciences
Carnegie Mellon University
Pittsburgh, PA 15213

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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