Relaxation and gradient methods for molecular orientation in liquid crystals

Robert Cohen, San Yih Lin, Mitchell Luskin

Research output: Contribution to journalArticlepeer-review

35 Scopus citations

Abstract

Relaxation and gradient methods have been developed during the past several years for the computation of molecular orientation in liquid crystals. These methods have contributed to the classification of stable defect structures and the description of some of the transitions that occur under the influence of electric and magnetic fields. The bulk energy of the liquid crystal depends on the orientation of the optic axis, and this gives the variational problem a nonconvex constraints. Further, minimum energy configurations can be discontinous and can have singularities. In this paper, new relaxation and gradient methods are proposed to handle this nonconvex constraint. The results of numerical experiments and error analysis are presented.

Original languageEnglish (US)
Pages (from-to)455-465
Number of pages11
JournalComputer Physics Communications
Volume53
Issue number1-3
DOIs
StatePublished - May 1989

Bibliographical note

Funding Information:
The work of this author was supported by ARO grant DAA1O3-88-K0170, the NSF and AFOSR through grants DMS 835-1080 and DMS 871-8881, the Cray Research Foundation and by a grant from the Minnesota Supercom-puter Institute,

Funding Information:
The work of this author was supported by the NSF, the ARO, the AFOSR, and the Cray Research Foundation.

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