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An efficient Q-tensor-based algorithm for liquid crystal alignment away from defects

An efficient Q-tensor-based algorithm for liquid crystal alignment away from defects
An efficient Q-tensor-based algorithm for liquid crystal alignment away from defects
We develop a fast and accurate approximation of the normally stiff equations which minimize the Landau–de Gennes free energy of a nematic liquid crystal. The resulting equations are suitable for all configurations in which defects are not present, making them ideal for device simulation. Specifically they offer an increase in computational efficiency by a factor of 100 while maintaining an error of order (10-4) when compared to the full stiff equations. As this approximation is based on a Q-tensor formalism, the sign reversal symmetry of the liquid crystal is respected. In this paper we derive these equations for a simple two-dimensional case, where the director is restricted to a plane, and also for the full three-dimensional case. An approximation of the error in the perturbation scheme is derived in terms of the first order correction, and a comparison to the full stiff equations is given.
Q-tensor, nematic liquid crystals, alignment, approximation methods, numerical methods
0036-1399
2844-2860
Daly, Keith R.
64f85c2e-2562-44df-9cb8-1be7fbc7e74c
D'Alessandro, Giampaolo
bad097e1-9506-4b6e-aa56-3e67a526e83b
Kaczmarek, Malgosia
408ec59b-8dba-41c1-89d0-af846d1bf327
Daly, Keith R.
64f85c2e-2562-44df-9cb8-1be7fbc7e74c
D'Alessandro, Giampaolo
bad097e1-9506-4b6e-aa56-3e67a526e83b
Kaczmarek, Malgosia
408ec59b-8dba-41c1-89d0-af846d1bf327

Daly, Keith R., D'Alessandro, Giampaolo and Kaczmarek, Malgosia (2010) An efficient Q-tensor-based algorithm for liquid crystal alignment away from defects. SIAM Journal on Applied Mathematics, 70 (8), 2844-2860. (doi:10.1137/100796467).

Record type: Article

Abstract

We develop a fast and accurate approximation of the normally stiff equations which minimize the Landau–de Gennes free energy of a nematic liquid crystal. The resulting equations are suitable for all configurations in which defects are not present, making them ideal for device simulation. Specifically they offer an increase in computational efficiency by a factor of 100 while maintaining an error of order (10-4) when compared to the full stiff equations. As this approximation is based on a Q-tensor formalism, the sign reversal symmetry of the liquid crystal is respected. In this paper we derive these equations for a simple two-dimensional case, where the director is restricted to a plane, and also for the full three-dimensional case. An approximation of the error in the perturbation scheme is derived in terms of the first order correction, and a comparison to the full stiff equations is given.

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Published date: 16 September 2010
Keywords: Q-tensor, nematic liquid crystals, alignment, approximation methods, numerical methods
Organisations: Quantum, Light & Matter Group, Applied Mathematics

Identifiers

Local EPrints ID: 164053
URI: https://eprints.soton.ac.uk/id/eprint/164053
ISSN: 0036-1399
PURE UUID: 8da3052a-a834-4c43-85de-431e32e2bc49
ORCID for Giampaolo D'Alessandro: ORCID iD orcid.org/0000-0001-9166-9356

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Date deposited: 20 Sep 2010 07:37
Last modified: 31 Jul 2019 00:51

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