Variational Theories for Liquid Crystals

Virga, Epifanio G.

doi:10.1007/978-1-4899-2867-2

Cited by 466 publications

(432 citation statements)

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“…Here, we want to refer, for example, to WARNER & TERENTJEV [67], STARK [54], and CESANA & DESIMONE [8]. Furthermore, we refer to the monograph VIRGA [66] for variational approaches to liquid crystals.…”

Section: Introductionmentioning

confidence: 99%

An electro‐elastic phase‐field model for nematic liquid crystal elastomers based on Landau‐de‐Gennes theory

Keip

Nadgir

2017

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The present contribution proposes a continuum-mechanical phase-field approach to model the electro-elastic behavior of nematic liquid crystal elastomers. The nemato-electro-elastic model is embedded into the fundamental Landau-de-Gennes theory for isotropic-nematic phase transition and employs a tensorial order parameter as the phase field. Nematic deformations are incorporated through a constitutive ansatz in terms of the order parameter. The phase-field formulation is implemented into the finite element method, so that the microstructure evolution of nematic elastomers under different boundary conditions can be studied. We show that the model is capable to capture characteristic features of nematic elastomers including mechanically and electrically induced microstructure evolution as well as the occurrence of stripe domains.

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Section: Introductionmentioning

confidence: 99%

An electro‐elastic phase‐field model for nematic liquid crystal elastomers based on Landau‐de‐Gennes theory

Keip

Nadgir

2017

GAMM-Mitteilungen

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“…Liquid crystals are mesophases, i.e., intermediate states of matter between the liquid and the crystal phase [15]. They exhibit characteristics of fluid flow and have optical properties typically associated with crystals.…”

Section: Introductionmentioning

confidence: 99%

“…In this paper we will specialize to stationary flow, and hence focus exclusively on the dynamics of the director field, a map n : R 3 → S 3 from the Euclidean space to the unit ball; see Saxton [14]. It is common to consider the Oseen-Franck expression for the internal energy (see [14], [15], [6])…”

Section: Introductionmentioning

confidence: 99%

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Convergent difference schemes for the Hunter–Saxton equation

2007

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Abstract. We propose and analyze several finite difference schemes for the Hunter-Saxton equationThis equation has been suggested as a simple model for nematic liquid crystals. We prove that the numerical approximations converge to the unique dissipative solution of (HS), as identified by Zhang and Zheng. A main aspect of the analysis, in addition to the derivation of several a priori estimates that yield some basic convergence results, is to prove strong convergence of the discrete spatial derivative of the numerical approximations of u, which is achieved by analyzing various renormalizations (in the sense of DiPerna and Lions) of the numerical schemes. Finally, we demonstrate through several numerical examples the proposed schemes as well as some other schemes for which we have no rigorous convergence results.

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“…Here we adopt the assumptions of [5] and use the methods of homogenization theory to derive a rigorous version of (2) in a dilute limit of the Ericksen free energy functional [6] supplemented by the Rapini-Papoular weak surface anchoring term [7].…”

Section: Introductionmentioning

confidence: 99%