Dynamic theory for smectic A liquid crystals

Stewart, I. W.

doi:10.1007/s00161-006-0035-4

Cited by 32 publications

(83 citation statements)

References 35 publications

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“…The SmA dynamic theory of Stewart [33], which allows n and a to separate, will be summarized in section 2.1 before we go on to discuss, in section 2.2, the geometrical set-up and the particular model equations for a pressure-driven flow of SmA confined between two fixed parallel plates. It will be shown that there are three governing dynamic equations, given below by (2.29), (2.35), and (2.37), and it will be solutions to these equations that will be investigated subject to a symmetry requirement and suitable boundary conditions.…”

Section: Dynamic Theory and Description Of The Problemmentioning

confidence: 99%

Boundary Layers in Pressure-driven Flow in Smectic A Liquid Crystals

Stewart¹,

Vynnycky²,

McKee³

et al. 2015

SIAM J. Appl. Math.

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Abstract. This article examines the steady flow of a smectic A liquid crystal sample that is initially aligned in a classical "bookshelf" geometry confined between parallel plates and is then subjected to a lateral pressure gradient which is perpendicular to the initial local smectic layer arrangement. The nonlinear dynamic equations are derived. These equations can be linearized and solved exactly to reveal two characteristic length scales that can be identified in terms of the material parameters and reflect the boundary layer behavior of the velocity and the director and smectic layer normal orientations. The asymptotic properties of the nonlinear equations are then investigated to find that these length scales apparently manifest themselves in various aspects of the solutions to the nonlinear steady state equations, especially in the separation between the orientations of the director and smectic layer normal. Non-Newtonian plug-like flow occurs and the solutions for the director profile and smectic layer normal share features identified elsewhere in static liquid crystal configurations. Comparisons with numerical solutions of the nonlinear equations are also made.

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Section: Dynamic Theory and Description Of The Problemmentioning

confidence: 99%

Boundary Layers in Pressure-driven Flow in Smectic A Liquid Crystals

Stewart¹,

Vynnycky²,

McKee³

et al. 2015

SIAM J. Appl. Math.

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“…These results track the subsequent response of the smectic to the refracted wave. Using the techniques of Landau and Lifshitz for sound in isotropic fluids [1], we extend the results for smectic C by Gill and Leslie [2] and perform the analogous calculations for a sample of smectic A using the dynamic theory of Stewart [3]. These calculations enable a comparison between the results for smectic A and an extension, by the present authors, to the known results for smectic C.…”

Section: Introductionmentioning

confidence: 69%

“…We now summarise the continuum theory in [3], in which n and a are allowed to separate, as considered by Ribotta and Durand [6]. The standard suffix notation for Cartesian vectors and tensors [7] is employed.…”

Section: Continuum Theory For Smectic a Liquid Crystalsmentioning

confidence: 99%

“…1. Section 2 will provide a brief outline of Stewart's dynamic theory for SmA [3]. Section 3 will provide, in an analogous manner to that adopted by Gill and Leslie [2] for smectic C (SmC), derivations of the dispersion relations for the reflected and refracted waves, together with the consequent interfacial conditions to be utilised in the analysis.…”

Section: Introductionmentioning

confidence: 99%

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Behaviour of a Shear-Wave at a Solid-Smectic Interface

Snow

Stewart

2015

Molecular Crystals and Liquid Crystals

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Results of theoretical investigations into the behaviour of a shear wave at the boundary between an isotropic solid and a smectic A liquid crystal are presented. These results track the subsequent response of the smectic to the refracted wave. Using the techniques of Landau and Lifshitz for sound in isotropic fluids [1], we extend the results for smectic C by Gill and Leslie [2] and perform the analogous calculations for a sample of smectic A using the dynamic theory of Stewart [3]. These calculations enable a comparison between the results for smectic A and an extension, by the present authors, to the known results for smectic C.Motivated by the work of Auernhammer, Brand, and Pleiner [4,5], mechanisms for determining the impact of perturbations upon the modes of response behaviour will be analysed, with plots demonstrating the amplitudes of these waves relative to that of the incident wave displayed for a range of typical physical parameters characteristic to smectic C and smectic A.

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“…These include certain alternate representations of Oseen-Frank in terms of dyadic tensors [2,10,21], generalizations of Oseen-Frank for nematics with nonuniform degree of orientational order [29,Chap. 6], several models of smectic liquid crystals (the second most common and important liquid crystal phase after the nematic) [27,28], and others. All of these models acquire an additional indefinite, saddle-point structure when they are coupled with an electric field, as discussed in the next section.…”

Section: Free Energy Modelsmentioning

confidence: 99%

A Preconditioned Nullspace Method for Liquid Crystal Director Modeling

Ramage¹,

Gartland²

2013

SIAM J. Sci. Comput.

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Abstract. We present a preconditioned nullspace method for the numerical solution of large sparse linear systems that arise from discretizations of continuum models for the orientational properties of liquid crystals. The approach effectively deals with pointwise unit-vector constraints, which are prevalent in such models. The indefinite, saddle-point nature of such problems, which can arise from either or both of two sources (pointwise unit-vector constraints, coupled electric fields), is illustrated. Both analytical and numerical results are given for a model problem.Key words. nullspace method, liquid crystals, saddle-point problems, unit-vector constraints AMS subject classifications. 65F08, 65F10, 65F50, 65H10, 65N22 DOI. 10.1137/120870219 1. Introduction. Many continuum models for the orientational properties of liquid crystals involve one or more state variables that are vector fields of unit length. The pointwise unit-vector constraints associated with discretizations of such models give rise to indefinite linear systems of saddle-point form, when these constraints are imposed via Lagrange multipliers. In problems such as these, indefiniteness also frequently manifests itself due to another influence (coupling with applied electric fields), and this leads to a double saddle-point structure. We are interested in the efficient numerical solution by iterative methods of large sparse linear systems of algebraic equations associated with such problems. We begin by presenting some background on these materials and models.

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Dynamic theory for smectic A liquid crystals

Cited by 32 publications

References 35 publications

Boundary Layers in Pressure-driven Flow in Smectic A Liquid Crystals

Boundary Layers in Pressure-driven Flow in Smectic A Liquid Crystals

Behaviour of a Shear-Wave at a Solid-Smectic Interface

A Preconditioned Nullspace Method for Liquid Crystal Director Modeling

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