Equilibrium configurations of nematic liquid crystals on a torus

Segatti, Antonio; Snarski, Michael; Veneroni, Marco

doi:10.1103/physreve.90.012501

Cited by 33 publications

(35 citation statements)

References 27 publications

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“…Again an additional geometric term enters in this equation if compared with the corresponding model in flat space. The term with the shape operator B results from the influence of the embedding (Napoli and Vergori, 2012;Nestler et al, 2018;Segatti et al, 2014). The coupled system eqs.…”

Section: The Ericksen-leslie Modelmentioning

confidence: 99%

Hydrodynamic interactions in polar liquid crystals on evolving surfaces

Nitschke

Reuther²,

Voigt

2019

Phys. Rev. Fluids

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We consider the derivation and numerical solution of the flow of passive and active polar liquid crystals, whose molecular orientation is subjected to a tangential anchoring on an evolving curved surface. The underlying passive model is a simplified surface Ericksen-Leslie model, which is derived as a thin-film limit of the corresponding three-dimensional equations with appropriate boundary conditions. A finite element discretization is considered and the effect of hydrodynamics on the interplay of topology, geometric properties and defect dynamics is studied for this model on various stationary and evolving surfaces. Additionally, we consider an active model. We propose a surface formulation for an active polar viscous gel and exemplarily demonstrate the effect of the underlying curvature on the location of topological defects on a torus.

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Section: The Ericksen-leslie Modelmentioning

confidence: 99%

Hydrodynamic interactions in polar liquid crystals on evolving surfaces

Nitschke

Reuther²,

Voigt

2019

Phys. Rev. Fluids

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“…These are problems yet to be solved. One already tackled is the equilibrium problem for the elastic energy density in (26) on a circular toroidal shell [18,49,50] (see also [62,63] for parallel treatments with only intrinsic, distortional energies, and [28] for an interesting application to toroidal shells of a promising Onsager excluded volume theory for wormlike polymer chains elaborated by Chen [64]). But, unfortunately, this problem has only been solved for the singular case where k 2 = k 3 , which by (27) implies that the fossil preferred direction coincides with the direction of minimal absolute curvature (that is, with either parallles or meridians).…”

Section: Conclusion and Discussionmentioning

confidence: 99%

“…A representation equivalent to (30) was also obtained in [49] (see their equation (5), then reiterated in (6.19) of [50]), though not endowed with the same meaning. In this form, W 0 appears like the potential energy for a torque on the nematic director, a torque that is not imparted by external agents, such as a field, but which stems from the curvature of the shell.…”

Section: A Fossil Energy and Curvature Potentialmentioning

confidence: 99%

Bistable curvature potential at hyperbolic points of nematic shells

Sonnet

Virga

2017

Soft Matter

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Nematic shells are colloidal particles coated with nematic liquid crystal molecules which may freely glide and rotate on the colloid's surface while keeping their long axis on the local tangent plane. We describe the nematic order on a shell by a unit director field on an orientable surface. Equilibrium fields can then be found by minimising the elastic energy, which in general is a function of the surface gradient of the director field. We learn how to extract systematically out of this energy a fossil component, related only to the surface and its curvatures, which expresses a curvature potential for the molecular torque. At hyperbolic points on the colloid's surface, and only there, the alignment preferred by the curvature potential may fail to be a direction of principal curvature. There the fossil energy becomes bistable.

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“…curvatures related to the geometry of the substrate itself, are relevant in the energetic balance [15,14,11,19]. The potential applications of these new theories in soft matter and their elegant mathematical formalism have produced a vivid research activity in the communities of both theoretical physicists [8,10,5,12,4] and applied mathematicians [20,21,17,22,18].…”

Section: Introductionmentioning

confidence: 99%

Influence of the extrinsic curvature on two-dimensional nematic films

Napoli

Vergori

2018

Phys. Rev. E

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Nematic films are thin fluid structures, ideally two dimensional, endowed with an in-plane degenerate nematic order. In this paper we examine a generalization of the classical Plateau problem to an axisymmetric nematic film bounded by two coaxial parallel rings. At equilibrium, the shape of the nematic film results from the competition between surface tension, which favors the minimization of the area, and the nematic elasticity, which instead promotes the alignment of the molecules along a common direction. We find two classes of equilibrium solutions in which the molecules are uniformly aligned along the meridians or parallels. Depending on two dimensionless parameters, one related to the geometry of the film and the other to the constitutive moduli, the Gaussian curvature of the equilibrium shape may be everywhere negative, vanishing, or positive. The stability of these equilibrium configurations is investigated.

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Equilibrium configurations of nematic liquid crystals on a torus

Cited by 33 publications

References 27 publications

Hydrodynamic interactions in polar liquid crystals on evolving surfaces

Hydrodynamic interactions in polar liquid crystals on evolving surfaces

Bistable curvature potential at hyperbolic points of nematic shells

Influence of the extrinsic curvature on two-dimensional nematic films

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