Related papers: Elastic energy of liquid crystals in convex polyhe…
Nematic liquid crystals in a polyhedral domain, a prototype for bistable displays, may be described by a unit-vector field subject to tangent boundary conditions. Here we consider the case of a rectangular prism. For configurations with…
Unit-vector fields $\nvec$ on a convex polyhedron $P$ subject to tangent boundary conditions provide a simple model of nematic liquid crystals in prototype bistable displays. The equilibrium and metastable configurations correspond to…
We consider a one-dimensional variational problem arising in connection with a model for cholesteric liquid crystals. The principal feature of our study is the assumption that the twist deformation of the nematic director incurs much higher…
The flexoelectric conversion of mechanical to electrical energy in nematic liquid crystals is investigated using continuum theory. Since the electrical energy produced cannot exceed the mechanical energy supplied, and vice-versa, upper…
The topology and the geometry of a surface play a fundamental role in determining the equilibrium configurations of thin films of liquid crystals. We propose here a theoretical analysis of a recently introduced surface Frank energy, in the…
We have written expressions for the free energy of a cholesteric liquid crystal in an approximation using the elasticity constants K_1, K_2, K_3 and the energy variation and the corresponding energy and energy gradient along the direction…
This review introduces the elasticity theory of two-dimensional crystals and nematic liquid crystals on curved surfaces, the energetics of topological defects (disclinations, dislocations and pleats) in these ordered phases, and the…
We consider the simplest one-constant model, put forward by J. Ericksen, for nematic liquid crystals with variable degree of orientation. The equilibrium state is described by a director field $\mathbf{n}$ and its degree of orientation $s$,…
Nematic elastomers and glasses deform spontaneously when subjected to temperature changes. This property can be exploited in the design of heterogeneously patterned thin sheets that deform into a non-trivial shape when heated or cooled. In…
We consider elastic flows of closed curves in Euclidean space. We obtain optimal energy thresholds below which elastic flows preserve embeddedness of initial curves for all time. The obtained thresholds take different values between…
Expressions are obtained for force and couple densities and stress tensors in macroscopic models for nematic liquid crystals subjected to electric fields. The coupling between the liquid crystal orientational properties and the electric…
A statistical theory of cholesteric liquid crystals composed of short rigid biaxial molecules is presented. It is derived in the thermodynamic limit at a small density and a small twist. The uniaxial (biaxial) cholesteric phase is regarded…
The nonlinear elastic properties of nematic liquid crystals have acquired new interest with the recent experimental observation of bulk modulated nematic phases which are composed by achiral molecules. We extend the Oseen-Zocher-Frank's…
Liquid crystals with molecules constrained to the tangent bundle of a curved surface show interesting phenomena resulting from the tight coupling of the elastic and bulk free energies of the liquid crystal with geometric properties of the…
We analyze an elastic surface energy which was recently introduced by G. Napoli and L.Vergori to model thin films of nematic liquid crystals. We show how a novel approach that takes into account also the extrinsic properties of the surfaces…
We consider a class of liquid crystal free-boundary problems for which both the equilibrium shape and internal configuration of a system must simultaneously be determined, for example in films with air- or fluid-liquid crystal interfaces…
We consider the axial compression of a thin elastic cylinder placed about a hard cylindrical core. Treating the core as an obstacle, we prove upper and lower bounds on the minimum energy of the cylinder that depend on its relative thickness…
The ground state of twist-bend nematic liquid crystals is a heliconical molecular arrangement in which the nematic director precesses uniformly about an axis, making a fixed angle with it. Both precession senses are allowed in the ground…
The elastic energy of a planar convex body is defined by $E(\Om)=\frac 12\,\int\_{\partial\Om} k^2(s)\,ds$where $k(s)$ is the curvature of the boundary. In this paper we are interested in the minimization problemof $E(\Om)$ with a…
The phase-field-crystal model for liquid crystals is solved numerically in two spatial dimensions. This model is formulated with three position-dependent order parameters, namely the reduced translational density, the local nematic order…