Related papers: Geometric frustration and compatibility conditions…

The interplay between geometry, topology and order can lead to geometric frustration that profoundly affects the shape and structure of a curved surface. In this commentary we show how frustration in this context can result in the faceting…

In the context of magnetism, frustration arises when a group of spins cannot find a configuration that minimizes all of their pairwise interactions simultaneously. We consider the effects of the geometric frustration that arises in a…

Geometric frustration offers a pathway to soft matter self-assembly with controllable finite sizes. While the understanding of frustration in soft matter assembly derives almost exclusively from continuum elastic descriptions, a current…

We study the formulation of bond-orientational order in an arbitrary two dimensional geometry. We find that bond-orientational order is properly formulated within the framework of differential geometry with torsion. The torsion reflects the…

We consider planar liquid crystal elastomers: two dimensional objects made of anisotropic responsive materials, that upon activation remain flat however change their planar shape. We derive a closed form, analytical solution based on the…

We derive a F\"{o}ppl-von K\'{a}rm\'{a}n-type constitutive model for solid liquid crystalline plates where the nematic director may or may not rotate freely relative to the elastic network. To obtain the reduced two-dimensional model, we…

We study the solution landscape and bifurcation diagrams of nematic liquid crystals confined on a rectangle, using a reduced two-dimensional Landau--de Gennes framework in terms of two geometry-dependent variables: half short edge length…

Topological defects in crystalline lattices are considered. In relation to physical realizability of such defects, criteria for geometric compatibility of the lattice distortions are formulated. For 2D lattices it is shown that the answer…

Nematic interfaces are thin fluid films, ideally two-dimensional, endowed with an in-plane degenerate nematic order. In this letter we examine a generalisation of the classical Plateau problem to an axisymmetric nematic interface bounded by…

We investigate a number of complex patterns driven by the electro-convection instability in a planarly aligned layer of a nematic liquid crystal. They are traced back to various secondary instabilities of the ideal roll patterns bifurcating…

Understanding and controlling the director field configuration, shape, and orientation in nematic and cholesteric liquid crystals is of fundamental importance in several branches of science. Liquid crystalline droplets, also known as…

Fluid interfaces, such as soap films, liquid droplets or lipid membranes, are known to give rise to several special geometries, whose complexity and beauty continue to fascinate us, as observers of the natural world, and challenge us as…

The defining property of electronic nematicity -- the spontaneous breaking of rotational symmetry -- implies an unavoidable coupling between the nematic order parameter and elastic strain fields, known as nemato-elasticity. While both…

The role of applied fields on the structure of liquid crystals confined to shell geometries has been studied in past theoretical work, providing strategies to produce liquid crystal shells with controlled defect structure or valence.…

We study droplets of chromonic liquid crystals squeezed between parallel plates inducing degenerate tangential anchoring on the nematic director. In the coexistence regime, where droplets in the nematic phase are at equilibrium with the…

Nematic tactoids are spindle-shaped droplets of a nematic phase nucleated in the co-existing isotropic phase. According to equilibrium theory, their internal structure and shape are controlled by a balance between the elastic deformation of…

Geometric frustration emerges when local interaction energies in an ordered lattice structure cannot be simultaneously minimized, resulting in a large number of degenerate states. The numerous degenerate configurations may lead to practical…

When flat or on a firm mechanical substrate, the atomic composition and atomistic structure of two-dimensional crystals dictate their chemical, electronic, optical, and mechanical properties. These properties change when the two-dimensional…

We examine a simple hard disc fluid with no long range interactions on the two dimensional space of constant negative Gaussian curvature, the hyperbolic plane. This geometry provides a natural mechanism by which global crystalline order is…

Phase inhomogeneity of otherwise chemically homogenous electronic systems is an essential ingredient leading to fascinating functional properties, such as high-$T_c$ superconductivity in cuprates, colossal magnetoresistance in manganites,…