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Colloidal particles in a liquid crystal (LC) behave very differently from their counterparts in isotropic fluids. Elastic nature of the orientational order and surface anchoring of the director cause long-range anisotropic interactions and…
Recent experiments have exploited elastic instabilities in membranes to create complex patterns. However, the rational design of such structures poses many challenges, as they are products of nonlinear elastic behavior. We pose a simple…
Although all members of the ophthalmic community agree that distortion is an aberration affecting the geometry of an image produced by the periphery of an ophthalmic lens, there are several approaches for analyzing and quantifying this…
We investigate the structure of nematic liquid crystal thin films described by the Landau--de Gennes tensor-valued order parameter with Dirichlet boundary conditions of nonzero degree. We prove that as the elasticity constant goes to zero a…
We study nematic liquid crystal configurations in a prototype bistable device - the Post Aligned Bistable Nematic (PABN) cell. Working within the Oseen-Frank continuum model, we describe the liquid crystal configuration by a unit-vector…
A survey is presented of the dynamic features of non-itinerant off-center defects in crystals, such as rotation-like reorientation of isolated species by either impurity or host ions. The occurrence of off-center displacements in…
The optical properties of liquid crystals serve as the basis for display, diagnostic, and sensing technologies. Such properties are generally controlled by relying on electric fields. In this work, we investigate the effects of microfluidic…
The homotopy theory of topological defects is a powerful tool for organizing and unifying many ideas across a broad range of physical systems. Recently, experimental progress has been made in controlling and measuring colloidal inclusions…
We present nonlinear dynamic equations for nematic and smectic $A$ liquid crystals in the presence of an alternating electric field and explain their derivation in detail. The local electric field acting in any liquid-crystalline system is…
We analyze stability of the planar orientational structure in a nematic liquid crystal (NLC) cell with planar anchoring conditions at both substrates. Specifically, we study the instabilities of the ground state caused by surface elasticity…
Ferroelectric nematic liquid crystals are formed by achiral molecules with large dipole moments. Its three-dimensional orientational order is universally described as unidirectionally polar. We demonstrate that the ground state of…
Recent experiments have found that a mechanically distorted blue phase can exhibit a primary linear electro-optic (Pockels) effect [F. Castles \textit{et al}. Nature Mater. \textbf{13}, 817 (2014)]. Here it is shown that flexoelectricity…
In linear elasticity, a fourth order elasticity (stiffness) tensor of 21 independent components completely describes deformation properties of a material. Due to Voigt, this tensor is conventionally represented by a $6\times 6$ symmetric…
Disclinations lines play a key role in many physical processes, from the fracture of materials to the formation of the early universe. Achieving versatile control over disclinations is key to developing novel electro-optical devices,…
Motivated by recent experimental observations [U. Delabre et al, Langmuir 24, 3998, 2008] we reconsider an instability of ultrathin nematic films, spread on liquid substrates. Within a continuum elastic theory of liquid crystals, in the…
Polar nematic liquid crystals are new classes of condensed-matter states where the inversion symmetry common to the traditional apolar nematics is broken. Establishing theoretical descriptions for the novel phase states is an urgent task.…
The mechanical properties of crystals on curved substrates mix elastic, geometric and topological degrees of freedom. In order to elucidate the properties of such crystals we formulate the low-energy effective action that combines metric…
The flow of a liquid crystal around a particle does not only depend on its shape and the viscosity coefficients but also on the direction of the molecules. We studied the resulting drag force on a sphere moving in a nematic liquid crystal…
The evaporation of a droplet induces variety of ordered patterns near the contact line between the droplet and a substrate. This pattern formation involves both the behavior of colloidal suspensions and interactions between a droplet and a…
Long-range e.g. Coulomb-like interactions for (quantized) topological charges are observed experimentally in liquid crystals, bringing open question this article is exploring: how far can we take this resemblance with particle physics?…