Related papers: Nematic liquid crystals in a rectangular confineme…
We analyze single-core and split-core defect structures in nematic liquid crystals within the Landau-de Gennes framework by studying minimizers of the associated energy functional. A bifurcation occurs at a critical temperature threshold,…
Substrates which are chemically or topographically patterned induce a variety of liquid crystal textures. The response of the liquid crystal to competing surface orientations, typical of patterned substrates, is determined by the anisotropy…
We apply a recently developed technique to determine adapted coordinates for the sixth degree Landau-deGennes potential, in which the potential is specially simple, to analyze the possibility of a direct transition between the fully…
Motivated by recent experiments on the rod-like virus bacteriophage fd, confined to circular and annular domains, we present a theoretical study of structural transitions in these geometries. Using the continuum theory of nematic liquid…
Disclination lines in three-dimensional nematic liquid crystals generically form closed loops whose topology is classified by homotopy theory. While this classification successfully captures global topological features, it does not encode…
The properties of liquid crystals can be modelled using an order parameter which describes the variability of the local orientation of rod-like molecules. Defects in the director field can arise due to external factors such as applied…
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 $s$,…
We present a theoretical study of the director fields and energetics of nematic liquid crystal shells with two pairs of surface defects. The pairs of defects can undergo abrupt transitions between a configuration of maximum separation to at…
Mono-layers of stearic and behenic acids and mixtures of them in different proportions, deposited with the Langmuir-Blodgett technique, were used to study the alignment and the alignment dynamics in nematic liquid crystal cells. A…
We study the weak anchoring condition for nematic liquid crystals in the context of the Landau-De Gennes model. We restrict our attention to two dimensional samples and to nematic director fields lying in the plane, for which the Landau-De…
The assembly of colloids in nematic liquid crystals via topological defects has been extensively studied for spherical particles, and investigations of other colloid shapes have revealed a wide array of new assembly behaviors. We show,…
The translation and shape deformations of a passive viscous Newtonian droplet immersed in an active nematic liquid crystal under circular confinement are analyzed using a linear stability analysis. We focus on the case of a sharply aligned…
Strong anchoring boundary conditions are conventionally modelled by imposing Dirichlet conditions on the order parameter in Landau-de Gennes theory, neglecting the finite surface energy of realistic anchoring. This work revisits the strong…
Motivated by recent studies of bifurcations in liquid crystals cells [1,2] we consider a nonlinear pendulum ordinary differential equation in the bounded interval $(-L, L)$ with non-homogeneous mixed boundary conditions (Dirichlet an one…
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…
Present work is a theoretical study on the stability of the thermotropic biaxial nematic liquid crystal phase in model systems. Its main aim is to present the phase diagrams of spatially uniform liquid mesophases and to identify the…
The biaxial phase in nematic liquid crystals has been elusive for several decades after its prediction in the 1970s. A recent experimental breakthrough was achieved by Liu et al. [PNAS 113, 10479 (2016)] in a liquid crystalline medium with…
We study nematic liquid crystal configurations in confined geometries within the continuum Landau--De Gennes theory. These nematic configurations are mathematically described by symmetric, traceless two-tensor fields, known as…
We study a class of symmetric critical points in a variational $2D$ Landau - de Gennes model where the state of nematic liquid crystals is described by symmetric traceless $3\times 3$ matrices. These critical points play the role of…