Related papers: A Moving Mesh Method for Modelling Defects in Nema…
Chiral nematic liquid crystals exhibit both a helical planar ground state with uniform twist and a metastable defect-rich focal conic texture, and can be switched between the two microstructures via application of transient voltage pulses.…
We consider the Beris-Edwards system modelling incompressible liquid crystal flows of nematic type. This couples a Navier-Stokes system for the fluid velocity with a parabolic reaction-convection-diffusion equation for the Q-tensors…
This paper investigates nematic liquid crystals in three-dimensional curved space, and determines which director deformation modes are compatible with each possible type of non-Euclidean geometry. Previous work by Sethna et al. showed that…
Numerical simulations based on radial basis functions have been developed for systems with complex geometries and have been successfully applied across various fields, including seismology, coastal hydrodynamics, and biology. However,…
From incompressible flows to electrostatics, harmonic functions can provide solutions to many two-dimensional problems and, similarly, the director field of a planar nematic can be determined using complex analysis. We derive a closed-form…
Nematic liquid crystals confined to geometrically as well as chemically patterned substrate on one end and a flat substrate with strong anchoring on the other is studied using non-Boltzmann Monte Carlo methods. We observe significant…
Liquid crystals inevitably possess topological defect excitations generated through boundary conditions, applied fields or in quenches to the ordered phase. In equilibrium pairs of defects coarsen and annihilate as the uniform ground state…
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…
A nematic liquid crystal (NLC) layer with the anisotropy axis modulated at a fixed rate q in the transverse direction is considered. If the layer locally constitutes a half-wave plate, then the thin-screen approximation predicts 100%…
In culture migrating and interacting amoeboid cells can form nematic liquid crystal phases. A polar nematic liquid crystal is formed if the interaction has a polar symmetry. One type of white blood cells (granulocytes) form clusters where…
Topological defects in systems with liquid-crystalline order are crucial in determining their large-scale properties. In active systems, they are known to have properties impossible at equilibrium: for example, $+1/2$ defects in…
This letter presents a closed-form integral-equation formulation that models the director tilting in nematic liquid crystals. The proposed formulation is computationally efficient compared to numerical methods and provides a physical…
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.…
The influence of controlable parameters like temperature and wavelength on the trajectories of light in a nematic liquid crystal with topological defects is studied through a geometric model. The model incorporates phenomenological details…
The present contribution investigates the well-posedness of a PDE system describing the evolution of a nematic liquid crystal flow under kinematic transports for molecules of different shapes. More in particular, the evolution of the {\em…
Recent theoretical research has developed a general framework to understand director deformations and modulated phases in nematic liquid crystals. In this framework, there are four fundamental director deformation modes: twist, bend, splay,…
We examine the equilibrium configurations of a nematic liquid crystal with an immersed body in two-dimensions. A complex variables formulation provides a means for finding analytical solutions in the case of strong anchoring. Local…
We study a nanosecond electro-optic response of a nematic liquid crystal in a geometry where an applied electric field $\textbf{E}$ modifies the tensor order parameter but does not change the orientation of the optic axis (director…
One objective of active matter science is to unveil principles by which chaotic microscale dynamics could be transformed into useful work. A nematic liquid crystal environment offers a number of possibilities, one of which is a directional…
In this paper, we investigate the Cauchy problem for the incompressible nematic liquid crystal flows in three-dimensional whole space. First of all, we establish the global existence of solution by energy method under assumption of small…