Related papers: A Moving Mesh Method for Modelling Defects in Nema…
Achieving control and tunability of lyotropic materials has been a long-standing goal of liquid crystal research. Here we show that the elasticity of a liquid crystal system consisting of a dense suspension of semiflexible biopolymers can…
This is a study of certain finite element methods designed for convection-dominated, time-dependent partial differential equations. Specifically, we analyze high order space-time tensor product finite element discretizations, used in a…
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…
In this paper we study a mathematical model describing the movement of a colloidal particle in a fixed, bounded three dimensional container filled with a nematic liquid crystal fluid. The motion of the fluid is governed by the Beris-Edwards…
This chapter is about the modeling of nematic liquid crystals (LCs) and their numerical simulation. We begin with an overview of the basic physics of LCs and discuss some of their many applications. Next, we delve into the modeling…
Engineering synthetic materials that mimic the remarkable complexity of living organisms is a fundamental challenge in science and technology. We study the spatiotemporal patterns that emerge when an active nematicfilm of microtubules and…
An adaptive moving mesh finite element method is studied for the numerical solution of the porous medium equation with and without variable exponents and absorption. The method is based on the so-called moving mesh partial differential…
Stabilizing defects in liquid-crystal systems is crucial for many physical processes and applications ranging from functionalizing liquid-crystal textures to recently reported command of chaotic behaviors of active matters. In this work, we…
Emerging technologies based on liquid crystal (LC) materials increasingly leverage the presence of nanoscale defects, unlike the canonical application of LCs -- LC displays. The inherent nanoscale characteristics of LC defects present both…
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…
There is now growing evidence of the emergence and biological functionality of liquid crystal features, including nematic order and topological defects, in cellular tissues. However, how such features that intrinsically rely on particle…
Phase field crystal (PFC) models constitute central tools for a microscopic understanding of the dynamics of complex systems in soft matter physics. They have found widespread application in the modeling of the uniaxial orientational…
An important ingredient of any moving-mesh method for fluid-structure interaction (FSI) problems is the mesh deformation technique (MDT) used to adapt the computational mesh in the moving fluid domain. An ideal technique is computationally…
An individual defect in a nematic liquid crystal moves not only in response to its interaction with other defects but also in response to an external field. We analyze the motion of a wedge disclination in the presence of an applied field…
Using Monte Carlo simulations of the Lebwohl--Lasher model we study the director ordering in a nematic cell where the top and bottom surfaces are patterned with a lattice of $\pm 1$ point topological defects of lattice spacing $a$. We find…
A nematic membrane is a sheet with embedded orientational order, which can occur in biological cells, liquid crystal films, manufactured materials, and other soft matter systems. By formulating the free energy of nematic films using tensor…
Stability is an important and fruitful avenue of research for liquid crystal elastomers. At constant temperature, upon stretching, the homogeneous state of a nematic body becomes unstable, and alternating shear stripes develop at very low…
We present a novel, self-consistent and robust theoretical model to investigate elastic interactions between topological defects in liquid crystal shells. Accounting for the non-concentric nature of the shell in a simple manner, we are able…
A moving mesh finite difference method based on the moving mesh partial differential equation is proposed for the numerical solution of the 2T model for multi-material, non-equilibrium radiation diffusion equations. The model involves…
Active fluids, such as cytoskeletal filaments, bacterial colonies and epithelial cell layers, exhibit distinctive orientational coherence, often characterized by nematic order and topological defects. By contrast, little is known about…