Related papers: Modeling and Computation of Liquid Crystals
Colloids are abundant in nature, science and technology, with examples ranging from milk to quantum dots and the "colloidal atom" paradigm. Similarly, liquid crystal ordering is important in contexts ranging from biological membranes to…
Liquid crystals are the prototype of the so-called soft condensed matter. In simple terms they are "structured liquids" that historically have received a lot of interest because they help to generate new concepts and knowledge in Physics,…
A review is given of some mathematical contributions, ideas and questions concerning liquid crystals.
Liquid crystals are phases of matter intermediate between crystals and liquids. Whereas classical liquid crystals have been known for a long time and are used in electro-optical displays, much less is known about their quantum counterparts.…
Liquid crystals are synthetic and biological viscoelastic anisotropic soft matter materials that combine liquid fluidity with crystal anisotropy and find use in optical devices, sensor/actuators, lubrication, super-fibers. Frequently…
These lecture notes discuss classical models of liquid crystals, and the different ways in which defects are described according to the different models.
The last decade has witnessed a rapid growth in understanding of the pivotal roles of mechanical stresses and physical forces in cell biology. As a result an integrated view of cell biology is evolving, where genetic and molecular features…
We use numerical simulation to examine the possibility of a reversible liquid-liquid transition in supercooled water and related systems. In particular, for two atomistic models of water, we have computed free energies as functions of…
We outline the main ideas behind the numerical modelling of soft-flowing crystals, with special attention to their application to microfluidic devices for the design of novel mesoscale porous materials.
Soft materials with a liquid component are an emerging paradigm in materials design. The incorporation of a liquid phase, such as water, liquid metals, or complex fluids, into solid materials imparts unique properties and characteristics…
The paper presents a teaching module about liquid crystals. Since liquid crystals are linked to everyday student experiences and are also a topic of a current scientific research, they are an excellent candidate of a modern topic to be…
This article investigates the interaction of nematic liquid crystals modeled by a simplified Ericksen-Leslie model with a rigid body. It is shown that this problem is locally strongly well-posed, and that it also admits a unique, global…
We outline the necessary background to understand the interaction of colloids in liquid crystals through boundary conditions and topology.
In contrast to the gaseous and the solid states, the liquid state does not have a simple model that could be developed into a quantitative theory. A central issue in the understanding of liquids is to estimate the energy state of liquids.…
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…
This is an expository introduction, for a general mathematics audience, to the modeling of the fluid/solid phase transition and in particular to complications created by the discovery of quasicrystals. One goal is to elucidate certain…
Liquid crystals are assemblies of rod-like molecules which self-organize to form mesophases, in-between ordinary liquids and anisotropic crystals. At each point, the molecules collectively orient themselves along a privileged direction,…
Liquid crystals in two dimensions undergo a first-order isotropic-to-quasi-nematic transition, provided the particle interactions are sufficiently ``sharp and narrow''. This implies phase coexistence between isotropic and quasi-nematic…
The bi-continuum model composed of two interpenetrating and dynamically coupled material continua is analysed as a simplified but relatively accurate way to describe some physical phenomena in crystalline solids. The essential novelty of…
Quantum spin liquids are an exciting playground for exotic physical phenomena and emergent many-body quantum states. The realization and discovery of quantum spin liquid candidate materials and associated phenomena lie at the intersection…