Related papers: Function spaces for liquid crystals
We use density--functional theory to study the structure of two-dimensional defects inside a circular nematic nanocavity. The density, nematic order parameter, and director fields, as well as the defect core energy and core radius, are…
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,…
A generalized notion of a nonlocal tensor order parameter is introduced within the framework of the phenomenological approach. This parameter has the form of a traceless tensor correlation function or a tensor integral operator. Based on…
We introduce a new class of non-isothermal models describing the evolution of nematic liquid crystals and prove their consistency with the fundamental laws of classical Thermodynamics. The resulting system of equations captures all…
We consider a thin film limit of a Landau-de Gennes Q-tensor model. In the limiting process we observe a continuous transition where the normal and tangential parts of the Q-tensor decouple and various intrinsic and extrinsic contributions…
We review and compare recent work on the properties of fluctuating interfaces between nematic and isotropic liquid-crystalline phases. Molecular dynamics and Monte Carlo simulations have been carried out for systems of ellipsoids and hard…
We study the hydrodynamics of compressible flows of active liquid crystals in the Beris-Edwards hydrodynamics framework, using the Landau-de Gennes $Q$-tensor order parameter to describe liquid crystalline ordering. We prove the existence…
We study the coarsening dynamics of two and three dimensional biaxial nematic liquid crystals, using Langevin dynamics. Unlike previous work, we use a model with no a priori relationship among the three elastic constants associated with…
Electro-hydrodynamic phenomena in liquid crystals constitute an old but still very active research area. The reason is that these phenomena play the key role in various applications of liquid crystals and due to the general interest of…
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…
Based on static and dynamical density functional theory, a phase-field-crystal model is derived which involves both the translational density and the orientational degree of ordering as well as a local director field. The model exhibits…
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?…
The phenomenological Landau-de Gennes (LdG) model is a powerful continuum theory to describe the macroscopic state of nematic liquid crystals. However, it is invariably less accurate and less physically informed than the molecular-level…
In this work we propose a mathematical model that describes the orientation of ventricular cardiac fibers. These fibers are commonly computed as the normalized gradient of certain harmonic potentials, so our work consisted in finding the…
From the theory of topological defect formation proposed for the early universe, the so called Kibble mechanism, it follows that the density correlation functions of defects and anti-defects in a given system should be completely determined…
Thin solids often develop elastic instabilities and subsequently complex, multiscale deformation patterns. Revealing the organizing principles of this spatial complexity has ramifications for our understanding of morphogenetic processes in…
A fluid of hard right isosceles triangles was studied using an extension of Scaled-Particle Density-Functional Theory which includes the exact third virial coefficient. We show that the only orientationally ordered stable liquid-crystal…
We use the classical version of the density-functional theory in the weighted-density approximation to build up the entire phase diagram and the interface structure of a two-dimensional lattice-gas model which is known, from previous…
Using numerical and analytical calculations we study the structure of vacancies and interstitials in two-dimensional colloidal crystals. In particular, we compare the displacement fields of the defect obtained numerically with the…
We discuss a dynamical theory for nematic liquid crystals describing the stage of evolution in which the hydrodynamic fluid motion has already equilibrated and the subsequent evolution proceeds via diffusive motion of the orientational…