相关论文: Half-integer point defects in the $Q$-tensor theor…
This paper is devoted to the full system of incompressible liquid crystals, as modeled in the Q-tensor framework. The main purpose is to establish the uniqueness of weak solutions in a two dimensional setting, without imposing an extra…
This paper focuses on the analysis of a free energy functional, that models a dilute suspension of magnetic nanoparticles in a two-dimensional nematic well. The {\it first part} of the article is devoted to the asymptotic analysis of global…
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…
In this paper, we consider the Q-tensor model of nematic liquid crystals, which couples the Navier-Stokes equations with a parabolic-type equation describing the evolution of the directions of the anisotropic molecules, in the half-space.…
We study the global existence of weak solutions to a multi-dimensional simplified Ericksen-Leslie system for compressible flows of nematic liquid crystals with large initial energy in a bounded domain $\Omega\subset \mathbb{R}^N$, where N=2…
We consider a nematic liquid crystal occupying the exterior region in R^3 outside of a spherical particle, with radial strong anchoring. Within the context of the Landau-de Gennes theory, we study minimizers subject to a strong external…
We consider several types of quantum critical phenomena from finite-density gauge-gravity duality which to different degrees lie outside the Landau-Ginsburg-Wilson paradigm. These include: (1) a "bifurcating" critical point, for which the…
We present a novel framework for the study of disclinations in two-dimensional active nematic liquid crystals, and topological defects in general. The order tensor formalism is used to calculate exact multi-particle solutions of the…
In this paper we study qualitative properties of global minimizers of the Ginzburg-Landau energy which describes light-matter interaction in the theory of nematic liquid crystals near the Friedrichs transition. This model is depends on two…
Anisotropic fluids, such as nematic liquid crystals, can form non-spherical equilibrium shapes known as tactoids. Predicting the shape of these structures as a function of material parameters is challenging and paradigmatic of a broader…
In this work, we present three linear numerical schemes to model nematic liquid crystals using the Landau-de Gennes $\textbf{Q}$-tensor theory. The first scheme is based on using a truncation procedure of the energy, which allows for an…
In this paper, we consider a complex fluid modeling nematic liquid crystal flows, which is described by a system coupling Navier-Stokes equations with a parabolic Q-tensor system. We first prove the global existence of weak solutions in…
We study the hydrodynamics of compressible active nematic liquid crystals in a three-dimensional and bounded domain, with a nonlinear viscosity tensor and nonhomogeneous boundary data, in a Landau-de Gennes framework. We prove the existence…
Uniaxial nematic liquid crystals whose molecular orientation is subjected to a tangential anchoring on a curved surface offer a non trivial interplay between the geometry and the topology of the surface and the orientational degree of…
We discuss a 3D model describing the time evolution of nematic liquid crystals in the framework of Landau-de Gennes theory, where the natural physical constraints are enforced by a singular free energy bulk potential proposed by J.M. Ball…
This paper outlines an energy-minimization finite-element approach to the computational modeling of equilibrium configurations for nematic liquid crystals under free elastic effects. The method targets minimization of the system free energy…
We investigate minimizers defined on a bounded domain $\Omega$ in $\mathbb{R}^2$ for singular constrained energy functionals that include Ball and Majumdar's modification of the Landau-de Gennes Q-tensor model for nematic liquid crystals.…
Disclination configurations of a nematic liquid crystal are studied within a self-consistent molecular field theory. The theory is based on a tensor order parameter, and can accommodate anisotropic elastic energies without the known…
Based on the Kosterlitz-Thouless-Halperin-Nelson-Young (KTHNY) theory of two-dimensional melting and the analogy between Laughlin states and the two-dimensional one-component plasma (2DOCP), we investigate the possibility of liquid…
We explore a method for regulating 2+1D quantum critical points in which the ultra-violet cutoff is provided by the finite density of states of particles in a magnetic field, rather than by a lattice. Such Landau level quantization allows…