Related papers: Nonlinear Methods for Shape Optimization Problems …
We consider three-dimensional reshaping of a thin nematoelastic film upon nematic-isotropic transition in the field of a charge one topological defect, leading to either cone or anticone (d-cone) shells. The analysis is based on the…
This paper outlines an energy-minimization finite-element approach to the modeling of equilibrium configurations for nematic liquid crystals in the presence of internal and external electric fields. The method targets minimization of system…
Real-world applications of computational fluid dynamics often involve the evaluation of quantities of interest for several distinct geometries that define the computational domain or are embedded inside it. For example, design optimization…
Topological defects, such as disclination lines in nematic liquid crystals, are fundamental to many physical systems and applications. In this work, we study the behavior of nematic disclinations in thin parallel-plate geometries with…
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…
Optimization techniques play a crucial role in estimating parameters and state information for nonlinear systems. However, some critical aspects of these problems have received little attention in previous research. In this paper, we…
In general, standard necessary optimality conditions cannot be formulated in a straightforward manner for semi-smooth shape optimization problems. In this paper, we consider shape optimization problems constrained by variational…
We study the effects of elastic anisotropy on the Landau-de Gennes critical points for nematic liquid crystals, in a square domain. The elastic anisotropy is captured by a parameter, $L_2$, and the critical points are described by three…
We explore the use of the Gauss-Newton method for optimization in shape learning, including implicit neural surfaces and geometry-informed neural networks. The method addresses key challenges in shape learning, such as the ill-conditioning…
Given recipe of qualitative, kinetic modelling by geometric methods of three-dimensional dendritic crystals. Characteristic features of the perturbations appearing on the surface of a spherical body, leading to different scenarios of the…
In this experimental and theoretical study, we examine the equilibrium shapes of quasitwo-dimensional twist-bend nematic (Ntb) drops formed within a planarly aligned nematic layer of the liquid crystal CB7CB. Initially, at the setting point…
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 construct a phenomenological Landau-de Gennes theory for hard colloidal rods by performing an order parameter expansion of the chemical-potential dependent grand potential. By fitting the coefficients to known results of Onsager theory,…
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…
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 planar nematic equilibria on a two-dimensional annulus with strong and weak tangent anchoring, within the Oseen-Frank and Landau-de Gennes theories for nematic liquid crystals. We analyse the defect-free state in the Oseen-Frank…
The ordering matrix, which was originally introduced by de Gennes, is a well-known mathematical device for describing orientational order of biaxial nematic liquid crystal. In this paper we propose a new interpretation of the ordering…
We study the fluid-mediated approach of a deformable axisymmetric object towards a rigid substrate, focusing on how its shape influences contact formation. For low approach velocities and large Stokes numbers, we show that sharper profiles…
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…
The ability to manipulate polar entities with multiple external fields opens exciting possibilities for emerging functionalities and novel applications in spin systems, photonics, metamaterials, and soft matter. Liquid crystals (LCs),…