Related papers: Saturn ring defect around a spherical particle imm…
Bound states of the Hamiltonian describing a quantum particle living on three dimensional straight strip of width $d$ are investigated. We impose the Neumann boundary condition on the two concentric windows of the radii $a$ and $ b$ located…
We present a theoretical study of the energetics of thin nematic shells with two charge one-half defects and one charge-one defect. We determine the optimal arrangement: the defects are located on a great circle at the vertices of an…
Topological defects -- locations of local mismatch of order -- are a universal concept playing important roles in diverse systems studied in physics and beyond, including the universe, various condensed matter systems, and recently, even…
We study the organization of topological defects in a system of nematogens confined to the two-dimensional sphere (S^2). We first perform Monte Carlo simulations of a fluid system of hard rods (spherocylinders) living in the tangent plane…
Recently, it was observed that water droplets suspended in a nematic liquid crystal form linear chains (Poulin et al., Science 275, 1770 (1997)). The chaining occurs, e.g., in a large nematic drop with homeotropic boundary conditions at all…
We study the Dirichlet problem for the semi--linear partial differential equations ${\rm div}\,(A\nabla u)=f(u)$ in simply connected domains $D$ of the complex plane $\mathbb C$ with continuous boundary data. We prove the existence of the…
The emergence of nematic order on deformable closed surfaces plays a pivotal role in the morphogenesis of active biological matter, such as the regeneration of Hydra. In this work, we present a continuum model that couples the…
We consider the interaction of a nonlinear Schrodinger soliton with a localized (point) defect in the medium through which it travels. Using numerical simulations, we find parameter regimes under which the soliton may be reflected,…
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…
We consider the evolution in full general relativity of a family of linearly unstable isolated spherical neutron stars under the effects of very small, perturbations as induced by the truncation error. Using a simple ideal-fluid equation of…
Topological defects can appear whenever there is some type of ordering. Its ubiquity in nature has been the subject of several studies, from early Universe to condensed matter. In this work, we investigated the annihilation dynamics of…
We study $k$-radially symmetric solutions corresponding to topological defects of charge $\frac{k}{2}$ for integer $k \neq 0$ in the Landau-de Gennes model describing liquid crystals in two-dimensional domains. We show that the solutions…
The aim of this article is twofold. First, in the large-body limit and when the temperature is below the nematic-isotropic transition threshold, we verify that the $\mathbb{S}^2$-valued energy-minimizing harmonic map on a bounded smooth…
Starting from a continuum theory of defects, that is the analogous to three-dimensional Einstein-Cartan-Sciama-Kibble gravity, we consider a charged particle with spin 1/2 propagating in a uniform magnetic field coincident with a wedge…
The problem of heterogeneous nucleation of second-phase in alloys in the vicinity of elastic defects is considered. The defect can be a dislocation line or a crack tip residing in a crystalline solid. We use the Ginzburg-Landau equation to…
Saturn's rings are composed of icy grains, most in the mm to m size ranges, undergoing several collisions per orbit. Their collective behaviour generates a remarkable array of structure over many orders of magnitude, much of it not well…
In the Landau-de Gennes theory on nematic liquid crystals, the well-known Landau-de Gennes energy depends on four elastic constants; $L_1$, $L_2$, $L_3$, $L_4$. For the general case of $L_4\neq 0$, Ball-Majumdar \cite {BM} found an example…
We consider a four-elastic-constant Landau-de Gennes energy characterizing nematic liquid crystal configurations described using the $Q$-tensor formalism. The energy contains a cubic term and is unbounded from below. We study dynamical…
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…
The stationary states of nonlinear Schr{\"o}dinger equation on a ring with a defect is numerically analyzed. Unconventional connection conditions are imposed on the point defect, and it is shown that the system displays energy level…