Related papers: Liquid crystals and their defects
Basic ideas and results which characterize quantum diffusion of defects in quantum crystals like solid helium as a new phenomenon are presented. Quantum effects in such media lead to a delocalization of point defects (vacancies, impurities…
Defects influence the properties and functionality of all crystalline materials. For instance, point defects participate in electronic (e.g. carrier generation and recombination) and optical (e.g. absorption and emission) processes critical…
We review some essential aspects of classically integrable systems. The detailed outline of the lectures consists of: 1. Introduction and motivation, with historical remarks; 2. Liouville theorem and action-angle variables, with examples…
Microscopic understanding of liquid properties is essential for advancing a wide range of applications from energy applications such as nuclear reactors and batteries to biomedical applications including drug delivery and microfluidics.…
Lecture notes for an introductory course in elementary particles.
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…
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…
In these lectures we review the constraints on particle physics models arising from cosmic defects. This includes constraints on theories where stable cosmic string loops, or vortons result. These can arise in supersymmetric theories. We…
We introduce a new theoretical model of simple fluid, whose interactions, defined in terms of the Voronoi cells of the configurations, are local and many-body. The resulting system is studied both theoretically and numerically. We show that…
Review of the author's data, partly still unpublished, on studying of liquid tellurium and cesium are given. No proofs indicating phase transitions in liquids were found. New developments in studying the liquid-liquid phase transition are…
We consider some extensions of Gamow's liquid drop model for an atomic nucleus. We present a review of the classical model and then we illustrate some recent developments on a nonlocal variant, where the perimeter term is replaced by the…
Quantum fluid (or hydrodynamic) models provide an attractive alternative for the modeling and simulation of the electron dynamics in nano-scale objects. Compared to more standard approaches, such as density functional theory or phase-space…
In liquid crystal elastomers, the orientational order of liquid crystals is coupled with elastic distortions of crosslinked polymer networks. Previous theoretical research has described these materials through two different approaches: a…
We review some recent results on the equilibrium shapes of charged liquid drops. We show that the natural variational model is ill-posed and how this can be overcome by either restricting the class of competitors or by adding penalizations…
This paper is devoted to a discussion of specific properties of invariants in the theory of forms.
Purely real space versions of the differential equations describing the kinematics of a dislocated crystalline medium are considered. The differential geometric structures associated with them are revealed.
Dark solitons and localized defect modes against periodic backgrounds are considered in arrays of waveguides with defocusing Kerr nonlinearity constituting a nonlinear lattice. Bright defect modes are supported by local increase of the…
Here we briefly discuss lattices in Euclidean spaces and spaces of lattices, which are basic objects that can be described in terms of matrices and are important settings in classical analysis.
An alternative Lagrangian definition of an integrable defect is provided and analyzed. The new approach is sufficiently broad to allow a description of defects within the Tzitzeica model, which was not possible in previous approaches, and…
Stable array of point defects was generated in nematic liquid crystal. Point defects with topological charge of +1 and -1 (hedgehogs) were generated in vertically aligned liquid crystal cell. The hedgehogs were arranged in square or…