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A (linear) nonsingular solution for the edge dislocation in the translational gauge theory of defects is presented. The stress function method is used and a modified stress function is obtained. All field quantities are globally defined and…
An alternative method to the topological instanton solution for deriving an expression for the topological charge is presented. This alternative method involves the use of relativistic quantum field theory and covariant electrodynamics. In…
A matrix method is formulated in a Lagrangian representation for the solution of the characteristic value problem governing modes of oscillation and instability in a collisionless stellar system. The underlying perturbation equations govern…
In this paper, a method of local perturbations, previously successfully applied to decompose the problem of elasticity in the system of connected thin rods and beams [Kolpakov and Andrianov, 2013], is used to study the asymptotic behaviour…
A circular twist disclination is a nontrivial example of a defect in an elastic continuum that causes large deformations. The minimal potential energy and the corresponding displacement field is calculated by solving the…
A class of metrics solving Einstein's equations with negative cosmological constant and representing rotating, topological black holes is presented. All such solutions are in the Petrov type-$D$ class, and can be obtained from the most…
The classical equations of motion of a charged particle in a spherically symmetric distribution of magnetic monopoles can be transformed into a system of linear equations, thereby providing a type of integrability. In the case of a single…
In recent times some interesting field theoretical descriptions of the statistical mechanics of entangling polymers have been proposed by various authors. In these approaches, a single test polymer fluctuating in a background of static…
We compute the second-order correction to the electronic dispersion relation of a free electron gas interacting with an effective electron-dislocation potential, derived from a modern quantized theory of dislocations. Our results…
A network of optical parametric oscillators is used to simulate classical Ising and XY spin chains. The collective nonlinear dynamics of this network, driven by quantum noise rather than thermal fluctuations, seeks out the Ising / XY ground…
Hard sphere systems are often used to model simple fluids. The configuration spaces of hard spheres in a three-dimensional torus modulo various symmetry groups are comparatively simple, and could provide valuable information about the…
The paper is devoted to the questions connected with the investigation of the S.P. Novikov problem of the description of the geometry of level lines of quasiperiodic functions on a plane with different numbers of quasiperiods. We consider…
Recently a perturbative theory has been constructed, starting from the Feynman rules of the nonlinear sigma model at the tree level in the presence of an external vector source coupled to the flat connection and of a scalar source coupled…
Smectic liquid crystals are charcterized by layers that have a preferred uniform spacing and vanishing curvature in their ground state. Dislocations in the smectics play an important role in phase nucleation, layer reorientation, and…
The ring configurations for classical two-dimensional atoms are calculated within the Thomson model and compared with the results from `exact' numerical simulations. The influence of the functional form of the confinement potential and the…
Topology plays a central role in classifying solitonic configurations in field theories, providing robustness and a nonperturbative label, the so-called topological charge $Q$. In soliton-fermion coupled systems, the relation between the…
A rapid algorithm is derived for the Helmholtz--Hodge decomposition on the surface of the sphere in spherical coordinates. The algorithm uncouples modes of spherical harmonics with different absolute order, writes the conversion as…
We consider the $N$-vortex problem on the sphere assuming that all vortices have equal strength. We develop a theoretical framework to analyse solutions of the equations of motion with prescribed symmetries. Our construction relies on the…
In this work we discuss about the problem of an electrically charged particle placed on the symmetry axis of an electrically charged ring in a quantum viewpoint. This problem should be an expanded version of the usual quantum ring and…
The optical properties of a multilayer system of dielectric media with arbitrary $N$ layers is investigated. Each layer is one of two dielectric media, with thickness one-quarter the wavelength of light in that medium, corresponding to a…