Fermi-Bose Transmutation for Stringlike Excitations of Maxwell-Higgs Systems

We show that a closed Nielsen-Olesen string in presence of a point scalar source exhibits the phenomenon of Fermi-Bose transmutation. This provides physical support to previous claims about transmutation between bosonic and fermionic one-dimensional structures in (3+1) dimensions. In order to render the computations mathematically rigorous we have resorted to an Euclidean lattice regularization.Comment: 9 pages, LATEX fil

Схема расщепления для трехмерной задачи теплопроводности

В статье исследована схема расщепления для трехмерного уравнения теплопроводности, сводящаяся к трехточечным прогонкам. Проведена численная реализация схемы и показана практическая применимость. Численная реализация схемы, стабилизирующей поправки, и сравнение её со схемой расщепления показали практическую эффективность предложенного алгоритма. Результаты расчетов приведены в таблице и дан анализ

Modeling of a Static Incompressible Medium

In the article mathematical modeling of the solution of the static Stokes problem is considered by solving the static problem of the theory of elasticity, with Hooke’s law. We obtain estimates for the proximity of solutions of these problems under asymptotics, namely, when λ →∞, in this case the Poisson coefficient tends to 0,5, which corresponds to an incompressible medium. Further, it was proved that the estimate of the proximity of the solutions of the problems considered as unimprovable in order of 1/λ. This allows us to use previously differential schemes for the static problem of the theory of elasticity, as an approximate, it is obtained a method for solving the static Stokes problem on a sequence of grids

The Role of Vortex Strings in the Non-Compact Lattice Abelian Higgs Model

The non-compact lattice version of the Abelian Higgs model is studied in terms of its topological excitations. The Villain form of the partition function is represented as a sum over world-sheets of gauge-invariant ``vortex'' strings. The phase transition of the system is then related to the density of these excitations. Through Monte Carlo simulations the density of the vortex sheets is shown to be a good order parameter for the system. The vortex density essentially vanishes in the Higgs phase, and the Coulomb phase consists of a single vortex condensate.Comment: 11 pages LaTeX2e, 4 Postscript figures, uses epsf.sty, references adde

Two-dimensional thermo-viscoelastic waves in layered media

Dynamic problems of deformation of solids have been the subject of numerous studies in the CIS and abroad. The rejection of a number of simplifying assumptions made in the cited and other published works leads to the need for further refinement and improvement of mechanical and mathematical models describing the kinematics and stress state of both the drummer and the barrier. Further, the axisymmetric collision of a cylindrical indenter with an obstacle in the form of a package of isotropic plates containing free cavities and rigid inclusions is numerically investigated within the framework of the coupled theory of thermoviscoelasticity. Various formulations of the problems of the theory of elasticity and thermo - viscoelasticity are possible. However, the used formulation in velocities and stresses is one of the most universal, since it allows solving the main boundary value problems (including mixed ones) by a uniform way. The paper gives a grid - characteristic scheme and its convergence. In accordance with the theory of A.A. Samarskii, the stability in the energy norm of the grid problem is proved

Cosmic Strings on the Lattice

We develop a formalism for the quantization of topologically stable excitations in the 4-dimensional abelian lattice gauge theory. The excitations are global and local (Abrikosov-Nielsen-Olesen) strings and monopoles. The operators of creation and annihilation of string states are constructed; the string Green functions are represented as a path integral over random surfaces. Topological excitations play an important role in the early universe. In the broken symmetry phase of the $U(1)$ spin model, closed global cosmic strings arise, while in the Higgs phase of the noncompact gauge-Higgs model, local cosmic strings are present. The compact gauge-Higgs model also involves monopoles. Then the strings can break if their ends are capped by monopoles. The topology of the Euclidean string world sheets are studied by numerical simulations.Comment: 4 pages LaTex (espcrc2.sty), LATTICE'92 contribution, ITEP(1992

Approaching of the solution of a static compressible medium to the solution of an incompressible medium

A well - known analogy of the flow of viscous incompressible fluid and incompressible elastic medium. According to this analogy, the solution of the equations of the elasticity theory with the Poisson’s ratio v = 0, 5 and for any fixed shear modulus µ can be interpreted as a motion of a viscous incompressible fluid with viscosity µ. Thus, we can consider the usual static linear elasticity task with Hooke’s law at λ → ∞, as a mathematical model of approaching to incompressible medium. In this paper, we obtained the asymptotic λ → ∞. Estimation of the proximity of the solution of an elastic static problem with Hooke’s law to the solution of incompressible medium (Stokes problem). The final estimate allows to use well - known difference schemes and algorithms for an elastic compressible medium to solve incompressible medium. In this paper, an estimate of the proximity of the solutions of these problems is proved at λ → ∞, i.e. u→uH λ→∞ λ div u→-p λ→∞ σ→σH λ→∞. To substantiate this fact in [1-3], various methods for the first boundary value problem were investigated. For the static problem of the theory of elasticity, there is currently a whole series of papers devoted to numerical implementation using difference schemes. In paper [4], the estimate O(λ-α) where k = 0,5 was obtained, in the proposed paper the estimate O(λ-1), and in further work we will show that this estimate is best possible in order

Analysis of Treatment Results of the Thoracic Part of Oesophageal Cancer

AIM: This study aims to evaluate the methods of treatment of the thoracic part of oesophagal cancer and to predict the results of treatment depending on the factors of the prognosis. MATERIALS AND METHODS: The results of treatment of 366 patients with cancer of the thoracic part of the oesophagus for 10 years (2007-2016) by the department of thoracic oncology of the Karaganda oncological dispensary were studied. RESULTS: The overall five-year survival rate, regardless of the method of treatment, was only 8.72% (28 of 321), and in the 6-10 year period 8.41% (27 of 321) lived, p < 0.05. Analysis of the overall survival of patients with cancer of the thoracic part of oesophagus showed that the method of treatment does not have a significant effect on life expectancy. A multivariate analysis of 19 grades that affect the prognosis of the disease was carried out. CONCLUSION: Radical type of treatment of the middle and lower thoracic oesophagus is surgical, in which the median of cumulative survival is 19 months. Traditional radiotherapy should be used in a limited way, as it is palliative, with a median survival of no more than 9 months. The leading factor in the prognosis for thoracic part of oesophagal cancer is the presence of regional metastases, on which the choice of method of treatment depends

Numerical solution of a problem on bending oscillation of a rod

In article considered the problem of curved rod fluctuation with Jungs module. Shown the civility of the problem formulation. For solution used integro - interpolation method. Constructed implicit differential scheme, which realized by five - point sweep method. Conducted numerical calculations showed coincidence of theoretical calculation values of solution. Calculations conducted on the system of computer algebra Wolfram Mathematica. Results of calculations are given for two cases of fixing ends of the rod: both ends are fixed and one end is fixed other is free

Matter Fields in the Lagrangian Loop Representation: Scalar QED

We present the extension of the Lagrangian loop gauge invariant representation in such a way to include matter fields. The partition function of lattice compact U(1)-Higgs model is expressed as a sum over closed as much as open surfaces. We have simulated numerically the loop action equivalent to the Villain form of the action and mapped out the beta-gamma phase diagram of this model.Comment: 10 pages, LaTe