Electrically neutral Dirac particles in the presence of external fields: exact solutions

In the present article we present exact solutions of the Dirac equation for electric neutral particles with anomalous electric and magnetic moments. Using the algebraic method of separation of variables, the Dirac equation is separated in cartesian, cylindrical and spherical coordinates, and exact solutions are obtained in terms of special functions.Comment: 20pp, IVIC-CFLE-93/02 (this is a version without Tex problems, the first version was corrupted

Robust novel high‐order accurate numerical methods for singularly perturbed convection‐diffusion problems

For singularly perturbed boundary value problems, numerical methods convergent ϵ‐uniformly have the low accuracy. So, for parabolic convection‐diffusion problem the order of convergence does not exceed one even if the problem data are sufficiently smooth. However, already for piecewise smooth initial data this order is not higher than 1/2. For problems of such type, using newly developed methods such as the method based on the asymptotic expansion technique and the method of the additive splitting of singularities, we construct ϵ‐uniformly convergent schemes with improved order of accuracy. Straipsnyje nagrinejami nedidelio tikslumo ϵ‐tolygiai konvertuojantys skaitmeniniai metodai, singuliariai sutrikdytiems kraštiniams uždaviniams. Paraboliniam konvekcijos‐difuzijos uždaviniui konvergavimo eile neviršija vienos antrosios, jeigu uždavinio duomenys yra pakankamai glodūs. Tačiau trūkiems pradiniams duomenims eile yra ne aukštesne už 2−1. Šio tipo uždaviniams, naudojant naujai išvestus metodus, darbe sukonstruotos ϵ‐tolygiai konvertuojančios schemos aukštesniu tikslumu. First Published Online: 14 Oct 201

Field induced evolution of regular and random 2D domain structures and shape of isolated domains in LiNbO₃ and LiTaO₃

The shapes of isolated domains produced by application of the uniform external electric field in different experimental conditions were investigated experimentally in single crystalline lithium niobate LiNbO3 and lithium tantalate LiTaO3. The study of the domain kinetics by computer simulation and experimentally by polarization reversal of the model structure using two-dimensional regular electrode pattern confirms applicability of the kinetic approach to explanation of the experimentally observed evolution of the domain shape and geometry of the domain structure. It has been shown that the fast domain walls strictly oriented along X directions appear after domain merging

An efficient numerical scheme for 1D parabolic singularly perturbed problems with an interior and boundary layers

In this paper we consider a 1D parabolic singularly perturbed reaction-convection-diffusion problem, which has a small parameter in both the diffusion term (multiplied by the parameter e2) and the convection term (multiplied by the parameter µ) in the differential equation (e¿(0, 1], µ¿0, 1], µ=e). Moreover, the convective term degenerates inside the spatial domain, and also the source term has a discontinuity of first kind on the degeneration line. In general, for sufficiently small values of the diffusion and the convection parameters, the exact solution exhibits an interior layer in a neighborhood of the interior degeneration point and also a boundary layer in a neighborhood of both end points of the spatial domain. We study the asymptotic behavior of the exact solution with respect to both parameters and we construct a monotone finite difference scheme, which combines the implicit Euler method, defined on a uniform mesh, to discretize in time, together with the classical upwind finite difference scheme, defined on an appropriate nonuniform mesh of Shishkin type, to discretize in space. The numerical scheme converges in the maximum norm uniformly in e and µ, having first order in time and almost first order in space. Illustrative numerical results corroborating in practice the theoretical results are showed

Structure of 5-nitro-2-tosylaminobenzaldehyde di(morpholin-4-yl)aminal Complex with Carbon Tetrachloride

The 5-nitro-2-tosylaminobenzaldehyde di(morpholin-4-yl)aminal forms a stable complex with carbon tetrachloride in the crystal phase. X-ray structural study of this complex indicates an essentially shortened intermolecular contact of 2.89 Å between the oxygen atom of the nitro group and one of the chlorine atom of the CCI4 molecule. Quantum-chemical calculations by semiempirical AMI method showed that the formation of such complex did not cause considerable decrease of system energy or change of charge distribution in molecules. It was supposed that this associate has van der Waals character

Vacuum effects in an asymptotically uniformly accelerated frame with a constant magnetic field

In the present article we solve the Dirac-Pauli and Klein Gordon equations in an asymptotically uniformly accelerated frame when a constant magnetic field is present. We compute, via the Bogoliubov coefficients, the density of scalar and spin 1/2 particles created. We discuss the role played by the magnetic field and the thermal character of the spectrum.Comment: 17 pages. RevTe

Acid Polishing of Lead Crystal Glass

The industrial partner manufactures high quality lead crystal glassware. The cutting of decorative features in the glass damages the surface and the cuts are optically opaque; to restore transparency, the glass is polished in a solution of hydrofluoric (HF) and sulphuric acid (H2 SO4 .) The polishing process comprises three stages: 1. immersion in a polishing tank containing acid; 2. rinsing in a tank containing water; and 3. settlement of the solid reaction products in a settlement tank. The manufacturer hopes to optimise its polishing process to • minimise the health/environmental impact of the process; • maximise throughput; • maintain the sharpness of the cut edges while still polishing to an acceptable level of transparency. The study group was asked to focus on modelling three aspects of the process: • the chemical reactions involved in the etching at the glass-acid solution interface; • the removal of reaction products in the settlement tank; • flow within the polishing tank

Social Portrait of the Ural Private Entrepreneur of the NEP Period in Modern Historiography

The article examines the social portrait of the Ural NEPman through the historiographic aspect, analyzes the works of modern Russian historians, which examine the social status, demographic portrait, social role and other social characteristics of the Ural private entrepreneurs of the NEP era.В статье рассматривается социальный портрет уральского нэпмана через историографический аспект, анализируются работы современных российских историков, в которых рассматриваются социальный статус, демографический портрет, социальная роль и другие социальные характеристики уральских частных предпринимателей эпохи НЭПа