Mathematical Structure of Relativistic Coulomb Integrals

We show that the diagonal matrix elements $,$ where $O$ $={1,\beta,i\mathbf{\alpha n}\beta}$ are the standard Dirac matrix operators and the angular brackets denote the quantum-mechanical average for the relativistic Coulomb problem, may be considered as difference analogs of the radial wave functions. Such structure provides an independent way of obtaining closed forms of these matrix elements by elementary methods of the theory of difference equations without explicit evaluation of the integrals. Three-term recurrence relations for each of these expectation values are derived as a by-product. Transformation formulas for the corresponding generalized hypergeometric series are discussed.Comment: 13 pages, no figure

Thermoconvective flow velocity in a high-speed magnetofluid seal after it has stopped

Convective flow is investigated in the high-speed (linear velocity of the shaft seal is more than 1 m/s) magnetofluid shaft seal after it has been stopped. Magnetic fluid is preliminarily heated due to viscous friction in the moving seal. After the shaft has been stopped, nonuniform heated fluid remains under the action of a high-gradient magnetic field. Numerical analysis has revealed that in this situation, intense thermomagnetic convection is initiated. The velocity of magnetic fluid depends on its viscosity. For the fluid with viscosity of 2 × 10 -4 m 2/s the maximum flow velocity within the volume of magnetic fluid with a characteristic size of 1 mm can attain a value of 10 m/s

Motion of vortices in ferromagnetic spin-1 BEC

The paper investigates dynamics of nonsingular vortices in a ferromagnetic spin-1 BEC, where spin and mass superfluidity coexist in the presence of uniaxial anisotropy (linear and quadratic Zeeman effect). The analysis is based on hydrodynamics following from the Gross-Pitaevskii theory. Cores of nonsingular vortices are skyrmions with charge, which is tuned by uniaxial anisotropy and can have any fractal value between 0 and 1. There are circulations of mass and spin currents around these vortices. The results are compared with the equation of vortex motion derived earlier in the Landau-Lifshitz-Gilbert theory for magnetic vortices in easy-plane ferromagnetic insulators. In the both cases the transverse gyrotropic force (analog of the Magnus force in superfluid and classical hydrodynamics) is proportional to the charge of skyrmions in vortex cores.Comment: 19 pages, 2 figures, to be published in the special issue of Fizika Nizkikh Temperatur dedicated to A.M.Kosevich. arXiv admin note: substantial text overlap with arXiv:1801.0109

Raising and lowering operators, factorization and differential/difference operators of hypergeometric type

Starting from Rodrigues formula we present a general construction of raising and lowering operators for orthogonal polynomials of continuous and discrete variable on uniform lattice. In order to have these operators mutually adjoint we introduce orthonormal functions with respect to the scalar product of unit weight. Using the Infeld-Hull factorization method, we generate from the raising and lowering operators the second order self-adjoint differential/difference operator of hypergeometric type.Comment: LaTeX, 24 pages, iopart style (late submission

Galactic Rotation Parameters from Data on Open Star Clusters

Currently available data on the field of velocities Vr, Vl, Vb for open star clusters are used to perform a kinematic analysis of various samples that differ by heliocentric distance, age, and membership in individual structures (the Orion, Carina--Sagittarius, and Perseus arms). Based on 375 clusters located within 5 kpc of the Sun with ages up to 1 Gyr, we have determined the Galactic rotation parameters Wo =-26.0+-0.3 km/s/kpc, W'o = 4.18+-0.17 km/s/kpc^2, W''o=-0.45+-0.06 km/s/kpc^3, the system contraction parameter K = -2.4+-0.1 km/s/kpc, and the parameters of the kinematic center Ro =7.4+-0.3 kpc and lo = 0+-1 degrees. The Galactocentric distance Ro in the model used has been found to depend significantly on the sample age. Thus, for example, it is 9.5+-0.7 kpc and 5.6+-0.3 kpc for the samples of young (50 Myr) clusters, respectively. Our study of the kinematics of young open star clusters in various spiral arms has shown that the kinematic parameters are similar to the parameters obtained from the entire sample for the Carina-Sagittarius and Perseus arms and differ significantly from them for the Orion arm. The contraction effect is shown to be typical of star clusters with various ages. It is most pronounced for clusters with a mean age of 100 Myr, with the contraction velocity being Kr = -4.3+-1.0 km/s.Comment: 14 pages, 4 figures, 2 table

Electrochemical Studies of Corrosion in Liquid Electrolytes for Energy Conversion Applications at Elevated Temperatures

Stainless steels (AISI 316, 321 and 347), high-nickel alloys (Hasteloy®C-276 and Inconel®625), tantalum, nickel, titanium, tungsten, molybdenum, niobium, platinum, and gold were tested for corrosion resistance in molten KH2PO4 (or KH2PO4-K2H2P2O7) as a promising electrolyte for the intermediate-temperature (200–400°C) water electrolysis. Pt, Ta, Nb, Ti, Inconel®625, and Ni demonstrated high corrosion resistance. Au and the rest of the tested materials were not corrosion resistant. It means that Ni, Ti and Inconel®625 may be used as relatively cheap construction materials for the intermediate-temperature water electrolyzer