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

Arbitrary l-state solutions of the rotating Morse potential by the asymptotic iteration method

For non-zero $\ell$ values, we present an analytical solution of the radial Schr\"{o}dinger equation for the rotating Morse potential using the Pekeris approximation within the framework of the Asymptotic Iteration Method. The bound state energy eigenvalues and corresponding wave functions are obtained for a number of diatomic molecules and the results are compared with the findings of the super-symmetry, the hypervirial perturbation, the Nikiforov-Uvarov, the variational, the shifted 1/N and the modified shifted 1/N expansion methods.Comment: 15 pages with 1 eps figure. accepted for publication in Journal of Physics A: Mathematical and Genera

Orthogonal polynomials of discrete variable and Lie algebras of complex size matrices

We give a uniform interpretation of the classical continuous Chebyshev's and Hahn's orthogonal polynomials of discrete variable in terms of Feigin's Lie algebra gl(N), where N is any complex number. One can similarly interpret Chebyshev's and Hahn's q-polynomials and introduce orthogonal polynomials corresponding to Lie superlagebras. We also describe the real forms of gl(N), quasi-finite modules over gl(N), and conditions for unitarity of the quasi-finite modules. Analogs of tensors over gl(N) are also introduced.Comment: 25 pages, LaTe

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

Landau (\Gamma,\chi)-automorphic functions on \mathbb{C}^n of magnitude \nu

We investigate the spectral theory of the invariant Landau Hamiltonian \La^\nu acting on the space ${\mathcal{F}}^\nu_{\Gamma,\chi}$ of $(\Gamma,\chi)$-automotphic functions on \C^n, for given real number $\nu>0$, lattice $\Gamma$ of \C^n and a map $\chi:\Gamma\to U(1)$ such that the triplet $(\nu,\Gamma,\chi)$ satisfies a Riemann-Dirac quantization type condition. More precisely, we show that the eigenspace {\mathcal{E}}^\nu_{\Gamma,\chi}(\lambda)=\set{f\in {\mathcal{F}}^\nu_{\Gamma,\chi}; \La^\nu f = \nu(2\lambda+n) f}; \lambda\in\C, is non trivial if and only if $\lambda=l=0,1,2, ...$. In such case, ${\mathcal{E}}^\nu_{\Gamma,\chi}(l)$ is a finite dimensional vector space whose the dimension is given explicitly. We show also that the eigenspace ${\mathcal{E}}^\nu_{\Gamma,\chi}(0)$ associated to the lowest Landau level of \La^\nu is isomorphic to the space, {\mathcal{O}}^\nu_{\Gamma,\chi}(\C^n), of holomorphic functions on \C^n satisfying g(z+\gamma) = \chi(\gamma) e^{\frac \nu 2 |\gamma|^2+\nu\scal{z,\gamma}}g(z), \eqno{(*)} that we can realize also as the null space of the differential operator $\sum\limits_{j=1}\limits^n(\frac{-\partial^2}{\partial z_j\partial \bar z_j} + \nu \bar z_j \frac{\partial}{\partial \bar z_j})$ acting on $\mathcal C^\infty$ functions on \C^n satisfying $(*)$.Comment: 20 pages. Minor corrections. Scheduled to appear in issue 8 (2008) of "Journal of Mathematical Physics

The rotating Morse potential model for diatomic molecules in the tridiagonal J-matrix representation: I. Bound states

This is the first in a series of articles in which we study the rotating Morse potential model for diatomic molecules in the tridiagonal J-matrix representation. Here, we compute the bound states energy spectrum by diagonalizing the finite dimensional Hamiltonian matrix of H2, LiH, HCl and CO molecules for arbitrary angular momentum. The calculation was performed using the J-matrix basis that supports a tridiagonal matrix representation for the reference Hamiltonian. Our results for these diatomic molecules have been compared with available numerical data satisfactorily. The proposed method is handy, very efficient, and it enhances accuracy by combining analytic power with a convergent and stable numerical technique.Comment: 18 Pages, 6 Tables, 4 Figure

Influence of the preliminary annealing conditions on step motion at the homoepitaxy on the Si(100) surface

In this paper, the motion of steps SA and SB on the Si(100) surface in the process of Si Molecular beam epitaxy (MBE) is explored. The study was carried out by means of the reflection intensity dependence behavior analysis of reflection high-energy electron diffraction (RHEED) corresponding to the (2×1) and (1×2) reconstructions. Superstructural rearrangement from a two-domain to a single-domain surface is associated with the bilayer step formation, which occurs due to the different motion rates of the steps SA and SB. Based on the research conducted, the conditions under which the step doubling occurs were determined. A behavior analysis of the diffraction reflection intensity dependences showed that an increasing of preliminary annealing time and temperature facilitates to the faster convergence of the steps SA and SB, but to the slower recovery of the initial surface. The presented experimental results indicate that step movement rate difference depends on the step A edge kink density

Effect of diffusion of magnetic particles on the parameters of the magnetic fluid seal: A numerical simulation

In the paper, a motion of magnetic nanoparticles in a high gradient magnetic field and its correlation with the characteristics of the magnetic fluid seal are numerically studied. The neutral curve defining a range of parameters, where the liquid keeps fluidity, is found. It is shown that the concentration of particles during the initial time period grows linearly and then the exponent decreases to 0.5 with time. It is found that at a high enough value of magnetic field the area of close-packed particles is formed under the pole tip. Numerical simulation has shown that with some values of the parameters it is possible to decrease the magnetic particles' concentration essentially so that the basic fluid leaks out from the seal under gravity, i.e. the magnetic fluid seal fails. It has appeared that the characteristic time of the described processes depends on the properties of magnetic fluid and on the magnetic field value and has an order from several hours to several years