Harry A. Mavromatis

Heat convection from a sphere placed in an oscillating free stream

Abstract The problem of heat convection from a sphere placed in an oscillating viscous free stream is considered for the two cases of forced and mixed convection regimes. The sphere surface is assumed isothermal and the free-stream oscillations are always in the vertical direction resulting in axisymmetric flow and thermal fields for both regimes. The study is based on the solution of the unsteady Navier–Stokes and energy equations for a Boussinesq fluid of constant Prandtl number (Pr=0.71) . The main parameters considered are the Reynolds number, Grashof number, and Strouhal number. Comparison of results with published data shows a good agreement for the special case of steady forced and mixed convection. The details of the resulting thermal fields are presented in the form of isotherm patterns and the local Nusselt number distribution.

Remarks on some associated Laguerre integral results

Motivated essentially by their possible need in a fairly large number of physical and chemical contexts, Mavromatis and Alassar [1] derived several associated Laguerre integral results by eliminating an unnecessary constraint used in an earlier paper on the subject by Mavromatis [2]. The main object of the present sequel to these recent works is to investigate and apply much more general families of integral formulas, involving products of two or more Laguerre polynomials, which have been considered in the mathematical literature rather extensively.

A generalized formula for the integral of three associated Legendre polynomials

Abstract In this paper, a generalized formula for the definite integral of three associated Legendre polynomials of the first kind that arises in various physical applications is given in terms of the 3 F 2 hypergeometric function and the 3 − j symbols. The special case, when the integral reduces to a particularly simple familiar expression, is also mentioned.

An interesting new result involving associated laguerre polynomials

An interesting new integral expression involving two Associated Laguerre Polynomials is derived, and seven special cases of this expression are discussed.

Two new associated Laguerre integral results

New associated Laguerre integral results are obtained by eliminating an unnecessary restriction in [1]. The expression used to obtain these new results is compared to that given in [2] and shown to be different and of greater generality. Finally, some physical moments are discussed that require such integrals.

New summation expressions obtained by combining perturbation theory formalisms

New perturbation theory expressions obtained by Kim and Sukhatme [“Alternative approach to non-relativistic perturbation theory”, J. Phys. A 25 (1992) L647–L650] are equated to standard perturbation theory expressions in order to obtain new mathematical series results. Several such new results are derived and discussed.

A straightforward mapping of the arbitrary-dimensional coulomb problem into the isotropic oscillator

Abstract A simple transformation is given that relates the arbitrary-dimensional Coulomb problem and the N-dimensional isotropic oscillator.

Connection between q-deformed anharmonic oscillators and quasi-exactly soluble potentials

Abstract It is proved that quasi-exactly soluble potentials (QESPs) corresponding to an oscillator with harmonic, quartic and sextic terms, for which the n + 1 lowest levels of a given parity can be determined exactly, may be approximated by WKB equivalent potentials corresponding to deformed anharmonic oscillators of SU q (1,1) symmetry, which have been used for the description of vibrational spectra of diatomic molecules. This connection allows for the immediate approximate determination of all levels of the QESPs.

Nth (even)‐order minimum uncertainty products

This paper considers the problem of finding the quantum states that minimize the products of the (even) Nth‐order fluctuation of two canonically conjugate operators. The problem is first attacked in an abstract form and an equation derived for the desired states. A consideration of the N=2 case then leads to a connection with the new concept of ‘‘squeezed states’’ of the electromagnetic field, and the usual exact solution involving the coherent state. The concept of ‘‘higher‐order squeezing’’ is touched on to motivate the further discussion. The cases N=4, 6, and 8 are then taken up, and approximate solutions to them found via a new numerical technique. During these calculations, it is noted that only the first few terms in the expansion in number states figure in the solution; this observation is then exploited to find an approximate closed solution to the problem valid for all N.

On obtaining the scattering potential and its moments in the partial wave Born approximation

Mathematical techniques are used to invert the the partial wave Born approximation. Two expressions are obtained for the scattering potential. Additionally simple expressions are given for various moments of this scattering potential. These results are illustrated by some analytic examples. Finally a few numerical calculations are performed using both ‘‘Born approximation’’ and ‘‘experimental’’ phase shifts in the relevant expressions.