Acoustic scattering by a penetrable spheroid

The scattering of a plane acoustic wave from a penetrable prolate or oblate spheroid is considered. Two different methods are used for the evaluation. In the first, the pressure field is expressed in terms of spheroidal wave functions. In the second, a shape perturbation method, the field is expressed in terms of spherical wave functions only, while the equation of the spheroidal boundary is given in spherical coordinates. Analytical expressions are obtained for the scattered pressure field and the various scattering cross-sections when the solution is specialized to small values of the eccentricity h = d/(2a), (h ≪ 1), with d being the interfocal distance of the spheroid and 2a the length of its rotation axis. In this case, exact, closed-form expressions are obtained for the expansion coefficients g ⁽²⁾ and g ⁽⁴⁾ in the relation S(h) = S(0)[1 + g ⁽²⁾ h ² + g ⁽⁴⁾ h ⁴ + O(h ⁶)] expressing the scattered field and the scattering cross-sections. Numerical results are given for various values of the parameters. Published in Russian in Akusticheskiĭ Zhurnal, 2008, Vol. 54, No. 2, pp. 189–204. The text was submitted by the authors in English.     

Power series expansions for Mathieu functions with small arguments

Power series expansions for the even and odd angular Mathieu functions and , with small argument , are derived for general integer values of . The expansion coefficients that we evaluate are also useful for the calculation of the corresponding radial functions of any kind.

     

Optimization of the phase system in the analysis of polynuclear aromatics (PNA) from diesel engine exhaust by high performance liquid chromatography (HPLC)

Summary Polynuclear aromatics (PNA) were collected and enriched from diesel engine exhausts by means of a probe and an absorber system. Group separation of PNA from other constituents of exhaust was accomplished through elution with n-heptane on a silica column. A variety of phase systems ranging from unpolar to strong polar packings and eluents, respectively, were tested to resolve PNA into single species. Of these a n-octadecyl bonded silica packing and methanol/water was found to be the most optimal with regard to resolution for real PNA mixtures. Separation was completed within 2–3 h at isocratic conditions.Paper presented at Euroanalysis III, Dublin. August 20–25, 1978.     

Solitary wave solutions to nonlinear evolution equations in mathematical physics

This paper obtains solitons as well as other solutions to a few nonlinear evolution equations that appear in various areas of mathematical physics. The two analytical integrators that are applied to extract solutions are tan–cot method and functional variable approaches. The soliton solutions can be used in the further study of shallow water waves in (1+1) as well as (2+1) dimensions.     

Acoustic scattering from two spheres,one with a small radius

The scattering of a plane acoustic wave from an acoustically penetrable or impenetrable (soft or hard) sphere separated at a distance from another sphere, also penetrable or impenetrable (soft or hard), of acoustically small radius, is examined. The penetrable spheres and the surrounding medium are fluids or fluidlike; i.e., they do not support shear waves. Separation of variables, in conjunction with translational addition theorems for spherical wave functions, is used. Analytical expressions are obtained for the scattered pressure field and the scattering cross sections. Numerical results are given for penetrable and impenetrable spheres, showing the influence of the small sphere on the scattering cross sections of the other sphere. Published in Russian in Akusticheskiĭ Zhurnal, 2007, Vol. 53, No. 1, pp. 38–49. The text was submitted by the authors in English.     

Separation of unmodified α-amino acid enantiomers by reverse phase HPLC

Summary A novel chiral phase system is presented for the resolution of unmodified α-amino acid racemates which is composed of a reverse phase packing coated with N-alkyl-L-hydroxyproline (where alkyl is n-C₇H₁₅-, n-C₁₀H₂₁- and n-C₁₆H₃₃-) and a hydro-organic eluent containing copper(II)acetate. The factors controlling retention and enantioselectivity such as concentration of Cu(II)ion and pH of the eluent, addition of NH₄Ac to the eluent, type and content of organic solvent of hydro-organic eluent and column temperature were examined. The extremely high enantioselectivity observed (α up to 16) is assumed to be caused by a three site sorbate-sorbent interaction involving bidentate coordination of two amino acids to a Cu(II)ion and hydrophobic attractions between hydrocarbon side chains of amino acids and the n-octadecyl groups of the support. The efficiency and selectivity of the system permits resolution of up to 7 racemic amino acids into enantiomers within 35 minutes on a conventional HPLC apparatus. 13th publication in the series dealing with the ligand-exchange chromatography. Previous publication: ref. [1].