Gaussian Beams,the Hamilton-Jacobi Equations,and Finsler Geometry

Relationships between Gaussian beams and geometry are considered in the paper. We show that the main properties of the Gaussian beam solutions are determined by the natural geometry related to the problem under consideration. The geometry is determined by the Hamilton-Jacobi equation and the corresponding Hamiltonian. In particular, we find a geometric interpretation of the Riccati equation for the quadratic form of the phase function corresponding to a Gaussian beam in the case of Finsler geometry. Bibliography: 2 titles.__________Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 297, 2003, pp. 66–92.     

Numerical Prediction of the Strain State of Thermoset Matrix/Mineral Filler Composite Plates

The numerical prediction of the fields of inelastic strains (the linear invariant of the tensor of inelastic strains) in thermoset polyester/marble filler composite plates is discussed. A uniformly distributed load is applied to the plates, which lie on a steel base. The strain fields are predicted by means of the boundary element method by using creep test data for the composites and the polyester matrix itself. Identical creep tests were performed for two ages of the materials (1 month and 13 years), which allowed evaluating the aging effect. The study is carried out in two stages. At the first stage, the application of the generalized Maxwell-Gurevich equation to the thermoset matrix/mineral filler composite is demonstrated. The model parameters determined from the experimental creep data is used for the second stage, where the state of inelastic strains in the plates is predicted by applying the boundary element method. The influence of composite formulation (filler content) and physical aging of the polyester matrix on the state of inelastic strains in the plates is shown.__________Russian translation published in Mekhanika Kompozitnykh Materialov, Vol. 41, No. 2, pp. 145–156, March–April, 2005.     

Combined supercritical-fluid chromatography/mass spectrometry in the analysis of diuron in plasma using on-line phase-system switching

On-line sample pretreatment by means of the phase-system switching approach is an interesting technique for the analysis of aqueous samples, e.g., plasma, by means of supercritical-fluid chromatography. In order to analyse plasma samples the following analytical procedure is used. The plasma sample is injected on to a short precolumn, which is washed with water and subsequently dried with nitrogen. Next, the solutes are desorbed with the supercritical mobile phase, analysed with packed-column supercritical-fluid chromatography and detected with either a UV detector or a mass spectrometer, equipped with a moving-belt interface. The herbicide diuron is selected as a test compound to study the feasibility of this approach. Using a selective detector the procedure is sufficiently sensitive to detect diuron in plasma, but not appropriate to detect the diuron metabolites in a post-mortem plasma sample. These have been identified with liquid chromatography/mass spectrometry. The detection limit of diuron in plasma using the procedure described is about 30 ng/mL.     

On the continuation for variational inequalities depending on an eigenvalue parameter

In this paper we generalize recent theoretical results on the local continuation of parameter-dependent non-linear variational inequalities. The variational inequalities are rather general and describe, for example, the buckling of beams, plates or shells subject to obstacles. Under a technical hypothesis that is satisfied by the simply supported beam, we obtain the existence of a continuation of both the solution and the eigenvalue with respect to a local parameter. A numerical continuation method is presented that easily overcomes turning points. Numerical results are presented for the non-linear beam.     

Sound radiation from a joint of plates of different thickness

A method of solving the problem of sound radiation from a plate with elements of different thickness in its plane is proposed, and the results obtained with this method are presented. It is shown that the main sources of sound radiation are the inhomogeneous flexural fields formed in the elements on both sides of their joint.     

Study of removal processes of <Superscript>7</Superscript>Be and <Superscript>137</Superscript>Cs from the atmosphere

In order to understand better the way in which radioactive contamination may be transferred from the atmosphere to other ecological compartments it is necessary to obtain information of the deposition mechanisms of radionuclides. Concentration and speciation of ¹³⁷Cs and ⁷Be in the atmospheric aerosol and deposition were studied. The mixed deposition velocities of water-soluble and insoluble ¹³⁷Cs and ⁷Be were determined. The relation between activity concentrations of insoluble ⁷Be in the atmosphere and its amount in deposition was observed. It is supposed that in the deposition process of radiocesium the precipitation plays an important role in scavenging of water-soluble radiocesium by falling raindrops, in contrast to insoluble ¹³⁷Cs where the dry deposition becomes predominant.     

Asymptotics of collision integral matrix elements in the isotropic case

The method of nonlinear moments, when used to solve the Boltzmann equation, necessitates the calculation of collision integral matrix elements. The matrix elements are hard to calculate numerically, especially at large indices. The asymptotics of the matrix elements are constructed. In terms of the model of pseudopower particle interaction, a formula free of summation is derived. This makes it possible to find the asymptotic behavior of linear and nonlinear elements when two indices are large. For an arbitrary interaction cross section, asymptotic expansions of linear and nonlinear matrix elements in one index are obtained. For Maxwellian molecules, asymptotic formulas are derived for three large indices.     

The structure of CeAlO3 by Rietveld refinement of X-ray powder diffraction data

The room temperature structure of perovskite CeAlO₃ has been reinvestigated by X-ray powder diffraction. The Rietveld refinement has confirmed the tetragonal symmetry; but revealed a super cell, a=5.32489(6) Å and c=7.58976(10) Å, with the space group I4/mcm. In CeAlO₃, the distortion from the ideal cubic perovskite is caused by the cooperative tilting of the AlO₆ octahedra around the primitive cubic [001]_p-axis.