Univariate Ore Polynomial Rings in Computer Algebra

We present some algorithms related to rings of Ore polynomials (or, briefly, Ore rings) and describe a computer algebra library for basic operations in an arbitrary Ore ring. The library can be used as a basis for various algorithms in Ore rings, in particular, in differential, shift, and q-shift rings. __________ Translated from Sovremennaya Matematika i Ee Prilozheniya (Contemporary Mathematics and Its Applications), Vol. 13, Algebra, 2004.     

Anisotropic and isotropic phases of polymer melts

The melting mechanism of polymer crystals is proposed. It is assumed that the melting happens due to forming supervacancies. This mechanism leads the appearance of anisotropic phase of a melt. It is shown that two phases—anisotropic and isotropic—can exist in polymer melts.     

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.     

Polarized Lidar Reflectance Measurements of Vegetation at Near-Infrared and Green Wavelengths

There is growing interest in the use of lidar for remote sensing of vegetation owing to the emergence of reliable and rugged lasers and highly sensitive detectors. Lidar remote sensing has a distinct advantage over conventional techniques in vegetation remote sensing due to its capability for three-dimensional characterization of vegetative targets. The Multiwavelength Airborne Polarimetric Lidar (MAPL) system was developed primarily for vegetation remote sensing applications from an airborne platform of up to 1,000 -m altitude. The lidar system has full waveform capture and polarimetric measurement capability at two wavelengths in the near-infrared (1064 nm) and the green (532 nm) spectral regions. This study presents preliminary ground-based lidar reflectance measurements on a variety of deciduous and coniferous trees under fully foliated conditions with a view towards tree species discrimination. Variations in the reflectance characteristics of selected deciduous trees under unfoliated and fully foliated conditions were also investigated. Our study reveals distinct differences in the reflectance characteristics of various trees.     

Eu- and Yb-induced reconstructions on a vicinal Si(1 0 0) surface

Early stages of rare-earth metal (Yb and Eu) growth on a vicinal, single-domain Si(1 0 0)2 × 1 surface have been studied in the coverage range of 0.1-0.3 monolayer (ML) by low energy electron diffraction, scanning tunneling microscopy, and synchrotron radiation photoemission spectroscopy. We show that Yb induces the 2 × 3 periodicity in the whole range of coverage studied. The 2 × 3 reconstruction coexists with the local 3 × 2/4 × 2 structure at about 0.2 ML of Yb. In contrast, Eu forms the 3 × 2 periodicity at 0.1-0.2 ML, whereas this structure is converted into the 2 × 3 phase at about 0.3 ML. The atomic arrangement and electronic properties of these reconstructions and the adsorbate-mediated modification of surface morphology are investigated.     

Hybrid numerical—experimental approach for investigation of dynamics of microcantilever relay system

The time average holography measurements of the vibrating microelectromechanical switch (MEMS) were performed in this study. Experimental measurement results exhibit good agreement with computer generated holographic interferogram analysis. The validation of experimental investigations versus numerical analysis provides the necessary background to analyze the dynamical characteristics of micromechanical systems in virtual numerical environments. Direct application of fringe counting techniques for reconstruction of motion from time average holograms cannot be straightforward if the analyzed micromechanical systems contain motion limiters. Modifications of a classical time average holographic technique enable qualitative analysis of MEMS and can be applied for investigation of dynamical properties of much broader classes of MEMS systems.     

Statistical Theory of the Phonon Drag Force Acting on a Conduction Electron

Within the framework of microscopic fluctuation-dissipation theory, we obtain the stochastic equation describing the Brownian motion of an electron in the phonon field of the crystal lattice. An expression for the Green’s function of the phonon field is found in general form and for the case of linear phonon-variable interaction of an electron with the phonon field with allowance for the potential screening of crystal-lattice nuclei. An expression for the phonon drag acting on a conduction electron in the lattice field is found and analyzed with allowance for the interaction. Frequency dependence of the coefficient of the phonon drag acting on a conduction electron is studied and the contribution of the electron-phonon interaction to the effective mass of a charge carrier is determined.__________Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 48, No. 3, pp. 249–268, March 2005.