The construction of a model of frequency independent damping using the amplitude characteristic of the absorption coefficient

Relations are obtained which connect the stresses and strains accompanying oscillations with the absorption coefficient and a procedure for modelling the frequency-independent scattering of energy is constructed based on them. Account is taken of the fact that damping lowers the resonance frequency and the accumulation of residual stresses and strains is not observed during oscillation. The models obtained using this procedure can be employed for any changes, including unsteady changes, in the load with respect to time. The case of a power dependence of the absorption coefficient on the amplitude, which is important in practice, is investigated in detail. The forced, transverse oscillations of a rod are considered as an example. Asymptotic and numerical solutions of the problem are obtained in the single-mode approximation.     

Optical properties of nanocrystalline silicon embedded in SiO2

Nanocrystalline silicon embedded SiO₂ matrix has been formed by annealing the a-SiO_x films fabricated by plasma enhanced chemical vapor deposition technique. Absorption and photoluminescence spectra of the films have been studied in conjunction with micro-Raman scattering spectra. It is found that absorption presents an exponential dependence of absorption coefficient to photon energy in the range of 1.5–3.0 eV, and a sub-band appears in the range of 1.0–1.5 eV. The exponential absorption is due to the indirect band-to-band transition of electrons in silicon nanocrys-tallites, while the sub-band absorption is ascribed to transitions between surfaces and/or defect states of the silicon nanocrystallites. The existence of Stokes shift between absorption and photoluminescence suggests that the phonon-assisted luminescence would be enhanced due to the quantum confinement effects.     

Wave function and the probability current distribution for a bound electron moving in a uniform magnetic field

We study the effects of electromagnetic fields on nonrelativistic charged spinning particles bound by a short-range potential. We analyze the exact solution of the Pauli equation for an electron moving in the potential field determined by the three-dimensional δ-well in the presence of a strong magnetic field. We obtain asymptotic expressions for this solution for different values of the problem parameters. In addition, we consider electron probability currents and their dependence on the magnetic field. We show that including the spin in the framework of the nonrelativistic approach allows correctly taking the effect of the magnetic field on the electric current into account. The obtained dependences of the current distribution, which is an experimentally observable quantity, can be manifested directly in scattering processes, for example.     

Correlation order, merging and diversification

We investigate the influence of the dependence between random losses on the shortfall and on the diversification benefit that arises from merging these losses.We prove that increasing the dependence between losses, expressed in terms of correlation order, has an increasing effect on the shortfall, expressed in terms of an appropriate integral stochastic order. Furthermore, increasing the dependence between losses decreases the diversification benefit.We also consider merging comonotonic losses and show that even in this extreme case a strictly positive diversification benefit will often arise.     

The calculation of the energy losses in a sliding elastic contact with friction and wear (the plane problem)

The plane problem of the sliding contact of a punch with an elastic foundation when there is friction and wear is considered. Assuming the existence of a steady solution in a moving system of coordinates, relations are derived between the sliding velocity, the wear, the contact stresses and the displacements for an arbitrary dependence of the wear rate on the contact pressure. Taking into account the presence of a deformation component of the friction force, an equation is written for the balance of the mechanical energy for the punch - elastic base system considered. It is shown that the equality of the work of the external force in displacing the punch to the losses due to friction and the change in the shape of the foundation due to wear is satisfied when the work done by the contact stresses on the increments of the boundary displacements is equal to zero, and the frictional losses must be determined taking into account the non-uniformity of the distributions of the shear contact stresses and the sliding velocity in the contact area. Two special cases of the foundation in the form of a wide and narrow strip are considered, for which the total coefficient of friction is calculated, taking into account the deformation component of the friction force.     

Two-dimensional Coulomb scattering of a quantum particle: Construction of radial wave functions

We prove that radial wave functions of a charged quantum particle moving in a two-dimensional plane of the three-dimensional coordinate space and scattering by a Coulomb center at rest in the same plane are governed by the Coulomb equation with a half-integer index. We investigate the structure of these functions and consider three physically interesting limits: the non-Coulomb limit and high- and low-energy limits. We explicate the basic differences between two- and three-dimensional Coulomb scattering.     

Global loss diversification in the insurance sector

We study the possibility for international diversification of catastrophe risk by the insurance sector. Adopting the argument that large insurance losses may be a ‘globalizing factor’ for the industry, we study the dependence of geographically distant insurance markets via equity returns. In particular, we employ conditional copula theory to model the bivariate dependence of the insurance industry. In contrast to earlier literature on this subject, we disentangle the causes of dependence stemming from the asset side from those from the liability side by conditioning on general market conditions. We find that for both Europe-America and Europe-Asia the dependence is significant. Moreover, we find asymmetric effects: the international dependence is particularly high for losses, even after conditioning for the asset side dependence. Finally, we investigate the time variation in copula parameters and find evidence that dependence in the insurance sector has increased over time, thus reducing the scope for international diversification of large losses in this sector.     

Electron in the Aharonov-Bohm potential and in the Coulomb field in 2+1 dimensions

We obtain exact solutions of the Dirac equation in 2+1 dimensions and the electron energy spectrum in the superposition of the Aharonov-Bohm and Coulomb potentials, which are used to study the Aharonov-Bohm effect for states with continuous and discrete energy spectra. We represent the total scattering amplitude as the sum of amplitudes of scattering by the Aharonov-Bohm and Coulomb potentials. We show that the gauge-invariant phase of the wave function or the energy of the electron bound state can be observed. We obtain a formula for the scattering cross section of spin-polarized electrons scattered by the Aharonov-Bohm potential. We discuss the problem of the appearance of a bound state if the interaction between the electron spin and the magnetic field is taken into account in the form of the two-dimensional Dirac delta function. __________ Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 149, No. 3, pp. 502–517, December, 2006. An erratum to this article is available at .     

Dynamics of phonon clouds of correlated polarons

We investigate the Anderson-Holstein model with strong repulsion of impurity electrons using a strongcoupling approximation. The strong electron-phonon interaction determines the formation of polarons with heavy clouds of phonons surrounding the impurity electrons. We describe the collective mode of phonon clouds and the relation between electron propagators and correlation functions. We obtain the dependence of the collective mode energy on the hybridization parameter in the case T = 0 and prove that it is suppressed by increasing hybridization.     

The energy conservation law in acoustics of a moving nonstationary inhomogeneous medium

Expressions for the energy density of a sound wave and the sound energy flow vector in a moving nonstationary inhomogeneous medium are obtained. The energy conservation law is stated.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova, Vol. 179, pp. 52–57, 1989.     

水中孤立气泡对声波的耗散作用

本文从气泡壁面线性运动方程出发,对水中孤立气泡的声耗散机理进行了分析。结果表明:气泡对声波具有明显的耗散作用;耗散作用由声散射和声吸收两部份组成;热传导在气泡对声波的耗散作用中起决定性作用;气泡处于谐振时,对声波具有最大的耗散作用。     

Scattering Problem for a Classical Particle with Spin in a Coulomb Field

We investigate the scattering problem for a relativistic electron with spin in a Coulomb field in the framework of pseudoclassical mechanics. We obtain an analytic expression for the scattering angle and limiting estimates for the scattering parameters for the spinless and nonrelativistic cases. For small angles, the pseudoclassical model under consideration leads to the well-known quantum-mechanical Mott formula.     

Scattering of an acoustic pulse by a rigid sphere on a sedimentary (fluid) bottom

We study the problem of scattering of acoustic pulses on a rigid sphere located near the interface of two media in one of which (the bottom) sound absorption is taken into account. To find the amplitudes of the echo-signal in the distal field we apply the Fourier transform with respect to time and the method of T-matrices. Translated fromMatematichni Metodi ta Fiziko-Mekhanichni Polya, Vol. 40, No. 2, 1997, pp. 137–141.     

Acoustic Wave Propagation in an Underwater Sound Channel 1. Qualitative Theory

We give a qualitative study of wave propagation in an inhomogeneousmedium principally by geometrical optics and ray theory. Theinhomogeneity is represented by a sound-speed profile whichis dependent upon one coordinate, namely the depth; and we discussthe general characteristics of wave propagation which resultfrom a source placed on the sound channel axis. We show thatour mathematical model of the sound-speed in the ocean actuallypredicts some of the behaviour of the observed physical phenomenain the underwater sound channel. Using ray theoretic techniqueswe investigate the implications of our profile on the followingcharacteristics of SOFAR propagation: (i) the sound energy travellingfurther away from the axis takes less time to travel from sourceto receiver than sound energy travelling closer to the axis,(ii) the focusing of sound energy in the sound channel at certainranges, (iii) the overall ray picture in the sound channel.     

Thermalization of Displacement Cascades in Solids and the Thermal Spike Model

We investigate the thermalization of low-energy cascades of displacements in solids using methods of nonequilibrium statistical thermodynamics. We investigate the time evolution of the quasi temperature of cascade particles taking the phonon scattering on dislodged atoms and the thermal recombination of defects into account. We use the obtained quasi-temperature time dependence to study the activated process—sputtering in the thermal spike region.     

Two-dimensional Coulomb scattering of a quantum particle: Low-energy asymptotic behavior

We consider a charged quantum particle moving in a two-dimensional plane in the three-dimensional coordinate space and scattering on an immovable Coulomb center in the same plane. We derive and investigate expansions of the wave function and of all radial wave functions of the particle in integer powers of the wave number and in Bessel functions of a real order. We prove that finite sums of such expansions are asymptotic in the low-energy limit.     

On the analytical solution for MHD natural convection flow and heat generation fluid in porous medium

Homotopy analysis method (HAM) is employed to investigate the momentum, heat and mass transfer characteristics of MHD natural convection flow and heat generation fluid driven by a continuously moving permeable surface immersed in a fluid saturated porous medium. The solution is found to be dependent on several governing parameters, including the magnetic field strength parameter, Prandtl number, Darcy number, the dimensionless inertia coefficient, the dimensionless heat generation/absorption coefficient and the dimensionless suction/blowing coefficient. A parametric study of all governing parameters is carried out and representative results are illustrated to reveal a typical tendency of the solutions. Representative results are presented for velocity and temperature distributions as well as the local friction coefficient and local Nusselt number. Finally, a proper discussion is derived on the obtained results and some remarkable conclusions are mentioned.     

High-energy bounds on helicity amplitudes in elastic pp scattering in the small-angle domain

Bounds on helicity amplitudes in elastic pp scattering follow from the unitarity and analyticity conditions. We discuss the maximum admissible energy dependence, corresponding to saturating the obtained unitarity restrictions, of the spin parameters of elastic pp scattering. __________ Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 149, No. 3, pp. 473–482, December, 2006.     

Asymptotic theory for varying coefficient regression models with dependent data

The varying coefficient models (VCMs) are extremely important tools in the statistical literature and are widely used in many subject areas for data modeling and exploration. In linear VCMs, typically the errors are assumed to be independent. However, in many situations, especially in spatial or spatiotemporal settings, this is not a viable assumption. In this article, we consider nonparametric VCMs with a general dependent error structure which allows for both spatially autoregressive and spatial moving average models as special cases. We investigate asymptotic properties of local polynomial estimators of the model components. Specifically, we show that the estimates of the unknown functions and their derivatives are consistent and asymptotically normally distributed. We show that the rate of convergence and the asymptotic covariance matrix depend on the error dependence structure and we derive the explicit formula for the convergence results.     

Soft-mode related origin of the boson peak and acoustic-phonon broadening in glasses

We study the origin of the boson peak and an associated mechanism for acoustic-phonon broadening (below the peak) in glasses exhibiting a high-frequency sound above the peak. The origin is related to the Ioffe-Regel crossover for inelastic (resonant) scattering of acoustic phonons from harmonic soft-mode vibrations. The broadening mechanism is due to the resonant interaction of a harmonic soft-mode vibration with acoustic phonons, which results in the resonant scattering. We find that the associated width of the phonon is independent of temperature and is characterized by a power-law frequency dependence with the exponent varying from ϰ=2 just below the boson peak to ϰ=4 at lower frequencies. The dependences seem to partly agree with some recent experimental data for the glasses under consideration. __________ Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 154, No. 1, pp. 77–90, January, 2008.