High-frequency asymptotic behavior of the dipole field in a three-layer dielectric medium

Translated from Metody Matematicheskogo Modelirovaniya i Vychislitel'noi Diagnostiki, pp. 171–174, Izd. Moskovskogo Universiteta, Moscow, 1990.     

Casimir energy of the quantum field in a dispersive and absorptive medium

We calculate the Casimir energy for a quantum field between two metallic plates separated by a dielectric in the microscopic framework with the medium modeled by a set of oscillators with continuously distributed frequencies. We study the case of one spatial dimension and compare the results for the additional energy and force due to interaction with the medium with the results obtained in the framework of the phenomenological approach similar to the well-known Lifshitz formula: they have opposite signs.     

Eigenvalue approach to study the effect of rotation and relaxation time in generalized magneto-thermo-viscoelastic medium in one dimension

The fundamental equations of the problems of generalized thermoelasticity with one relaxation parameter including heat sources in infinite rotating magneto-thermo-viscoelastic media have been derived in the form of a vector matrix differential equation in the Laplace transform domain for a one dimensional problem. These equations have been solved by the eigenvalue approach to determine deformations, stress, and temperature. The results have been compared to those available in the existing literature. The graphs have been drawn to show the effect of rotation in the medium.     

The effect of thermal relaxation on rayleight surface waves in a thermoelastic medium

We study the problem of propagation of Rayleigh surface waves in thermoelastic media on the basis of the generalized coupled theory of thermoelasticity, which takes account of the phenomenon of thermal relaxation for sharply nonsteady thermal loads, thereby eliminating the paradox of infinite velocity of propagation of heat. It thus makes it possible to take account of the finite velocity of propagation of heat in the study of the process of propagation of Rayleigh surface waves. Translated fromMatematichni Metodi i Fiziko-mekhanichni Polya, Vol. 40, No. 1, 1997, pp. 85–89.     

Fractal spectrum of periodic quantum systems in a magnetic field

Models of two-dimensional periodic quantum-mechanical systems in a uniform magnetic field are considered. Results of the numerical analysis of the energy spectrum for these models are presented. The flux–energy diagrams for the magnetic Bloch bands are obtained. Evidence for a fractal structure of these diagrams is given.     

Using the Renyi entropy to describe quantum dissipative systems in statistical mechanics

We develop a formalism for describing quantum dissipative systems in statistical mechanics based on the quantum Renyi entropy. We derive the quantum Renyi distribution from the principle of maximum quantum Renyi entropy and differentiate this distribution (the temperature density matrix) with respect to the inverse temperature to obtain the Bloch equation. We then use the Feynman path integral with a modified Mensky functional to obtain a Lindblad-type equation. From this equation using projection operators, we derive the integro-differential equation for the reduced temperature statistical operator, an analogue of the Zwanzig equation in statistical mechanics, and find its formal solution in the form of a series in the class of summable functions. __________ Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 156, No. 3, pp. 444–453, September, 2008.     

The effect of ultraviolet radiation on the stress relaxation rate of polymers

The effect of UV radiation on the stress relaxation rate for four different polymers was investigated. A reversible increase in the stress relaxation rate was noted: the rate increased during irradiation and declined after its termination. It is assumed that this effect involves the rupture of stressed polymer macromolecules by the action of UV rays.Mekhanika Polimerov, Vol. 3, No. 4, pp. 615–618, 1967     

Functional approach to the theory of two-dimensional quantum Fermi systems in an external periodic field

The behavior of an adsorbed layer of Fermi particles in a weak external field with symmetry of the centered quadratic lattice is investigated. Instability of the weakly inhomogeneous state of the system with respect to small fluctuations in the vicinity ofa ^*=2k _F is established; herea ^* is the magnitude of the vectors of the neighbors closest to the point in the inverse lattice; k_F is the Fermi momentum.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 169, pp. 29–43, 1988.It remains to thank V. N. Popov for constant interest in the work.     

Localization of the essential spectrum of the energy operators ofn-particle quantum systems in a magnetic field

Theorems on the localization of the essential spectrum of givenSO(2) symmetry forn-particle Hamiltonians in an external magnetic field are proved. The energy operators are studied for systems of arbitrary particles in the absence of an external potential field and for systems of identical particles in an external potential field. Some of the results were announced in earlier papers [1,2].Radiophysics Research Institute. Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 97, No.1, pp. 94–112, October, 1993.     

Perturbation analysis of radiative effect on free convection flows in porous medium in the presence of pressure work and viscous dissipation

The effect of thermal radiation with a regular three-parameter perturbation analysis has been studied for the effects in some free convection flows of Newtonian fluid-saturated porous medium. The effects of the thermal radiation, permeability of the porous medium, pressure stress work and viscous dissipation on the flows and temperature fields have been included in the analysis. Four different vertical flows have been analyzed, those adjacent to an isothermal surface, uniform heat flux surface, a plane plume and flow generated from a horizontal line energy source, and, a vertical adiabatic surface. Rosseland approximation is used to describe the radiative heat flux in the energy equation. The numerical results of the perturbation analysis for four conditions are solved numerically by the fourth-order Runge–Kutta integration scheme. Numerical values of the main physical quantities are the skin friction and a heat transfer and total heat and mass convected downstream are presented in a tabular form with the parameters characterizing the radiation, permeability of the porous medium, pressure stress work and viscous dissipation. The obtained results are compared and a representative set is displayed graphically to illustrate the influences of the radiation, permeability of the porous medium, pressure stress work and viscous dissipation on the velocity and the temperature profiles.     

On the computation of a wave field in a multilayer medium

In this paper, theoretical seismograms of waves propagating in a medium comprising four layers that rest on a half-space are presented. The seismograms are computed by the method of summation of kinematic and dynamic wave analogs. On the basis of these computations, some conclusions concerning the behavior of the wave field at large distances are drawn. Bibliography: 5 titles. Translated fromZapiski Nauchnykh Seminarov POMI, Vol. 230, 1995, pp. 243–252. Translated by N. S. Smirnova.     

Modeling the field of a cable in a two-dimensional nonhomogeneous medium

In this article we model the electromagnetic field of a cable on the surface of a two-dimensional nonhomogeneous medium used for electromagnetic sounding. The model of the medium represents the sea. Calculations are reported describing the coast effect on the electromagnetic field. An iterative field calculation method is proposed, which reduces the computing effort. The effect of sub-seafloor nonhomogeneities on the electromagnetic field measured at the seafloor is investigated numerically.     

A method and an algorithm for computing the electromagnetic field in a stratified medium with a local nonhomogeneity in an arbitrary layer

Translated from Metody Matematicheskogo Modelirovaniya i Vychislitel'noi Diagnostiki, pp. 133–142, Izd. Moskovskogo Universiteta, Moscow, 1990.     

Estimate of convergence rate in local limit theorem for the particle number in spin systems

For classical lattice spin systems with vacuum, an estimate is obtained of the convergence rate in a local limit theorem for the number of particles in a region A. The estimate has the order of the square rooot of the volume of A.Institute of Mathematics, Armenian Academy of Sciences. Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 95, No. 3, pp. 497–512, June, 1993.     

Modeling the electromagnetic field of distant sources in a nonhomogeneous medium

Asymptotic formulas are derived for calculating the far-zone field inside a layered medium induced by a vertical magnetic dipole located on the surface of a horizontally homogeneous layered Earth with a three-dimensional nonhomogeneity. The asymptotic solution is compared with the exact solution. The far-zone dipole field is simulated for the model of a horizontally homogeneous layered earth with a three-dimensional nonhomogeneity. The simulation results show that the 3D-nonhomogeneity is easily detected from electromagnetic measurements with an artificial dipole source on the Earth’s surface.