Showing papers by "Voronezh State University published in 1997"

The Langevin Equation

Abstract: The generalized Langevin equation describes processes in a mechanical system with both deterministic and random forces which have comparable magnitudes (i.e., neither the deterministic nor random part can be neglected) and the random force is a transformed white noise. Examples of such processes are well known in physics. In this chapter, we use integral operators with Riemannian parallel translation in order to study the Langevin equations arising in geometric mechanics. Note that in the case under consideration the trajectories of the process are a.s. smooth. This makes the analysis of such systems technically much simpler than that of the general ones studied in Chap. 4.

Territory covered by N Lévy flights on d-dimensional lattices

Abstract: We study the territory covered by N L\'evy flights by calculating the mean number of distinct sites, 〈${\mathrm{S}}_{\mathrm{N}}$(n)〉, visited after n time steps on a d-dimensional, d\ensuremath{\geqslant}2, lattice. The L\'evy flights are initially at the origin and each has a probability A${\mathrm{\ensuremath{\ell}}}^{\mathrm{\ensuremath{-}}(\mathrm{d}+\mathrm{\ensuremath{\alpha}})}$ to perform an \ensuremath{\ell}-length jump in a randomly chosen direction at each time step. We obtain asymptotic results for different values of \ensuremath{\alpha}. For d=2 and N\ensuremath{\rightarrow}\ensuremath{\infty} we find 〈${\mathrm{S}}_{\mathrm{N}}$(n)〉\ensuremath{\propto}${\mathrm{C}}_{\mathrm{\ensuremath{\alpha}}}$${\mathrm{N}}^{2\mathrm{/}(2+\mathrm{\ensuremath{\alpha}})}$${\mathrm{n}}^{4\mathrm{/}(2+\mathrm{\ensuremath{\alpha}})}$, when \ensuremath{\alpha}2 and 〈${\mathrm{S}}_{\mathrm{N}}$(n)〉\ensuremath{\propto}${\mathrm{N}}^{2\mathrm{/}(2+\mathrm{\ensuremath{\alpha}})}$${\mathrm{n}}^{2\mathrm{/}\mathrm{\ensuremath{\alpha}}}$, when \ensuremath{\alpha}g2. For d=2 and n\ensuremath{\rightarrow}\ensuremath{\infty} we find 〈${\mathrm{S}}_{\mathrm{N}}$(n)〉\ensuremath{\propto}Nn for \ensuremath{\alpha}2 and 〈${\mathrm{S}}_{\mathrm{N}}$(n)〉\ensuremath{\propto}Nn/ln n for \ensuremath{\alpha}g2. The last limit corresponds to the result obtained by Larralde et al. [Phys. Rev. A 45, 7128 (1992)] for bounded jumps. We also present asymptotic results for 〈${\mathrm{S}}_{\mathrm{N}}$(n)〉 on d\ensuremath{\geqslant}3 dimensional lattices.

The effect of pulsed magnetic fields on Cz-Si crystals

Abstract: It has been established that short-term effects of pulsed magnetic fields initiate long-term low-temperature decay of a supersaturated solid solution of oxygen in silicon crystals grown by the Czochralski method (Cz-Si), which results in the generation of oxygen-containing defects in the form of O-V centers and more complicated SixOyVz complexes, where V is a vacancy The process of defect formation after the action of the pulsed magnetic fields culminates in the formation of spatially ordered oxygen-vacancy clusters and/or the precipitation of oxide phases, depending on the original defects present in the crystal The action of such fields also initiates crystallization of an amorphized layer when it is present on the surface of the original crystal The detected effects are characterized by a threshold field strength, are accumulate with successive pulses, and reach saturation in terms of these parameters of the action The effects induced in Cz-Si crystals by pulsed magnetic fields are analyzed in terms of a possible cause consisting of the excitation of the Si-O bond of an interstitial oxygen by nonequilibrium population of the vibrational levels of a metastable electronic term of the bond

Topological properties of the set of fixed points of a?multivalued map

Abstract: This paper is a study of the topological properties of the set of fixed points of a multivalued map. Some theorems are proved on the topological dimension of this set, and conditions are studied under which the set is connected or acyclic. The theorems obtained are applied to the investigation of the set of solutions of differential and integral inclusions.

Electron emission from ferroelectric plate stimulated by switching

Abstract: The behavior of a ferroelectric sample in the form of a thin plate in an electric field is considered in the work. It is assumed that the reason of the appearance of emission is the presence of the electric field due to non-compensated charges arising with the displacement of the domain wall on the ferroelectric surface in the place of the domain wall exit at the sample surface as well as on the surface of the domain wall itself sagged in the external electric field. The value of the equilibrium displacement for domain boundaries in the external field is calculated in the frames of models of free domain boundaries and domain walls pinned by defects. This is the basis for determination of electric fields accompanying the shifts of domain boundaries. The value of the emission current stimulated by switching of a material is also calculated.

Estimates of the rate of convergence of projective and projective-difference methods for weakly solvable parabolic equations

Abstract: We consider a weakly solvable parabolic problem in a separable Hilbert space. We seek approximations to the exact solution by projective and projective-difference methods. In this connection the discretization of the problem with respect to the spatial variables is carried out by the semidiscrete method of Galerkin, and with respect to time by the implicit method of Euler. In this paper we establish a coercive mean-square error estimate for the approximate solutions. We illustrate the effectiveness of these estimates with parabolic equations of second order with Dirichlet or Neumann boundary conditions in projective subspaces of finite element type.

The polarization-angular structure and elliptical dichroism of the cross sections for three-photon bound-bound transitions in atoms

Abstract: Using the electric dipole approximation, we present, in invariant form, the cross section of an arbitrary three-photon transition between the discrete states of an atom with total angular momenta Ji and Jf. The cross section contains scalar and mixed products of the photon polarization vectors, and invariant atomic parameters dependent only on the photon frequencies. We determine the number of independent atomic parameters at fixed values of Ji and Jf and obtain their explicit expressions in terms of the reduced composite dipole matrix elements. The polarization dependence of the cross sections is expressed in terms of the degrees l and ξ of linear and circular photon polarizations. We analyze the phenomenon of dissipation-induced circular dichroism in three-photon processes, i.e., the difference Δ of the cross sections for opposite signs of the degree of circular polarization of all the photons. We study in detail the case of two identical photons and the phenomenon of elliptical dichroism, when Δ∼lξ holds and dichroism occurs only when the photons are elliptically polarized, with 0<|ξ|<1. Finally, we discuss the dissipation-induced effects of atom polarization in three-photon processes involving linearly polarized or unpolarized photons.

Tunneling ionization of Rydberg molecules

Abstract: The theory of tunneling ionization of atoms is generalized to ionization of symmetric top molecules, either polar or nonpolar. Low-lying excited states of molecules, for which the ordinary Born-Oppenheimer approximation holds, and high-lying excited states, for which the inverse Born-Oppenheimer approximation holds, are discussed. Ionization in a constant external field is analyzed, as is ionization in an alternating field. It is shown that the orientation of the molecule’s axis along the field does not lead to any appreciable increase in the ionization probability as compared to other orientations.

Analytical Solution of the Logistic Equation

Abstract: An analytical solution for the well-known quadratic recursion, also known as the logistic map, is presented. Our derivation makes use of the analogy between this equation and Galton–Watson processes. The latter can be treated in a linear way using the transfer matrix technique. The solution is represented as a power of an appropriate transfer matrix.

Evolution of domain structure in ferroelectrics in the presence of polarization screening by charges bound to surface states and by free charge carriers

Abstract: The influence of screening by charges bound to surface states and by free charge carriers on the width of a plane-parallel domain structure is investigated. The period of the domain structure is determined on the basis of its identification with the period of the modulated polarization distribution created by the mechanism of destabilization in a ferroelectric crystal of finite dimensions. The influence of the parameters of surface electron states, the nonferroelectric surface layer, and screening by free carriers on the period is described.

Education as a Factor of Humanistic Security and Social Development

Abstract: Over the past few decades, two opposite and at the same time inseparably connected tendencies have emerged in world educational practice. On the one hand, the role of education is steadily increasing in the lives of peoples, countries, and individuals. On the other hand, there is an ongoing crisis of education and its structures, one that is quite frequently caused by a shortage of financial support. This latter factor is characteristic of backward and poorly developed countries. To some extent, this component of the crisis is also to be observed in present-day Russia. Budget spending on education in this country has come to be among the lowest in the world.

Investigation of interfacial states in MIS structures by a single-frequency admittance method

Abstract: Two models of tunneling charge exchange on interfacial states buried in the insulator are examined. In one model the spatial distribution of these states is assumed to be uniform and in the other model the volume density of traps decreases exponentially with increasing depth. Analytical expressions are obtained for the width and position of the peak in the normalizedconductance curves in both models, and the accuracy and limitations of these expressions are indicated. A new procedure for investigating interfacial states by the admittance method is proposed, based on the use of G-V characteristics of metal-insulator-semiconductor (MIS) structures measured at a fixed frequency.

Identification of the multicomponent nature of E 0 photoreflectance spectra from moderately doped GaAs substrates

Abstract: The paper considers methods used to identify the multicomponent character of photoreflectance (PR) spectra in the vicinity of the E0 transition measured at room temperature from moderately doped GaAs substrates. It is shown that that if an E0 PR spectrum contains an excitonic component, its presence can be established from both a mathematical and phase analysis, as well as from measurements performed at different laser excitation densities.

Formation of a polarized state in polydiethylsiloxane during structural phase transitions

Abstract: The interrelation between structural rearrangements and a stable induced polarization state in polydiethylsiloxane (PDES) is studied. At the temperatures of crystallization and crystal-crystal transitions in PDES, thermally-induced polarization currents are observed whose temperature dependence is determined by the magnitude of the polarizing field and the choice of polarization temperature interval. This implies the existence of a mesophase state in PDES.

Calculated Spectral Properties of YBa2Cu3O7 - Thin Films

Abstract: The present paper reports the results of theoretical valence band structure investigations of high-temperature YBa 2 Cu 3 O 7-δ thin films obtained by calculation of the X-ray emission (XES) and photoelectron (PES) spectra. The XES and PES spectra were obtained on the basis of energy band structure calculations which were realized in the framework of a local density functional approximation using the film linearized augmented plane wave method. The calculated spectra are compared with the experimental data. The main characteristic properties of the experimental spectra are interpreted on the basis of the performed computations.

Strong-norm error estimates for the projective-difference method for approximately solving abstract parabolic equations

Abstract: Solutions continuously differentiable with respect to time of parabolic equations in Hilbert space are obtained by the projective-difference method approximately. The discretization of the problem is carried out in the spatial variables using Galerkin's method, and in the time variable using Euler's implicit method. Strong-norm error estimates for approximate solutions are obtained. These estimates not only allow one to establish the convergence of the approximate solutions to the exact ones but also yield numerical characteristics of the rates of convergence. In particular, order-sharp error estimates for finite element subspaces are obtained.

Functional properties of silicon/non-native-oxide heterostructures

Abstract: It is shown possible to use Al/SnO2/Si and Al/WO3/Si metal-oxide-semiconductor structures as photodiodes with a large-area heterojunction. For structures with a film of amorphous tungsten trioxide (a-WO3) they show promise for applications associated with the development of varicaps and photovaricaps and also chemical sensors of the capacitance type.

Nonlinear dynamics in an electrical circuit containing a ferroelectric

Abstract: Nonlinear effects in a series oscillator circuit containing a ferroelectric capacitor are investigated as a function of the temperature and the amplitude of the applied field. A relation is established between the circuit parameters and the resonance shift in samples of a pure triglycine sulfate crystal and in samples containing chromium impurity ions. The observed effects are explained on the basis of a feature in the domain structure of the samples and the influence of point defects on it.

Fourier-Haar Multipliers

Abstract: In this section we investigate multipliers with respect to the H.s. A sequence λ n , k , (n, k) ∈ Ω generates the operator $$ \Lambda (\sum\limits_{(n,k) \in \Omega } {{a_{n,k}}x_n^k} ) = \sum {{\lambda _{n,k}}{c_{n,k}}x_n^k} $$ (1) on the polynomials with respect to the H.s. Such operators are said to be multipliers. Recall that the norm of Λ from L p into L p (L p ) is denoted by ‖Λ‖p,q (‖Λ‖ p ). The main result of Chapter 5 (Corollary 5.8) may be formulated in the following way. If , then (2)

Information processing as an intrinsic property of biological systems: Origin and dynamics of information

Abstract: Information processing is a main property which distinguishes life from inorganic matter. Its background is the recognition activity of biomacro‐molecules based on quantum non‐demolition measurements. Reflective arrows in the set of mappings appearing from quantum measurements do form a hypercyclic structure which realizes information transfer and allows a system to self‐reproduce and evolve. These arrows correspond to Goedel numbers created inside a system.

Photoelectron spectra of thin films of the high-Tc superconductor YBa2Cu3O7−δ

Abstract: The results of calculations of the energy band structure of thin films are used to obtain theoretical photoelectron spectra of the valence band of the compound YBa2Cu3O7−δ for δ=0 and δ=1 at various photon energies; the spectra are averaged over the photoelectron emission angles. The principal structural features of the spectra are determined by the d states of copper atoms, while the variation of the shape of the spectra with increasing photon energy is attributed to a relative decrease in the contribution from the p states of oxygen atoms. The density of d states around the Fermi level for YBa2Cu3O6 films is observed to increase relative to YBa2Cu3O7 films.