Experimental study of the emission spread at gyrotron cathodes by current-voltage characteristics

A scheme for automated study of current-voltage characteristics of gyroresonance devices is developed. The effective emission spread at the cathodes of powerful gyrotrons is studied by analysis of current-voltage characteristics. Experimental data on the effective emission spread parameter for different modes are given. The permissible emission spread at the cathodes of powerful gyrotrons is estimated, and the dependence of the electron beam parameters on the cathode emission spread is presented. A complex measurement technique showing the contribution of different physical mechanisms to the cathode emission spread is proposed. Institute of Applied Physics, Russian Academy of Sciences, Nizhny Novgorod, Russia. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 40, No. 4, pp. 506–516, April, 1997.     

Hausdorff dimension of a random invariant set

The notion of random attractor for a dissipative stochastic dynamical system has recently been introduced. It generalizes the concept of global attractor in the deterministic theory. It has been shown that many stochastic dynamical systems associated to a dissipative partial differential equation perturbed by noise do possess a random attractor. In this paper, we prove that, as in the case of the deterministic attractor, the Hausdorff dimension of the random attractor can be estimated by using global Lyapunov exponents. The result is obtained under very natural assumptions. As an application, we consider a stochastic reaction-diffusion equation and show that its random attractor has finite Hausdorff dimension.     

Fischer--Tropsch, hydrotreating and superClaus catalysts

In modern society the application of catalysts, and hence, research in the field of catalysis, is becoming more and more important. In the strongly increasing chemical industry most reaction processes are performed with the aid of catalysts. Knowledge about the structure of the active sites present at the surface of catalysts will facilitate the design of new catalysts with better performances. Such knowledge can be obtained by Mössbauer spectroscopy, which is an excellent in-situ characterization technique due to the high penetrating power of the γ-radiation used and the sensitivity of the spectral parameters for the chemical state and local environment of the Mössbauer atoms.     

On asymptotic approximations for slow wave processes in nonlinear dispersive media

We consider the application of asymptotic methods of nonlinear mechanics (the Krylov-Bogolyubov-Mitropol'skii method) and the method of separation of motions in nonlinear systems for the construction of an approximate solution of a nonlinear equation that describes a nonstationary wave process. Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 50, No. 3, pp. 357–371, March, 1998.     

Random oscillations in the Van der Pol system under the action of a broadband random process

We construct the second approximation for random oscillations described by the Van der Pol equation which are under the action of a broadband random process. Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 50, No. 11, pp. 1517–1521, November, 1998.     

Investigation of acceptor centers in semiconductors with the diamond crystal structure by the μ − SR method

The residual polarization of negative muons in crystal silicon samples with phosphorus (P: 1.6×10¹³ cm⁻³) and antimony (Sb: 2×10¹⁸ cm⁻³) impurities is investigated. The measurements are made in a 1000 G magnetic field oriented in a direction transverse to the muon spin in the temperature range 4–300 K. The relaxation rate and shift of the precession frequency in the silicon sample with the phosphorus impurity are measured more accurately than previously. It is found that in antimony-doped silicon the acceptor center _μ A1 at temperatures below 30 K can be in both ionized and neutral states. The experimental data are interpreted on the basis of spin-lattice relaxation of the magnetic moment of an acceptor center, formation of acceptor-donor pairs, and recombination of charge carriers at the acceptor. Preliminary measurements showed a nonzero residual polarization of negative muons in germanium. Pis’ma Zh. éksp. Teor. Fiz. 68, No. 1, 61–66 (10 July 1998)     

String representation of SU(3) gluodynamics in the Abelian projection

A dual Ginzburg-Landau model corresponding to SU(3) gluodynamics in the Abelian projection is studied. A string theory describing QCD string dynamics is obtained in this model. The interaction of static quarks in mesons and baryons is investigated in an approximation to leading order. Pis’ma Zh. éksp. Teor. Fiz. 68, No. 2, 109–114 (25 July 1998)     

Random Homeomorphisms and Fourier Expansions

We prove that a random change of variable in general improves convergence properties of the Fourier expansions, and we give a precise quantitative estimate of the phenomenon. Submitted: December 1997, final version: May 1998     

Anomalous proximity effect in d-wave superconductors

The anomalous proximity effect between a d-wave superconductor and a thin disordered normal layer is studied theoretically in the framework of Eilenberger equations. It is shown that disorder of the quasiparticle reflection from this thin layer leads to the formation of an s-wave component localized near the boundary. The angular and spatial structure of the pair potential near the interface is studied. Pis’ma Zh. éksp. Teor. Fiz. 67, No. 7, 478–483 (10 April 1998) Published in English in the original Russian journal. Edited by Steve Torstveit.     

Exact solutions of the nonstationary Schrödinger equation

On the basis of exactly solvable stationary models for the Schrödinger equation, we develop a procedure for solving the nonstationary Schödinger equation in an explicit analytic form. We investigate the formation of the nonadiabatic geometric phase during cyclic evolution of a quantum system.