On the Influence of Magnetic Field on the Probability of Diffusing Particle Capture by Absorbing Traps

Journal of Experimental and Theoretical Physics - The influence of a magnetic field on the capture of diffusing particles into traps is considered. It is shown that the survival probability for...     

Drift in a random walk along self-similar clusters

This paper is a study of the relationship between diffusion and conductivity when the random walks of particles occur via Lévy hops. It shows that because of the unusual nature of Lévy hops the particle mobility is a nonlinear function of the electric field in arbitrarily weak fields. The crossover to ordinary diffusion by introduction of a finite displacement in each step is also discussed. Zh. éksp. Teor. Fiz. 115, 1016–1023 (March 1999)     

Erratum to: Temporal Asymptotic Form of the Survival Probability in the Effective Medium Approximation for Trapping of Particles in Media with Anomalous Diffusion

Journal of Experimental and Theoretical Physics - erratum     

Universal Temporal Dependence of Survival Probability for Diffusing Particles in Multidimensional Media with Absorbing Traps in an Electric Field

The effect of electric-field-induced reduction of the “effective” dimension is detected in the multidimensional problem of diffusion in a medium with absorbing traps. An effective transition to the 1D case occurs due to directional motion of a particle when it begins to dominate over diffusion. A universal “1D” dependence of the particle survival probability in a multidimensional medium with absorbing traps over long times has been established.     

New Temporal Asymptotics of the Survival Probability in the Capture of Particles in Traps in Media with Anomalous Diffusion

Journal of Experimental and Theoretical Physics - The problem of capture of particles experiencing normal diffusion as well as anomalous subdiffusion to absorbing traps has been investigated. It is...     

Quantum hall effect in inhomogeneous media: Effective characteristics and local current distribution

An analysis is made of the problem of current flow in heterophase inhomogeneous media in the quantum Hall effect regime. Duality relations are derived and expressions are obtained for the effective conductivity of inhomogeneous media over the entire range of concentrations. Local current distributions (fields) are determined in the quantum Hall effect regime.     

On the fixed points and invariants of Dykhne transformations and the stability of the solutions of the problem of the effective conductivity of randomly inhomogeneous two-phase media

The fixed points and invariants of Dykhne transformations are determined. It is established that they correspond to the exact solutions and duality relations for the effective characteristics of an inhomogeneous medium. The stability of the exact solutions for the effective conductivity, which are fixed points of the Dykhne transformations, is studied by bifurcation-theory methods, and a classification of these fixed points by stability type is given. It is shown that the effective conductivity tensor of a two-phase medium in magnetic and ac electric fields for certain parameters of the medium can be an unstable point of the “saddle” type.     

Bound values for Hall conductivity of heterogeneous medium under quantum Hall effect conditions

Bound values for Hall conductivity under quantum Hall effect (QHE) conditions in inhomogeneous medium has been studied. It is shown that bound values for Hall conductivity differ from bound values for metallic conductivity. This is due to the unusual character of current percolation under quantum Hall effect conditions.      

The effective conductivity of two-phase two-dimensional media as a function of the geometric parameters of the medium

The paper deals with the problem of current flow in doubly periodic two-dimensional media whose unit cell is a parallelogram. Local distributions of currents (fields) are found, and the effective conductivity of such media is calculated for equal phase concentrations. The dependence of conductivity on the angle of parallelogram is determined. This dependence is shown to be threshold in media of the metal-insulator type.