B. Ya. Balagurov

The conductivity of the 2D Rayleigh model in the critical region (near the metal–insulator phase transition point) is considered. The analytic expression describing effective conductivity σ_e of the model is derived for the entire pre-threshold critical region (up to the contact of circular inclusions). The data obtained for σ_e expansions are compared with the relevant results of the similarity hypothesis.

Low-frequency conductivity in LC-systems modeling disordered lattices with inductive (L) and capacitive (C) links in alternating electric field has been studied. Conditions are established under which real (ohmic)) energy losses in these systems are possible.

The conductivity of the two-dimensional Rayleigh model near a critical point, the percolation threshold, is investigated. The effective conductivity of the model with a metal–prefect conductor phase transition is calculated in the binary (pair) approximation. For the alternative model with a metal–insulator phase transition the corresponding effective conductivity is determined from the Keller–Dykhne reciprocity relation.

The problem for determining Green’s function G( r, r') for the time-independent Schrödinger equation is considered using the potential quantization method. The expression for G( r, r') is...

The problem of elastic scattering of particles has been considered by the potential quantization method. The properties of the eigenfunctions ϕν(+)( r) and eigenvalues αν(+)of this method for states...

The metal–insulator and metal–superconductor phase transitions related to the percolation thresholds in two-component composites are considered. The behavior of effective conductivity σ ein the...

The solution to the problem of the conductivity of the 3D model of a composite with inclusion having a shape of oblate ellipsoids of revolution (spheroids) has been obtained in a wide range of concentrations. The entire range of variation of the shape of inclusions (from a sphere to an infinitely thin circular disk) has been considered. The relation between the percolation thresholds in this model and the quantities characterizing its effective conductivity in the limit of low concentrations of inclusions has been established.