Alexander Morozovskiy

Effective Conductivity of Percolation Media

The analogy between percolation theory and theory of second-order phase transition is introduced. Effective conductivity is considered as the order parameter of phase transitions. Calculations of critical indexes are provided. Different models of percolation media are considered. Hierarchical model of percolation structure is introduced.

Nonlinear Properties of Composites

Up to now, in the calculation of the effective properties of composites it has been always assumed that local volt-ampere characteristics are linear, i.e., Ohm’s law is valid for each of the phases.

Continual Percolation Problem

Types of continual percolation problem are discussed (including Swiss Cheese models). Solutions to relevant models are presented.

Effective Properties of Ferromagnetic Composites

Theory of composites is applied to inhomogeneous ferromagnetic media. Nonlinearity of ferromagnets near percolation threshold is described. Influence of hysteresis on effective magnetic properties is discussed.

Conductivity of Percolation Layer

The effective conductivity of percolation systems with sizes larger and smaller than percolation length is considered. Statement of the problem and solution is provided. Scaling solution is described.

Temperature Coefficient of Resistance and Third Harmonic Generation Close to Percolation Threshold

Temperature coefficient of resistance near percolation threshold is provided. Relation to the third harmonic generation is discussed.

Percolation-Similar Description of Abrikosov Vortex

Superconductivity on percolation structures is discussed. Pinning of Abricosov vortexes in films is introduced. Formulae for wide pinning force distribution are provided.

Elements of Geometrical Theory of Percolation

Problem of percolation is introduced. Basic features of geometric theory of percolation are discussed.

The Methods of Description of Random Media

Methods and treatments of random media have been discussed. Conditions for self-averaging are provided. Main characteristics of random media are introduced.

Instability and Chaos in the Macroscopically Inhomogeneous Media with Weak Dissipation

Instability in macroscopically inhomogeneous media with low dissipation is discussed for dual media and ladder filter. Problematic statement in Feynman lectures is also discussed.