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Article
New exact solution of the Dirac equation. XI
A study in finding new exact solutions of relativistic wave equations, started in [1], is continued. Exact solutions of the Dirac, Klein-Gordon, and classical relativistic equations of motion in four new types...
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Article
New exact solutions of the dirac equation. XII
The search for exact solutions of the Dirac equation begun in [1] is continued. We find three new types of external electromagnetic fields where the Dirac equation, Klein-Gordon equation, and classical Lorentz...
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Article
Lagrangian formulation of a general Hamiltonian theory with constraints
A Lagrangian formulation is constructed for a general Hamiltonian theory with constraints. A modification is proposed of the standard procedure of the “Hamiltonianization” of a Lagrangian theory in the case wh...
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Article
Green's functions in an external electromagnetic field
The possibility is discussed of using eigenfunctions to find different propagators in quantum electrodynamics (QED) with an external electromagnetic field.
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Article
Investigation of Green's functions in an external electromagnetic field by the eigenfunction method
This paper contains a study of Green's functions in a quantum electrodynamics (QED) with an external electromagnetic field that disrupts vacuum stability. Representations are found for the Green's functions of...
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Article
Electromagnetic radiation of charges with fractal distribution
The radiation of charges with fractal distributions is studied in the framework of classical electrodynamics. The properties of the form factork(x) of the density of the fractal distribution are investigated. It ...
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Article
Transmission of quantum particles through a one-dimensional fractal potential barrier
We consider scattering of a nonrelativistic quantum particle by a one-dimensional fractal potential barrier carried by a generalized Cantor set. We obtain recurrence relations for the reflection coefficient an...
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Article
Interaction of electromagnetic waves with fractal structures
A review and analysis is presented of the state of theoretical and experimental investigations of the problem of the interaction of electromagnetic waves with different inhomogeneous media possessing fractal p...
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Article
Relationship between dielectric strength and the multifractal nature of charge distribution on the surface of an electrode
A study is made of the manner in which the nonuniformity of the charge distribution on the surface of an electrode affects the dependence of mean breakdown lag time on electrode area.
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Article
Fractal characteristics of near-electrode formations during electrical discharge in water
In this work we have investigated the characteristic features of optically dense near-electrode formations appearing during electrical discharge in water. We have established that they have a fractal surface. ...
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Article
Relation between the distribution of initiation sites of a discharge and the field nonuniformity at an electrode
The connection between the field nonuniformity at an electrode and the distribution of discharge initiation sites over its surface is described. The results of experiments on the breakdown of transformer oil i...
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Article
Modeling the development of the stepped leader of a lightning discharge
A stochastic-deterministic model is presented for the propagation of a downward-moving leader. Lightning formation is described by a stochastic growth of branching discharge channels which is determined by the...
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Article
Stochastic modeling of the development of the taylor instability in liquid filtration in a porous medium
A modified model of stochastic growth that is controlled by the pressure gradient is used for a numerical study of the instability of the displacement front of liquids with different densities and viscosities ...
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Article
Influence of local heterogeneities on discharge channel trajectory at electric pulse destruction of materials
A stochastically deterministic model of electric discharge development in nonuniform dielectrics is proposed. The results of computer modeling and experimental studies of discharge channel orientation are pres...
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Article
Simulation of Radiation-Chemical Decomposition of Organic Impurities in Liquid Radioactive Wastes at Depth Disposal
A mathematical model is developed to describe the behavior of organic impurities in liquid radioactive wastes at depth geological disposal. The model includes description of the migration of radionuclides and ...
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Article
Dynamics of the Thermal Instability Evolution in Dielectric Breakdown
A mathematical model of the dynamics of temperature, electric field strength, and charge density in thermal dielectric breakdown is examined. The characteristics of the evolution of a thermal instability initi...
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Article
The simulation of dendrite growth and partial discharges in epoxy resin
A self-consistent model of the development of dendrites and partial discharges in a dielectric solid under a variable voltage is suggested. Dendrites originate at sites with the enhanced local field strength a...
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Article
Stochastic‐Deterministic Modeling of the Development of Hydrodynamic Instability in Filtration of Mixing Fluids
The stochastic‐deterministic approach to modeling of the Saffman–Taylor hydrodynamic instability in filtration of mixing fluids in a porous medium is considered. The numerical model is used to study the dynami...
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Article
Modeling of discharges in spatially charged dielectrics
A stochastic-deterministic model of a discharge induced by space charge in dielectric is developed. The spatiotemporal and current characteristics of the discharge are simulated numerically. The simulation res...
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Article
Simulation of the Dynamics of Radiation and Temperature Fields with Deep Burial of Liquid Wastes
A mathematical model of the migration of radionuclides and the dynamics of the temperature field with deep disposal of liquid radioactive wastes in deep porous geological formations is presented. The model inc...
