Clusterization of Stochastically Wandering Particles in Potential Fields

Computer models belonging to the class of models of growth controlled by a gradient are investigated. A theoretical approach to the construction of model algorithms of this class allows us to obtain a wide variety of clusters with different structures, including fractal ones. A consideration of gradient increments to the potential leads to the formation of vertical, nonbranching, and insulated clusters corresponding to a long-range potential with large gradient.     

Solution of the Electrodiffusion Equations in the Quasi-Stationary Approximation

The electrodiffusion equations are solved together with the equation for the current running through the boundary of the examined system with the environment. The complete system of equations allows the volt-ampere characteristic of the system to be obtained for an arbitrary time dependence of the external potential. The procedure of finding the first-order approximation is developed to solve the system of electrodiffusion equations.     

Tomography of Binomial States of the Radiation Field

The symplectic, optical, and photon-number tomographic symbols of binomial states of the radiation field are studied. Explicit relations for all tomograms of the binomial states are obtained. Two measures for nonclassical properties of these states are discussed.     

Localization of nonlinear waves in elastic bodies with inclusions

By the example of the problem of the motion of a semi-infinite string lying on an elastic base, a method for describing wave localization near inclusions is proposed for the case of a cubic nonlinearity of the base. The method applies the perturbation technique to the amplitude of a localized mode. The nature of the divergences is revealed, and the secular terms are found to belong to one of two types: inphase or antiphase with the localized wave. It is shown that a combination of the renormalization method and multiscale method provides a convergence of the solutions, which are sought for in the form of power series in the amplitude of the localized mode. It is found that the localization process is determined by the type of the discrete spectrum, type of the nonlinearity, and type of dispersion. The nonlinearity of the elastic base produces two characteristic effects. First, the frequency of the localized wave becomes dependent on the wave amplitude. Second, the system can generate traveling waves at multiple frequencies, which withdraw energy from the localized wave and cause it to decay. The decay behavior is determined by the minimum frequency of these traveling waves (because it must be higher than the cutoff frequency). The lifetime of the localized wave as a function of the mass of a dynamic inclusion exhibits a number of maxima. In particular, the first maximum corresponds to the minimum amplitude of the traveling wave at the triple frequency.     

Scattering of high-frequency waves by surfaces in continuous media with allowance for rereflections

This study is devoted to the development of the ray theory of diffraction in application to arbitrary (nonconvex) smooth obstacles in the scalar case. A three-dimensional problem is considered. An asymptotic method of estimating the diffraction integrals is described. The method is based on the multidimensional stationary phase approach. The diffraction integrals are obtained on the basis of the generalization of the Kirchhoff physical theory of diffraction. Explicit expressions are derived for the pressure in the reflected wave in the cases of its single and double reflections.     

Physical processes underlying the development of shear turbulence

A physical model of the development of turbulence in free shear flows is proposed. The model is based on the results of numerical simulations of turbulent flow development. The main ideas of the proposed theory of turbulence are stated as follows: the onset of turbulence begins with the formation of large vortices; spectral energy transfer involves both direct and inverse cascades; and the inertial range of the energy spectrum develops as a result of concurrent direct and inverse cascades. The dominant physical factors that determine the spectrum include Joukowski forces.