Vol 10, No 5 (2018)

Model allowing analytical and numerical studies of a dusty plasma system is used to describe the dynamics of a monolayer of dusty particles. The mechanism of energy transfer between horizontal and vertical particle motion based on parametric resonance is described by the extended Mathieu equation. The resonance regions and growth rates of dust particles energy are obtained. The conditions for the occurrence of resonance and the initial stage of energy transfer are described more precisely based on the analysis of the obtained data. It is shown that a wide spectrum of dust particle oscillations participates in the system heating. The harmonics contributing the most to this process are determined.

The kinetic Monte Carlo (kMC) method is an indispensable method for studying atomic and molecular systems, which makes it possible to solve a wide range of problems associated with atomic diffusion, the formation of defects and chemical compounds of various types, as well as the growth and self-organization of nanostructures. In this paper, we consider the fundamentals of the kMC and its modern modifications, both rigid-lattice and off-lattice. Particular attention is focused on constructing self-learning algorithms based on different methods for finding the saddle points of potential energy and on the techniques for the acceleration of the Monte Carlo method. Every considered method is illustrated by relevant examples mostly associated with the physics of metal surfaces.

The plane steady-state filtration in a phreatimetric formation to an imperfect gallery in the presence of evaporation from the free surface of groundwater is considered. In order to study the evaporation effect, a multiparameter mixed boundary-value problem of the theory of analytic functions is posed and solved by the Polubarinova-Kochina method. Based on the proposed model, we develop an algorithm to compute the seepage flow characteristics and provide the hydrodynamic analysis of the impact of the dependences of all the physical parameters of the scheme on the flow rate of the gallery and the ordinate of the exit point of the depression curve on an impermeable screen.

The gravitational instability of a homogeneous isotropic infinite gravitating gaseous medium is investigated in order to study the physical processes that take place during the formation of the solar planetary system. The analytical and numerical solutions of the motion equations of such a medium are considered in two approximations: cold gas and gas at a finite temperature. The real solutions describing the behavior of both wave density disturbances of a homogeneous medium and single disturbances are obtained. Waves of gravitational instability whose amplitude grows exponentially and whose highs and lows, as well as their nodal points, retain their positions in space follow the basic laws of Jean’s model. The authors interpret this wave of instability as an analogue of protoplanetary rings, which can be formed in protoplanetary disks. According to the numerical calculation results, the reaction of a homogeneous gravitating medium to the single initial perturbation of its density is significantly different from the laws of Jean’s model. The instability localized in single initial perturbations extends to the region λ < λ_J, although in this case the growth of the perturbation density is considerably less than for λ > λ_J. It is discovered that the gravitational instabilities in the region λ > λ_J suppress sound. It is shown that, without taking into account the rotation of the Sun’s protoplanetary disk medium, its critical density in the event of a large-scale gravitational instability is about four orders of magnitude smaller than the critical density in accordance with the theory of planet formation by the accumulation of solids and particles.

The aim of this work is to study the spatial dynamic of wave propagation in rock formations, taking into account ravines and caverns. The dynamics of the seismic and acoustic waves generated by explosions of different types is investigated using seismograms measured by several reception lines. The research uses the numerical experiments using the full-wave joint simulation of acoustic and seismic wave propagation in heterogeneous mixed acoustic and linear-elastic media. The grid-characteristic method is used to obtain the mathematically and physically correct description of spatial dynamic wave processes taking the boundary and contact surfaces, including the interfaces between the linearelastic and the acoustic environments, into consideration. The influence of the type of explosion on the spatial dynamic wave patterns and seismograms is analyzed for the cases of horizontal and vertical reception lines. The dependences of spatial dynamic wave patterns and seismograms recorded by the horizontal and vertical reception lines on the distance of the karst caverns from the ravine are studied. The basic types of waves that different types of explosions generate in the rock formations, ravines, and caverns are investigated. The basic laws that characterize the emerging wave patterns and their influence on seismograms are found.

We consider a two-dimensional nonstationary inverse scattering problem in a layered homogeneous acoustic medium. The data consist of a scattered wavefield from a surface point source registered on the boundary of the half-plane. We prove the uniqueness of the recovery of an acoustic impedance and velocity in a medium from the scattering data. An algorithm for solving an inverse twodimensional scattering problem as a one-dimensional problem with the parameter based on the τ–p Radon transformation is constructed. Also, the numerical modeling results for the direct scattering problem and solutions of a pair of inverse scattering problems in a layered homogeneous acoustic medium are presented. The proposed algorithm is applicable to data processing in geophysical prospecting both for surface seismics and vertical seismic profiling.