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The article is devoted to the numerical study of shock-wave flows in inhomogeneous media–gas mixtures. In this work, a two-speed two-temperature model is used, in which the dispersed component of the mixture has its own speed and temperature. To describe the change in the concentration of the dispersed component, the equation of conservation of “average density” is solved. This study took into account interphase thermal interaction and interphase pulse exchange. The mathematical model allows the carrier component of the mixture to be described as a viscous, compressible and heat-conducting medium. The system of equations was solved using the explicit Mac-Cormack second-order finite-difference method. To obtain a monotone numerical solution, a nonlinear correction scheme was applied to the grid function. In the problem of shock-wave flow, the Dirichlet boundary conditions were specified for the velocity components, and the Neumann boundary conditions were specified for the other unknown functions. In numerical calculations, in order to reveal the dependence of the dynamics of the entire mixture on the properties of the solid component, various parameters of the dispersed phase were considered — the volume content as well as the linear size of the dispersed inclusions. The goal of the research was to determine how the properties of solid inclusions affect the parameters of the dynamics of the carrier medium — gas. The motion of an inhomogeneous medium in a shock duct divided into two parts was studied, the gas pressure in one of the channel compartments is more important than in the other. The article simulated the movement of a direct shock wave from a high-pressure chamber to a low–pressure chamber filled with a dusty medium and the subsequent reflection of a shock wave from a solid surface. An analysis of numerical calculations showed that a decrease in the linear particle size of the gas suspension and an increase in the physical density of the material from which the particles are composed leads to the formation of a more intense reflected shock wave with a higher temperature and gas density, as well as a lower speed of movement of the reflected disturbance reflected wave.

The article reports the findings of an investigation into pollution migration processes at the municipal solid waste (MSW) landfill located in the water protection zone of Lake Seliger (Tver Region). The distribution of pollutants is investigated and migration parameters are determined in field and laboratory conditions at the landfill site. A mathematical model describing physical and chemical processes of substance migration in soil strata is constructed. Pollutant migration is found to be due to a variety of factors. The major ones, having a significant impact on the migration of MSW ingredients and taken into account mathematically, include convective transport, diffusion and sorption processes. A modified mathematical model differs from its conventional counterparts by considering a number of parameters reflecting the decrease in the concentration of ammonium and nitrate nitrogen ions in ground water (transpiration by plant roots, dilution with infiltration waters, etc.). An analytical solution to assess the pollutant spread from the landfill is presented. The mathematical model provides a set of simulation models helping to obtain a computational solution of specific problems, vertical and horizontal migration of substances in the underground flow. Numerical experiments, analytical solutions, as well as field and laboratory data was studied the dynamics of pollutant distribution in the object under study up to the lake. A long-term forecast for the spread of landfill pollution is made. Simulation experiments showed that some zones of clean groundwater interact with those of contaminated groundwater during the pollution migration from the landfill, each characterized by a different pollutant content. The data of a computational experiments and analytical calculations are consistent with the findings of field and laboratory investigations of the object and give grounds to recommend the proposed models for predicting pollution migration from a landfill. The analysis of the pollution migration simulation allows to substantiate the numerical estimates of the increase in $NH_4^+$ and $NO_3^-$ ion concentration with the landfill operation time. It is found that, after 100 years following the landfill opening, toxic filtrate components will fill the entire pore space from the landfill to the lake resulting in a significant deterioration of the ecosystem of Lake Seliger.

In this work, we consider a special approximation of the general perturbation formula for the electromagnetic field by a set of electrically small inhomogeneities located in the domain of interest. The problem considered in this paper arises in many applications of technical electrodynamics, radar technologies and subsurface remote sensing. In the general case, it is formulated as follows: at some point in the perturbed domain, it is necessary to determine the amplitude of the electromagnetic field. The perturbation of electromagnetic waves is caused by a set of electrically small scatterers distributed in space. The source of electromagnetic waves is also located in perturbed domain. The problem is solved by introducing the far field approximation and through the formulation for the scatterer radar cross section value. This, in turn, allows one to significantly speed up the calculation process of the perturbed electromagnetic field by a set of a spherical inhomogeneities identical to each other with arbitrary electrophysical parameters. In this paper, we consider only the direct scattering problem; therefore, all parameters of the scatterers are known. In this context, it may be argued that the formulation corresponds to the well-posed problem and does not imply the solution of the integral equation in the generalized formula. One of the features of the proposed algorithm is the allocation of a characteristic plane at the domain boundary. All points of observation of the state of the system belong to this plane. Set of the scatterers is located inside the observation region, which is formed by this surface. The approximation is tested by comparing the results obtained with the solution of the general formula method for the perturbation of the electromagnetic field. This approach, among other things, allows one to remove a number of restrictions on the general perturbation formula for E-filed analysis.

There are conditions of uneven combustion for tubular powder elements of large elongation used in artillery propelling charges. Here it is necessary to consider in parallel the processes of combustion and movement of powder gases inside and outside the channels of the powder tubes. Without this, it is impossible to adequately formulate and solve the problems of ignition, erosive combustion and stress-strain state of tubular powder elements in the shot process. The paper presents a physical and mathematical formulation of the main problem of the internal ballistics of an artillery shot for a charge consisting of a set of powder tubes. Combustion and movement of a bundle of powder tubes along the barrel channel is modeled by an equivalent tubular charge of all-round combustion. The end and cross-sectional areas of the channel of such a charge (equivalent tube) are equal to the sum of the areas of the ends and cross-sections of the channels of the powder tubes, respectively. The combustion surface of the channel is equal to the sum of the inner surfaces of the tubes in the bundle. The outer combustion surface of the equivalent tube is equal to the sum of the outer surfaces of the tubes in the bundle. It is assumed that the equivalent tube moves along the axis of the bore. The speed of motion of an equivalent tubular charge and its current position are determined from Newton’s second law. To calculate the flow parameters, we used two-dimensional axisymmetric equations of gas dynamics, for the solution of which an axisymmetric orthogonalized difference mesh is constructed, which adapts to the flow conditions. When the tube moves and burns, the difference grid is rearranged taking into account the changing regions of integration. The control volume method is used for the numerical solution of the system of gas-dynamic equations. The gas parameters at the boundaries of the control volumes are determined using a self-similar solution to the Godunov problem of decay for an arbitrary discontinuity. The developed technique was used to calculate the internal ballistics parameters of an artillery shot. This approach is considered for the first time and allows a new approach to the design of tubular artillery charges, since it allows obtaining the necessary information in the form of fields of velocity and pressure of powder gases for calculating the process of gradual ignition, unsteady erosive combustion, stress-strain state and strength of powder elements during the shot. The time dependences of the parameters of the internal ballistics process and the distribution of the main parameters of the flow of combustion products at different times are presented.

Rugose spiraling whitefly (RSW) is one of the major pests which affects the coconut trees. It feeds on the tree by sucking up the water content as well as the essential nutrients from leaves. It also forms sooty mold in leaves due to which the process of photosynthesis is inhibited. Biocontrol of pest is harmless for trees and crops. The experimental results in literature reveal that Pseudomallada astur is a potential predator for this pest. We investigate the dynamics of predator, Pseudomallada astur’s interaction with rugose spiralling whitefly, Aleurodicus rugioperculatus in coconut trees using a mathematical model. In this system of ordinary differential equation, the pest-predator interaction is modeled using Holling type III functional response. The parametric values are calculated from the experimental results and are tabulated. An approximate analytical solution for the system has been derived. The homotopy analysis method proves to be a suitable method for creating solutions that are valid even for moderate to large parameter values, hence we employ the same to solve this nonlinear model. The $\hbar$-curves, which give the admissible region of $\hbar$, are provided to validate the region of convergence. We have derived the approximate solution at fifth order and stopped at this order since we obtain a more approximate solution in this iteration. Numerical simulation is obtained through MATLAB. The analytical results are compared with numerical simulation and are found to be in good agreement. The biological interpretation of figures implies that the use of a predator reduces the whitefly’s growth to a greater extent.

This work is devoted to the study of the problem of modeling and analyzing complex oscillatory modes, both regular and chaotic, in systems of interacting populations in the presence of random perturbations. As an initial conceptual deterministic model, a Volterra system of three differential equations is considered, which describes the dynamics of prey populations of two competing species and a predator. This model takes into account the following key biological factors: the natural increase in prey, their intraspecific and interspecific competition, the extinction of predators in the absence of prey, the rate of predation by predators, the growth of the predator population due to predation, and the intensity of intraspecific competition in the predator population. The growth rate of the second prey population is used as a bifurcation parameter. At a certain interval of variation of this parameter, the system demonstrates a wide variety of dynamic modes: equilibrium, oscillatory, and chaotic. An important feature of this model is multistability. In this paper, we focus on the study of the parametric zone of tristability, when a stable equilibrium and two limit cycles coexist in the system. Such birhythmicity in the presence of random perturbations generates new dynamic modes that have no analogues in the deterministic case. The aim of the paper is a detailed study of stochastic phenomena caused by random fluctuations in the growth rate of the second population of prey. As a mathematical model of such fluctuations, we consider white Gaussian noise. Using methods of direct numerical modeling of solutions of the corresponding system of stochastic differential equations, the following phenomena have been identified and described: unidirectional stochastic transitions from one cycle to another, trigger mode caused by transitions between cycles, noise-induced transitions from cycles to the equilibrium, corresponding to the extinction of the predator and the second prey population. The paper presents the results of the analysis of these phenomena using the Lyapunov exponents, and identifies the parametric conditions for transitions from order to chaos and from chaos to order. For the analytical study of such noise-induced multi-stage transitions, the technique of stochastic sensitivity functions and the method of confidence regions were applied. The paper shows how this mathematical apparatus allows predicting the intensity of noise, leading to qualitative transformations of the modes of stochastic population dynamics.

A two-dimensional mathematical model was developed for estimating the stresses in welded joints formed during multipass welding of multilayer steels. The basis of the model is the system of equations that includes the Lagrange variational equation of incremental plasticity theory and the variational equation of heat conduction, which expresses the principle of M. Biot. Variational-difference method was used to solve the problems of heat conductivity and calculation of the transient temperature field, and then at each time step – for the quasi-static problem of thermoplasticity. The numerical scheme is based on triangular meshes, which gives a more accuracy in describing the boundaries of structural elements as compared to rectangular grids.

Numerical investigation of mixing non-isothermal streams of sodium coolant in a T-branch is carried out in the FlowVision CFD software. This study is aimed at argumentation of applicability of different approaches to prediction of oscillating behavior of the flow in the mixing zone and simulation of temperature pulsations. The following approaches are considered: URANS (Unsteady Reynolds Averaged Navier Stokers), LES (Large Eddy Simulation) and quasi-DNS (Direct Numerical Simulation). One of the main tasks of the work is detection of the advantages and drawbacks of the aforementioned approaches.

Numerical investigation of temperature pulsations, arising in the liquid and T-branch walls from the mixing of non-isothermal streams of sodium coolant was carried out within a mathematical model assuming that the flow is turbulent, the fluid density does not depend on pressure, and that heat exchange proceeds between the coolant and T-branch walls. Model LMS designed for modeling turbulent heat transfer was used in the calculations within URANS approach. The model allows calculation of the Prandtl number distribution over the computational domain.

Preliminary study was dedicated to estimation of the influence of computational grid on the development of oscillating flow and character of temperature pulsation within the aforementioned approaches. The study resulted in formulation of criteria for grid generation for each approach.

Then, calculations of three flow regimes have been carried out. The regimes differ by the ratios of the sodium mass flow rates and temperatures at the T-branch inlets. Each regime was calculated with use of the URANS, LES and quasi-DNS approaches.

At the final stage of the work analytical comparison of numerical and experimental data was performed. Advantages and drawbacks of each approach to simulation of mixing non-isothermal streams of sodium coolant in the T-branch are revealed and formulated.

It is shown that the URANS approach predicts the mean temperature distribution with a reasonable accuracy. It requires essentially less computational and time resources compared to the LES and DNS approaches. The drawback of this approach is that it does not reproduce pulsations of velocity, pressure and temperature.

The LES and DNS approaches also predict the mean temperature with a reasonable accuracy. They provide oscillating solutions. The obtained amplitudes of the temperature pulsations exceed the experimental ones. The spectral power densities in the check points inside the sodium flow agree well with the experimental data. However, the expenses of the computational and time resources essentially exceed those for the URANS approach in the performed numerical experiments: 350 times for LES and 1500 times for ·DNS.

The paper develops a new mathematical method of the joint signal and noise calculation at the Rice statistical distribution based on combing the maximum likelihood method and the method of moments. The calculation of the sough-for values of signal and noise is implemented by processing the sampled measurements of the analyzed Rician signal’s amplitude. The explicit equations’ system has been obtained for required signal and noise parameters and the results of its numerical solution are provided confirming the efficiency of the proposed technique. It has been shown that solving the two-parameter task by means of the proposed technique does not lead to the increase of the volume of demanded calculative resources if compared with solving the task in one-parameter approximation. An analytical solution of the task has been obtained for the particular case of small value of the signal-to-noise ratio. The paper presents the investigation of the dependence of the sought for parameters estimation accuracy and dispersion on the quantity of measurements in experimental sample. According to the results of numerical experiments, the dispersion values of the estimated sought-for signal and noise parameters calculated by means of the proposed technique change in inverse proportion to the quantity of measurements in a sample. There has been implemented a comparison of the accuracy of the soughtfor Rician parameters’ estimation by means of the proposed technique and by earlier developed version of the method of moments. The problem having been considered in the paper is meaningful for the purposes of Rician data processing, in particular, at the systems of magnetic-resonance visualization, in devices of ultrasonic visualization, at optical signals’ analysis in range-measuring systems, at radar signals’ analysis, as well as at solving many other scientific and applied tasks that are adequately described by the Rice statistical model.

A dynamic game theoretic model of struggle against corruption in resource allocation is considered. It is supposed that the system of resource allocation includes one principal, one or several supervisors, and several agents. The relations between them are hierarchical: the principal influences to the supervisors, and they in turn exert influence on the agents. It is assumed that the supervisor can be corrupted. The agents propose bribes to the supervisor who in exchange allocates additional resources to them. It is also supposed that the principal is not corrupted and does not have her own purposes. The model is investigated from the point of view of the supervisor and the agents. From the point of view of agents a non-cooperative game arises with a set of Nash equilibria as a solution. The set is found analytically on the base of Pontryagin maximum principle for the specific class of model functions. From the point of view of the supervisor a hierarchical Germeyer game of the type Г_2t is built, and the respective algorithm of its solution is proposed. The punishment strategy is found analytically, and the reward strategy is built numerically on the base of a discrete analogue of the initial continuous- time model. It is supposed that all agents can change their strategies in the same time instants only a finite number of times. Thus, the supervisor can maximize his objective function of many variables instead of maximization of the objective functional. A method of qualitatively representative scenarios is used for the solution. The idea of this method consists in that it is possible to choose a very small number of scenarios among all potential ones that represent all qualitatively different trajectories of the system dynamics. These scenarios differ in principle while all other scenarios yield no essentially new results. Then a complete enumeration of the qualitatively representative scenarios becomes possible. After that, the supervisor reports to the agents the rewardpunishment control mechanism.