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It is known that the sound speed in medium that contain highly compressible inclusions, e.g. air pores in an elastic medium or gas bubbles in the liquid may be significantly reduced compared to a homogeneous medium. Effective nonlinear parameter of medium, describing the manifestation of nonlinear effects, increases hundreds and thousands of times because of the large differences in the compressibility of the inclusions and the medium. Spatial change in the concentration of such inclusions leads to the variable local sound speed, which in turn calls the spatial-temporal redistribution of acoustic energy in the wave and the distortion of its temporal profiles and cross-section structure of bounded beams. In particular, focal areas can form. Under certain conditions, the sound channel is formed that provides waveguide propagation of acoustic signals in the medium with similar inclusions. Thus, it is possible to control spatial-temporal structure of acoustic waves with the introduction of highly compressible inclusions with a given spatial distribution and concentration. The aim of this work is to study the propagation of acoustic waves in a rubberlike material with non-uniform spatial air cavities. The main objective is the development of an adequate theory of such structurally inhomogeneous media, theory of propagation of nonlinear acoustic waves and beams in these media, the calculation of the acoustic fields and identify the communication parameters of the medium and inclusions with characteristics of propagating waves. In the work the evolutionary self-consistent equation with integro-differential term is obtained describing in the low-frequency approximation propagation of intense acoustic beams in a medium with highly compressible cavities. In this equation the secondary acoustic field is taken into account caused by the dynamics of the cavities oscillations. The method is developed to obtain exact analytical solutions for nonlinear acoustic field of the beam on its axis and to calculate the field in the focal areas. The obtained results are applied to theoretical modeling of a material with non-uniform distribution of strongly compressible inclusions.

Within the framework of the actual problem of comet-asteroid danger, the physical processes causing the destruction and fragmentation of meteor bodies in the Earth’s atmosphere are numerically investigated. Based on the developed physicalmathematical models that determines the movements of space objects of natural origin in the atmosphere and their interaction with it, the fall of three, one of the largest and by some parameters unusual bolides in the history of meteoritics, are considered: Tunguska, Vitim and Chelyabinsk. Their singularity lies in the absence of any material meteorite remains and craters in the area of the alleged crash site for the first two bodies and the non-detection, as it is assumed, of the main mother body for the third body (due to the too small amount of mass of the fallen fragments compared to the estimated mass). The effect of aerodynamic loads and heat flows on these bodies are studied, which leads to intensive surface mass loss and possible mechanical destruction. The velocities of the studied celestial bodies and the change in their masses are determined from the modernized system of equations of the theory of meteoric physics. An important factor that is taken into account here is the variability of the meteorite mass entrainment parameter under the action of heat fluxes (radiation and convective) along the flight path. The process of fragmentation of meteoroids in this paper is considered within the framework of a progressive crushing model based on the statistical theory of strength, taking into account the influence of the scale factor on the ultimate strength of objects. The phenomena and effects arising at various kinematic and physical parameters of each of these bodies are revealed. In particular, the change in the ballistics of their flight in the denser layers of the atmosphere, consisting in the transition from the fall mode to the ascent mode. At the same time, the following scenarios of the event can be realized: 1) the return of the body back to outer space at its residual velocity greater than the second cosmic one; 2) the transition of the body to the orbit of the Earth satellite at a residual velocity greater than the first cosmic one; 3) at lower values of the residual velocity of the body, its return after some time to the fall mode and falling out at a considerable distance from the intended crash site. It is the implementation of one of these three scenarios of the event that explains, for example, the absence of material traces, including craters, in the case of the Tunguska bolide in the vicinity of the forest collapse. Assumptions about the possibility of such scenarios have been made earlier by other authors, and in this paper their implementation is confirmed by the results of numerical calculations.

Self-organization of molecules on a solid surface is one of the promising directions for materials generation with unique magnetic, electrical, and optical properties. They can be widely used in fields such as electronics, optoelectronics, catalysis, and biology. However, the structure and physicochemical properties of adsorbed molecules are influenced by many parameters that must be taken into account when studying the self-organization of molecules. Therefore, the experimental study of such materials is expensive, and quite often it is difficult for various reasons. In such situations, it is advisable to use the mathematical modeling. One of the parameters in the considered adsorption systems is the multiparticle interaction, which is often not taken into account in simulations due to the complexity of the calculations. In this paper, we evaluated the influence of multiparticle interactions on the total energy of the system using the transfer-matrix method and the Materials Studio software package. The model of monocentric adsorption with nearest interactions on a triangular lattice was taken as the basis. Phase diagrams in the ground state were constructed and a number of thermodynamic characteristics (coverage $\theta$, entropy $S$, susceptibility $\xi$) were calculated at nonzero temperatures. The formation of all four ordered structures (lattice gas with $\theta=0$, $(\sqrt{3} \times \sqrt{3}) R30^{\circ}$ with $\theta = \frac{1}{3}$, $(\sqrt{3} \times \sqrt{3})R^{*}30^{\circ}$ with $\theta = \frac{2}{3}$ and densest phase with $\theta = 1$) in a system with only pairwise interactions, and the absence of the phase  $(\sqrt{3}\times \sqrt{3}) R30^\circ$ when only three-body interactions are taken into account, were found. Using the example of an atomistic model of the trimesic acid adsorption layer by quantum mechanical methods we determined that in such a system the contribution of multiparticle interactions is 11.44% of the pair interactions energy. There are only quantitative differences at such values. The transition region from the  $(\sqrt{3} \times \sqrt{3}) R^{*}30^\circ$ to the densest phase shifts to the right by 38.25% at $\frac{\varepsilon}{RT} = 4$ and to the left by 23.46% at $\frac{\varepsilon}{RT} = −2$.

Superplastic forming of Ni and Ti based alloys is widely used in aerospace industry. The main advantage of using the effect of superplasticity in sheet metal forming processes is a feasibility of forming materials with a high amount of plastic strain in conditions of prevailing tensile stresses. This article is dedicated to study commercial FEM software SFTC DEFORM application for prediction thickness deviation during low temperature superplastic forming of UFG Ti-6-4 alloy. Experimentally, thickness deviation during superplastic forming can be observed in the local area of plastic deformation and this process is aggravated by local softening of the metal and this is stipulated by microstructure coarsening. The theoretical model was prepared to analyze experimentally observed metal flow. Two approaches have been used for that. The first one is the using of integrated creep rheology model in DEFORM. As superplastic effect is observed only in materials with fine and ultrafine grain sizes the second approach is carried out using own user procedures for rheology model which is based on microstructure evolution equations. These equations have been implemented into DEFORM via Fortran user’s solver subroutines. Using of FEM simulation for this type of forming allows tracking a strain rate in different parts of a workpiece during a process, which is crucial for maintaining the superplastic conditions. Comparison of these approaches allows us to make conclusions about effect of microstructure evolution on metal flow during superplastic deformation. The results of the FEM analysis and theoretical conclusions have been approved by results of the conducted Erichsen test. The main issues of this study are as follows: a) the DEFORM software allows an engineer to predict formation of metal shape under the condition of low-temperature superplasticity; b) in order to augment the accuracy of the prediction of local deformations, the effect of the microstructure state of an alloy having sub-microcristalline structure should be taken into account in the course of calculations in the DEFORM software.

Optimal management of fuel supply system boils down to choosing an energy development strategy which provides consumers with the most efficient and reliable fuel and energy supply. As a part of the program on switching the heat supply distributed management system of the Udmurt Republic to renewable energy sources, an “Information-analytical system of regional alternative fuel supply management” was developed. The paper presents the mathematical model of optimal management of fuel supply logistic system consisting of three interconnected levels: raw material accumulation points, fuel preparation points and fuel consumption points, which are heat sources. In order to increase effective the performance of regional fuel supply system a modification of information-analytical system and extension of its set of functions using the methods of quick responding when emergency occurs are required. Emergencies which occur on any one of these levels demand the management of the whole system to reconfigure. The paper demonstrates models and algorithms of optimal management in case of emergency involving break down of such production links of logistic system as raw material accumulation points and fuel preparation points. In mathematical models, the target criterion is minimization of costs associated with the functioning of logistic system in case of emergency. The implementation of the developed algorithms is based on the usage of genetic optimization algorithms, which made it possible to obtain a more accurate solution in less time. The developed models and algorithms are integrated into the information-analytical system that enables to provide effective management of alternative fuel supply of the Udmurt Republic in case of emergency.

Now days the main research activity in the field of nanotechnology is aimed at the creation, study and application of new materials and new structures. Recently, much attention has been attracted by the possibility of controlling magnetic properties using a superconducting current, as well as the influence of magnetic dynamics on the current–voltage characteristics of hybrid superconductor/ferromagnet (S/F) nanostructures. In particular, such structures include the S/F/S Josephson junction or molecular nanomagnets coupled to the Josephson junctions. Theoretical studies of the dynamics of such structures need processes of a large number of coupled nonlinear equations. Numerical modeling of hybrid superconductor/magnet nanostructures implies the calculation of both magnetic dynamics and the dynamics of the superconducting phase, which strongly increases their complexity and scale, so it is advisable to use heterogeneous computing systems.

In the course of studying the physical properties of these objects, it becomes necessary to numerically solve complex systems of nonlinear differential equations, which requires significant time and computational resources.

The currently existing micromagnetic algorithms and frameworks are based on the finite difference or finite element method and are extremely useful for modeling the dynamics of magnetization on a wide time scale. However, the functionality of existing packages does not allow to fully implement the desired computation scheme.

The aim of the research is to develop a unified environment for modeling hybrid superconductor/magnet nanostructures, providing access to solvers and developed algorithms, and based on a heterogeneous computing paradigm that allows research of superconducting elements in nanoscale structures with magnets and hybrid quantum materials. In this paper, we investigate resonant phenomena in the nanomagnet system associated with the Josephson junction. Such a system has rich resonant physics. To study the possibility of magnetic reversal depending on the model parameters, it is necessary to solve numerically the Cauchy problem for a system of nonlinear equations. For numerical simulation of hybrid superconductor/magnet nanostructures, a computing environment based on the heterogeneous HybriLIT computing platform is implemented. During the calculations, all the calculation times obtained were averaged over three launches. The results obtained here are of great practical importance and provide the necessary information for evaluating the physical parameters in superconductor/magnet hybrid nanostructures.

Course “Natural models of parallel computing”, given for senior students of the Faculty of Computational Mathematics and Cybernetics, Moscow State University, is devoted to the issues of supercomputer implementation of natural computational models and is, in fact, an introduction to the theory of natural computing, a relatively new branch of science, formed at the intersection of mathematics, computer science and natural sciences (especially biology). Topics of the natural computing include both already classic subjects such as cellular automata, and relatively new, introduced in the last 10–20 years, such as swarm intelligence. Despite its biological origin, all these models are widely applied in the fields related to computer data processing. Research in the field of natural computing is closely related to issues and technology of parallel computing. Presentation of theoretical material of the course is accompanied by a consideration of the possible schemes for parallel computing, in the practical part of the course it is supposed to perform by the students a software implementation using MPI technology and numerical experiments to investigate the effectiveness of the chosen schemes of parallel computing.