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When a supersonic air flow interacts with a transverse secondary jet injected into this flow through an orifice on a flat wall, a special flow structure is formed. This flow takes place during fuel injection into combustion chambers of supersonic aircraft engines; therefore, in recent years, various approaches to intensifying gas mixing in this type of flow have been proposed and studied in several countries. The approach proposed in this work implies using spark discharges for pulsed heating of the gas and generating the instabilities in the shear layer at the boundary of the secondary jet. Using simulation in the software package FlowVision 3.13, the characteristics of this flow were obtained in the absence and presence of pulsed-periodic local heat release on the wall on the windward side of the injector opening. A comparison was made of local characteristics at different periodicities of pulsed heating (corresponding to the values of the Strouhal number 0.25 and 0.31). It is shown that pulsed heating can stimulate the formation of perturbations in the shear layer at the jet boundary. For the case of the absence of heating and for two modes of pulsed heating, the values of an integral criterion for mixing efficiency were calculated. It is shown that pulsed heating can lead both to a decrease in the average mixing efficiency and to its increase (up to 9% in the considered heating mode). The calculation method used (unsteady Reynolds-averaged Navier – Stokes equations with a modified $k-\varepsilon$ turbulence model) was validated by considering a typical case of the secondary transverse jet interaction with a supersonic flow, which was studied by several independent research groups and well documented in the literature. The grid convergence was shown for the simulation of this typical case in FlowVision. A quantitative comparison was made of the results obtained from FlowVision calculations with experimental data and calculations in other programs. The results of this study can be useful for specialists dealing with the problems of gas mixing and combustion in a supersonic flow, as well as the development of engines for supersonic aviation.

The paper proposes and investigates a mathematical model of a distributed computing system of parallel interacting processes competing for the use of a limited number of copies of a structured software resource. In cases of unlimited and limited parallelism by the number of processors of a multiprocessor system, the problems of determining operational and exact values of the execution time of heterogeneous and identically distributed competing processes in a synchronous mode are solved, which ensures a linear order of execution of blocks of a structured software resource within each of the processes without delays. The obtained results can be used in a comparative analysis of mathematical relationships for calculating the implementation time of a set of parallel distributed interacting competing processes, a mathematical study of the efficiency and optimality of the organization of distributed computing, solving problems of constructing an optimal layout of blocks of an identically distributed system, finding the optimal number of processors that provide the directive execution time of given volumes of computations. The proposed models and methods open up new prospects for solving problems of optimal distribution of limited computing resources, synchronization of a set of interacting competing processes, minimization of system costs when executing parallel distributed processes.

The influence of solar activity on various processes on Earth has long been the subject of close study, which resulted in the appearance of the term “space weather”. The most striking manifestation of solar activity are the so-called “solar flares”, which are explosive releases of energy in the solar atmosphere, resulting in a flow of photons and charged particles reaching the Earth with a slight delay. After two or three days, a plasma flow reaches the Earth. Thus, a solar flare is an event stretched out in time for several days. The impact of solar flares on human health and the technosphere is a popular subject for discussion and scientific research. This article provides a quantitative assessment of the trigger effect of solar flares on the release of energy as a result of seismic events. The article provides an estimate in the form of a “percentage” of the released seismic energy of the trigger effect of solar flares on the release of seismic energy worldwide and in 8 areas of the Pacific Fire Ring. The initial data are a time series of solar flares from July 31, 1996 to the end of 2024. The time points of the greatest local extremes of solar flare intensity and released seismic energy were studied in successive time intervals of 1 day. For each pair of time sequences in sliding time windows, the “lead measures” of each time sequence relative to the other were estimated using a parametric model of the intensity of interacting point processes. The difference between the “direct” lead measure of the time points of local extremes of solar flare intensity relative to the moments of maximum released seismic energy and the “reverse” lead measure was calculated. The average value of the difference in lead measures provides an estimate of the share of the intensity of seismic events for which solar flares are a trigger.

The solution of problems of heat conductivity by means of a method of continuous asynchronous cellular automats is considered in the article. Coordination of distribution of temperature in a sample at a given time between cellular automat model and the exact analytical solution of the equation of heattransfer is shown that speaks about expedient use of this method of modelling. Dependence between time of one cellular automatic interaction and dimension of a cellular automatic field is received.

Protein-protein interactions are of central importance for virtually every process in living matter. Modeling the dynamics of protein association is crucial for understanding their functionality. This paper proposes novel simulation software ProKSim (Protein Kinetics Simulator) for modeling of protein interactions by means of the multi-particle Brownian Dynamics. Effect of long-range electrostatic interactions on the process of transient encounter complex formation is numerically estimated. Investigation of transient encounter complex formation was performed for three pairs of proteins: ferredoxin and ferredoxin:NADP⁺-redustase, plastocyanin and cytochrome f, barnase and barstar.

In the context of problems of hydrogen and thermonuclear power engineering intensive research of the hydrogen isotopes properties is being conducted. Mathematical models help to specify physical-chemical ideas about the interaction of hydrogen isotopes with structural materials, to discover the limiting factors. Classical diffusion models are often insufficient. The paper is devoted to the models and numerical solution of the boundary-value problems of hydrogen thermodesorption and permeability taking into account nonlinear sorption-desorption dynamics on the surface and reversible capture of hydrogen atoms in the bulk. Algorithms based on difference approximations. The results of computer simulation of the hydrogen flux from a structural material sample are presented.

А discrete element model is applied to the problem of a spherical projectile penetration into a massive obstacle. According to the model both indenter and obstacle are described by a set of densely packed particles. To model the interaction between the particles the two-parameter Lennard–Jones potential is used. Computer implementation of the model has been carried out using parallelism on GPUs, which resulted in high spatial — temporal resolution. Based on the comparison of the results of numerical simulation with experimental data the binding energy has been identified as a function of the dynamic hardness of materials. It is shown that the use of this approach allows to accurately describe the penetration process in the range of projectile velocities 500–2500 m/c.

The paper is devoted to the analysis of the proximity of the population system to dangerous boundaries. An intersection of these boundaries results in the collapse of the stable coexistence of interacting populations. As a reason of such destruction one can consider random perturbations inevitably presented in any living system. This study is carried out on the example of the well-known model of interaction between predator and prey populations, taking into account both a stabilizing factor of the competition of predators for another than prey resources, and also a destabilizing saturation factor for predators. To describe the saturation of predators, we use the second type Holling trophic function. The dynamics of the system is studied as a function of the predator saturation, and the coefficient of predator competition for resources other than prey. The paper presents a parametric description of the possible dynamic regimes of the deterministic model. Here, local and global bifurcations are studied, and areas of sustainable coexistence of populations in equilibrium and the oscillation modes are described. An interesting feature of this mathematical model, firstly considered by Bazykin, is a global bifurcation of the birth of limit cycle from the separatrix loop. We study the effects of noise on the equilibrium and oscillatory regimes of coexistence of predator and prey populations. It is shown that an increase of the intensity of random disturbances can lead to significant deformations of these regimes right up to their destruction. The aim of this work is to develop a constructive probabilistic criterion for the proximity of the population stochastic system to the dangerous boundaries. The proposed approach is based on the mathematical technique of stochastic sensitivity functions, and the method of confidence domains. In the case of a stable equilibrium, this confidence domain is an ellipse. For the stable cycle, this domain is a confidence band. The size of the confidence domain is proportional to the intensity of the noise and stochastic sensitivity of the initial deterministic attractor. A geometric criterion of the exit of the population system from sustainable coexistence mode is the intersection of the confidence domain and the corresponding separatrix of the unforced deterministic model. An effectiveness of this analytical approach is confirmed by the good agreement of theoretical estimates and results of direct numerical simulations.

The application of a conservative numerical method of fluxes is examined for studying the vortex structures in the massive, fast-turned compact astrophysical objects, which are in self-gravity conditions. The simulation is accomplished for the objects with different mass and rotational speed. The pictures of the vortex structure of objects are visualized. In the calculations the gas-dynamic model is used, in which gas is accepted perfected and nonviscous. Numerical procedure is based on the finite-difference approximation of the conservation laws of the additive characteristics of medium for the finite volume. The “upwind” approximations of the densities of distribution of mass, components of momentum and total energy are applied. For the simulation of the objects, which possess fast-spin motion, the control of conservation for the component of moment of momentun is carried out during calculation. Evolutionary calculation is carried out on the basis of the parallel algorithms, realized on the computer complex of cluster architecture. Algorithms are based on the standardized system of message transfer Message Passing Interface (MPI). The blocking procedures of exchange and non-blocking procedures of exchange with control of the completion of operation are used. The parallelization on the space in two or three directions is carried out depending on the size of integration area and parameters of computational grid. For each subarea the parallelization based on the physical factors is carried out also: the calculations of gas dynamics part and gravitational forces are realized on the different processors, that allows to raise the efficiency of algorithms. The real possibility of the direct calculation of gravitational forces by means of the summation of interaction between all finite volumes in the integration area is shown. For the finite volume methods this approach seems to more consecutive than the solution of Poisson’s equation for the gravitational potential. Numerical calculations were carried out on the computer complex of cluster architecture with the peak productivity 523 TFlops. In the calculations up to thousand processors was used.

A variant of import into ANSYS Mechanical APDL system of the model of behavior of flexible woven composite materials with reinforcing weaving cloth of linen at static stretching along the reinforcement yarns is offered. The import was carried out using an integration module based on the use of an analytical model of deformation of the material under study. The model is presented in the articles published earlier and takes into account the changes in the geometric structure occurring in the reinforcing layer of the material during the deformation process, the formation of irreversible deformations and the interaction of cross-lying reinforcing fabric threads. In the introduction input characteristics of the plain weave of the reinforcing fabric and the analytical model imported into ANSYS are briefly described. The input parameters of the module are the mechanical characteristics of the materials that make up the composite (binder and material of reinforcement yarns), the geometric characteristics of the interlacing of the reinforcing fabric. The algorithm for importing the model is based on the calculation and transfer in ANSYS of the calculated points of the material stress-strain diagram for uniaxial stretching along the reinforcement direction and using the Multilinear Kinematich Hardening model material embedded in the ANSYS. The analytical model imported with the help of the presented module allows to model a composite material with reinforcing fabric without a detailed description of the geometry of the interlacing of threads during modeling of the material as a whole. The imported model was verified. For verification full-scale experimental studies and numerical simulation of the stretching of samples from flexible woven composites were carried out. The analysis of the obtained results showed good qualitative and quantitative agreement of calculations.