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The paper presents a physical and numerical analysis of the dynamics and radiation of explosion products formed during the Russian-American experiment in the ionosphere using an explosive generator based on hexogen (RDX) and trinitrotoluene (TNT). The main attention is paid to the radiation of the perturbed region and the dynamics of the products of explosion (PE). The detailed chemical composition of the explosion products is analyzed and the initial concentrations of the most important molecules capable of emitting in the infrared range of the spectrum are determined, and their radiative constants are given. The initial temperature of the explosion products and the adiabatic exponent are determined. The nature of the interpenetration of atoms and molecules of a highly rarefied ionosphere into a spherically expanding cloud of products is analyzed. An approximate mathematical model of the dynamics of explosion products under conditions of mixing rarefied ionospheric air with them has been developed and the main thermodynamic characteristics of the system have been calculated. It is shown that for a time of 0,3–3 sec there is a significant increase in the temperature of the scattering mixture as a result of its deceleration. In the problem under consideration the explosion products and the background gas are separated by a contact boundary. To solve this two-region gas dynamic problem a numerical algorithm based on the Lagrangian approach was developed. It was necessary to fulfill special conditions at the contact boundary during its movement in a stationary gas. In this case there are certain difficulties in describing the parameters of the explosion products near the contact boundary which is associated with a large difference in the size of the mass cells of the explosion products and the background due to a density difference of 13 orders of magnitude. To reduce the calculation time of this problem an irregular calculation grid was used in the area of explosion products. Calculations were performed with different adiabatic exponents. The most important result is temperature. It is in good agreement with the results obtained by the method that approximately takes into account interpenetration. The time behavior of the IR emission coefficients of active molecules in a wide range of the spectrum is obtained. This behavior is qualitatively consistent with experiments for the IR glow of flying explosion products.

The creation of a virtual laboratory stand that allows one to obtain reliable characteristics that can be proven as actual, taking into account errors and noises (which is the main distinguishing feature of a computational experiment from model studies) is one of the main problems of this work. It considers the following task: there is a rectangular waveguide in the single operating mode, on the wide wall of which a technological hole is cut, through which a sample for research is placed into the cavity of the transmission line. The recovery algorithm is as follows: the laboratory measures the network parameters (S₁₁ and/or S₂₁) in the transmission line with the sample. In the computer model of the laboratory stand, the sample geometry is reconstructed and an iterative process of optimization (or sweeping) of the electrophysical parameters is started, the mask of this process is the experimental data, and the stop criterion is the interpretive estimate of proximity (or residual). It is important to note that the developed computer model, along with its apparent simplicity, is initially ill-conditioned. To set up a computational experiment, the Comsol modeling environment is used. The results of the computational experiment with a good degree of accuracy coincided with the results of laboratory studies. Thus, experimental verification was carried out for several significant components, both the computer model in particular and the algorithm for restoring the target parameters in general. It is important to note that the computer model developed and described in this work may be effectively used for a computational experiment to restore the full dielectric parameters of a complex geometry target. Weak bianisotropy effects can also be detected, including chirality, gyrotropy, and material nonreciprocity. The resulting model is, by definition, incomplete, but its completeness is the highest of the considered options, while at the same time, the resulting model is well conditioned. Particular attention in this work is paid to the modeling of a coaxial-waveguide transition, it is shown that the use of a discrete-element approach is preferable to the direct modeling of the geometry of a microwave device.

Hemostasis system is one of the key body’s defense systems, which is presented in all the liquid tissues and especially important in blood. Hemostatic response is triggered as a result of the vessel injury. The interaction between specialized cells and humoral systems leads to the formation of the initial hemostatic clot, which stops bleeding. After that the slow process of clot dissolution occurs. The formation of hemostatic plug is a unique physiological process, because during several minutes the hemostatic system generates complex structures on a scale ranging from microns for microvessel injury or damaged endothelial cell-cell contacts, to centimeters for damaged systemic arteries. Hemostatic response depends on the numerous coordinated processes, which include platelet adhesion and aggregation, granule secretion, platelet shape change, modification of the chemical composition of the lipid bilayer, clot contraction, and formation of the fibrin mesh due to activation of blood coagulation cascade. Computer modeling is a powerful tool, which is used to study this complex system at different levels of organization. This includes study of intracellular signaling in platelets, modelling humoral systems of blood coagulation and fibrinolysis, and development of the multiscale models of thrombus growth. There are two key issues of the computer modeling in biology: absence of the adequate physico-mathematical description of the existing experimental data due to the complexity of the biological processes, and high computational complexity of the models, which doesn’t allow to use them to test physiologically relevant scenarios. Here we discuss some key unresolved problems in the field, as well as the current progress in experimental research of hemostasis and thrombosis. New findings lead to reevaluation of the existing concepts and development of the novel computer models. We focus on the arterial thrombosis, venous thrombosis, thrombosis in microcirculation and the problems of fibrinolysis and thrombolysis. We also briefly discuss basic types of the existing mathematical models, their computational complexity, and principal issues in simulation of thrombus growth in arteries.

The problem is constructing the differences that arise on ${\mathrm{\LaTeX}}$ documents editing. Each document is represented as a parse tree whose nodes are called tokens. The smallest possible text representation of the document that does not change the syntax tree is constructed. All of the text is splitted into fragments whose boundaries correspond to tokens. A map of the initial text fragment sequence to the similar sequence of the edited document corresponding to the minimum distance is built with Hirschberg algorithm A map of text characters corresponding to the text fragment sequences map is cunstructed. Tokens, that chars are all deleted, or all inserted, or all not changed, are selected in the parse trees. The map for the trees formed with other tokens is built using Zhang–Shasha algorithm.

One of problems in developing the gas condensate fields lies on the fact that the condensed hydrocarbons in the gas-bearing layer can get stuck in the pores of the formation and hence cannot be extracted. In this regard, research is underway to increase the recoverability of hydrocarbons in such fields. This research includes a wide range of studies on mathematical simulations of the passage of gas condensate mixtures through a porous medium under various conditions.

In the present work, within the classical approach based on the Darcy law and the law of continuity of flows, we formulate an initial-boundary value problem for a system of nonlinear differential equations that describes a depletion of a multicomponent gas-condensate mixture in porous reservoir. A computational scheme is developed on the basis of the finite-difference approximation and the fourth order Runge .Kutta method. The scheme can be used for simulations both in the spatially one-dimensional case, corresponding to the conditions of the laboratory experiment, and in the two-dimensional case, when it comes to modeling a flat gas-bearing formation with circular symmetry.

The computer implementation is based on the combination of C++ and Maple tools, using the MPI parallel programming technique to speed up the calculations. The calculations were performed on the HybriLIT cluster of the Multifunctional Information and Computing Complex of the Laboratory of Information Technologies of the Joint Institute for Nuclear Research.

Numerical results are compared with the experimental data on the pressure dependence of output of a ninecomponent hydrocarbon mixture obtained at a laboratory facility (VNIIGAZ, Ukhta). The calculations were performed for two types of porous filler in the laboratory model of the formation: terrigenous filler at 25 .„R and carbonate one at 60 .„R. It is shown that the approach developed ensures an agreement of the numerical results with experimental data. By fitting of numerical results to experimental data on the depletion of the laboratory reservoir, we obtained the values of the parameters that determine the inter-phase transition coefficient for the simulated system. Using the same parameters, a computer simulation of the depletion of a thin gas-bearing layer in the circular symmetry approximation was carried out.

Represented study considers numerical simulation of corium cooling driven by natural convection within a horizontal hemicylindrical cavity, boundaries of which are assumed isothermal. Corium is a melt of ceramic fuel of a nuclear reactor and oxides of construction materials.

Corium cooling is a process occurring during severe accident associated with core melt. According to invessel retention conception, the accident may be restrained and localized, if the corium is contained within the vessel, only if it is cooled externally. This conception has a clear advantage over the melt trap, it can be implemented at already operating nuclear power plants. Thereby proper numerical analysis of the corium cooling has become such a relevant area of studies.

In the research, we assume the corium is contained within a horizontal semitube. The corium initially has temperature of the walls. In spite of reactor shutdown, the corium still generates heat owing to radioactive decays, and the amount of heat released decreases with time accordingly to Way–Wigner formula. The system of equations in Boussinesq approximation including momentum equation, continuity equation and energy equation, describes the natural convection within the cavity. Convective flows are taken to be laminar and two-dimensional.

The boundary-value problem of mathematical physics is formulated using the non-dimensional nonprimitive variables «stream function – vorticity». The obtained differential equations are solved numerically using the finite difference method and locally one-dimensional Samarskii scheme for the equations of parabolic type.

As a result of the present research, we have obtained the time behavior of mean Nusselt number at top and bottom walls for Rayleigh number ranged from 10³ to 10⁶. These mentioned dependences have been analyzed for various dimensionless operation periods before the accident. Investigations have been performed using streamlines and isotherms as well as time dependences for convective flow and heat transfer rates.

The article presents the numerical modeling and study of the kinetic model of propane pyrolysis. The study of the reaction kinetics is a necessary stage in modeling the dynamics of the gas flow in the reactor.

The kinetic model of propane pyrolysis is a nonlinear system of ordinary differential equations of the first order with parameters, the role of which is played by the reaction rate constants. Math modeling of processes is based on the use of the mass conservation law. To solve an initial (forward) problem, implicit methods for solving stiff ordinary differential equation systems are used. The model contains 60 input kinetic parameters and 17 output parameters corresponding to the reaction substances, of which only 9 are observable. In the process of solving the problem of estimating parameters (inverse problem), there is a question of non-uniqueness of the set of parameters that satisfy the experimental data. Therefore, before solving the inverse problem, the possibility of determining the parameters of the model is analyzed (analysis of identifiability).

To analyze identifiability, we use the orthogonal method, which has proven itself well for analyzing models with a large number of parameters. The algorithm is based on the analysis of the sensitivity matrix by the methods of differential and linear algebra, which shows the degree of dependence of the unknown parameters of the models on the given measurements. The analysis of sensitivity and identifiability showed that the parameters of the model are stably determined from a given set of experimental data. The article presents a list of model parameters from most to least identifiable. Taking into account the analysis of the identifiability of the mathematical model, restrictions were introduced on the search for less identifiable parameters when solving the inverse problem.

The inverse problem of estimating the parameters was solved using a genetic algorithm. The article presents the found optimal values of the kinetic parameters. A comparison of the experimental and calculated dependences of the concentrations of propane, main and by-products of the reaction on temperature for different flow rates of the mixture is presented. The conclusion about the adequacy of the constructed mathematical model is made on the basis of the correspondence of the results obtained to physicochemical laws and experimental data.

Recently many investigations have been devoted to theoretical models in new areas concerning description of different biological, sociological and historical processes. In the present paper we investigate the nazi Germany invasion in Poland, France and USSR from the kinetic theory point of view. We model this process with the Cauchy boundary problem for the two-element kinetic equations with spatial uniform initial conditions. The solution of the problem is given in the form of the traveling wave and the propagation velocity of a frontline depends on the quotient between initial forces concentrations. Moreover it is obtained that the general solution of the model can be obtained in terms of the quadratures and elementary functions. Finally it is shown that the frontline velocities are complied with the historical data.

In the present article we explore the process of changing the level of approval of a political leader under the influence of the processes taking place in online platforms (social networks, forums, etc.). The driver of these changes is the interaction of users, through which they can exchange opinions with each other and formulate their position in relation to the political leader. In addition to interpersonal interaction, we will consider such factors as the information impact, expressed in the creation of an information flow with a given power and polarity (positive or negative, in the context of influencing the image of a political leader), as well as the presence of a group of agents (opinion leaders), supporting the leader, or, conversely, negatively affecting its representation in the media space.

The mathematical basis of the presented research is the Kirman model, which has its roots in biology and initially found its application in economics. Within the framework of this model it is considered that each user is in one of the two possible states, and a Markov jump process describing transitions between these states is given. For the problem under consideration, these states are 0 or 1, depending on whether a particular agent is a supporter of a political leader or not. For further research, we find its diffusional approximation, known as the Jacoby process. With the help of spectral decomposition for the infinitesimal operator of this process we have an opportunity to find an analytical representation for the transition probability density.

Analyzing the probabilities obtained in this way, we can assess the influence of individual factors of the model: the power and direction of the information flow, available to online users and relevant to the tasks of rating formation, as well as the number of supporters or opponents of the politician. Next, using the found eigenfunctions and eigenvalues, we derive expressions for the evaluation of conditional mathematical expectations of a politician’s rating, which can serve as a basis for building forecasts that are important for the formation of a strategy of representing a political leader in the online environment.

Collective behavior can serve as a mechanism of thermoregulation and play a key role in the joint survival of a group of organisms. In higher animals, such phenomena are usually the subject of study of biology since sudden transitions to collective behavior are difficult to differentiate from the psychological and social adaptation of animals. However, in this paper, we indicate several important examples when a flock of higher animals demonstrates phase transitions similar to known phenomena in liquids and gases. This issue can also be studied experimentally within the framework of synthetic systems consisting of self-propelled robots that act according to a certain given algorithm. Generalizing both of these cases, we consider the problem of phase transitions in a dense group of interacting selfpropelled agents. Within the framework of microscopic theory, we propose a mathematical model of the phenomenon, in which agents are represented as bodies interacting with each other in accordance with an effective potential of a special type, expressing the desire of agents to move in the direction of the gradient of the joint thermal field. We show that the number of agents in the group, the group power, is the control parameter of the problem. A discrete model with individual dynamics of agents reproduces most of the phenomena observed both in natural flocks of higher animals engaged in collective thermoregulation and in synthetic complex systems. A first-order phase transition is observed, which symbolizes a change in the aggregate state in a group of agents. One observes the self-assembly of the initial weakly structured mass of agents into dense quasi-crystalline structures. We demonstrate also that, with an increase in the group power, a second-order phase transition in the form of thermal convection can occur. It manifests in a sudden liquefaction of the group and a transition to vortex motion, which ensures more efficient energy consumption in the case of a synthetic system of interacting robots and the collective survival of all individuals in the case of natural animal flocks.With an increase in the group power, secondary bifurcations occur, the vortex structure in agent medium becomes more complicated.