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The difference scheme for numerical solution of a time-dependant system of two Schrödinger equations with the operator of a spin-orbit interaction for a two-component spinor wave function is offered on the basis of a split method for a time-dependant Schrödinger equations. The computer simulation of the external neutrons’ wave functions evolution with different values of the full moment projection upon internuclear axis and probabilities of their transfer are executed for head-on collisions of ¹⁸O and ⁵⁸Ni nuclei.

The paper describes the results of computer simulation of time-dependent temperature fields arising in polar dielectrics irradiated by focused electron bunches with average electron energy when analyzing with electron microscopy techniques. The mathematical model was based on solving several-dimensional nonstationary heat conduction equation with use of numerical finite element method. The approximation of thermal source was performed taking into account the estimation of initial electron distribution determined by Monte-Carlo simulation of electron trajectories. The simulation program was designed in Matlab. The geometrical modeling and calculation results demonstrated the main features of model sample heating by electron beam were presented at the given experimental parameters as well as source approximation.

An algorithm of applied problem solving was described to calculate electrical characteristics of electrical field effects in ferroelectrics electron-beam charged. The algorithm was based on implementation of the deterministic model using finite element method as well as taking into account Monte-Carlo simulation results of electron transport. The program application was developed to perform computing experiments.

The physical and mathematical model of combustion of the polydisperse suspension of coal dust was developed. The formulation of the problem takes into account the evaporation of particle volatile components during the heating, the particle emitting and the gas heat transfer to a surrounding area via the sphere volume side surface, heat transfer coefficient as a function of temperature. The polydisperse of coal-dust is taken into consideration. N — the number of fraction. Fractions are subdivided into inert and reacting particles. The oxidizer mass balance equation takes into consideration the oxidizer consumption per each reaction (heterogeneous on the particle surface and homogenous in the gas). Exothermic chemical reactions in gas are determined by Arrhenius equation with second-order kinetics. The heterogeneous reaction on the particle surface was first-order reaction. The numerical simulation was solved by Runge–Kutta–Merson method. Reliability of the calculations was verified by solving the partial problems. During the numerical calculation the percentage composition of inert and reacting particles in coal-dust and their total mass were changed for each simulation. We have determined the influence of the percentage composition of inert and reacting particles on burning characteristics of polydisperse coal-dust methane-air mixture. The results showed that the percent increase of volatile components in the mixture lead to the increase of total pressure in the volume. The value of total pressure decreases with the increasing of the inert components in the mixture. It has been determined that there is the extremism radius value of coarse particles by which the maximum pressure reaches the highest value.

The article describes a mathematical model that simulates performance of a hierarchical organization during an early stage of a crisis. A distinguished feature of this stage of crisis is presence of so called early warning signals containing information on the approaching event. Employees are capable of catching the early warnings and of preparing the organization for the crisis based on the signals’ meaning. The efficiency of the preparation depends on both parameters of the organization and parameters of the crisis. The proposed simulation agentbased model is implemented on Java programming language and is used for conducting experiments via Monte- Carlo method. The goal of the experiments is to compare how centralized and decentralized organizational structures perform during sudden and smoldering crises. By centralized organizations we assume structures with high number of hierarchy levels and low number of direct reports of every manager, while decentralized organizations mean structures with low number of hierarchy levels and high number of direct reports of every manager. Sudden crises are distinguished by short early stage and low number of warning signals, while smoldering crises are defined as crises with long lasting early stage and high number of warning signals not necessary containing important information. Efficiency of the organizational performance during early stage of a crisis is measured by two parameters: percentage of early warnings which have been acted upon in order to prepare organization for the crisis, and time spent by top-manager on working with early warnings. As a result, we show that during early stage of smoldering crises centralized organizations process signals more efficiently than decentralized organizations, while decentralized organizations handle early warning signals more efficiently during early stage of sudden crises. However, occupation of top-managers during sudden crises is higher in decentralized organizations and it is higher in centralized organizations during smoldering crises. Thus, neither of the two classes of organizational structures is more efficient by the two parameters simultaneously. Finally, we conduct sensitivity analysis to verify the obtained results.

In this paper we present Rayleigh formulas obtained from Kirchhoff integral formulas, which can later be used to obtain migration images. The relevance of the studies conducted in the work is due to the widespread use of migration in the interests of seismic oil and gas seismic exploration. A special feature of the work is the use of an elastic approximation to describe the dynamic behaviour of a geological environment, in contrast to the widespread acoustic approximation. The proposed approach will significantly improve the quality of seismic exploration in complex cases, such as permafrost and shelf zones of the southern and northern seas. The complexity of applying a system of equations describing the state of a linear-elastic medium to obtain Rayleigh formulas and algorithms based on them is a significant increase in the number of computations, the mathematical and analytical complexity of the resulting algorithms in comparison with the case of an acoustic medium. Therefore in industrial seismic surveys migration algorithms for the case of elastic waves are not currently used, which creates certain difficulties, since the acoustic approximation describes only longitudinal seismic waves in geological environments. This article presents the final analytical expressions that can be used to develop software systems using the description of elastic seismic waves: longitudinal and transverse, thereby covering the entire range of seismic waves: longitudinal reflected PP-waves, longitudinal reflected SP-waves, transverse reflected PS-waves and transverse reflected SS-waves. Also, the results of comparison of numerical solutions obtained on the basis of Rayleigh formulas with numerical solutions obtained by the grid-characteristic method are presented. The value of this comparison is due to the fact that the method based on Rayleigh integrals is based on analytical expressions, while the grid-characteristic method is a method of numerical integration of solutions based on a calculated grid. In the comparison, different types of sources were considered: a point source model widely used in marine and terrestrial seismic surveying and a flat wave model, which is also sometimes used in field studies.

Experimental, theoretical and numerical investigations of equatorial spread F, equatorial plasma bubbles (EPBs), plasma depletion shells, and plasma clouds are continued at new variety articles. Nonlinear growth, bifurcation, pinching, atomic and molecular ion dynamics are considered at there articles. But the authors of this article believe that not all parameters of EPB development are correct. For example, EPB bifurcation is highly questionable.

A maximum speed inside EPBs and a development time of EPB are defined and studied. EPBs starting from one, two or three zones of the increased density (initial plasma clouds). The development mechanism of EPB is the Rayleigh-Taylor instability (RTI). Time of the initial stage of EPB development went into EPB favorable time interval (in this case the increase linear increment is more than zero) and is 3000–7000 c for the Earth equatorial ionosphere.

Numerous computing experiments were conducted with use of the original two-dimensional mathematical and numerical model MI2, similar USA standard model SAMI2. This model MI2 is described in detail. The received results can be used both in other theoretical works and for planning and carrying out natural experiments for generation of F-spread in Earth ionosphere.

Numerical simulating was carried out for the geophysical conditions favorable for EPBs development. Numerical researches confirmed that development time of EPBs from initial irregularities with the increased density is significantly more than development time from zones of the lowered density. It is shown that developed irregularities interact among themselves strongly and not linearly even then when initial plasma clouds are strongly removed from each other. In addition, this interaction is stronger than interaction of EPBs starting from initial irregularities with the decreased density. The numerical experiments results showed the good consent of developed EPB parameters with experimental data and with theoretical researches of other authors.

In real problems of exploration seismology we deal with a heterogeneity of the nature of elastic waves interaction with the surface of a fracture by the propagation through it. The fracture is a complex heterogeneous structure. In some locations the surfaces of fractures are placed some distance apart and are separated by filling fluid or emptiness, in some places we can observe the gluing of surfaces, when under the action of pressure forces the fracture surfaces are closely adjoined to each other. In addition, fractures can be classified by the nature of saturation: fluid or gas. Obviously, for such a large variety in the structure of fractures, one cannot use only one model that satisfies all cases.

This article is concerned with description of developed mathematical fracture models which can be used for numerical solution of exploration seismology problems using the grid-characteristic method on unstructured triangular (in 2D-case) and tetrahedral (in 3D-case) meshes. The basis of the developed models is the concept of an infinitely thin fracture, whose aperture does not influence the wave processes in the fracture area. These fractures are represented by bound areas and contact boundaries with different conditions on contact and boundary surfaces. Such an approach significantly reduces the consumption of computer resources since there is no need to define the mesh inside the fracture. On the other side, it allows the fractures to be given discretely in the integration domain, therefore, one can observe qualitatively new effects, such as formation of diffractive waves and multiphase wave front due to multiple reflections between the surfaces of neighbor fractures, which cannot be observed by using effective fracture models actively used in computational seismology.

The computational modeling of seismic waves propagation through layers of mesofractures was produced using developed fracture models. The results were compared with the results of physical modeling in problems in the same statements.

A cluster method of mathematical modeling of interval-stochastic thermal processes in complex electronic systems (ES), is developed. In the cluster method, the construction of a complex ES is represented in the form of a thermal model, which is a system of clusters, each of which contains a core that combines the heat-generating elements falling into a given cluster, the cluster shell and a medium flow through the cluster. The state of the thermal process in each cluster and every moment of time is characterized by three interval-stochastic state variables, namely, the temperatures of the core, shell, and medium flow. The elements of each cluster, namely, the core, shell, and medium flow, are in thermal interaction between themselves and elements of neighboring clusters. In contrast to existing methods, the cluster method allows you to simulate thermal processes in complex ESs, taking into account the uneven distribution of temperature in the medium flow pumped into the ES, the conjugate nature of heat exchange between the medium flow in the ES, core and shells of clusters, and the intervalstochastic nature of thermal processes in the ES, caused by statistical technological variation in the manufacture and installation of electronic elements in ES and random fluctuations in the thermal parameters of the environment. The mathematical model describing the state of thermal processes in a cluster thermal model is a system of interval-stochastic matrix-block equations with matrix and vector blocks corresponding to the clusters of the thermal model. The solution to the interval-stochastic equations are statistical measures of the state variables of thermal processes in clusters - mathematical expectations, covariances between state variables and variance. The methodology for applying the cluster method is shown on the example of a real ES.

In this work, we develop a model of the immune response to respiratory viral infections taking into account some particular properties of the SARS-CoV-2 infection. The model represents a system of ordinary differential equations for the concentrations of epithelial cells, immune cells, virus and inflammatory cytokines. Conventional analysis of the existence and stability of stationary points is completed by numerical simulations in order to study dynamics of solutions. Behavior of solutions is characterized by large peaks of virus concentration specific for acute respiratory viral infections.

At the first stage, we study the innate immune response based on the protective properties of interferon secreted by virus-infected cells. On the other hand, viral infection down-regulates interferon production. Their competition can lead to the bistability of the system with different regimes of infection progression with high or low intensity. In the case of infection outbreak, the incubation period and the maximal viral load depend on the initial viral load and the parameters of the immune response. In particular, increase of the initial viral load leads to shorter incubation period and higher maximal viral load.

In order to study the emergence and dynamics of cytokine storm, we consider proinflammatory cytokines produced by cells of the innate immune response. Depending on parameters of the model, the system can remain in the normal inflammatory state specific for viral infections or, due to positive feedback between inflammation and immune cells, pass to cytokine storm characterized by excessive production of proinflammatory cytokines. Furthermore, inflammatory cell death can stimulate transition to cytokine storm. However, it cannot sustain it by itself without the innate immune response. Assumptions of the model and obtained results are in qualitative agreement with the experimental and clinical data.