and Computational Methods

#### 533.95:539.17 Simulating atomic and molecular physics processes based on the quantum scattering theory

**Pozdneev S. A. (Tashkent institute of railway engineering/The Lebedev Physical Institute of the Russian Academy of Sciences)**

doi: 10.18698/2309-3684-2017-1-321

The article introduces the methods and techniques of simulating various characteristics (such as cross-section, reaction rate etc.) of atomic and molecular physics elementary processes based on the quantum scattering theory within the system of several particles. We have analyzed the results of simulating the electrons and atoms processes of scattering by the diatomic and polyatomic molecules being in specific excited rovibrational states. The article considers different approximations necessary for constructing adequate models of the real physical systems consisting of several bodies which are applicable for both forward reactions and the reactions accompanied by the formation of the intermediate transition complex. We have compared the results of simulating the cross sections of the collisions between the electrons, atoms and molecules as well as between the molecules to the existing experimental data and calculations results of other researchers.

Pozdneev S. Simulating atomic and molecular physics processes based on the quantum scattering theory. Маthematical Modeling and Coтputational Methods, 2017, №1 (13), pp. 3-21

#### 51-72:519.688 Simulating a fractal composite and studying its electrical characteristics

**Korchagin S. A. (Yuri Gagarin State Technical University of Saratov), Terin D. V. (Yuri Gagarin State Technical University of Saratov), Klinaev Y. V. (Yuri Gagarin State Technical University of Saratov)**

doi: 10.18698/2309-3684-2017-1-2231

The study tested a model of a layered hierarchically constructed composite, whose structure has a morphology similar to fractal formation. In our research we developed an algorithm for studying the interaction of an alternating electric field with a fractal composite, as well as a software package that allows simulating fractal characteristics of the composite under study and calculating the electrical parameters of the composite medium. Moreover, we studied the boundaries of the developed model application: the maxand min-dimensions of the composite, at which fractal properties appear. We investigated the frequency dependences of the permittivity of a fractal composite.

The results of the research can be used in designing the materials with predefined electrophysical parameters and characteristics, as well as in developing the elements and devices that possess absorbing and selective properties.

Korchagin S., Terin D., Klinaev Y. Simulating a fractal composite and studying its electrical characteristics. Маthematical Modeling and Coтputational Methods, 2017, №1 (13), pp. 22-31

#### 539.3 Incompressible layered composites with finite deformations on the basis of the asymptotic averaging method

**Dimitrienko Y. I. (Bauman Moscow State Technical University), Gubareva E. A. (Bauman Moscow State Technical University), Kolzhanova D. Y. (Bauman Moscow State Technical University), Karimov S. B. (Bauman Moscow State Technical University)**

doi: 10.18698/2309-3684-2017-1-3254

The article considers the modeling results of incompressible layered composites with finite strains deformation according to the individual layers characteristics. The article proposes an asymptotic averaging method version for layered nonlinearly elastic incompressible composites with finite deformations and periodic structure. We are using a universal representation of the defining relations for incompressible composite layers, proposed by Yu.I. Dimitrienko, which allows us to simulate simultaneously for a complex of various nonlinear elastic media models characterizedby the choice of a pair of energy tensors. We proved that if all composite layers are incompressible, the composite as a whole is also an incompressible, but anisotropic, medium. The article considers the problem of laminated plate uniaxial stretching from incompressible layers with finite deformations. Using the developed method, we calculated the effective deformation diagrams connecting the averaged Piola — Kirchhoff stress tensors components and the strain gradient, as well as the stress distribution in the composite layers.

The developed method for calculating effective deformation diagrams and stresses in composite layers can be used in the design of elastomeric composites with specified properties.

Dimitrienko Y., Gubareva E., Kolzhanova D., Karimov S. Incompressible layered composites with finite deformations on the basis of the asymptotic averaging method. Маthematical Modeling and Coтputational Methods, 2017, №1 (13), pp. 32-54

#### 629.762 Simulating mass-consuming characteristics of power devices providing gas-dynamic ejection of the flying vehicle with setup parameters

**Plyusnin A. V. (JSC MIC NPO Mashinostroyenia)**

doi: 10.18698/2309-3684-2017-1-5577

The article introduces and provides a rationale for the mathematical theory which defines the mass-consuming characteristics of the power devices designed for providing the gas-dynamic ejection of the flying vehicle from the launcher-container with the set-up restrictions on parameters. We present a visual geometrical interpretation of the offered method. The calculations of the gas-dynamic emission parameters and the intraballistic computation of the power device with the propellant grain operation confirm the correctness of the theoretical constructions and their practical feasibility.

Plyusnin A. Simulating mass-consuming characteristics of power devices providing gas-dynamic ejection of the flying vehicle with setup parameters. Маthematical Modeling and Coтputational Methods, 2017, №1 (13), pp. 55-77

#### 532.5:551.465 Numerical simulation of the point pulse source impact in a liquid on the ice cover

**Savin A. S. (Bauman Moscow State Technical University), Gorlova N. E. (Bauman Moscow State Technical University), Strunin P. A. (Bauman Moscow State Technical University)**

doi: 10.18698/2309-3684-2017-1-7890

The research examines the planar and three-dimensional problems of an ice cover perturbed by a point pulse source localized in the depth of an infinitely deep liquid. We studied the ice cover of different thickness and carried out numerical study of its perturbations by sources located at different depths. The main attention is paid to the ice cover perturbations that arise directly above the source.

Savin A., Gorlova N., Strunin P. Numerical simulation of the point pulse source impact in a liquid on the ice cover. Маthematical Modeling and Coтputational Methods, 2017, №1 (13), pp. 78-90

#### 519.8 “Mixed” probabilistic models of bilateral military operations of numerous groups

**Chuev V. U. (Bauman Moscow State Technical University), Dubogray I. V. (Bauman Moscow State Technical University), Dyakova L. N. (Bauman Moscow State Technical University)**

doi: 10.18698/2309-3684-2017-1-91101

The purpose of this work was to develop "mixed" probabilistic models of bilateral military operations according to the theory of continuous Markov processes. In our research we obtained calculation formulas for estimating the main combat indices of groups small in number. Moreover, we developed a numerical algorithm to calculate the main combat indices of numerous groupings and made a comparison with the results of combat simulation using a deterministic model of two-way combat operations, the model being developed according to themean-value method dynamics. Findings of the research show that the correlation of the forces of the opposing sides, rather than their initial numbers, affects the errors in the mean-value method dynamics.

Chuev V., Dubogray I., Dyakova L. “Mixed” probabilistic models of bilateral military operations of numerous groups. Маthematical Modeling and Coтputational Methods, 2017, №1 (13), pp. 91-101

#### 519.248 Cox model validity checking for several progressively censored samples

**Timonin V. I. (Bauman Moscow State Technical University), Tyannikova N. D. (Bauman Moscow State Technical University)**

doi: 10.18698/2309-3684-2017-1-102117

The article proposes a nonparametric criterion of the Kiefer — Gihman type to test the Cox model validity for several progressively censored samples. As estimates of the reliability function for each sample we are using the Kaplan — Meyer ones. The paper proves that if the hypothesis is valid, the Kiefer — Gihman distribution can be used as an approximation of the asymptotic distribution of the criterionstatistics. Based on the particle random walk model over a multidimensional cells array, the paper has developed the method for calculating the exact statistics distributions. The article presents obtained probability values tables of the proposed statistics exact distributions for a wide range of samples possible values. Statistical modeling methods show Cox parameters estimating method consistency, based on the statistics minimization. We present the obtained estimates histograms for the developments exponential distribution to failure. The research results are used when analyzing the redundant technical systems of different multiplicity tests results operating in different operating conditions.

Analyzed systems find applications in all industries — from machine building to radio electronic.

Timonin V., Tyannikova N. Cox model validity checking for several progressively censored samples. Маthematical Modeling and Coтputational Methods, 2017, №1 (13), pp. 102-117