Rubric: "01.01.00 Mathematics"
Andrianov I. K. (Комсомольский-на-Амуре государственный технический университет), Grinkrug M. S. (Комсомольский-на-Амуре государственный технический университет)
doi: 10.18698/2309-3684-2016-2-2438
The paper considers a mathematical model of the heat exchange process occurring in the thin-walled curved shells of turbomachines. We propose an algorithm for calculating the thermal state on the boundary surfaces of the shell and of the coating according to the desired thermal condition. We present the calculation results of the temperature distribution in the given temperature field for the most terminally loaded shell surface caused by the heat effect.
Andrianov I., Grinkrug M. Parametric identification of a mathematical model of heat exchange process for thin-walled curved shells of turbomachines. Маthematical Modeling and Coтputational Methods, 2016, №2 (10), pp. 24-38
519.237.07 Factorial modeling using neural network
Chauvigny V. A. (Sobolev Institute of Mathematics, Omsk branch, Siberian Branch of the Russian Academy of Sciences), Goltiapin V. V. (Sobolev Institute of Mathematics, Omsk branch, Siberian Branch of the Russian Academy of Sciences)
doi: 10.18698/2309-3684-2016-2-85103
The paper deals with the factorial modeling of the initial stage arterial hypertension. The modeling was carried out by the factorization method based on the neural network and the back propagation of error algorithm. This factorization method is an alternative to the classical factor analysis. We implemented an algorithm for constructing the factorial structure based on the neural network in software. This method has been improved for the factor rotation and obtaining an interpretable solution. The hypertension factorial structure obtained by this factorization method is in accordance with the results of the factorial modeling by other methods.
Chauvigny V., Goltiapin V. Factorial modeling using neural network. Маthematical Modeling and Coтputational Methods, 2016, №2 (10), pp. 85-103
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
Rodnikov A. V. (Bauman Moscow State Technical University)
doi: 10.18698/2309-3684-2016-3-110118
We suggest a numerical and analytical algorithm of searching for stationary space station orbits in the vicinity of an oblate asteroid, when these orbits correspond to relative equilibrium positions of the space station on the plane defined by the asteroid precession and proper rotation axes, in the case of the asteroid being represented by a solid body of an approximately dynamically symmetric shape, compressed along the axis of dynamic symmetry. The algorithm is based on representing the asteroid gravitational potential by a composition of two complex conjugate point masses and consists of sequential variable substitution steps, reducing the problem to solving algebraic equations analytically and numerically. We supply a number of facts concerning evolution of stationary orbits in cases of changes in precession angular velocity.
Rodnikov A. Modelling the search for stationary space station orbits in the vicinity of an oblate-shaped asteroid. Маthematical Modeling and Coтputational Methods, 2016, №3 (11), pp. 110-118
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
Frolov A. V. (Water Problems Institute of the Russian Academy of Sciences)
doi: 10.18698/2309-3684-2016-3-7992
The paper considers long-term fluctuations of the Caspian Sea level as a nonlinear system output with positive and negative feedbacks. The Caspian Sea model with due consideration of an outflow into the Kara-Bogaz-Gol Bay is designed. Density distribution of the sea level is obtained as a solution to the corresponding Fokker — Planck — Kolmogorov equation. The bimodal probability density of the sea level distribution, which meets the endorheic Caspian Sea (if you cut off the Kara-Bogaz-Gol Bay), is shown to turn into the single-mode probability density in case of simultaneous influence of evaporation and seawater outflow into the Kara-Bogaz-Gol Bay on the sea level.
Frolov A. Modelling influence of outflow into the Kara-Bogaz-Gol Bay on probability density of the Caspian Sea level fluctuations. Маthematical Modeling and Coтputational Methods, 2016, №3 (11), pp. 79-92
Volkov V. Y. (JSC OKB GIROPRESS,), Golibrodo L. A. (JSC OKB GIROPRESS,), Zorina I. G. (Bauman Moscow State Technical University), Kudryavtsev O. V. (JSC OKB GIROPRESS,), Krutikov A. A. (JSC OKB GIROPRESS,), Skibin A. A. (JSC OKB GIROPRESS,)
doi: 10.18698/2309-3684-2016-4-3446
For modeling piping systems we made a transition from the mass balance equations, based on 1m and 2m Kirchhoff laws, to the mathematical description of a hydraulic network using the continuity equation discretization. For this purpose we applied a controlvolume method. This paper introduces an extension of the developed control-volume method for extended period simulations in hydraulic networks. This extension is developed for slow time-varying conditions in the hydraulic networks and is not intended to calculate rapidly occurring local phenomena such as waterhammer. The control-volume method was successfully applied to test tasks.
Volkov V., Golibrodo L., Zorina I., Kudryavtsev O., Krutikov A., Skibin A. Applying the control−volume method to extended period simulations in pipe network hydraulics. Маthematical Modeling and Coтputational Methods, 2016, №4 (12), pp. 34-46
Polyanin A. D. (Ishlinsky Institute for Problems in Mechanics), Zhurov A. I. (Cardiff University/Ishlinsky Institute for Problems in Mechanics)
doi: 10.18698/2309-3684-2015-4-337
We present a number of new simple separable, generalized separable, and functional separable solutions to one-dimensional nonlinear delay reaction-diffusion equations with varying transfer coefficients of the formut = [G(u)ux ]x F(u,w),where w = u(x,t) and w = u(x,t ), with denoting the delay time. All of the equations considered contain one, two, or three arbitrary functions of a single argument. The generalized separable solutions are sought in the form =1 = () () N
n n n u x t , withn (x) and n (t) to be determined in the analysis using a new modification of the functional constraints method. Some of the results are extended to nonlinear delay reaction-diffusion equations with time-varying delay = (t). We also present exact solutions to more complex, three-dimensional delay reactiondiffusion equations of the formut = div[G(u)u] F(u,w).Most of the solutions obtained involve free parameters, so they may be suitable for solving certain problems as well as testing approximate analytical and numerical methods for non-linear delay PDEs.
Polyanin A., Zhurov A. Nonlinear delay reaction-diffusion equations with varying transfer coefficients: generalized and functional separable solutions. Маthematical Modeling and Coтputational Methods, 2015, №4 (8), pp. 3-37
Parkhomenko V. P. (ФИЦ ИУ РАН/Bauman Moscow State Technical University)
doi: 10.18698/2309-3684-2016-3-93109
The paper analyzes some factors affecting the parallel implementation performance of the atmospheric general circulation model designed on a cluster type multiprocessor computer. It considers several modifications of the initial parallel code of this model in order to improve both its computational efficiency and processor load balancing. The numerical scheme is modified according to the time of the atmospheric general circulation model for parallel computing of dynamics and physics blocks. The proposed procedure is used along with the procedures of paralleling the dynamics and physics blocks based on decomposition of the computational domain. It allows both optimizing the processor load balancing and increasing the paralleling efficiency. The data obtained while using the scheme for the physics block load balancing allow for complication of the physics block without increasing the total computational time. The results of numerical experiments are given.
Parkhomenko V. Algorithm for computational performance improvement and processor load balancing to simulate the general atmosphere circulation. Маthematical Modeling and Coтputational Methods, 2016, №3 (11), pp. 93-109