and Computational Methods

Rubric: "05.13.00 Computer science, computer facilities and management"

doi: 10.18698/2309-3684-2014-3-89110

We propose a full solution for Manna model, two-dimensional conservative sand pile model with isotropic rules of grains redistribution on average. We determined the general properties indices of avalanches distribution (size, area, perimeter, duration, the multiplicity of topplings) for the model both analytically and numerically. The solution is based on spatio-temporal decomposition of avalanches described in terms of toppling layers and waves and on division of the motion of grains into directed and undirected types. The former of the two is treated as the dynamics of active particles with some physical properties described.

Podlazov A. Two-dimensional self-organized critical Мanna model. Маthematical Modeling and Coтputational Methods, 2014, №3 (3), pp. 89-110

doi: 10.18698/2309-3684-2016-4-103121

The article centers on developing the models of complex engineering structures for monitoring their operational status. In order to organize effective monitoring of the structures state, we often need to restore the state parameters values according to the measuremen tresults and use monitoring object models. The study suggests using a model built by calculation and reduced to small size. Among the state parameters there may be either load values and their combinations on which direct restrictions are imposed, or limit states defined by their values. The work proposes both criteria for assessing the quality of the reduced model, and an efficient algorithm for searching them.

Meschikhin I., Gavryushin S. Quality criteria and algorithm for selecting reduced finite element models for technical design monitoring. Маthematical Modeling and Coтputational Methods, 2016, №4 (12), pp. 103-121

doi: 10.18698/2309-3684-2016-4-316

The study examined the formation and evolution of stationary and moving breathers of a two-dimensional O(3) nonlinear sigma model. We detected analytical form of trial functions of two-dimensional sine-Gordon equations, which over time evolve into periodic (breather) solutions. According to the solutions found, by adding the rotation to an A3-field vector in isotopic space S^2 we obtained the solutions for the O(3) nonlinear sigma model. Furthermore, we conducted the numerical study of the solutions dynamics and showed their stability in a stationary and a moving state for quite a long time, although in the presence of a weak radiation.

Shokirov F. Mathematical modeling of breathers of two-dimensional O(3) nonlinear sigma model. Маthematical Modeling and Coтputational Methods, 2016, №4 (12), pp. 3-16

doi: 10.18698/2309-3684-2015-1-316

The article presents a developed mathematical model of electric describing the coaxial electrogenerating elements (EGE) with isothermal cathode and a variety of ways for current collecting. To analyze their internal state and output parameters in the arc mode we used a two-parameter local linear current-voltage characteristic (CVC). It was shown that in the case of one-sided current collection maximum power of EGE and generated magnetic field asymptotically approach to their maximum values as the length of the electrodes goes into infinity. In the case of versatile current collection maximum values of these parameters can be achieved at the final length of the electrodes. In both methods of the current collection the acceptable value of EGE electrical power loss of 25% due to electrode non-equipotentionality was achieved at their universal critical length. The calculation of which is presented.

Loshkarev A., Oblakova T. Mathematical modeling of coaxial electrogenerating elements. Маthematical Modeling and Coтputational Methods, 2015, №1 (5), pp. 3-16

doi: 10.18698/2309-3684-2015-1-94108

The article considers a model of the climate, including interacting blocks of the ocean, atmosphere and sea ice. The model describes the deep thermohaline circulation of the oceans and the main characteristics of the other elements of the climate system. The paper presents model operating in the mode of the seasonal variations of solar radiation. The changes in atmospheric temperature in XXI century for different scenarios of CO2 concentration variations are calculated.

Parkhomenko V. Global climate model including description of thermohaline circulation of the World Ocean. Маthematical Modeling and Coтputational Methods, 2015, №1 (5), pp. 94-108

doi: 10.18698/2309-3684-2014-1-None

Aleksandrov A., Dimitrienko Y. Математическое и компьютерное моделирование — основа современных инженерных наук. Маthematical Modeling and Coтputational Methods, 2014, №1 (1), pp. 3-4

doi: 10.18698/2309-3684-2015-3-6888

The article considers the problems of coolant flow computational diagnostics in a closed circulation loop. The mathematical models of acoustic waves in two-phase flow are developed. Indirect diagnostic information, contained in the flow vibrational spectra recorded by regular systems is used. The inverse eigenvalue problem is formulated. Solving it the optimization approach is implemented. It is supposed that partial criteria are presented by continuous, Lipschitz, not everywhere differentiable, multi-extremal functions. Search of global solutions was performed using a new hybrid algorithms integrating stochastic algorithm of variable space viewing and deterministic methods of local search. A numerical example of model diagnosing the phase composition of the coolant in the circulation loop of nuclear reactor plant is presented.

Sulimov V., Shkapov P. Hybrid methods of computer diagnosis of two-phase flow in the circulation loop. Маthematical Modeling and Coтputational Methods, 2015, №3 (7), pp. 68-88

doi: 10.18698/2309-3684-2014-1-131144

The paper deals with the citation index and h-index, which are the main scientometric indices, currently used for evaluating the performance of scientists and university professors. The author indicates their main disadvantages and considers a number of illustra-tive examples. The study shows that the normalized citation index (taking into account the presence of co-authors) has a number of important advantages in comparison with other scientometric indices. The author proposes new indices — the maximum citation indices, which can be easily calculated, have a simple and clear interpretation and have a number of distinct advantages in comparison with the h-index.

Polyanin A. Disadvantages of citation index and Hirsch and using other scientometrics. Маthematical Modeling and Coтputational Methods, 2014, №1 (1), pp. 131-144

doi: 10.18698/2309-3684-2014-1-517

The paper gives grounds for applying mathematical modeling in the development and improvement of modern technical instruments and systems. It also shows typical stages of mathematical modeling and the sequence of their execution. The authors describe special features and basic methods in quantitative analysis of mathematical models of systems with distributed parameters (in continuous systems).

Zarubin V., Kuvyrkin G. Special features of mathematical modeling of technical instruments. Маthematical Modeling and Coтputational Methods, 2014, №1 (1), pp. 5-17