Rubric: "05.13.00 Computer science, computer facilities and management"
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
Based on the theory of Markov processes the model of "poorly organized" battle was developed. Formulae for calculating its basic parameters at different initial numbers of the opposing sides were obtained. A comparison of the results of modeling a battle using probabilistic and deterministic models was performed. It was found that the dynamics model errors of the average are primarily affected by the balance of forces of the opposing sides in the beginning of the battle. It was shown that in case of military groups of similar forces the first-strike attack is of significant importance. When one of the warring parties at the beginning of the battle has a great advantage, the influence of first-strike attack is negligible. An increase in the influence of first-strike attack on the expected losses of a strong hand, and a reduction of its impact on the expected losses of the weaker party, as the number of groups involved in the fight increases proportionally, is also shown.
Chuev V., Dubogray I. Models of bilateral warfare of numerous groups. Маthematical Modeling and Coтputational Methods, 2016, №1 (9), pp. 89-104
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
In this paper we prove constitutive equations for calculation and estimation of life’s features of the objects working in normal mode through life’s features of objects working in another self-similar mode where life consumption is modeled according to the law of the additive damage accumulation.
Sadykhov G., Krapotkin V., Kazakova O. Additive damage accumulation approach to calculation and estimation of objects’ life feartures. Маthematical Modeling and Coтputational Methods, 2014, №1 (1), pp. 82-98
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
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
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
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
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