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361. Zakharov P.V., Eremin A.M., Starostenkov M.D., Markidonov A.V.
     Computer simulation of nonlinear localized vibrational modes of large amplitude in the crystal Pt₃Al with bivacancies Pt
     Computer Research and Modeling, 2015, v. 7, no. 5, pp. 1089-1096

     By method of molecular dynamics investigated the interaction of nonlinear localized modes with bivacancies Pt crystal Pt₃Al. Identified dependences of the lifetime of the nonlinear localized modes from the initial temperature of the crystal model, the initial atom Al deviation from its equilibrium position, as well as the distance to the introduced bivacancy Pt in (111) plane of the crystal.

     Keywords: molecular dynamics, discrete breathers, localized mode.
     Views (last year): 4. Citations: 9 (RSCI).
362. Alekseenko A.E., Kholodov Y.A., Kholodov A.S., Goreva A.I., Vasilev M.O., Chekhovich Y.V., Mishin V.D., Starozhilets V.M.
     Development, calibration and verification of mathematical model for multilane urban road traffic flow. Part I
     Computer Research and Modeling, 2015, v. 7, no. 6, pp. 1185-1203

     In this paper, we propose the unified procedure for the development and calibration of mathematical model for multilane urban road traffic flow. We use macroscopic approach, describing traffic flow with the system of second-order nonlinear hyperbolic equations (for traffic density and velocity). We close the resulting model with the equation of vehicle flow as a function of density, obtained empirically for each segment of road network using data from traffic detectors and vehicles’ GPS tracks. We verify the developed new model and calibration methods by using it to model segment of Moscows Ring Road.

     Keywords: traffic flow modeling, fundamental diagram, second-order hydrodynamic models.
     Views (last year): 4. Citations: 2 (RSCI).
363. Ghazaryan M., Yakushkina T.S., Saakian D.B.
     Exact evolutionary dynamics on multi dimensional fitness landscape
     Computer Research and Modeling, 2015, v. 7, no. 6, pp. 1269-1277

     Crow–Kimura model is one of the famous models of population genetics. Last decade models with low-dimensional fitness landscape have been investigated. We consider the Crow–Kimura model of evolutionary dynamics on multi-dimensional fitness landscape with a single peak. We deduce exact solution for the dynamics, confirmed well by the numerics.

     Keywords: model Crow–Kimura, evolution model, mutidimensional fitness landscape.
     Views (last year): 4.
364. Risnik D.V., Levich A.P., Fursova P.V., Goncharov I.A.
     The algorithm of the method for calculating quality classes’ boundaries for quantitative systems’ characteristics and for determination of interactions between characteristics. Part 2. Calculation for three or more quality classes
     Computer Research and Modeling, 2016, v. 8, no. 1, pp. 37-54

     The method of calculation of the boundaries of quality classes for quantitative characteristics of systems with any properties is adapted to search for boundaries of three quality classes. In addition to other results, adaptation of the method allowed to determine boundaries between quality classes at simultaneous «unacceptability » of high and low values of indicator characteristic of the system condition and simultaneous «inadmissibility » of high and low values of factors affecting the system.

     Keywords: analysis of interaction, maximization of interaction power, indicators, factors, boundaries of quality classes, factor contribution.
     Views (last year): 4. Citations: 1 (RSCI).
365. Zhluktov S.V., Aksenov A.A., Karasev P.I.
     Modeling separated flow with use of two-equation turbulence model
     Computer Research and Modeling, 2016, v. 8, no. 1, pp. 79-88

     The article provides a development of recently published turbulence model KEFV. The submitted version of this model allows modeling transition in a separated flow. The model includes an adjustable mechanism for specifying generation of turbulence in laminar zones with high velocity gradients. The model is implemented in the FlowVision CFD software. Simulation of the air flow around low-Reynolds airfoil Eppler-387 is discussed in the article. The flow conditions are characterized by the Reynolds number Re = 200 000.

     Keywords: turbulent flow, laminar-turbulent transition, $k–\varepsilon$ turbulence model, low-Reynolds calculations.
     Views (last year): 4. Citations: 7 (RSCI).
366. Sukhinov A.I., Chistyakov A.E., Semenyakina A.A., Nikitina A.V.
     Numerical modeling of ecologic situation of the Azov Sea with using schemes of increased order of accuracy on multiprocessor computer system
     Computer Research and Modeling, 2016, v. 8, no. 1, pp. 151-168

     The article covered results of three-dimensional modeling of ecologic situation of shallow water on the example of the Azov Sea with using schemes of increased order of accuracy on multiprocessor computer system of Southern Federal University. Discrete analogs of convective and diffusive transfer operators of the fourth order of accuracy in the case of partial occupancy of cells were constructed and studied. The developed scheme of the high (fourth) order of accuracy were used for solving problems of aquatic ecology and modeling spatial distribution of polluting nutrients, which caused growth of phytoplankton, many species of which are toxic and harmful. The use of schemes of the high order of accuracy are improved the quality of input data and decreased the error in solutions of model tasks of aquatic ecology. Numerical experiments were conducted for the problem of transportation of substances on the basis of the schemes of the second and fourth orders of accuracy. They’re showed that the accuracy was increased in 48.7 times for diffusion-convection problem. The mathematical algorithm was proposed and numerically implemented, which designed to restore the bottom topography of shallow water on the basis of hydrographic data (water depth at individual points or contour level). The map of bottom relief of the Azov Sea was generated with using this algorithm. It’s used to build fields of currents calculated on the basis of hydrodynamic model. The fields of water flow currents were used as input data of the aquatic ecology models. The library of double-layered iterative methods was developed for solving of nine-diagonal difference equations. It occurs in discretization of model tasks of challenges of pollutants concentration, plankton and fish on multiprocessor computer system. It improved the precision of the calculated data and gave the possibility to obtain operational forecasts of changes in ecologic situation of shallow water in short time intervals.

     Keywords: mathematical model, scheme of high order of accuracy, bottom topography, transport of substances, aquatic ecology tasks, Azov Sea, multiprocessor computer system.
     Views (last year): 4. Citations: 31 (RSCI).
367. Ostrovskaya N.V., Skidanov V.A., Skvortsov M.S.
     Classification of dynamical switching regimes in a three-layered ferromagnetic nanopillar governed by spin-polarized injection current and external magnetic field. II. Perpendicular anisotropy
     Computer Research and Modeling, 2016, v. 8, no. 5, pp. 755-764

     The mathematical model of a three-layered Co/Cu/Co nanopillar for MRAM cell with one fixed and one free layer was investigated in the approximation of uniformly distributed magnetization. The anisotropy axis is perpendicular to the layers (so-called perpendicular anisotropy). Initially the magnetization of the free layer is oriented along the anisotropy axis in the position accepted to be “zero”. Simultaneous magnetic field and spinpolarized current engaging can reorient the magnetization to another position which in this context can be accepted as “one”. The mathematical description of the effect is based on the classical vector Landau–Lifshits equation with the dissipative term in the Gilbert form. In our model we took into account the interactions of the magnetization with an external magnetic field and such effective magnetic fields as an anisotropy and demagnetization ones. The influence of the spin-polarized injection current is taken into account in the form of Sloczewski–Berger term. The model was reduced to the set of three ordinary differential equations with the first integral. It was shown that at any current and field the dynamical system has two main equilibrium states on the axis coincident with anisotropy axis. It was ascertained that in contrast with the longitudinal-anisotropy model, in the model with perpendicular anisotropy there are no other equilibrium states. The stability analysis of the main equilibrium states was performed. The bifurcation diagrams characterizing the magnetization dynamics at different values of the control parameters were built. The classification of the phase portraits on the unit sphere was performed. The features of the dynamics at different values of the parameters were studied and the conditions of the magnetization reorientation were determined. The trajectories of magnetization switching were calculated numerically using the Runge–Kutta method. The parameter values at which limit cycles exist were determined. The threshold values for the switching current were found analytically. The threshold values for the structures with longitudinal and perpendicular anisotropy were compared. It was established that in the structure with the perpendicular anisotropy at zero field the switching current is an order lower than in the structure with the longitudinal one.

     Keywords: MRAM, uniaxial anisotropy, magnetization, free layer, fixed layer, the Landau–Lifshits–Gilbert equation, magnetization reversal.
     Views (last year): 4. Citations: 1 (RSCI).
368. Khavinson M.J., Kulakov M.P., Frisman Y.Y.
     Mathematical modeling of the age groups of employed peoples by the example of the southern regions of the Russian Far East
     Computer Research and Modeling, 2016, v. 8, no. 5, pp. 787-801

     The article focuses on a nonlinear mathematical model that describes the interaction of the different age groups of the employed population. The interactions are treated by analogy with population relationship (competition, discrimination, assistance, oppression, etc). Under interaction of peoples we mean the generalized social and economic mechanisms that cause related changes in the number of employees of different age groups. Three age groups of the employed population are considered. It is young specialists (15–29 years), workers with experience (30–49 years), the employees of pre-retirement and retirement age (50 and older). The estimation of model’s parameters for the southern regions of the Far Eastern Federal District (FEFD) is executed by statistical data. Analysis of model scenarios allows us to conclude the observed number fluctuations of the different ages employees on the background of a stable total employed population may be a consequence of complex interactions between these groups of peoples. Computational experiments with the obtained values of the parameters allowed us to calculate the rate of decline and the aging of the working population and to determine the nature of the interaction between the age groups of employees that are not directly as reflected in the statistics. It was found that in FEFD the employed of 50 years and older are discriminated against by the young workers under 29, employed up to 29 and 30–49 years are in a partnership. It is shown in most developed regions (Primorsky and Khabarovsk Krai) there is “uniform” competition among different age groups of the employed population. For Primorsky Krai we were able to identify the mixing effect dynamics. It is a typical situation for systems in a state of structural adjustment. This effect is reflected in the fact the long cycles of employed population form with a significant decrease in migration inflows of employees 30–49 years. Besides, the change of migration is accompanied by a change of interaction type — from employment discrimination by the oldest of middle generation to discrimination by the middle of older generation. In less developed regions (Amur, Magadan and Jewish Autonomous Regions) there are lower values of migration balance of almost all age groups and discrimination by young workers up 29 years of other age groups and employment discrimination 30–49 years of the older generation.

     Keywords: mathematical model, employed population, interaction, age groups, Russian Far East.
     Views (last year): 4. Citations: 3 (RSCI).
369. Editor's note
     Computer Research and Modeling, 2019, v. 11, no. 4, pp. 559-561
     Views (last year): 4.
370. Lavrova A.I., Plusnina T.Yu., Ukrainetz A.V., Riznichenko G.Yu., Rubin A.B.
     Nonlinear dynamic of the transmembrane potential and pH along the cell membrane of Chara alga
     Computer Research and Modeling, 2009, v. 1, no. 2, pp. 233-239

     The model of potential dependent proton transfer trough the cell membrane of Chara alga developed in [1] is considered. In the last version of the model we considered two variables: proton concentration near the surface cell and transmembrane potential. In present version we introduce the new variable — proton concentration in cytoplasm. Oscillative and chaotic dynamic of transmembrane potential was obtained in calculations. The physiological role of these patterns is discussed.

     Keywords: Chara alga, transmembrane potential, pH, oscillations.
     Views (last year): 3. Citations: 1 (RSCI).

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