Most viewed papers

151. Yakovleva T.V.
     Signal and noise calculation at Rician data analysis by means of combining maximum likelihood technique and method of moments
     Computer Research and Modeling, 2018, v. 10, no. 4, pp. 511-523

     The paper develops a new mathematical method of the joint signal and noise calculation at the Rice statistical distribution based on combing the maximum likelihood method and the method of moments. The calculation of the sough-for values of signal and noise is implemented by processing the sampled measurements of the analyzed Rician signal’s amplitude. The explicit equations’ system has been obtained for required signal and noise parameters and the results of its numerical solution are provided confirming the efficiency of the proposed technique. It has been shown that solving the two-parameter task by means of the proposed technique does not lead to the increase of the volume of demanded calculative resources if compared with solving the task in one-parameter approximation. An analytical solution of the task has been obtained for the particular case of small value of the signal-to-noise ratio. The paper presents the investigation of the dependence of the sought for parameters estimation accuracy and dispersion on the quantity of measurements in experimental sample. According to the results of numerical experiments, the dispersion values of the estimated sought-for signal and noise parameters calculated by means of the proposed technique change in inverse proportion to the quantity of measurements in a sample. There has been implemented a comparison of the accuracy of the soughtfor Rician parameters’ estimation by means of the proposed technique and by earlier developed version of the method of moments. The problem having been considered in the paper is meaningful for the purposes of Rician data processing, in particular, at the systems of magnetic-resonance visualization, in devices of ultrasonic visualization, at optical signals’ analysis in range-measuring systems, at radar signals’ analysis, as well as at solving many other scientific and applied tasks that are adequately described by the Rice statistical model.

     Keywords: probability density function, Rice distribution, maximum likelihood technique, method of moments, samples of measurements, signal to noise ratio.
     Views (last year): 11.
152. Korolev S.A., Maykov D.V.
     Identification of a mathematical model and research of the various modes of methanogenesis in mesophilic environments
     Computer Research and Modeling, 2012, v. 4, no. 1, pp. 131-141

     A mathematical model for the production of biogas from animal waste was developed. An algorithm for identification of model parameters was developed. The accuracy of model identification was performed. The result of simulation for batch and continuous modes of supply of substrate was shown. The optimum flow rate of the substrate for continuous operation was found.

     Keywords: methanogenesis, biogas, mathematical model, set of ordinary differential equations, identification of mathematical model, genetic algorithm.
     Views (last year): 10. Citations: 10 (RSCI).
153. Zhуkharevуch V.V., Shumуlyak L.M.
     Approximation of the solution of the non-stationary equation of heat conductivity by the method of probabilistic continuous asynchronous cellular automats for a one-dimensional case
     Computer Research and Modeling, 2012, v. 4, no. 2, pp. 293-301

     The solution of problems of heat conductivity by means of a method of continuous asynchronous cellular automats is considered in the article. Coordination of distribution of temperature in a sample at a given time between cellular automat model and the exact analytical solution of the equation of heattransfer is shown that speaks about expedient use of this method of modelling. Dependence between time of one cellular automatic interaction and dimension of a cellular automatic field is received.

     Keywords: heat conductivity equation, cellular automat, time of interaction.
     Views (last year): 10. Citations: 4 (RSCI).
154. Skalko Y.I., Karasev R.N., Akopyan A.V., Tsybulin I.V., Mendel M.A.
     Space-marching algorithm for solving radiative transfer problem based on short-characteristics method
     Computer Research and Modeling, 2014, v. 6, no. 2, pp. 203-215

     A procedure of approximate solving of the radiation transfer problem is presented. The approximated solution is being built successively from the domain border along the direction of radiation propagation. The algorithm was tested for model problem of hot ball radiation.

     Keywords: radiative transfer problem, space-marching algorithm, short-characteristics method.
     Views (last year): 10. Citations: 3 (RSCI).
155. Bratsun D.A., Zakharov A.P., Pismen L.M.
     Multiscale mathematical modeling occurrence and growth of a tumour in an epithelial tissue
     Computer Research and Modeling, 2014, v. 6, no. 4, pp. 585-604

     In this paper we propose a mathematical model of cancer tumour occurrence in a quasi twodimensional epithelial tissue. Basic model of the epithelium growth describes the appearance of intensive movement and growth of tissue when it is damaged. The model includes the effects of division of cells and intercalation. It is assumed that the movement of cells is caused by the wave of mitogen-activated protein kinase (MAPK), which in turn activated by the chemo-mechanical signal propagating along tissue due to its local damage. In this paper it is assumed that cancer cells arise from local failure of spatial synchronization of circadian rhythms. The study of the evolutionary dynamics of the model could determine the chemo-physical properties of a tumour, and spatial relationship between the occurrence of cancer cells and development of the entire tissue parameters coordinating its evolution through the exchange of chemical and mechanical signals.

     Keywords: mathematical modeling, cancer growth, circadian rhythms, gene regulation, synchronization, complex systems.
     Views (last year): 10. Citations: 12 (RSCI).
156. Orlova E.V.
     Model for economic interests agreement in duopoly’s making price decisions
     Computer Research and Modeling, 2015, v. 7, no. 6, pp. 1309-1329

     The model of market pricing in duopoly describing the prices dynamics as a two-dimensional map is presented. It is shown that the fixed point of the map coincides with the local Nash-equilibrium price in duopoly game. There have been numerically identified a bifurcation of the fixed point, shown the scheme of transition from periodic to chaotic mode through a doubling period. To ensure the sustainability of local Nashequilibrium price the controlling chaos mechanism has been proposed. This mechanism allows to harmonize the economic interests of the firms and to form the balanced pricing policy.

     Keywords: two-dimensional map, stability of fixed point, bifurcation analysis, price competition, control of market prices, strategic interaction of firms, Nash-equilibrium.
     Views (last year): 10. Citations: 2 (RSCI).
157. Grabarnik P.Ya., Logofet D.O.
     Non-linear World of A.S. Komarov
     Computer Research and Modeling, 2016, v. 8, no. 2, pp. 205-212
     Views (last year): 10.
158. Safiullina L.F., Gubaydullin I.M.
     Research and reduction of mathematical model of chemical reaction by Sobol’ method
     Computer Research and Modeling, 2016, v. 8, no. 4, pp. 633-646

     The technique of simplification of mathematical model of a chemical reaction by reducing the number of steps of the reaction scheme, based on an analysis of sensitivity to changes in the objective function of the model parameters, is proposed. The reduced scheme of model reaction of formaldehyde oxidation is received. Functional characterizes the measure of proximity to the calculated values for the initial kinetic reaction scheme and the scheme resulting disturbance of its parameters. The advantage of this technique is the ability to analyze complex kinetic schemes and reduction of kinetic models to a size suitable for practical use. The results of computational experiments under different reaction conditions can be included in the functional and thus to receive the reduce scheme, which is consistent the detailed scheme for the desired range of conditions. Sensitivity analysis of the functional model allows to identify those parameters, which provide the largest (or smallest) the contribution to the result of the process simulation. The mathematical model can contain parameters, which change of values do not affect the qualitative and quantitative description of the process. The contribution of these parameters in the functional value won’t be of great importance. Thus it can be eliminated from consideration, which do not serve for modeling kinetic curves substances. The kinetic scheme of formaldehyde oxidation, the detailed mechanism which includes 25 stages and 15 substances, were investigated using this method. On the basis of the local and global sensitivity analysis, the most important stage of the process that affect the overall dynamics of the target concentrations of the reaction. The reduced scheme of model reaction of formaldehyde oxidation is received. This scheme also describes the behavior of the main substances, as detailed scheme, but has a much smaller number of reaction stages. The results of the comparative analysis of modeling of formaldehyde oxidation on detailed and reduced schemes are given. Computational aspects of the problems of chemical kinetics by Sobol’ global method an example of this reaction are specified. The comparison results are local, global and total sensitivity indices are given.

     Keywords: sensitivity analysis, mathematical model of reaction, reducing the reaction scheme, formaldehyde oxidation reaction.
     Views (last year): 10. Citations: 4 (RSCI).
159. Gorshkov A.V., Prosviryakov Y.Y.
     Layered Bénard–Marangoni convection during heat transfer according to the Newton’s law of cooling
     Computer Research and Modeling, 2016, v. 8, no. 6, pp. 927-940

     The paper considers mathematical modeling of layered Benard–Marangoni convection of a viscous incompressible fluid. The fluid moves in an infinitely extended layer. The Oberbeck–Boussinesq system describing layered Benard–Marangoni convection is overdetermined, since the vertical velocity is zero identically. We have a system of five equations to calculate two components of the velocity vector, temperature and pressure (three equations of impulse conservation, the incompressibility equation and the heat equation). A class of exact solutions is proposed for the solvability of the Oberbeck–Boussinesq system. The structure of the proposed solution is such that the incompressibility equation is satisfied identically. Thus, it is possible to eliminate the «extra» equation. The emphasis is on the study of heat exchange on the free layer boundary, which is considered rigid. In the description of thermocapillary convective motion, heat exchange is set according to the Newton’s law of cooling. The application of this heat distribution law leads to the third-kind initial-boundary value problem. It is shown that within the presented class of exact solutions to the Oberbeck–Boussinesq equations the overdetermined initial-boundary value problem is reduced to the Sturm–Liouville problem. Consequently, the hydrodynamic fields are expressed using trigonometric functions (the Fourier basis). A transcendental equation is obtained to determine the eigenvalues of the problem. This equation is solved numerically. The numerical analysis of the solutions of the system of evolutionary and gradient equations describing fluid flow is executed. Hydrodynamic fields are analyzed by a computational experiment. The existence of counterflows in the fluid layer is shown in the study of the boundary value problem. The existence of counterflows is equivalent to the presence of stagnation points in the fluid, and this testifies to the existence of a local extremum of the kinetic energy of the fluid. It has been established that each velocity component cannot have more than one zero value. Thus, the fluid flow is separated into two zones. The tangential stresses have different signs in these zones. Moreover, there is a fluid layer thickness at which the tangential stresses at the liquid layer equal to zero on the lower boundary. This physical effect is possible only for Newtonian fluids. The temperature and pressure fields have the same properties as velocities. All the nonstationary solutions approach the steady state in this case.

     Keywords: convection of Benard–Maragoni, analytical solutions, nonstationary problem.
     Views (last year): 10. Citations: 3 (RSCI).
160. Dyadkin A.A., Pavlov A.O., Simakova T.V., Chetkin S.V.
     Analysis of the possibility of investigation of hydrodynamic responses and landing dynamics of space module impacting water with FlowVision CFD software
     Computer Research and Modeling, 2017, v. 9, no. 1, pp. 47-55

     The results of verification carried out for investigations of hydrodynamic effect on reentry conicalsegmental space vehicle are presented in the paper. The program complex Flow Vision is used for this analysis. The purpose of the study is verification of using Flow Vision program complex for problem solving mentioned above on the base of comparison between calculated and experimental data, obtained on the Apollo landing models and new development reentry spacecraft of manned transporting spaceship designed by RSC Energia. The comparison was carried out through the data of pressure values on spacecraft model surfaces during its water landing and inertia center motion parameters.

     The results of study show good agreement between experimental and calculated data of force effects on vehicle construction during water landing and its motion parameters in the water medium. Computer simulation sufficiently well reproduces influence of initial velocities & water entry angles variations on water landing process.

     Using of computer simulation provides simultaneous acquisition of all data information needed for investigation of water landing peculiarities during construction design, notably, hydrodynamic effects for structural strength calculations, parameters and dynamics of center mass motion and vehicle revolution around center mass for estimation water landing conditions, as well as vehicle stability after landing.

     Obtained results confirm suitability of using Flow Vision program complex for water landing vehicle investigations and investigations of influence of different landing regimes through wide initial condition change range, that permits considerably decrease extent of expensive experimental tests and realize landing conditions which are sufficiently complicated for realizing in model physical experiments.

     Keywords: computational fluid dynamics, computer simulation, water landing.
     Views (last year): 10.

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