Most viewed papers

221. Sviridenko A.B., Zelenkov G.A.
     Correlation and realization of quasi-Newton methods of absolute optimization
     Computer Research and Modeling, 2016, v. 8, no. 1, pp. 55-78

     Newton and quasi-Newton methods of absolute optimization based on Cholesky factorization with adaptive step and finite difference approximation of the first and the second derivatives. In order to raise effectiveness of the quasi-Newton methods a modified version of Cholesky decomposition of quasi-Newton matrix is suggested. It solves the problem of step scaling while descending, allows approximation by non-quadratic functions, and integration with confidential neighborhood method. An approach to raise Newton methods effectiveness with finite difference approximation of the first and second derivatives is offered. The results of numerical research of algorithm effectiveness are shown.

     Keywords: Newton methods, quasi-Newton methods, Cholesky factorization, step scaling, method of confidence neighborhoods, finite difference approximation, algorithm, numerical research, absolute optimization.
     Views (last year): 7. Citations: 5 (RSCI).
222. Zhdanova O.L., Frisman Y.Y.
     Mathematical modeling of the mechanism of a reproductive strategies differentiation in natural populations (on the example of arctic fox, Alopex lagopus)
     Computer Research and Modeling, 2016, v. 8, no. 2, pp. 213-228

     This paper considers the integrated approach to modeling the dynamics of genetic structure and the number of natural population. A set of dynamic models with different types of natural selection is used to describe a possible mechanism for the fixing of a genetic diversity in size of the litter in coastal, continental and farmed populations of arctic fox (Alopex lagopus, Canidae, Carnivora) observed now. The most interesting results have been obtained with the model of population consisting of two stages of development. At that with the frame of this model a dynamics of population genetic structure on genotypes was analyzed to consider different reproductive abilities and fitnesses of pups on the early stage of lifecycle which defined by the single diallelic gene. This model allows to receive a monomorphism for coastal populations of arctic fox, where food resources are practically constant. As well the model allows polymorphism with cyclical fluctuations in the number and frequency of the gene in the continental populations due to regular fluctuating of rodent number, the major component of its food. In farmed populations by selective selection carried out by farmers to increase the reproductive success, this gene is a pleiotropic one (i. e., determining the survival rate of individuals both early and late stages of their life cycle); so an application of appropriate model (with the selection of pleiotropic gene) allows to get an adequate rate of elimination for small litters allele.

     Keywords: evolution, age structure, natural selection, polymorphism, monomorphism.
     Views (last year): 7. Citations: 5 (RSCI).
223. Bashashin M.V., Zemlyanay E.V., Rahmonov I.R., Shukrinov J.M., Atanasova P.C., Volokhova A.V.
     Numerical approach and parallel implementation for computer simulation of stacked long Josephson Junctions
     Computer Research and Modeling, 2016, v. 8, no. 4, pp. 593-604

     We consider a model of stacked long Josephson junctions (LJJ), which consists of alternating superconducting and dielectric layers. The model takes into account the inductive and capacitive coupling between the neighbor junctions. The model is described by a system of nonlinear partial differential equations with respect to the phase differences and the voltage of LJJ, with appropriate initial and boundary conditions. The numerical solution of this system of equations is based on the use of standard three-point finite-difference formulae for discrete approximations in the space coordinate, and the applying the four-step Runge-Kutta method for solving the Cauchy problem obtained. Designed parallel algorithm is implemented by means of the MPI technology (Message Passing Interface). In the paper, the mathematical formulation of the problem is given, numerical scheme and a method of calculation of the current-voltage characteristics of the LJJ system are described. Two variants of parallel implementation are presented. The influence of inductive and capacitive coupling between junctions on the structure of the current-voltage characteristics is demonstrated. The results of methodical calculations with various parameters of length and number of Josephson junctions in the LJJ stack depending on the number of parallel computing nodes, are presented. The calculations have been performed on multiprocessor clusters HybriLIT and CICC of Multi-Functional Information and Computing Complex (Laboratory of Information Technologies, Joint Institute for Nuclear Research, Dubna). The numerical results are discussed from the viewpoint of the effectiveness of presented approaches of the LJJ system numerical simulation in parallel. It has been shown that one of parallel algorithms provides the 9 times speedup of calculations.

     Keywords: Josephson junctions, finite difference approximation, parallel computing.
     Views (last year): 7. Citations: 6 (RSCI).
224. Shumov V.V.
     Consideration of psychological factors in models of the battle (conflict)
     Computer Research and Modeling, 2016, v. 8, no. 6, pp. 951-964

     The course and outcome of the battle is largely dependent on the morale of the troops, characterized by the percentage of loss in killed and wounded, in which the troops still continue to fight. Every fight is a psychological act of ending his rejection of one of the parties. Typically, models of battle psychological factor taken into account in the decision of Lanchester equations (the condition of equality of forces, when the number of one of the parties becomes zero). It is emphasized that the model Lanchester type satisfactorily describe the dynamics of the battle only in the initial stages. To resolve this contradiction is proposed to use a modification of Lanchester's equations, taking into account the fact that at any moment of the battle on the enemy firing not affected and did not abandon the battle fighters. The obtained differential equations are solved by numerical method and allow the dynamics to take into account the influence of psychological factor and evaluate the completion time of the conflict. Computational experiments confirm the known military theory is the fact that the fight usually ends in refusal of soldiers of one of the parties from its continuation (avoidance of combat in various forms). Along with models of temporal and spatial dynamics proposed to use a modification of the technology features of the conflict of S. Skaperdas, based on the principles of combat. To estimate the probability of victory of one side in the battle takes into account the interest of the maturing sides of the bloody casualties and increased military superiority.

     Keywords: model battlefield, function technology of the conflict, the function of representation and perception, psychology of combat, social and information management and confrontation.
     Views (last year): 7. Citations: 4 (RSCI).
225. Radjuk A.G., Titlianov A.E., Skripalenko M.M.
     Computer simulation of temperature field of blast furnace’s air tuyere
     Computer Research and Modeling, 2017, v. 9, no. 1, pp. 117-125

     Study of work of heating equipment is an actual issue because it allows determining optimal regimes to reach highest efficiency. At that it is very helpful to use computer simulation to predict how different heating modes influence the effectiveness of the heating process and wear of heating equipment. Computer simulation provides results whose accuracy is proven by many studies and requires costs and time less than real experiments. In terms of present research, computer simulation of heating of air tuyere of blast furnace was realized with the help of FEM software. Background studies revealed possibility to simulate it as a flat, axisymmetric problem and DEFORM-2D software was used for simulation. Geometry, necessary for simulation, was designed with the help of SolidWorks, saved in .dxf format. Then it was exported to DEFORM-2D pre-processor and positioned. Preliminary and boundary conditions were set up. Several modes of operating regimes were under analysis. In order to demonstrate influence of eah of the modes and for better visualization point tracking option of the DEFORM-2D post-processor was applied. Influence of thermal insulation box plugged into blow channel, with and without air gap, and thermal coating on air tuyere’s temperature field was investigated. Simulation data demonstrated significant effect of thermal insulation box on air tuyere’s temperature field. Designed model allowed to simulate tuyere’s burnout as a result of interaction with liquid iron. Conducted researches have demonstrated DEFORM-2D effectiveness while using it for simulation of heat transfer and heating processes. DEFORM-2D is about to be used in further studies dedicated to more complex process connected with temperature field of blast furnace’s air tuyere.

     Keywords: blast furnace, air tuyere, thermal insulation box, thermal coating, DEFORM-2D, temperature field, burnout of tuyere.
     Views (last year): 7.
226. Kurushina S.E., Shapovalova E.A.
     Origin and growth of the disorder within an ordered state of the spatially extended chemical reaction model
     Computer Research and Modeling, 2017, v. 9, no. 4, pp. 595-607

     We now review the main points of mean-field approximation (MFA) in its application to multicomponent stochastic reaction-diffusion systems.

     We present the chemical reaction model under study — brusselator. We write the kinetic equations of reaction supplementing them with terms that describe the diffusion of the intermediate components and the fluctuations of the concentrations of the initial products. We simulate the fluctuations as random Gaussian homogeneous and spatially isotropic fields with zero means and spatial correlation functions with a non-trivial structure. The model parameter values correspond to a spatially-inhomogeneous ordered state in the deterministic case.

     In the MFA we derive single-site two-dimensional nonlinear self-consistent Fokker–Planck equation in the Stratonovich's interpretation for spatially extended stochastic brusselator, which describes the dynamics of probability distribution density of component concentration values of the system under consideration. We find the noise intensity values appropriate to two types of Fokker–Planck equation solutions: solution with transient bimodality and solution with the multiple alternation of unimodal and bimodal types of probability density. We study numerically the probability density dynamics and time behavior of variances, expectations, and most probable values of component concentrations at various noise intensity values and the bifurcation parameter in the specified region of the problem parameters.

     Beginning from some value of external noise intensity inside the ordered phase disorder originates existing for a finite time, and the higher the noise level, the longer this disorder “embryo” lives. The farther away from the bifurcation point, the lower the noise that generates it and the narrower the range of noise intensity values at which the system evolves to the ordered, but already a new statistically steady state. At some second noise intensity value the intermittency of the ordered and disordered phases occurs. The increasing noise intensity leads to the fact that the order and disorder alternate increasingly.

     Thus, the scenario of the noise induced order–disorder transition in the system under study consists in the intermittency of the ordered and disordered phases.

     Keywords: mean field approximation, reaction-diffusion systems, nonlinear self-consistent Fokker–Planck equation, dynamical phase transitions, disorder.
     Views (last year): 7.
227. Sviridenko A.B.
     Direct multiplicative methods for sparse matrices. Newton methods
     Computer Research and Modeling, 2017, v. 9, no. 5, pp. 679-703

     We consider a numerically stable direct multiplicative algorithm of solving linear equations systems, which takes into account the sparseness of matrices presented in a packed form. The advantage of the algorithm is the ability to minimize the filling of the main rows of multipliers without losing the accuracy of the results. Moreover, changes in the position of the next processed row of the matrix are not made, what allows using static data storage formats. Linear system solving by a direct multiplicative algorithm is, like the solving with $LU$-decomposition, just another scheme of the Gaussian elimination method implementation.

     In this paper, this algorithm is the basis for solving the following problems:

     Problem 1. Setting the descent direction in Newtonian methods of unconditional optimization by integrating one of the known techniques of constructing an essentially positive definite matrix. This approach allows us to weaken or remove additional specific difficulties caused by the need to solve large equation systems with sparse matrices presented in a packed form.

     Problem 2. Construction of a new mathematical formulation of the problem of quadratic programming and a new form of specifying necessary and sufficient optimality conditions. They are quite simple and can be used to construct mathematical programming methods, for example, to find the minimum of a quadratic function on a polyhedral set of constraints, based on solving linear equations systems, which dimension is not higher than the number of variables of the objective function.

     Problem 3. Construction of a continuous analogue of the problem of minimizing a real quadratic polynomial in Boolean variables and a new form of defining necessary and sufficient conditions of optimality for the development of methods for solving them in polynomial time. As a result, the original problem is reduced to the problem of finding the minimum distance between the origin and the angular point of a convex polyhedron, which is a perturbation of the $n$-dimensional cube and is described by a system of double linear inequalities with an upper triangular matrix of coefficients with units on the main diagonal. Only two faces are subject to investigation, one of which or both contains the vertices closest to the origin. To calculate them, it is sufficient to solve $4n – 4$ linear equations systems and choose among them all the nearest equidistant vertices in polynomial time. The problem of minimizing a quadratic polynomial is $NP$-hard, since an $NP$-hard problem about a vertex covering for an arbitrary graph comes down to it. It follows therefrom that $P = NP$, which is based on the development beyond the limits of integer optimization methods.

     Keywords: $NP$-hard problem, sparse matrices, Newton methods, direct multiplication algorithm, the direction of descent, a new mathematical formulation, necessary and sufficient conditions of optimality, minimization pseudo Boolean functions, pseudo Boolean programming, linear programming.
     Views (last year): 7. Citations: 1 (RSCI).
228. Krasilnikov P.M.
     Role of hydrogen bonds in molecular relaxation during electron transport processes in biological systems
     Computer Research and Modeling, 2009, v. 1, no. 3, pp. 297-320

     In molecular systems with hydrogen bonds the mechanism of proton relaxation can take place. It is caused by redistribution of protons between two steady positions in double walls potential along the line of the hydrogen bond. This redistribution occurs at change of parameters of the double walls potential of the hydrogen bond which is caused by change of an electronic state of molecular system. The relaxation process is carried out due to a tunnel transfer of protons along the line of bonds. It is shown, that relaxation process can define temperature dependence of power parameters (either of the free energy differences ΔG or of the reorganization energy λ) of charge recombination P⁺Q^-_A from RC of Rhodobacter sphaeroides.

     Keywords: hydrogen bonds, electron transport, proton relaxation.
     Views (last year): 6. Citations: 3 (RSCI).
229. Bratsun D.A., Zakharov A.P.
     Modelling spatio-temporal dynamics of circadian rythms in Neurospora crassa
     Computer Research and Modeling, 2011, v. 3, no. 2, pp. 191-213

     We derive a new model of circadian oscillations in Neurospora crassa, which is suitable to analyze both temporal and spatial dynamics of proteins responsible for mechanism of rythms. The model is based on the non-linear interplay between proteins FRQ and WCC which are products of transcription of frequency and white collar genes forming a feedback loop comprised both positive and negative elements. The main component of oscillations mechanism is supposed to be time-delay in biochemical reactions of transcription. We show that the model accounts for various features observed in Neurospora’s experiments such as entrainment by light cycles, phase shift under light pulse, robustness to action of fluctuations and so on. Wave patterns excited during spatial development of the system are studied. It is shown that the wave of synchronization of biorythms arises under basal transcription factors.

     Keywords: time-delay, stochastic systems, circadian rythms, gene regulation.
     Views (last year): 6. Citations: 20 (RSCI).
230. Yevin I.A., Koblyakov A.A., Savricov D.V., Shuvalov N.D.
     Cognitive Networks
     Computer Research and Modeling, 2011, v. 3, no. 3, pp. 231-239

     Traditional classification of real complex networks on biological, technological and social is incomplete, as there is a huge variety of artworks, which structure also can be presented in the form of networks. In this paper the review of researches of the complex networks, modeling some literary, musical and painting works is given. Corresponding networks are offered for naming cognitive networks. The possible directions of studying of such networks are discussed.

     Keywords: scale-free networks, assortativity, clasterisation.
     Views (last year): 6. Citations: 16 (RSCI).

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