No 3.2 (2010)

By an example of the generalized Korteweg-Burgers equation by means of a numerical analysis it was found that for the weakly dissipative media with dispersion and nonlinearity there are three types of discontinuity structures: stationary, periodic on time and stochastic ones. The stationary weakly dissipative structures inside themselves contain dissipation-free discontinuity structures such as transitions between homogeneous or wave states. A technique of research of branches of doubly periodic solutions of the generalized Korteweg-de Vries equation has been developed. A correspondence has been revealed between the types of the internal discontinuity structure and the pictures of the branches arrangement. Research was conducted on the dependence of the type of discontinuity upon its amplitude and dissipation parameter.

In previous papers we presented algorithm for parallel calculation of Gr.obner and Janet bases that works in terms of parallel normal forms computations. The realization was quite promising but faced problem of "starvation" (e.g. in some moments of time only few processors was fully loaded). In this talk one approach to raise scalability and avoid "starvation" will be presented. Experimental results of parallel computations on eight core SMP machine will be shown. Work was partially supported by the RFBR grant 07-01-00660 and by the grant 1027.2008.2 of the Ministry of Education and Science of the Russian Federation.

Further development of the thermal explosion model (TEM) describing track formation processes in high- superconductors is suggested. Information on the temperature dependence of electron thermal diffusivity in YBa2Cu3O7− is obtained by solving an inverse problem of reproducing measured track radii within the framework of TEM.

A statistical model is applied to data processing and simulation of processes of magmatism and tectonics. With the help of a model of forming volcanic channels, the empirical dependence describing the capacity of lava streams of plateau basalt volcanism by Fibonacci series of numbers is explained. Oriented features of the types of separateness and directions of imposed fracturing of Valaam sill are established. By processing the events of catalogue NEIC, received were spatiotemporal and magnitude characteristics of the present-day seismicity. It is shown that earthquakes occur more often when tangential acceleration of the Earth is nonzero.

Nowadays there exists a large variety of forecasting methods based on neural networks technologies which allow to adequately simulate the nonlinear processes with noisy data in slowly varying markets. However, in the conditions of strong turbulence they are not capable to promptly response to swiftly changing environment, and, hence, to market conjuncture changes. It has grown in a very serious problem, as the decisions accepted on the basis of these technologies can be resulted in movement of hundreds billion dollars in the financial markets, and any incorrectly revealed tendency can lead to large losses.We will notice that this problem has recently arisen due to joining of new world players to the common economics, and due to, as a consequence, decrease in controllability of the international system. In the presented work the dynamic approach will be considered which properly operates in swiftly changing markets. It is based on a combination of neural networks technologies with algorithms of quantum mechanics calculations.

A high order finite difference scheme for the Schr̈odinger equation with the degenerate potential U(x) = x2r, r N, which describes phase transitions in quantum systems, have been constructed. The eigenvalues are found for some values of r

An approach has been developed for organizing massive calculations of the maps of a molecular surface of helical proteins and nucleic acids in the distributed computing media. Three new program codes SURFACE-2008-compact, PROT-Zcompact and DNA-RNA-Zcompact that represent modified Linux versions of codes SURFACE-2008, PROT-Z and DNA-RNA-Z were elaborated to calculate the surface maps of the helical protein molecules and the helical DNA-RNA molecules. In order to organize massive computing of a large set of molecules, the graphical interface and the input of control parameters in a dialog mode are eliminated from the SURFACE-2008, PROT-Z and DNA-RNA-Z codes. To input the control parameters and to run codes SURFACE-2008-compact, PROT-Zcompact and DNA-RNA-Zcompact, a special script-program has been implemented. For graphical presentation and further analysis of the maps obtained in such a way corresponding full versions of codes SURFACE-2008, PROT-Z and DNA-RNA-Z are used. The investigation has been supported by a grant of the RFBR 07-07-234.

A set of calculation models has been developed and computations have been performed with the use of the TYPHOON code for ITER cryopumps to study behaviour of eddy currents and EM loads. A computational approach is described that allows detailed simulation of a cryopump components with respect to surrounding conducting elements of the tokamak.

Получена новая форма разложения полинома Pn(x) по базисным элементам - трём квадратичным и одной кубической параболами. Базисные элементы определяются через x-координаты, связанные специальным правилом сложного отношения четырёх точек. В задачах полиномиальной аппроксимации и сглаживания такое разложение позволяет повышать эффективность и качество вычислений.

The questions of the recognition graphic pattern are considered on discrete image. The organized study of the influence amount gradation on brightness on quality of the recognition graphic image. It Is shown that increase the number gradation with 28 on 216 brings to essential expansion of the range to correct classification in condition raised level of noise.

The operation of a high-energy ion facility provokes secondary radiation along an accelerator ring and especially at the local sites of maximum beam losses (outlet devices, targets, and beam dumps). An essential condition for the commissioning of a relativistic heavy ion accelerator is appropriate radiation shielding for every radiation element of the complex. The shielding design is connected with two crucial problems: the estimation of the source term and the prognostication of the neutron fluence and equivalent dose distributions around the shielding. As regards the first problem, the experimental data on the double differential cross section and secondary neutron production in thick targets for a primary uranium beam with the energy of several GeV/n are practically lacking. Few Monte Carlo multipurpose codes able to simulate the uranium ion interaction with, and transport into, the matter are now available. A comparison of FLUKA, GEAT4, and SHIELD simulations with unique experimental data on neutron production in a 1GeV/n 238U beam interaction with a thick Fe target was performed to find the most suitable code. As a result, the GEANT4 code was chosen to carry out a simulation of the NICA (Nuclotron-Based Ion Facility at JINR) complex radiation shielding. Forming the secondary radiation field inside and behind the ordinary concrete shielding was analyzed as well. Some regularities of the secondary neutron field generation in a 4.5 GeV/n uranium beam interaction with thick targets are discussed. As concerns the second problem, it was found that the crucial point determining the NICA shielding design is that the yearly equivalent dose at the border of the Laboratory site must not exceed 1 mSv. The radiation situation at long distances from NICA will be formed by neutrons which escaped from the shielding of the NICA radiation sources and were then multiscattered in the air and ground ("skyshine" neutrons). The GEANT4 calculations of the "skyshine" neutron radial distributions around all the elements of the NICA complex were carried out, and guidelines for the shielding construction were worked out for different operation modes of the complex.

An advanced computer code VENECIA is introduced intended for simulation of thermohydraulic transients. The code uses an extended database for a range of compressible coolants and capable of prediction of behaviour of both superconducting and warm magnet systems. Basic features of the VENECIA thermo-diffusion and thermohydraulic modelling are described. A computational model for the ITER toroidal field coil is presented.

We study localised attractors of the parametrically driven damped nonlinear SchrЁodinger equation. Time-periodic solitons of this equation are obtained as solutions of the boundaryvalue problem on a two-dimensional domain. We classify stability and bifurcations of periodic solitons and their complexes.

The objective of this investigation is to prove the possibility of representation of the 3 interaction between particles in various reacting three-body systems by analytical function with a set of adjusting parameters in natural collision coordinates. Realization of this idea implies the procedure of fitting 3 numerical data by 3 analytical function or more precisely, calculation of adjusting parameters in mentioned analytical function. In the work Levenberg Marquardt algorithm is used on the basis of which the numerical method is developed. The possibility of implementation of 3 fitting with the big accuracy, on the example of reaction + 2 is shown.