# No 3.2 (2010)

**Year:**2010**Articles:**29**URL:**https://journals.rudn.ru/miph/issue/view/515

## Articles

6-9

### Prediction Technique of the Discontinuity Structure in Weakly Dissipative Media with Dispersion

#### Abstract

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.

**Discrete and Continuous Models and Applied Computational Science**. 2010;(3.2):10-13

10-13

### Investigation of Solutions of Boundary Problems for the Differential Equation of High Order in a Coulomb Field

#### Abstract

An algorithm to find eigenvalues and eigenfunctions of one boundary problem for the equation of high order (6th, 8th, 10th and 12th orders) with an arbitrary parameter .. at the higher derivatives in the Coulomb potential field is proposed. At .. ЃЁ 0 , some solutions of these equations coincide with the solution of Schroedinger equation. The investigations of the properties of eigenvalues and eigenfunctions with different values of .. have been conducted. The algorithm is implemented using the system of symbolic calculations MAPLE.

**Discrete and Continuous Models and Applied Computational Science**. 2010;(3.2):14-18

14-18

### Reduction-Level Parallel Computations of Gr.obner and Janet Bases

#### Abstract

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.

**Discrete and Continuous Models and Applied Computational Science**. 2010;(3.2):19-24

19-24

### Extraction of Data Features for Neuro-Classifier Input

#### Abstract

The problem of essential data compression to be input to ANN-classifier without loosing significant information is considered on the example of the quite substantial task of the genetic protein structure analysis, which is important for genetic biology researches in radiobiology and, especially, in agricultural. Such analysis is usually carried out by studying ElectroPhoretic Spectra (EPS) of gliadin (alcohol soluble protein) of the inspected grain cultivar. EPS digitization produces a densitogram with 4 thousands counts, which most informative features must be extracted to be input to ANN. Besides these data require special preprocessing for densitogram smoothing, pedestal eliminating, as well as compensating such digitization orocess defects as signal noise, variability of spectrum borders and illumination, their non-linear starches due to electrophoresis nonstationarity.
Several alternative approaches to features extracting were studied: (1) the densitogram coarsing into 200 averaged measurements; (2) the principal component analysis; (3) recognition of all well-pronounced peaks in order to evaluate their parameters to be input to ANN; (4)-(5) data compression by both discrete Fourier (DFT) and wavelet (DWT) transformations. These methods have been used for feature extraction from samples formed by experts for 30 different sorts. Then extracted features were used to train ANN of three-layer perceptron type. The comparative study of the recognition efficiency with data compressed by the methods listed above shows their high sensitivity to the number of sorts to be classified. Only DFT and DWT approaches could keep the efficiency on the level 95-97% up to 20 sorts.
A further development of feature extraction methods and a study of possibility to develop a hierarchy of classifying ANNs are intended.

**Discrete and Continuous Models and Applied Computational Science**. 2010;(3.2):25-31

25-31

### Mathematical Modeling of Track Formation in YBa2Cu3O7− Superconductor

#### Abstract

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.

**Discrete and Continuous Models and Applied Computational Science**. 2010;(3.2):32-36

32-36

### Computational Approaches for 2D and 3D Modeling of the Macro-Architecture of Native Chromosomes in Sperm Genome of Drosophila Melanogaster

#### Abstract

As a first justified concept over 125 years of the history of the basic scientific ideas on the large-scale arrangement of eukaryotic interphase chromatin in cell nucleus, 2D and 3D spatial macro-architecture of haploid chromosomes in Drosophila sperm nucleus was sequentially reconstructed using the detected non-random distribution of -ray- and neutron-induced inversion and translocation breakpoints along the euchromatic chromosome maps with their clastering around heterochromatin.

**Discrete and Continuous Models and Applied Computational Science**. 2010;(3.2):37-40

37-40

### Geophysical Applications of Statistical Model

#### Abstract

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.

**Discrete and Continuous Models and Applied Computational Science**. 2010;(3.2):41-44

41-44

### Mathematical Model and Toolkit for Regional Social and Economic Monitoring

#### Abstract

The problem of monitoring the social and economic situation in regions has always been a currently central one for our country due to the vast territory and variety of life conditions in different areas. This urgency severely increases in crisis conditions. For acceptance of reasonable well-grounded managerial decisions monitoring should not be reduced to sociological research, but it should be founded on a deep mathematical base. Whereas the problem of description of economic subjects interaction is more or less clear, the social processes are much more difficult for analysis. In the presented discourse the attempt is made on the basis of leading political psychologists' latest research to formulate a model of social and economic processes in a region. The analysis of results of this model application allows one to reveal such characteristic modes which correspond to real processes in the society. Prototypes of information systems which can be used for monitoring in real conditions are offered. The problem of regional elections forecast is analyzed as an example for such system application.

**Discrete and Continuous Models and Applied Computational Science**. 2010;(3.2):45-50

45-50

### Hybrid Information System for Estimation of Risks in Financial Markets

#### Abstract

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.

**Discrete and Continuous Models and Applied Computational Science**. 2010;(3.2):51-57

51-57

### Application of Polynomial Approximation Method to Drop Water Evaporation

#### Abstract

In the paper our method for construction of orthonormal polynomials - orthonormal polynomial expansion method [OPEM] - is applied to water contact angle variations. Some special features of the method are developed for this purpose. The total variance method is demonstrated to include the errors in both dependent and independent variables. Two polynomial expansions are presented for approximating function: orthonormal and "usual" ones.

**Discrete and Continuous Models and Applied Computational Science**. 2010;(3.2):63-67

63-67

### Numerical Solutions for the Schr¨odinger Equation with a Degenerate Polynomial Potential of Even Power

#### Abstract

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

**Discrete and Continuous Models and Applied Computational Science**. 2010;(3.2):58-62

58-62

### Model Description of Thermoelastic Tensions in Materials Exposed toHigh Energy Heavy Ions

#### Abstract

Our previous studies dealt with the formation and evolution of thermoelastic waves arising in metals under irradiation with pulsed ion beams, within the system of thermoelasticity equations. The present work proposes a numerical research of this phenomenon within a two-temperature model, with introduction of temperature of electrons and a crystal lattice (a thermal spike model). A comparative analysis of the received results with the results of previous research works is presented.

**Discrete and Continuous Models and Applied Computational Science**. 2010;(3.2):68-71

68-71

### On Massive Calculations of Maps of Molecular Surface of Helical Proteins and Nucleic Acids

#### Abstract

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.

**Discrete and Continuous Models and Applied Computational Science**. 2010;(3.2):72-76

72-76

### Fast Ring Recognition Algorithm for the RICH Detector of the CBM Experiment at FAIR

#### Abstract

The Compressed Baryonic Matter (CBM) experiment at the future FAIR facility at Darmstadt will measure dileptons emitted from the hot and dense phase in heavy-ion collisions. Measuring di-electron, a high purity of identified electrons is required in order to suppress the background. Electron identification in CBM will be performed by a Ring Imaging Cherenkov (RICH) detector and Transition Radiation Detectors (TRD).
In this contribution we will present algorithms which were developed for event reconstruction in the RICH detector. Efficient and fast ring recognition is based on the Hough Transform method which was accelerated considerably compared to a standard implementation. Ring quality selection is done using an Artificial Neural Network. Ellipse fitting algorithm was developed for RICH ring fitting. These reconstruction methods allow for a high purity and efficiency of reconstructed electron rings.

**Discrete and Continuous Models and Applied Computational Science**. 2010;(3.2):77-80

77-80

### Numerical Simulations of Electro-Magnetic Transients in ITER Cryopumps with Use of TYPHOON Code

#### Abstract

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.

**Discrete and Continuous Models and Applied Computational Science**. 2010;(3.2):81-86

81-86

### Quasi-3D Numerical Simulation of TF Coil Thermal-Hydraulic Parameters During the Fast Energy Discharge

#### Abstract

Results of ITER TF coil thermohydraulic simulations during the fast energy discharge are presented. The simulations were performed for the reference discharge scenario and allowed preliminary assessment of basic dimensions for relief valves and quench lines.

**Discrete and Continuous Models and Applied Computational Science**. 2010;(3.2):87-92

87-92

### Polynomial Decomposition on the Basis of Cubic andQuadratic Parabolas

#### Abstract

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.

**Discrete and Continuous Models and Applied Computational Science**. 2010;(3.2):93-100

93-100

### Software Complex for Modelling Problems of Continuum Mechanics with the Help of Modern Multiprocessor Systems

#### Abstract

This work presents a program complex for solving problems arising in continuum mechanics. The complex contains the tools allowing the user to solve a specific problem from the beginning (design of computational domain, formulation of boundary conditions) up to the end (viewing end results). These tools are focused on using modern multiprocessor systems. The complex comprises 4 basic components: geometry editor, grid generator, a visual analyzer of result and a shell which unites 3 remaining components in a uniform interface and controls data transfer between each other and the multiprocessor system. The user directly cooperates only with the shell, i.e. the user does not need to know how the components interoperate and operate with the computing system. The solution of any problem consists of 4 basic stages: design of computational domain, formulation of boundary conditions in the editor, creation of a suitable grid with the help of the grid generator, start-up of calculation on a computing cluster, viewing of results in the built-in visual analyzer. All these stages can be prformed with the help of the shell.

**Discrete and Continuous Models and Applied Computational Science**. 2010;(3.2):101-104

101-104

### About Influence of the Accuracy of Image Representation on the Graphic Recognition Quality

#### Abstract

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.

**Discrete and Continuous Models and Applied Computational Science**. 2010;(3.2):105-108

105-108

### Network Libraries of Computable Models as the Reactive Distributed Systems

#### Abstract

For computable models and numerical methods on the basis of the reactive distributed systems with a graphic interface the concept and the architecture of network object-oriented information libraries are discussed. Calculation of modelling situations is driven by the events and workflow constructed by the user using components saved in library and their data.
The library is intended for saving, easy access and the calculation of wide range set of models solved by iterations, including complex models on the basis of systems of equations of private and ordinary derivatives.
The example of calculation of complex system of mass transfer model and population dynamic model by means of working system Niva is shown.

**Discrete and Continuous Models and Applied Computational Science**. 2010;(3.2):109-114

109-114

### GEANT4 Code Application for Radiation Environment Prediction at the NICA Complex

#### Abstract

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.

**Discrete and Continuous Models and Applied Computational Science**. 2010;(3.2):115-122

115-122

### Modernization of the SP-40 Magnet of the NIS Spectrometer with the Purpose of Increasing the Homogeneous Field Volume

#### Abstract

This work is aimed to generalize experience of the mathematical simulation of magnetic systems of various type physical and electromechanical installations and to work out some recommendations of the optimal use of some software products for the numerical modeling of magnetostatic problems. This work also presents some results of a numerical analysis of the magnetic systems of the JINR's physical installation NIS with the purpose of studying an opportunity of designing magnetic systems with predetermined characteristics of the magnetic field.

**Discrete and Continuous Models and Applied Computational Science**. 2010;(3.2):123-126

123-126

### VENECIA: New Code for Simulation of Thermohydraulics in Complex Superconducting Systems

#### Abstract

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.

**Discrete and Continuous Models and Applied Computational Science**. 2010;(3.2):127-131

127-131

### Methods to Reveal Hidden Structures of Signals and their Applications

#### Abstract

As the result of the application of the maximum entropy method for reveal the structure of blurred spectra new information about characteristics of materials had been obtained. The methods based on the account of the signal entropy and the wavelet transformation had been developed to seismic signals treatment and to determ the processes bifurcation points.

**Discrete and Continuous Models and Applied Computational Science**. 2010;(3.2):132-135

132-135

### Time-Periodic Solitons in the Damped-Driven Nonlinear Schr¨odinger Equation

#### Abstract

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.

**Discrete and Continuous Models and Applied Computational Science**. 2010;(3.2):136-142

136-142

### Critical Dependencies in Three-Layered Josephson Junctions

#### Abstract

Sakai-Bodin-Pedersen model is used to investigate numerically the dynamics of the Josephson phases in three stacked long Josephson Junctions. It is shown that the critical currents of the individual junctions depend on the damping and the coupling parameters and that there is a domain in vicinity of zero magnetic field where the junctions switch to nonzero voltage simultaneously, i.e. current locking takes place.

**Discrete and Continuous Models and Applied Computational Science**. 2010;(3.2):143-147

143-147

### Fitting of 3D Reaction Surface of Three-Atomic System in the Natural Collision Coordinates

#### Abstract

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.

**Discrete and Continuous Models and Applied Computational Science**. 2010;(3.2):148-154

148-154

### Our authors

**Discrete and Continuous Models and Applied Computational Science**. 2010;(3.2):155-159

155-159