ЖВТ. 2009. Т. 14, № 5. С. 3-17.
Application **of the genetic algorithm to solution of the optimal sensors location problem**
Astrakova A.S., Bannikov D.V., Lavrentiev M.M. (Jr.), Cherny S.G.

A problem of the optimal configuration of sensors for early detection of tsunami waves is considered. The aim is to record a tsunami wave as soon as possible from any arbitrary point of a subduction zone, using a given number of sensors. Mathematically the problem reduces to finding a minimum of the functional, which calculates the sensor's detection time from the most distant point of the region where wave is formed. In construction of the functional, we use the long wavelength approximation for the wave velocity versus depth. The problem is solved using the genetic algorithm. A systematic verification of the proposed computational algorithm is carried out. The problem of the optimal sensor placement for the Alaska-Aleutan subduction zone has been solved.

Key words: genetic algorithm, optimal sensors location, tsunami waves, the earliest tsunami wave detections, Alaska-Aleutan subduction zone.

**ЖВТ. **2009. **T. **14, № 5. C. 18-29.

**A ****3D ****code for modelling of the ultra relativistic beams**

Boronina M.A., Vshivkov V.A., Levichev E.B., Nikitin S.A., Simonov E.A., Snitnikov V.N.

An algorithm for modeling of a collision of beams of charged particles is presented for the three-dimensional ultra relativistic case. A new algorithm for imposing of boundary and initial conditions, based on a new artificial potential, is proposed. A comparison with calculations on the Guines-Pig code for the case of focusing colliding beams is presented.

Key words: relativistic factor, charged beam, electromagnetic fields, particles in cell method, Maxwell equations.

**ЖВТ. **2009. **T. **14, № 5. C. 30-39.

**Pixel technology for a discretization of the World Ocean area**

Kireev I.V., Pyataev S.F.

In this article a discretization method for the World Ocean area is proposed using a mesh refinement procedure near the shoreline. This method relies on computer graphics algorithms whose grid elements are either squares or 45° right triangles.

Key words: triangulation, mesh, computer graphics, bathymetry.

**ЖВТ. **2009. **T. **14, № 5. C. 40-48.

**The dynamic method for construction of the triangular grids in the multiply connected areas**

Kraus E.I., Fomin V.M., Shabalin **I.I.**

The dynamic method for construction of the regular 2D triangular grids is often applied for the multiply connected areas. The calculation algorithm for contact surfaces is modified by accounting a number of the elementary acts of interaction for each boundary grid knot. It has allowed successful calculation of an impact of model reactor blocks of a nuclear power installation on a deformable surface.

Key words: triangular grids, dynamic method, multiply connected areas.

**ЖВТ. **2009. **T. **14, № 5. C. 49-65.

**A unification of the stochastic and interval approaches for solution of the global optimization problem for a function**

Panov N.V.

Interval methods of global optimization are considered. The problems for which the existing methods are ineffective are analyzed and the causes are revealed. On this basis, new computationally effective methods, combining conclusiveness of the interval and the flexibility of stochastic approaches, are proposed.

Key words: interval, interval analysis, global optimization, genetic algorithm, the method of simulated annealing, minimum.

**ЖВТ. **2009. **T. **14, № 5. C. 66-78.

**Development of webometric research tools for hyperlinks of scientific sites**

Pechnikov A.A., Lugovaja N.B., Chuyko Ju.V., Kosinets I.E.

This article describes a database that contains information about the structure of hyperlinks for the web sites of scientific institutions. The choice of a target set is justified, the principles used for algorithms of the crawler are stated, the structure and capabilities of the database are described, and results of hyperlink analysis are presented.

Key words: Web, webometrics, web links, data base, web spider, crawler, classification.

**ЖВТ. **2009. **T. **14, № 5. C. 79-91.

**Modelling of evolution for the cross section of a sandy channel**

Potapov I.I., Bondarenko B.V.

A transient problem for development of the cross section of a sandy channel is formulated for various mechanical and granulometric properties of a sand bed. An algorithm and a numerical method for its realization are offered. It is shown that after typical time of the watercourse passage, the sand bed profile can be approximated by power series, which is in a good agreement with the experimental data.

Key words: numerical simulation, geomorphology, sediment transport, bank erosion, bedload transport.

**ЖВТ. **2009. **Т. **14, № 5. С. 92-101.

**On initial conditions for a numerical simulation of a solitary wave Protopopov **B.E.

It has been shown, by means of a numerical experiment, what kind of initial conditions should be used to better simulate, with high accuracy, а** **solitary wave on the surface of an incompressible inviscid fluid. It is shown that the wave speed and the stretching parameter of the wave profile are better to be determined using the known exact relations. A modification of formulas for calculation the coefficients of the wave profile expansion upon the basis functions is proposed which further increases the accuracy of the numerical simulation of a solitary wave.

Key words: a solitary wave, numerical simulation.

**ЖВТ. **2009. **T. **14, № 5. C. 102-113.

**An inductive generation of the regression volatility models**

Strijov V.V., Sologub H.A.

Volatility of the European-type options depends on their strike and maturity. The authors suppose that volatility of regression models based not only on the expert knowledge, but also on the measured data. A model generation algorithm is proposed. It inductively generates the volatility models of the optimal structure using implied volatility data and expert considerations. The models are shown to satisfy expert assessments.

Key words: Nonlinear regression, model generation, model selection, analysis of model parameters, stock options, volatility modelling.

**ЖВТ. **2009. **T. **14, № 5. C. 114-121.

**Numerical modelling of convection under cratons of Central Asia**

Chervov V.V., Chernykh G.G., Chervov A.V.

Results of the 3D modeling of convection under cratons of Central Asia are presented. Our numerical model is based on "vorticity**—**potential vector" variables and the method of fractional steps. The results of numerical experiments show the structure of a convective flow.

Key words: thermal convection in Earth mantle, cratons of Central Asia, numerical modelling.