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Shary S.P.,Institute of Computational Technologies
Studies in Computational Intelligence | Year: 2014

The work advances a new class of global optimization methods, called graph subdivision methods, that are based on simultaneous adaptive subdivision of both the function's domain of definition and the range of values. An application to interval linear systems is given. © 2014 Springer International Publishing Switzerland.

Shary S.P.,Institute of Computational Technologies
Journal of Global Optimization | Year: 2015

The work is devoted to application of global optimization in data fitting problem under interval uncertainty. Parameters of the linear function that best fits intervally defined data are taken as the maximum point for a special (“recognizing”) functional which is shown to characterize consistency between the data and parameters. The new data fitting technique is therefore called “maximum consistency method”. We investigate properties of the recognizing functional and present interpretation of the parameter estimates produced by the maximum consistency method. © 2015 Springer Science+Business Media New York

Turitsyn S.K.,Aston University | Rubenchik A.M.,Lawrence Livermore National Laboratory | Fedoruk M.P.,Institute of Computational Technologies
Optics Letters | Year: 2010

The modulation instability (MI) in optical fiber amplifiers and lasers with anomalous dispersion leads to cw radiation breakup. This can be both a detrimental effect limiting the performance of amplifiers and an underlying physical mechanism in the operation of MI-based devices. Here we revisit the analytical theory of MI in fiber optical amplifiers. The results of the exact theory are compared with the previously used adiabatic approximation model, and the range of applicability of the latter is determined. © 2010 Optical Society of America.

Rubenchik A.M.,Lawrence Livermore National Laboratory | Turitsyn S.K.,Aston University | Fedoruk M.P.,Institute of Computational Technologies
Optics Express | Year: 2010

The modulation instability (MI) is one of the main factors responsible for the degradation of beam quality in high-power laser systems. The so-called B-integral restriction is commonly used as the criteria for MI control in passive optics devices. For amplifiers the adiabatic model, assuming locally the Bespalov-Talanov expression for MI growth, is commonly used to estimate the destructive impact of the instability. We present here the exact solution of MI development in amplifiers. We determine the parameters which control the effect of MI in amplifiers and calculate the MI growth rate as a function of those parameters. The safety range of operational parameters is presented. The results of the exact calculations are compared with the adiabatic model, and the range of validity of the latest is determined. We demonstrate that for practical situations the adiabatic approximation noticeably overestimates MI. The additional margin of laser system design is quantified. © 2010 Optical Society of America.

Medvedev S.,Institute of Computational Technologies | Zeitlin V.,Ecole Normale Superieure de Paris
IUTAM Bookseries | Year: 2010

We revisit the well-known analogy between the effects of stratification and rotation in hydrodynamics, and between both and the external magnetic field in magnetohydrodynamics. After sketching the similarities among models in what concerns linear and nonlinear stationary waves, we show that the Hamiltonian structure of the 2D versions of the models is the same, and use this fact to 1) find a canonical (skew-diagonal) form of the Hamiltonian equations, and 2) to treat in a unified manner the problem of weak turbulence of, respectively, internal gravity, gyroscopic, and Alfvén waves in scale-invariant limits. We thus find stationary energy spectra in the long- and short-wave limits for all three types of waves. © 2010 Springer Science+Business Media B.V.

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