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Kotta U.,Institute of Cybernetics
European Control Conference, ECC 1999 - Conference Proceedings | Year: 2015

The paper deals with nonlinear system described by the set of higher-order difference equations in the inputs and the outputs. A theorem for transforming such a system around a regular equilibrium point into a locally equivalent one, but having the so-called row- and column-reduced form, is formulated. The importance of this form comes from the fact that this is a suitable starting point for studing the realization problem for a set of nonlinear multi-input multi-output difference equations. © 1999 EUCA.

Didenkulova I.,Institute of Cybernetics | Didenkulova I.,Institute of Applied Physics | Pelinovsky E.,Institute of Applied Physics | Sergeeva A.,Institute of Applied Physics
Coastal Engineering | Year: 2011

The random long wave runup on a beach of constant slope is studied in the framework of the rigorous solutions of the nonlinear shallow water theory. These solutions are used for calculation of the statistical characteristics of the vertical displacement of the moving shoreline and its horizontal velocity. It is shown that probability characteristics of the runup heights and extreme values of the shoreline velocity coincide in the linear and nonlinear theory. If the incident wave is represented by a narrow-band Gaussian process, the runup height is described by a Rayleigh distribution. The significant runup height can also be found within the linear theory of long wave shoaling and runup. Wave nonlinearity nearshore does not affect the Gaussian probability distribution of the velocity of the moving shoreline. However the vertical displacement of the moving shoreline becomes non-Gaussian due to the wave nonlinearity. Its statistical moments are calculated analytically. It is shown that the mean water level increases (setup), the skewness is always positive and kurtosis is positive for weak amplitude waves and negative for strongly nonlinear waves. The probability of the wave breaking is also calculated and conditions of validity of the analytical theory are discussed. The spectral and statistical characteristics of the moving shoreline are studied in detail. It is shown that the probability of coastal floods grows with an increase in the nonlinearity. Randomness of the wave field nearshore leads to an increase in the wave spectrum width. © 2010 Elsevier B.V.

Didenkulova I.,Institute of Cybernetics | Didenkulova I.,Institute of Applied Physics | Pelinovsky E.,Institute of Applied Physics
Pure and Applied Geophysics | Year: 2011

The problem of tsunami wave shoaling and runup in U-shaped bays (such as fjords) and underwater canyons is studied in the framework of 1D shallow water theory with the use of an assumption of the uniform current on the cross-section. The wave shoaling in bays, when the depth varies smoothly along the channel axis, is studied with the use of asymptotic approach. In this case a weak reflection provides significant shoaling effects. The existence of traveling (progressive) waves, propagating in bays, when the water depth changes significantly along the channel axis, is studied within rigorous solutions of the shallow water theory. It is shown that traveling waves do exist for certain bay bathymetry configurations and may propagate over large distances without reflection. The tsunami runup in such bays is significantly larger than for a plane beach. © 2010 Springer Basel AG.

Gonzalez-Fernandez Y.,Institute of Cybernetics | Gonzalez-Fernandez Y.,York University | Soto M.,Institute of Cybernetics
Journal of Statistical Software | Year: 2014

The use of copula-based models in EDAs (estimation of distribution algorithms) is currently an active area of research. In this context, the copulaedas package for R provides a platform where EDAs based on copulas can be implemented and studied. The package offers complete implementations of various EDAs based on copulas and vines, a group of well-known optimization problems, and utility functions to study the performance of the algorithms. Newly developed EDAs can be easily integrated into the package by extending an S4 class with generic functions for their main components. This paper presents copulaedas by providing an overview of EDAs based on copulas, a description of the implementation of the package, and an illustration of its use through examples. The examples include running the EDAs defined in the package, implementing new algorithms, and performing an empirical study to compare the behavior of different algorithms on benchmark functions and a real-world problem. © 2014, American Statistical Association. All rights reserved.

Didenkulova I.,Institute of Cybernetics | Didenkulova I.,Institute of Applied Physics | Anderson C.,University of Sheffield
Natural Hazards and Earth System Science | Year: 2010

We present a statistical analysis of freak waves 1 measured during the 203 h of observation on sea surface elevation at a location in the coastal zone of the Baltic Sea (2.7 m depth) during June-July 2008. The dataset contains 97 freak waves occurring in both calm and stormy weather conditions. All of the freak waves are solitary waves, 63% of them having positive shape, 17.5% negative shape and 19.5% sign-variable shape. It is suggested that the freak waves can be divided into two groups. Those of the first group, which includes 92% of the freak waves, have an amplification factor (ratio of freak wave height to significant wave height) which does not vary from significant wave height and has values largely within the range of 2.0 to 2.4; while for the second group, which contain the most extreme freak waves, amplification factors depend strongly on significant wave height and can reach 3.1. Analysis based on the Generalised Pareto distribution is used to describe the waves of the first group and lends weight to the identification of the two groups. It is suggested that the probable mechanism of the generation of freak waves in the second group is dispersive focussing. The time-frequency spectra of the freak waves are studied and dispersive tracks, which can be interpreted as dispersive focussing, are demonstrated. © 2010 Author(s).

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