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Slunyaev A.,Keele University | Didenkulova I.,RAS Institute of Mathematics and Mechanics | Pelinovsky E.,RAS Institute of Applied Physics
Contemporary Physics | Year: 2011

In this essay we give an overview on the problem of rogue or freak wave formation in the ocean. The matter of the phenomenon is a sporadic occurrence of unexpectedly high waves on the sea surface. These waves cause serious danger for sailing and sea use. A number of huge wave accidents, resulting in damages, ship losses and people injuries and deaths, are known. Now marine researchers do believe that these waves belong to a specific kind of sea wave, not taken into account by conventional models for sea wind waves. This paper addresses the nature of the rogue wave problem from a general viewpoint based on wave process ideas. We start by introducing some primitive elements of sea wave physics with the purpose of paving the way for further discussion. We discuss linear physical mechanisms which are responsible for high wave formation, at first. Then, we proceed with a description of different sea conditions, starting from the open deep sea, and approaching the sea coast. Nonlinear effects which are able to cause rogue waves are emphasised. In conclusion we briefly discuss the generality of the physical mechanisms suggested for the rogue wave explanation; they are valid for rogue wave phenomena in other media such as solid matters, superconductors, plasmas and nonlinear optics. © 2011 Taylor and Francis Group, LLC.


Matviychuk O.G.,RAS Institute of Mathematics and Mechanics
Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) | Year: 2014

The problem of estimating reachable sets of linear impulsive dynamical control systems with uncertainty in initial data is considered. It is assumed that the impulsive controls in the dynamical system belong to the intersection of a special cone with a generalized ellipsoid both taken in the space of functions of bounded variation. The algorithms for constructing the ellipsoidal estimates of reachable sets for such control systems are given. Numerical simulation results relating to the proposed procedures are also given. © 2014 Springer-Verlag.


Vasin V.V.,RAS Institute of Mathematics and Mechanics
Automation and Remote Control | Year: 2012

An ill-posed problem is considered in the form of a nonlinear operator equation with a discontinuous inverse operator. It is known that in investigating a high convergence of the methods of the type of Levenberg-Marquardt (LM) method, one is forced to impose very severe constraints on the problem operator. In the suggested article the LM method convergence is set up not for the initial problem, but for the Tikhonov-regularized equation. This makes it possible to construct a stable Fejer algorithm for approximation of the solution of the initial irregular problem at the conventional, comparatively nonburdensome conditions on the operator. The developed method is tested on the solution of an inverse problem of geophysics. © 2012 Pleiades Publishing, Ltd.


Gusev M.I.,RAS Institute of Mathematics and Mechanics
Automation and Remote Control | Year: 2012

Consideration was given to formation of the external estimates of the reachability sets of the nonlinear controlled systems in the form of the level sets of the functions satisfying the differential Hamilton-Jacobi inequalities. The trajectories of the nonlinear system are estimated by modifying the estimates of its linear part. The constructions proposed are based on comparing the systems of differential inequalities. Applications of the reachability sets of the multivariable controlled systems with nonlinear cross connections to the ellipsoidal estimates were examined. © 2012 Pleiades Publishing, Ltd.


Avdyushev V.A.,RAS Institute of Mathematics and Mechanics
Celestial Mechanics and Dynamical Astronomy | Year: 2011

Determination of orbital parameters from observations is formally a nonlinear inverse problem for solving which evidently nonlinear methods are required. Meanwhile, an accompanying stage in solving the inverse problem is the evaluation of parametric accuracy to which, however, linear methods are conventionally applied. This is quite justified if parametric errors caused by observation errors are rather small, otherwise this is not at all since the nonlinearity of the inverse problem can be considerable to influence on the evaluations of parametric accuracy especially when the observations are very few. With the advent of quick-operating and multiprocessor computers, recently one tends to employ statistic simulation of virtual parameter values for investigating uncertainties in orbits determined from observations. In the paper are just discussed the methods designed specially for nonlinear statistic simulation of virtual parameter values. Their efficiency is investigated in application to estimating uncertainties in the orbit of Jovian satellite S/2003 J04 whose orbital parameters are ill-determined owing to scanty available observations. Indices of nonlinearity are introduced for making decision in the choice between linear and nonlinear methods. © 2011 Springer Science+Business Media B.V.


Gusev M.I.,RAS Institute of Mathematics and Mechanics
Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) | Year: 2010

The problem of optimal choice of inputs is considered for identification of control system parameters by the results of measurements. The integral of information function is accepted as a criterion of optimality. It is shown that the problem may be reduced to an optimal control problem for the bundle of trajectories of the control system generated by the set of unknown parameters. © 2010 Springer-Verlag Berlin Heidelberg.


Filippova T.F.,RAS Institute of Mathematics and Mechanics
Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) | Year: 2010

The paper is devoted to state estimation problems for nonlinear dynamic control systems with states being compact sets. The studies are motivated by the theory of dynamical systems with unknown but bounded uncertainties without their statistical description. The trajectory tubes of differential inclusions are introduces as the set-valued analogies of the classical isolated trajectories of uncertain dynamical systems. Applying results related to discrete-time versions of the funnel equations and techniques of ellipsoidal estimation theory developed for linear control systems we present approaches that allow to find estimates for such set-valued states of uncertain nonlinear control systems. © 2010 Springer-Verlag Berlin Heidelberg.


Kostousova E.K.,RAS Institute of Mathematics and Mechanics
AIP Conference Proceedings | Year: 2012

The paper deals with polyhedral (parallelotope-valued) estimates for reachable sets of linear differential systems and is devoted to investigation of so called tight estimates. First, we construct the new families of tight internal and external estimates. Second, we study properties of boundedness and unboundedness on the infinite time interval of external estimates for reachable sets of systems with stable matrices and present new results concerning the family of the tight external estimates. © 2012 American Institute of Physics.


Matviychuk O.G.,RAS Institute of Mathematics and Mechanics
AIP Conference Proceedings | Year: 2012

The paper deals with the state estimation problem for the linear control system containing impulsive control terms (or measures). The problem is studied here under uncertainty conditions when the initial system state is unknown but bounded, with given bound. It is assumed also that the system states should belong to the given ellipsoid in the state space. So the main problem of estimating the reachable set of the control system is studied here under more complicated assumption related to the case of state constraints. It is assumed additionally that impulsive controls in the dynamical system must belong to the intersection of a special cone with a generalized ellipsoid both taken in the space of functions of bounded variation. The last constraint is motivated by problems of impulsive control theory and by models from applied areas when not every direction of control impulses is acceptable in the system. We present here the state estimation algorithms that use the special structure of the control system and take into account additional restrictions on states and controls. The algorithms are based on ellipsoidal techniques for estimating the trajectory tubes of uncertain dynamical systems. Numerical simulation results related to proposed procedures are also given. © 2012 American Institute of Physics.


Vaganova N.,RAS Institute of Mathematics and Mechanics
AIP Conference Proceedings | Year: 2014

Thermal fields testing at the ground surface above a pipeline are considered. One method to obtain and investigate an ideal thermal field in different environments is a direct numerical simulation of heat transfer processes taking into account the most important physical factors. In the paper a mathematical model of heat propagation from an underground source is described with accounting of physical factors such as filtration of water in soil and solar radiation. Thermal processes are considered in 3D origin where the heat source is a pipeline with constant temperature and non-uniform isolated shell (with «damages»). This problem leads to solution of heat diffusivity equation with nonlinear boundary conditions. Approaches to analysis of thermal fields are considered to detect damages. © 2014 AIP Publishing LLC.

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