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Modelling of postcritical states of slender structures
Mašek, Jan ; Eliáš, Jan (referee) ; Frantík, Petr (advisor)
The aim of the presented thesis is to create a compact publication which deals with properties, solution and examination of behavior of dynamical systems as models of mechanical structures. The opening portion of the theoretical part leads the reader through the subject of description of dynamical systems, offers solution methods and investigates solution stability. As the introduction proceeds, possible forms of structure loading, damping and response are presented. Following chapters discuss extensively the possible approaches to system behavior observation and identification of nonlinear and chaotic phenomena. The attention is also paid to displaying methods and color spaces as these are essential for the examination of complex and sensitive systems. The theoretical part of the thesis ends with an introduction to fractal geometry. As the theoretical background is laid down, the thesis proceeds with an application of the knowledge and shows the approach to numerical simulation and study of models of real structures. First, the reader is introduced to the single pendulum model, as the simplest model to exhibit chaotic behavior. The following double pendulum model shows the obstacles of observing systems with more state variables. The models of free rod and cantilever serve as examples of real structure models with many degrees of freedom. These models show even more that a definite or at least sufficiently relevant monitoring of behavior of such deterministic systems is a challenging task which requires sophisticated approach.
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Equivalent circuit realizations of the simple chaotic oscillators
Kobza, Jaromír ; Dostál, Tomáš (referee) ; Petržela, Jiří (advisor)
The aim of this paper is to introduce with basic theory the problems encountered when considering the circuit implementation of autonomous RC chaotic oscillator with nonlinearity. All oscillator prototypes are based on one type of universal oscillator circuit. This circuit is able to generate a lot of attractors on condition of different entrance parameters. The design is based on a mathematical simulation, which includes the generation of electronic circuit values. The work is focused the transformation of these values to operational circuit configuration and simulation in a circuit simulator. The final task is to acquire chaotic attractors. Oscilloscope and spectrum analyser photos will verify the operation.
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The Control of Chaos: Methods and Applications
Hůlka, Tomáš ; Dvořák, Jiří (referee) ; Matoušek, Radomil (advisor)
This thesis focuses on deterministic chaos and selected methods of chaos control. It briefly describes the matter of deterministic chaos and presents commonly used tools of analysis of dynamical systems exhibiting chaotic behavior. A list of frequently studied chaotic systems is presented and followed by a description of methods of chaos control and the optimization of these methods. The practical part is dedicated to the stabilization of two model systems and one real system with described methods.
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Nonlinear dynamical systems and chaos
Tesař, Lukáš ; Opluštil, Zdeněk (referee) ; Nechvátal, Luděk (advisor)
The diploma thesis deals with nonlinear dynamical systems with emphasis on typical phenomena like bifurcation or chaotic behavior. The basic theoretical knowledge is applied to analysis of selected (chaotic) models, namely, Lorenz, Rössler and Chen system. The practical part of the work is then focused on a numerical simulation to confirm the correctness of the theoretical results. In particular, an algorithm for calculating the largest Lyapunov exponent is created (under the MATLAB environment). It represents the main tool for indicating chaos in a system.
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The Control of Chaos: Methods and Applications
Švihálková, Kateřina ; Dvořák, Jiří (referee) ; Matoušek, Radomil (advisor)
The diploma thesis is focused on the use of heuristic and metaheuristic methods to stabilization and controlling the selected systems distinguished by the deterministic chaos behavior. There are discussed parameterization of chosen optimization methods, which are the genetic algorithm, simulated annealing and pattern search. The thesis also introduced the suitable controlling methods and the definition of the objective function. In the theoretical part of the thesis there is a brief introduction to the deterministic chaos theory. The next chapters describes the most common and deployed methods in~the~control theory, especially OGY and Pyragas methods. The practical part of the thesis is divided into two chapters. The first one describes the~stabilization of the artifical chaotic systems with the time delayed Pyragas method - TDAS and its modification ETDAS. The second chapter shows the real chaotic system control. The Duffing oscillator system was chosen to serve this purpose.
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THE CONTROL OF CHAOS: METHODS AND APPLICATIONS
Kořenek, Miroslav ; Dvořák, Jiří (referee) ; Matoušek, Radomil (advisor)
This thesis deals with methods of stabilizing deterministic chaos. The first part provides a brief overview of the problem of deterministic chaos, including the framework used to describe and analyze chaotic systems. Furthermore, the most well-known chaotic systems are described in detail, with the logistic map and the Hénon map selected for experimental stabilization. The description of conventional methods for chaos stabilization, namely TDAS and ETDAS, follows. The principle of their optimization is also explained. Next chapter is dedicated to describing genetic programming and its potential use in chaos stabilization. In the practical part of the thesis, conventional methods and various implementations of genetic programming were applied to stabilize the selected systems. The utilization and experimentation with genetic programming to find stabilizing sequences are the most significant contributions of this work.
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Transition from regular to chaotic motion in black hole magnetospheres
Kopáček, Ondřej ; Karas, Vladimír (advisor) ; Kulhánek, Petr (referee) ; Rezzolla, Luciano (referee)
Cosmic black holes can act as agents of particle acceleration. We study properties of a system consisting of a rotating black hole immersed in a large-scale organized magnetic field. Electrically charged particles in the immediate neighborhood of the horizon are influenced by strong gravity acting together with magnetic and induced electric components. We relax several constraints which were often imposed in previous works: the magnetic field does not have to share a common symmetry axis with the spin of the black hole but they can be inclined with respect to each other, thus violating the axial symmetry. Also, the black hole does not have to remain at rest but it can instead perform fast translational motion together with rotation. We demonstrate that the generalization brings new effects. Starting from uniform electro-vacuum fields in the curved spacetime, we find separatrices and identify magnetic neutral points forming in certain circumstances. We suggest that these structures can represent signatures of magnetic reconnection triggered by frame-dragging effects in the ergosphere. We further investigate the motion of charged particles in these black hole magnetospheres. We concentrate on the transition from the regular motion to chaos, and in this context we explore the characteristics of chaos in...
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Diffusion of Particles from Tokamak by Stochastization of Magnetic Field Lines
Cahyna, Pavel ; Krlín, Ladislav (advisor) ; Rohlena, Karel (referee) ; Suttrop, Wolfgang (referee)
The thesis summarizes the current state of research of thermonuclear fusion with magnetic confinement and decribes the possible role of stochastization of magnetic field lines and magnetic perturbations in solving some of the problems that are encountered on the road to the exploitation of fusion. It presents a theoretical introduction to deterministic chaos and explains the connection of this theory to magnetic perturbations in tokamak. The results are presented mainly in the form of publications in journals and conference proceedings. Among them are: the comparison of chaotic diffusion of particles and field lines, where significant differences were found; the application of chaotic diffusion of particles to the problem of runaway electrons originating in disruptions, where our simulations contributed to explaining the experimental results from the JET tokamak; the calculation of spectra of perturbations for the COMPASS tokamak, done as a preparation for the upcoming experiments; and modelling of screening of perturbations by plasma, where the observations of divertor footprints show as a promising method to detect the screening.
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Diffusion of Particles from Tokamak by Stochastization of Magnetic Field Lines
Cahyna, Pavel
Diffusion of particles from tokamak by stochastization of magnetic field lines Pavel Cahyna Abstract: The thesis summarizes the current state of research of ther- monuclear fusion with magnetic confinement and decribes the possible role of stochastization of magnetic field lines and magnetic perturbations in solv- ing some of the problems that are encountered on the road to the exploitation of fusion. It presents a theoretical introduction to deterministic chaos and explains the connection of this theory to magnetic perturbations in tokamak. The results are presented mainly in the form of publications in journals and conference proceedings. Among them are: the comparison of chaotic dif- fusion of particles and field lines, where significant differences were found; the application of chaotic diffusion of particles to the problem of runaway electrons originating in disruptions, where our simulations contributed to ex- plaining the experimental results from the JET tokamak; the calculation of spectra of perturbations for the COMPASS tokamak, done as a preparation for the upcoming experiments; and modelling of screening of perturbations by plasma, where the observations of divertor footprints show as a promising method to detect the screening. 1
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