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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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Theory-guided design of novel Fe-Al-based superalloys
Friák, Martin ; Holec, D. ; Jirásková, Yvonna ; Palm, M. ; Stein, F. ; Janičkovič, D. ; Pizúrová, Naděžda ; Dymáček, Petr ; Dobeš, Ferdinand ; Šesták, Pavel ; Fikar, Jan ; Šremr, Jiří ; Nechvátal, Luděk ; Oweisová, S. ; Homola, V. ; Titov, Andrii ; Slávik, Ondrej ; Miháliková, Ivana ; Pavlů, Jana ; Buršíková, V. ; Neugebauer, J. ; Boutur, D. ; Lapusta, Y. ; Šob, Mojmír
Our modern industrialized society increasingly requires new structural materials\nfor high-temperature applications in automotive and energy-producing industrial\nsectors. Iron-aluminides are known to possess excellent oxidation and sulfidation\nresistance as well as sufficient strength at elevated temperatures. New Fe-Al-based\nmaterials will have to meet multiple casting, processing and operational criteria\nincluding high-temperature creep strength, oxidation resistance and room-temperature\nductility. Such desirable combination of materials properties can be achieved in multi-phase\nmulti-component superalloys with a specific type of microstructure (the matrix contains\ncoherent particles of a secondary phase - a superalloy microstructure). In order to design\nnew Fe-Al-based superalloys, we employ a state-ofthe-art theory-guided materials design\nconcept to identify suitable combinations of solutes.
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Time discretization method of solving PDE
Myška, Michal ; Zatočilová, Jitka (referee) ; Nechvátal, Luděk (advisor)
This thesis deals with solving evulution partial differential equations by the time discretization method. It originates form the Rothe's method (methond of lines). The thesis is divided into three parts. The first one shows principle of the method. The second part focuses on teoretical aspects, in particular, on existence and convergence theorem along with an error estimate. Some function analysis tools are presented here as well. In the last part, a MATLAB code is listed.
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Analysis of the Rössler dynamical system
Nechutová, Vendula ; Nechvátal, Luděk (referee) ; Čermák, Jan (advisor)
In this bachelor thesis, there is analysed Rössler dynamical system, especially stability and type of its fixed points. Theoretical calculations are supported with visualizations illustrating notions of bifurcation and chaotic behaviour. In the last part, stabilization of chaotic Rössler dynamic system by delayed feedback control is discussed.
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Newton and numerical mathematics
Obrátil, Štěpán ; Nechvátal, Luděk (referee) ; Zatočilová, Jitka (advisor)
Topic of this bachelor thesis are Newton's methods for numerical solutions of various problems. Especially the problems of solving nonlinear equations and systems of nonlinear equations, as well as numerical integration are explained. The Newton's method for solving nonlinear equations is presented, as well as its many modifications and its generalisation for systems of nonlinear equations. Usefulness of methods is demonstrated on various examples. In the end, Newton-Cotes quadrature formulae for numerical integration are presented.
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Solutions of inverse problems in the area of material and heat exchangers
Kůdelová, Tereza ; Nechvátal, Luděk (referee) ; Čermák, Jan (advisor)
This master’s thesis deals with the dynamic behaviour of the heat exchangers which is described by a system of differential equations. In this connection, it contains general informations about heat transfer, heat exchangers and their arrangements. The main aim of this thesis is to solve the inverse problem of the antiparallel arrangement and discuss the question of the controllability, observability and identifiability of its parameters.
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Continuous and discrete time attitude control of a vehicle
Najvarová, Lucie ; Nechvátal, Luděk (referee) ; Gennaro, Stefano Di (advisor)
Kontrola řízení vozidla se stala významným problémem v automatizačních aplikacích v automobilovém průmyslu. Ta se stala reálnou díky zavedení různých "by-wire" subsystémů, jako je např. "steer-by-wire," "break-by-wire," atd. Tyto subsystémy reprezentují elektronické ekvivalenty již existujících mechanických a hydraulických subsystémů. Především pak může být zavedeno číslicové řízení, určené na základě vzorkování dynamiky vozidla. Výhodou periodického snímání vstupních veličin je vyvarování se určitých poruch spojitého řízení.
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