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Dynamical Simulation of a System with Contact Problem
Raisinger, Jan ; Keršner, Zbyněk (referee) ; Frantík, Petr (advisor)
This work deals with the simulation of a dynamical system with a contact problem represented by the contact of a bicycle tube with a tire during inflation and loading of a bicycle wheel. In the first part the work defines the basics of dynamical systems a contact problems and introduces the methods used for following simulations. The practical part of the work desribes the process of converting a real system of rim-tube-tire objects to a computional model by determining its geometry and material characteristics as a continuous object and its subsequent discretization, introduces the program used for the subsequent simulations (FyDiK 2D) and shows the results of said simulations.
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TESTING THE METHOD OF MULTIPLE SCALES AND THE AVERAGING PRINCIPLE FOR MODEL PARAMETER ESTIMATION OF QUASIPERIODIC TWO TIME-SCALE MODELS
Papáček, Štěpán ; Matonoha, Ctirad
Some dynamical systems are characterized by more than one timescale, e.g. two well separated time-scales are typical for quasiperiodic systems. The aim of this paper is to show how singular perturbation methods based on the slow-fast decomposition can serve for an enhanced parameter estimation when the slowly changing features are rigorously treated. Although the ultimate goal is to reduce the standard error for the estimated parameters, here we test two methods for numerical approximations of the solution of associated forward problem: (i) the multiple time-scales method, and (ii) the method of averaging. On a case study, being an under-damped harmonic oscillator containing two state variables and two parameters, the method of averaging gives well (theoretically predicted) results, while the use of multiple time-scales method is not suitable for our purposes.
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Dynamical Simulation of a System with Contact Problem
Raisinger, Jan ; Keršner, Zbyněk (referee) ; Frantík, Petr (advisor)
This work deals with the simulation of a dynamical system with a contact problem represented by the contact of a bicycle tube with a tire during inflation and loading of a bicycle wheel. In the first part the work defines the basics of dynamical systems a contact problems and introduces the methods used for following simulations. The practical part of the work desribes the process of converting a real system of rim-tube-tire objects to a computional model by determining its geometry and material characteristics as a continuous object and its subsequent discretization, introduces the program used for the subsequent simulations (FyDiK 2D) and shows the results of said simulations.
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Analýza atraktorů zobecněných Newtonovských tekutin v 3d oblastech
Žabenský, Josef ; Pražák, Dalibor (advisor) ; Bulíček, Miroslav (referee)
We investigate a system of nonlinear partial differential equations, specifically the so-called Ladyzhenskaya model, in three spatial dimensions. It will be shown that after inclusion of a perturbation of a higher order, the model exhibits a considerably better behavior, in particular it will become quite straightforward to prove differentiability of solutions with respect to the initial condition. Due to this fact we may consequently employ the method of Lyapunov exponents to estimate the fractal dimension of the exponential attractor. First, however, it will be necessary to show existence and uniqueness of solutions, improved regularity and existence of a compact invariant set for the entire system.
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Physical and Mathematical modelling of Chimney Demolition
Ficker, Tomáš ; Keršner, Zbyněk (referee) ; Frantík, Petr (advisor)
The thesis deals with physical and numerical modelling of downsized model of chimney and its demolition. The properties of downsized physical model, which is made of wooden cubes, are being researched and experimentally tested. The physical experiments are then designed using software FyDiK. Numerical Model is simplified to 2D problem, whereas the problem includes dynamic effects. Conformity of designed software model and physical experiment is tested. The aim of this thesis is to achive the best possible conformity of physical and numerical models.
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Model Of Chaotic Single Stage Transistor Amplifier In Class C
Rujzl, Miroslav
This article deals with design and experimental verification of a single stage transistoramplifier in class C which is introduced to chaotic state. The basic procedure of deriving differentialequations and representation of dynamical system is presented. Equivalent circuit of transistor stagewas transformed to the real model based on operation amplifier integrators. Chaotic behavior wasconfirmed by strange attractors captured by oscilloscope.
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Delay Differential Equations in Dynamic Systems
Dokyi, Martha ; Šremr, Jiří (referee) ; Opluštil, Zdeněk (advisor)
Tato práce je přehledem zpožděných diferenciálních rovnic v dynamických systémech. Počínaje obecným přehledem zpožděných diferenciálních rovnic představujeme koncept zpožděných diferenciálů a použití jeho modelů, od biologie a populační dynamiky po fyziku a inženýrství. Poskytneme také přehled Dynamické systémy a diferenciální rovnice zpoždění v dynamických systémech. Oblastí pro modelování s rovnicemi zpožďovacích diferenciálů je Epidemiologie. Důraz je kladen na vývoj epidemiologického modelu Susceptible-Infected-Removed (SIR) bez časového zpoždění. Analyzujeme naše dva modely v rovnováze a lokální stabilitě pomocí předpokládaných dat COVID -19. Výsledky by byly porovnány mezi modelem bez zpoždění a modelem se zpožděním.
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Analysis and circuit realization of special chaotic systems
Rujzl, Miroslav ; Hruboš, Zdeněk (referee) ; Petržela, Jiří (advisor)
This master‘s thesis deals with analysis of electronic dynamical systems exhibiting chaotic solution. In introduction, some basic concepts for better understanding of dynamical systems are explained. After introduction, current knowledge from the world of circuits exhibiting chaotic solutions are discussed. The best-known chaotic systems are analyzed numerically in Matlab software. Numerical analysis and experimental verification were demonstrated at C class transistor amplifier, which confirmed the chaotic behavior and generation of a strange attractor.
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REGULATORY NETWORK OF DRUG-INDUCED ENZYME PRODUCTION: PARAMETER ESTIMATION BASED ON THE PERIODIC DOSING RESPONSE MEASUREMENT
Papáček, Štěpán ; Lynnyk, Volodymyr ; Rehák, Branislav
The common goal of systems pharmacology, i.e. systems biology applied to the eld of pharmacology, is to rely less on trial and error in designing an input-output systems, e.g. therapeutic schedules. In this paper we present, on the paradigmatic example of a regulatory network of drug-induced enzyme production, the further development of the study published by Duintjer Tebbens et al. (2019) in the Applications of Mathematics. Here, the key feature is that the nonlinear model in form of an ODE system is controlled (or periodically forced) by an input signal being a drug intake. Our aim is to test the model features under both periodic and nonrecurring dosing, and eventually to provide an innovative method for a parameter estimation based on the periodic dosing response measurement.
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