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Solution of integral equations for separable interactions
Hvizdoš, Dávid ; Horáček, Jiří (advisor) ; Kolorenč, Přemysl (referee)
Title: Solution of integral equations for separable interactions Author: Dávid Hvizdoš Department: Institute of Theoretical Physics Supervisor: prof. RNDr. Jiří Horáček, DrSc., Institute of Theoretical Physics Abstract: This work deals with the most fundamental types of integral equations (Fredholm and Volterra). Their occurrence in quantum mechanics is illustrated and the process that leads to the so-called regular and Jost solution is presented. Further their solutions in the case of separable interactions are studied. Analytical solutions on model separable potentials are sought. Analytical extensions of these solutions to the complex energy plane are provided and the properties of these functions are examined. The method of analytical continuation in the coupling constant based on the extension of the coupling constant as a function of is introduced. For some examples of separable potentials the Taylor expansion of the function and from it the inverse series √ are calculated. These series are then used to determine the resonance parameters of the potential and the accuracy of these calculations is discussed. Key words: integral equations, scattering theory, resonances, separable potential
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Fir Filter Resonance Compensation For Random Vibration Generation
Kunz, Jan
This paper deals with a random vibration generation on vibration shakers using a FIR filter. Every shaker has its resonances and anti-resonances which causes troubles in random vibration generation, for instance in presented shaker the difference between maximum and minimum in frequency characteristic is nearly 50 dB. Therefore, we decided to create a FIR filter with inverse characteristic with respect to the shaker to minimize those differences. To design such a filter a freqeuncy characteristic of the shaker has to be measured, then the characteristic is simplified using Ramer–Douglas–Peucker algorithm. Finally, the characteristic is inverted and FIR filter is designed using Remez algorithm. Using this FIR filter the difference in frequency characteristic drops from 50 dB to less 2 dB.
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Interactions of migrating giant planets and small solar-system bodies
Chrenko, Ondřej ; Brož, Miroslav (advisor)
Changes of semimajor axes of giant planets, which took place 4 billion years ago and evolved the Solar System towards its present state, affected various populations of minor Solar-System bodies. One of these populations was a group of dynamically stable asteroids in the 2:1 mean-motion resonance with Jupiter which reside in two islands of the phase space, denoted A and B, and exhibit lifetimes comparable to the age of the Solar System. The origin of stable asteroids has not been explained so far. Our main goal is to create a viable hypothesis of their origin. We update the resonant population and its physical properties on the basis of up-to-date observational data. Using an N-body model with seven giant planets and the Yarkovsky effect included, we demonstrate that the depletion of island A is faster compared to island B. We then investigate: (i) survivability of primordial resonant asteroids and (ii) capture of the population during planetary migration, using a recently described scenario with an escaping fifth giant planet and a jumping-Jupiter instability. We employ simulations with prescribed migration, smooth late migration and we statistically evaluate the results using dynamical maps. We also model collisions during the last 4 billion years. We conclude that the long-lived group was created by a...
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Milne method and phase-amplitude method
Matějková, Markéta ; Soldán, Pavel (advisor) ; Čurík, Roman (referee)
Bound and quasi-bound states of one-dimensional systems play an important role in quantum physics. In this thesis we solve the Schrödinger equation numerically via the Milne method. We show the relation between the Schrödinger and the Milne equation. The quantum action and the quantum number function are defined. We find bound-state energies of chosen symmetrical and unsymmetrical potentials. Dependence of bound- state energies on the number of points and the step size is studied. We also analyze the influence of the choice of trial energies and the number of iterations. Then we modify the Milne equation and using the phase-amplitude method we illustrate the search of resonances on the example of a diatomic molecule. 1
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Switched Mode Power Supplies
Španěl, Petr ; Lettl,, Jiří (referee) ; Kadaník,, Petr (referee) ; Procházka, Petr (advisor)
This thesis deals with switched mode power supplies based on resonant principle to achieve high efficiency. Several ways of switched mode power supplies optimalisation are described as part of the work to achieve better efficiency. Priparily, the new generation of switching elements based on SiC and resonant topology are used to achieve significant switching loss minimization. The selected resonant topology is simualted in detail and then built with focus on high efficiency. The main content of the work consists in the design and realization of the switched mode power supply with selected control algorithms and their comparison. The problems associated with usage of new SiC MOSFET generation in TO-247-4L package are being solved within the design and implementation of the power source. To solve the main problems, new 3rd SiC MOSFET gate driver was developer for working with switching frequencies in hundreds of kHz and resisting very high voltage stress on the controlled transistor. The next part of the gate driver is the overcurrent protection. The overcurrent limit can be set easily by changing one component. This protection reacts very quickly in hundreds of nanoseconds, so it is capable of saving the converter even in branch failure and going to hard short circuit. The functional sample of the series resonant converter was built and revated in the work. The converter based on 3. Generation of SiC MOSFET transistors from Cree in a modern case TO-247-4L was built. For this inverter, it was also necessary to develop both the control scheme and the resonance frequency tracking to achieve accurate switching and thus achieve the use of the resonant principle of the converter to the maximum extent possible. The result of this work is up to 3 kW converter with adjustable output voltage while maintaining high efficiency up to 96%.
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Optimization of modal properties of the body in the air flow
Matějka, Jan ; Švancara, Pavel (referee) ; Skalka, Petr (advisor)
The bachelor thesis deals with dynamic analysis of the rod body, which is excited by the Karmán vortices. In this thesis a method of countermeasure is also verified, which could be possibly used in order to supress the state of resonance in the body and which could minimalize the influence of the Karmán vortices on the structure. This method consists in change of the mass in specific parts of the body in order to change modal properties of this body. The main goal of the thesis is to find suitable configurations of the mass distribution depending on air flow velocity for purpose of minimalization the influence of the Karmán vortices on the construction. This is achieved by optimization of modal properties. The optimization is based on results of harmonic analysis and is considering possibility of practical use.
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The comparison of acoustic properties of guitars from the same product line
Trávníčková, Hana ; Indrák, Michal (referee) ; Jirásek, Ondřej (advisor)
This work is dealing with acoustic features of Furch guitars. In theoretical introduction is possible to find an information about basic characteristics of a tone. Following chapter about acoustic guitars is dealing even with mostly used types of woods for their manufacturing. In special chapter are described spectres of signals, LPC analysis, sound radiation of instruments and Chladni figures. Mentioned terms have been evaluated from measurements and are available in practical part of this work also including description of implementation of the measurement. As an output of this work is a comparison of acoustic features of measured guitars, their colours and modes.
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Feedback
Koniar, Martin ; Solčáni, Ján (referee) ; Rathouský, Luděk (advisor)
My diploma work is an installation, made from multiple instances of a device iniciating string resonance via electromagnetic field. These devices along with strings are placed on the wall in geometrical shape. Installation creates loop on multiple levels. Except the fact that installation have a circular shape, position of each string starts at the end of another string. Second, more inconspicious loops takes place in the electromagnetic device resonating the strings, that do that with feedback loop. Strings consist every step of chromatic scale, that repeats itself, just an octave higher. Amplification of the final sound of strings is done purely acoustically, with help of the wall on wich the piece is installed. This piece is in its nature concerned with spirituality in music, not necessarily in sense of evoking a spiritual experience, but rather demonstrating metaphors and parallels, that exists between physical aspects of tonal music and different religious ideas. The symmetrical shape of installation refer to religious and occult visuality, built f.e. in cabal on Fibonacci numbers, that is present not only in nature ( for example, the veins of the leaves grow by these numbers), but also in tonal music system (ancient philosophers were working with this concept, see Plato's Music of the Spheres). Strings in this piece produce drone sound, that is naturally evoking spirituality (most visible in buddhist monk meditation). This sound in the piece demonstrates immutability and constancy, the fact that all the chromatic tones are playing demonstrates wholeness (this fact may produce interesting resonances emerging between chromatic steps), so to speak, the unchangeable laws of physics, or to put it in religious lingo, the god law. The symbol of loop also refers to religion, like the eternal return of the same, the periodicity of history. Strings can be viewed as astrophysical symbol. Everything stated is nothing but my recourse, that should not ultimately determine the perception of the piece by viewer. The goal of the work is to offer experience without need to be put into context
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Suppression of Resonances from Vibration Signal using Vold-Kalman Filter
Čala, Martin
Presented paper describes usage of Vold-Kalman filter of the first generation compared with time-frequency method as the short-time Fourier transform or order tracking technique based on resampling. Advantages of Vold-Kalman filter will be showed on extraction of order signal for variable rotor speed. Additionally, ability to extract multiple orders will be demonstrated as well as utilization of removing resonances from a real vibration signal during the rotor startup and coastdown.
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Mutual interaction of pressure pulsations and pulsations of undirect pipe
Hrazdíra, Zdeněk ; Pochylý, František (referee) ; Habán, Vladimír (advisor)
This thesis deals with mathematical modeling of multiphysics FSI (fluid-structure interaction) problem, describing mutual interaction of pressure pulsations and vibrations of indirect pipe in a 2D region. Firstly, physical partial differential equations are derived separately for both media, which are in turn coupled and solved analytically. Results of mentioned models include natural frequency values, amplitude-frequency characteristics and both natural and driven damped oscillations of pipe and liquid.
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