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Computational modeling of radial hydrodynamic bearings for water machines
Pokorný, Jan ; Šimek,, Jiří (referee) ; Návrat, Tomáš (advisor)
The aim of this thesis is to calculate the stiffness and damping coefficients for radial hydrodynamic bearings. Cylindrical and lemon hydrodynamic bearings are considered. The solution to this problem mainly depends on the hydrodynamic pressure in the bearing. The numerical solution of the Reynolds equation is used to calculate the pressure. The effect of variable viscosity and density of the lubricant due to temperature changes is considered. The static equilibrium position of the journal centre is also solved. The stiffness and damping coefficients are determined using small amplitude journal motions about the equilibrium position. Three methods for determining these coefficients are presented. The outcome of this thesis is an algorithm for the calculation of stiffness and damping coefficients for cylindrical and lemon bearings. Results for lemon bearings are presented and comparison with the commercial software DynRot BR is made. The benefit of this thesis is the creation of an algorithm for the calculation of journal centre equilibrium position, a new way of incorporating the temperature changes in the viscosity and the density of the lubricant, and the modification of a method for calculating stiffness and damping coefficients based on experimental analogy.
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Low Earth orbit trajectory prediction using a machine learning approach
Janda, Přemek ; Vlk, Jan (referee) ; Novák, Jiří (advisor)
Přesné orbitální predikce orbit satelitů na nízé oběžné dráze Země jsou nezbytné pro každodení provádění operací, tak aby se předešlo jejich srážkám. Tato práce se zaměřuje na analýzu histrorických dat trajektorií, tvořených z klacických dráhových elementů. S využitím strojového učení, data jsou sdružena, zpracována a na závěr užita pro predikci dráhy orbity. Nejlepších výsledků předpovědí bylo dosaženo s neuronovou sítí s doulodobou a krátkodobou pamětí (LSTM).
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Ray-based Born approximation
Šachl, Libor ; Klimeš, Luděk (advisor) ; Bulant, Petr (referee)
Title: Ray-based Born approximation Author: Libor Šachl Department: Department of Geophysics Supervisor: RNDr. Luděk Klimeš, DrSc. Supervisor's e-mail address: klimes@seis.karlov.mff.cuni.cz Abstract: One of the aims of this thesis was coding of program grdborn.for for computing the 2D and 3D ray-based Born approximation of the first order in an inhomoge- nous isotropic medium without attenuation. The computation of 3D amplitudes using the 2D Born approximation is based on the correction term, which is de- rived. The program is further used in computing the Born approximation in various models. We test its performance in three simple models. We study the effect of the discretization, the spurious waves introduced by the finite size of the grid etc. In the next step, we focus on the computations in more compli- cated models. We compute the Born seismograms in 2D heterogenous models. We study the diffracted waves, the effects of caustics etc. Keywords: Born approximation, ray theory, velocity model, perturbation 1
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Ray-based Born approximation
Šachl, Libor
Title: Ray-based Born approximation Author: Libor Šachl Department: Department of Geophysics Supervisor: RNDr. Luděk Klimeš, DrSc. Supervisor's e-mail address: klimes@seis.karlov.mff.cuni.cz Abstract: One of the aims of this thesis was coding of program grdborn.for for computing the 2D and 3D ray-based Born approximation of the first order in an inhomoge- nous isotropic medium without attenuation. The computation of 3D amplitudes using the 2D Born approximation is based on the correction term, which is de- rived. The program is further used in computing the Born approximation in various models. We test its performance in three simple models. We study the effect of the discretization, the spurious waves introduced by the finite size of the grid etc. In the next step, we focus on the computations in more compli- cated models. We compute the Born seismograms in 2D heterogenous models. We study the diffracted waves, the effects of caustics etc. Keywords: Born approximation, ray theory, velocity model, perturbation 1
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Interpretation of the sources of the known solutions of Teukolsky equations
Mikeska, Václav ; Kofroň, David (advisor) ; Ledvinka, Tomáš (referee)
Many realistic astrophysical problems can be treated as perturbations. It turns out that the NP formalism is a very successful tool in electromagnetic perturbations on Kerr background. We investigate stationary axisymmetric test electromagnetic field generated by static axisymmetric charge distribution and stationary axisymmetric tangential cur- rents around Kerr black hole. We found a simple relation between electromagnetic field NP scalars φ0 and φ2 and then we got an explicit formula for the third NP scalar φ1 by solving Maxwell equations with electromagnetic sources. Next, we investigate the problem of visualisation of electromagnetic field and develop a visualisation method on arbitrary background, which emphasize local field measured by an observer. We illustrate this method with several examples of electromagnetic fields. 1
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Computational modeling of radial hydrodynamic bearings for water machines
Pokorný, Jan ; Šimek,, Jiří (referee) ; Návrat, Tomáš (advisor)
The aim of this thesis is to calculate the stiffness and damping coefficients for radial hydrodynamic bearings. Cylindrical and lemon hydrodynamic bearings are considered. The solution to this problem mainly depends on the hydrodynamic pressure in the bearing. The numerical solution of the Reynolds equation is used to calculate the pressure. The effect of variable viscosity and density of the lubricant due to temperature changes is considered. The static equilibrium position of the journal centre is also solved. The stiffness and damping coefficients are determined using small amplitude journal motions about the equilibrium position. Three methods for determining these coefficients are presented. The outcome of this thesis is an algorithm for the calculation of stiffness and damping coefficients for cylindrical and lemon bearings. Results for lemon bearings are presented and comparison with the commercial software DynRot BR is made. The benefit of this thesis is the creation of an algorithm for the calculation of journal centre equilibrium position, a new way of incorporating the temperature changes in the viscosity and the density of the lubricant, and the modification of a method for calculating stiffness and damping coefficients based on experimental analogy.
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Gravitational waves in cosmology
Kadlecová, Alžběta ; Svítek, Otakar (advisor) ; Žofka, Martin (referee)
In this work, we study the backreaction of high-frequency gravitational waves on cosmological backgrounds. To describe the wave, we use the Isa- acson formalism, specifically the WKB approximation, which allows us to express the backreaction through an effective stress-energy tensor of the gra- vitational wave. First, we consider the inhomogeneous cosmological model of Charach and Malin, which contains gravitational waves and a massless scalar field mini- mally coupled to gravity. We show that although this is a spatially compacti- fied solution, it is possible to add a high-frequency perturbation and solve Einstein's equations with the effective stress-energy tensor in a consistent way. The bacreaction is of the same order as the influence of the scalar field. Second, we add multiple incoherent high-frequency waves to the homoge- neous Kasner background, and discuss the relation to the late-time limit of the Gowdy (vacuum Charach and Malin) model. 1
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Interaction of gravitational radiation with matter
Tintěra, Tomáš ; Svítek, Otakar (advisor) ; Žofka, Martin (referee)
In the present work we study gravitational waves in the approximation of high frequency, and their interaction with matter waves with comparable frequency. We generalize the formalism of R. A. Isaacson to the case of non-vacuum spacetimes. We formulate and study a technique of so called averaging, which helps us to separate slow changes and high-frequency fluctuations of various tensor fields. The described methods are used in examples with a given particular metric - so called background metric. We thus study the interaction of high-frequency gravitational waves on the Robinson- Trautman background and the high-frequency electromagnetic waves. Further, we seek a perfect fluid with high-frequency energy-momentum tensor that could coexist with high-frequency gravitational waves on the flat Friedmann-Lemaˆıtre-Robertson-Walker background; again, we examine the relation between those potential gravitational and matter waves.
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Ray-based Born approximation
Šachl, Libor
Title: Ray-based Born approximation Author: Libor Šachl Department: Department of Geophysics Supervisor: RNDr. Luděk Klimeš, DrSc. Supervisor's e-mail address: klimes@seis.karlov.mff.cuni.cz Abstract: One of the aims of this thesis was coding of program grdborn.for for computing the 2D and 3D ray-based Born approximation of the first order in an inhomoge- nous isotropic medium without attenuation. The computation of 3D amplitudes using the 2D Born approximation is based on the correction term, which is de- rived. The program is further used in computing the Born approximation in various models. We test its performance in three simple models. We study the effect of the discretization, the spurious waves introduced by the finite size of the grid etc. In the next step, we focus on the computations in more compli- cated models. We compute the Born seismograms in 2D heterogenous models. We study the diffracted waves, the effects of caustics etc. Keywords: Born approximation, ray theory, velocity model, perturbation 1
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Ray-based Born approximation
Šachl, Libor ; Klimeš, Luděk (advisor) ; Bulant, Petr (referee)
Title: Ray-based Born approximation Author: Libor Šachl Department: Department of Geophysics Supervisor: RNDr. Luděk Klimeš, DrSc. Supervisor's e-mail address: klimes@seis.karlov.mff.cuni.cz Abstract: One of the aims of this thesis was coding of program grdborn.for for computing the 2D and 3D ray-based Born approximation of the first order in an inhomoge- nous isotropic medium without attenuation. The computation of 3D amplitudes using the 2D Born approximation is based on the correction term, which is de- rived. The program is further used in computing the Born approximation in various models. We test its performance in three simple models. We study the effect of the discretization, the spurious waves introduced by the finite size of the grid etc. In the next step, we focus on the computations in more compli- cated models. We compute the Born seismograms in 2D heterogenous models. We study the diffracted waves, the effects of caustics etc. Keywords: Born approximation, ray theory, velocity model, perturbation 1
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