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Model Problems of the Theory of Gravitation
Pilc, Marián ; Bičák, Jiří (advisor) ; Langer, Jiří (referee) ; Balek, Vladimír (referee)
Title: Model Problems of the Theory of Gravitation Author: Marián Pilc Department: Institute of Theoretical Physics Faculty of Mathematics and Physics Supervisor: prof. RNDr. Jiří Bičák, DrSc., dr. h. c., Institute of Theoretical Physics Faculty of Mathematics and Physics Abstract: Equations of motion for general gravitational connection and orthonormal coframe from the Einstein-Hilbert type action of the Einstein-Cartan theory are derived. Ad- ditional gauge freedom is geometrically interpreted. Our formulation does not fix coframe to be tangential to spatial section hence Lorentz group is still present as part of gauge freedom. 3+1 decomposition introduces tangent Minkowski structures hence Hamilton-Dirac approach to dynamics works with Lorentz connection over spatial sec- tion. The second class constraints are analyzed and Dirac bracket is defined.Reduction of phase space is performed and canonical coordinates are introduced. The second part of this thesis is dedicated to quantum formulation of Einstein-Cartan theory. Point version of Einstein-Cartan phase space is introduced. Basic variables, crucial for quan- tization, are derived via groups acting on the phase space and their selfadjoint represen- tation is found. Representation of basic variables of Einstein-Cartan theory is derived via infinite...
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Selected problems in relativistic cosmology
Kerachian, Morteza ; Bičák, Jiří (advisor) ; Balek, Vladimír (referee) ; Vikman, Alexander (referee)
In this work, we studied three selected problems in FRW spacetime. In the first part, we analysed the motion of a test particle in the homogeneous and isotropic universe. We presented a framework in which one can derive the uniformly accelerated trajectory and geodesic motion if a scale factor for a given spacetime is provided as a function of coordinate time. By applying the confomal time transformation, we were able to convert second order differential equations of motion in FRW spacetime to first order differential equations. From this, we managed to obtain a formalism to derive the uniformly accelerated trajectory of a test particle in spatially curved FRW spacetime. The second part of this work is devoted to dynamical cosmology. In particular, we analyse the cases of barotropic fluids and non-minimally coupled scalar field in spatially curved FRW spacetime. First, we set up the dynamical systems for an unspecified EoS of a barotropic fluid case and an unspecified positive potential for a non-minimal coupled scalar field case. For both of these systems, we determined well-defined dynamical variables valid for all curvatures. In the framework of these general setups we discovered several characteristic features of the systems, such as invariant subsets, symmetries, critical points and their...
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Inhomogeneous cosmology and averaging methods
Kašpar, Petr ; Svítek, Otakar (advisor) ; Balek, Vladimír (referee) ; Carloni, Sante (referee)
In this work we have examined different methods of averaging in general relativity and cosmology. We developed the method based on Cartan scalars. We computed the backreaction term for a flat LTB model with a special ansatz for the radial function. We found out that it behaves as a positive cosmological constant. In the next part of this thesis we were interested in averaging inside LRS class II dust model. For this family we averaged all the Einstein equations and the resulting system generalizes the Buchert equations. We numerically worked out two concrete examples where deceleration parameter changes its sign from positive to negative. Powered by TCPDF (www.tcpdf.org)
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Model Problems of the Theory of Gravitation
Pilc, Marián ; Bičák, Jiří (advisor) ; Langer, Jiří (referee) ; Balek, Vladimír (referee)
Title: Model Problems of the Theory of Gravitation Author: Marián Pilc Department: Institute of Theoretical Physics Faculty of Mathematics and Physics Supervisor: prof. RNDr. Jiří Bičák, DrSc., dr. h. c., Institute of Theoretical Physics Faculty of Mathematics and Physics Abstract: Equations of motion for general gravitational connection and orthonormal coframe from the Einstein-Hilbert type action of the Einstein-Cartan theory are derived. Ad- ditional gauge freedom is geometrically interpreted. Our formulation does not fix coframe to be tangential to spatial section hence Lorentz group is still present as part of gauge freedom. 3+1 decomposition introduces tangent Minkowski structures hence Hamilton-Dirac approach to dynamics works with Lorentz connection over spatial sec- tion. The second class constraints are analyzed and Dirac bracket is defined.Reduction of phase space is performed and canonical coordinates are introduced. The second part of this thesis is dedicated to quantum formulation of Einstein-Cartan theory. Point version of Einstein-Cartan phase space is introduced. Basic variables, crucial for quan- tization, are derived via groups acting on the phase space and their selfadjoint represen- tation is found. Representation of basic variables of Einstein-Cartan theory is derived via infinite...
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Physical and biological treatment of barley seeds
BÁLEK, Václav
Barley is the second oldest cereal after wheat, which began to be cultivated. The area, which was sown with barley in 2015 amounted to nearly 366,000 hectares, which was by 15 thousand hectares more than in the previous year. These numbers indicate that even nowadays it is an important and attractive crop. The aim of my thesis was to study the influence of treating of malt barley varieties Francin by low temperature plasma to technological quality malting barley. It has been evaluated several parameters. Parameters achieved the following results: turbidity 12 ° (10,68 12,15%) and 90 ° (8,86 9,56 %), the viscosity of 8.6% (1,46 mPa), the pH of the wort (5,57 - 5,65), extract flour dry matter (78,2 78,6 %), relative extract at 45 ° C (31,2 33,4 %), the color of the wort (15,5 16,5 j. EBC), nitrogenous substances in dry matter (11,71 12,11 %), soluble nitrogen substances (3,9 4 %), Kolbach index (32,5 34,2 %), beta glucans (69 97 mg/l), diastatic power (147 152 Wk), apparent final attenuation (70 71,8).
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Diseases and pests of grasses
BÁLEK, Václav
In the search I selected diseases and pests that are harmful to grasses specifying the damage to the health of plants, methods of diagnosis and economic threshold of harmfulness. In addition, I mention about the resistance, which is very important in this issue, because today is already grown and bred resistant varieties and the subsequent intervention against diseases and pests by pesticides or any other form of protection is not usually needed.
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