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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 EinsteinHilbert type action of the EinsteinCartan 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 HamiltonDirac 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 EinsteinCartan theory. Point version of EinsteinCartan 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 EinsteinCartan theory is derived via infinite...


Notation of Czech Sign Language
Okrouhlíková, Lenka ; Hrubý, Jaroslav (advisor) ; Souralová, Eva (referee) ; Langer, Jiří (referee)
The thesis deals with possibilities of recording sign language vocabulary, especially the possible ways of notation of Czech sign language signs. The introductory chapter describes the first attempts to put the data down on paper in the 18th and 19th century in Europe. These ones were the first verbal descriptions of signs, sign notations and signs drawn in figures. Furthermore, the chapter gives a detailed description of the first notation system based on linguistic principles  William Stokoe's notation system, which was established in 1960 for American sign language and has become a basis and inspiration for many other notation systems which are also briefly described. A great deal of the paper is focused on possible ways to record Czech sign language lexicon. First, the thesis describes the "non notational" ways of recording signs that were previously used in papers dealing with Czech sign language  description, figures, photographs, videos and computer simulations. After these, we focus on the particular standardized notational systems that can be used for our purposes  Czech notation system for sign language and its modifications, the Edinburgh non manual notation system, Hamburg notation system, SignWriting and Berkeley transcription system. The last chapter provides an evaluation of...

 

Billiard time machine
Dolanský, Jindřich ; Langer, Jiří (advisor) ; Novotný, Jan (referee) ; Hledík, Stanislav (referee)
Title: Billiard time machine Author: Jindřich Dolanský Department: Institute of Theoretical Physics Supervisor: doc. RNDr. Jiří Langer, CSc. Supervisor's email address: Jiri.Langer@mff.cuni.cz Abstract: In this work we investigate a simple interacting system of an elastic particle in the nonrelativistic spacetime with a nontrivial causal structure realized by a worm hole with a time shift. We require that standard local physical laws hold, and search for their globally consistent solutions, i.e, we assume the validity of the principle of selfconsistency. If there were nontrivial set of initial conditions which would violate this principle, the system would be logically inconsistent. We show that the investigated system is not inconsistent in this sense, i.e., that all standard initial conditions have a globally consistent evolution. Even for the so called dangerous initial conditions which threaten to result into the paradoxical situation a consistent solution exists. In this case, the paradoxical collisionfree trajectory is superseded by a special consistent selfcolliding trajectory. Moreover, we demonstrate that more than one globally consistent evolution exists for a wide class of initial conditions. Thus, the evolution of the described system is not unique due to the nontrivial causal structure...


Asymptotic properties of the Cmetric
Sládek, Pavel ; Krtouš, Pavel (advisor) ; Langer, Jiří (referee) ; Ortaggio, Marcello (referee)
Asymptotic properties of the Cmetric are analyzed, using a method developed in work of Tafel and coworkers[1],[2],[3]. By nding an appropriate conformal factor , it allows the investigation of the asymptotic properties of a given asymptotically at spacetime. The news function and the Bondi mass aspect are computed and their general properties are analyzed, as well as the small mass, small acceleration, small and large Bondi time limits.


Structure and dynamics of shell sources in general relativity
Turnovec, Aleš ; Žofka, Martin (advisor) ; Langer, Jiří (referee)
Cylindrically symmetric shell sources are studied and a general form of induced energymomentum tensor of a collapsing shell is presented. The actual movement of the shell is numerically solved for a case when dynamics of the system is determined by energy conservation per unit length. It is then shown that additional assumptions can prevent the collapse, e. g. induced energymomentum tensor as perfect fluid or null dust of counterrotating particles. Collapse can be prevented also by introducing Thorne's Cenergy into the system.

 

Anomalous Ion Diffusion in Models of Turbulent Edge Tokamak Plasma
Papřok, Richard ; Krlín, Ladislav (advisor) ; Svoboda, Vojtěch (referee) ; Langer, Jiří (referee)
Enhanced particle and energy transport from edge plasma is observed and may cause a problem for a future operation of a thermonuclear reactor. Plasma edge turbulence presents a complex problem which is not fully theoretically understood. We chose a simple, mathematically simply described potential, which represents first approximation of the realistic one. Resulting dynamics led, for certain class of parameters, to a phenomenon known as Lévy walks, which is the cause of an anomalous enhanced diffusion. It is shown that for typical tokamak's parameters it is in this class and therefore it can be a cause of an anomalous transport in plasma.
