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Interactions of migrating giant planets and small solar-system bodies
Chrenko, Ondřej ; Brož, Miroslav (advisor) ; Wünsch, Richard (referee)
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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Collisional evolution of the Main Asteroid Belt over 4 billion years
Cibulková, Helena ; Brož, Miroslav (advisor) ; Ďurech, Josef (referee)
In this work, we constructed a new model for the collisional evolution of the Main Asteroid Belt. Our goals are to test the scaling law from the work of Benz & Asphaug (1999) and ascertain if it can be used for the whole belt. We want to find initial size-frequency distributions (SFDs) for the considered six parts of the belt, and to verify if the number of asteroid families created during the simulation matches the number of observed families as well. We used new observational data from the WISE satellite (Masiero et al., 2011) to construct the observed SFDs. We simulated mutual collisions of asteroids with a modified Boulder code (Morbidelli et al., 2009), in which the results of hydrodynamic (SPH) simulations from the work of Durda et al. (2007) are included. Because material characteris- tics can affect breakups, we created two models - for monolithic asteroids and for rubble-piles (Benavidez et al., 2012). The results for monolithic and rubble- -pile asteroids are comparable and in both cases the number of created families is, within uncertainties, consistent with the observations. A disagreement of the SFDs for a limited size range D 1 to 5 km a is a good motivation to conduct new SPH simulations with relatively small targets. 1
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Properties of near-horizon geometry of spacetimes
Daněk, Jiří ; Žofka, Martin (advisor) ; Svítek, Otakar (referee)
Nowadays, the near-horizon regions of black holes have enjoyed great attention thanks to their role in the popular AdS/CFT correspondence and their specific geometry suitable for formulations of uniqueness theorems in higher dimensions. A strictly general-relativistic point of view reveals also many interesting phenomena taking place near black-hole horizons. Our aim was to investigate how horizon multiplicity affects near-horizon geometry, geodesical distance, radial motion of photons and massive, charged particles, and also the possibility of collision processes leading to unbound collision energies near the horizon. We chose the Reissner-Nordström-de Sitter metric, which, on the one hand, is simple thanks to being static and spherically symmetric but which, on the other hand, is rich enough to enable the existence of up to a doubly degenerate ultra-extreme horizon. After discussing the physical feasibility of the near-horizon limit, we applied it to single, double, and triple horizons, their near-horizon geometries, and local collision processes. We found continuous coordinate systems covering all types of horizons and analytic solutions for motion of radial photons and special or critical, massive, charged particles in their vicinity. We addressed particle collisions in the immediate vicinity of horizons...
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Hash functions - characteristics, implementation and collisions
Karásek, Jan ; Sobotka, Jiří (referee) ; Lambertová, Petra (advisor)
Hash functions belong to elements of modern cryptography. Their task is to transfer the data expected on the entry into a unique bite sequence. Hash functions are used in many application areas, such as message integrity verification, information authentication, and are used in cryptographic protocols, to compare data and other applications. The goal of the master’s thesis is to characterize hash functions to describe their basic characteristics and use. Next task was to focus on one hash function, in particular MD5, and describe it properly. That means, to describe its construction, safety and possible attacks on this function. The last task was to implement this function and collisions. The introductory chapters describe the basic definition of hash function, the properties of the function. The chapters mention the methods preventing collisions and the areas were the hash functions are used. Further chapters are focused on the characteristics of various types of hash functions. These types include basic hash functions built on basic bit operations, perfect hash functions and cryptographic hash functions. After concluding the characteristics of hash functions, I devoted to practical matters. The thesis describes the basic appearance and control of the program and its individual functions which are explained theoretically. The following text describes the function MD5, its construction, safety risks and implementation. The last chapter refers to attacks on hash functions and describes the hash function tunneling method, brute force attack and dictionary attack.
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Passive and active safety features in passenger cars
Jahoda, Patrik ; Kučera, Pavel (referee) ; Píštěk, Václav (advisor)
This bachelor thesis deals with safety elements of all kinds in personal vehicles and their general introduction. This elements are divided and broadened and roughly described. My work contains short summary of history of safety elements. Conclusion contains evaluation of individual elements. Video with crash test is inserted in this graduate work.
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