http://hdl.handle.net/11089/6914 2026-04-03T18:16:55Z http://hdl.handle.net/11089/55609 Zagadnienia propagacji światła w polu grawitacyjnym Piwnik, Joanna Rozprawa poświęcona jest analizie propagacji światła w zakrzywionych czasoprzestrzeniach ogólnej teorii względności, w przybliżeniu optyki geometrycznej. Jej główną ideą jest zastosowanie do tego klasycznego problemu, nierozerwalnie związanego z głównymi wątkami ogólnej teorii względności, efektywnych metod teorii układów dynamicznych. W płaskiej czasoprzestrzeni użytecznym narzędziem opisu propagacji promieni świetlnych jest zasada najkrótszego czasu Fermata. Jednym z głównych wyników rozprawy jest podanie nowej wersji zasady Fermata dla dowolnych pól grawitacyjnych. Punktem wyjścia jest pewne proste twierdzenie udowodnione w rozprawie, na podstawie którego można zdefiniować funkcję Lagrange’a, opisującą zredukowane trajektorie w przestrzeni konfiguracyjnej, zależną od zmiennej działania. Takie uogólnienie opisane jest tzw. formalizmem Herglotza. Dzięki temu zaproponowana w rozprawie wersja zasady Fermata dostarcza efektywne narzędzia do analizy różnych problemów szczegółowych. Drugi główny wynik oparty jest na obserwacji, że w przypadku geometrii opisujących czarne dziury, równania wynikające z zasady Fermata opisują małe drgania nieliniowe. Prawidłowe rozwinięcie rozwiązań równań ruchu opisane jest przez algorytm Lindstedta-Poincare. Zastosowanie tego algorytmu do zagadnienia propagacji promieni świetlnych w obszarze asymptotycznym prowadzi do opisu oddającego jakościowe i ilościowe charakterystyki trajektorii. Ostatni problem rozważany w rozprawie dotyczy propagacji promieni świetlnych w metryce Kerra. W omawianej rozprawie zerowe geodezyjne analizowane są w ramach zasady Fermata, w taki sposób, że otrzymuje się dwuwymiarowy układ dynamiczny. Opisujący go hamiltonian jest dość skomplikowany, lecz problem można uprościć przez zastosowanie tzw. metody metamorfozy stałej sprzężenia. W ten sposób otrzymuje się dużo prostszy opis zerowych geodezyjnych w metryce Kerra w ramach dwuwymiarowego układu całkowalnego w sensie Arnolda-Liouville’a.; The dissertation is devoted to the analysis of light propagation in curved spacetimes of general relativity, in the approximation of geometrical optics. Its main idea is to apply effective methods of dynamical systems theory to this classical problem, inextricably linked to the main threads of general relativity. One of the main results of the dissertation is the provision of a new version of Fermat's principle for arbitrary gravitational fields. The starting point is a certain simple theorem proved in the dissertation, on the basis of which one can define the Lagrange function, describing reduced trajectories in configuration space, dependent on the action variable. Such a generalization is described by the so-called Herglotz formalism. The second main result is based on the observation that in the case of black hole geometries, the equations resulting from Fermat's principle describe small nonlinear oscillations. The correct expansion of the solutions is described by the Lindstedt-Poincare algorithm. Applying this algorithm to the problem of propagation of light rays in the asymptotic region leads to a description that correctly captures the characteristics of the trajectory. The last problem concerns the propagation of light rays in the Kerr metric. The null geodesics are analyzed in the framework of Fermat's principle, in such a way that a two-dimensional dynamical system is obtained. The Hamiltonian describing it is quite complicated, but the problem can be simplified by using the so-called coupling constant metamorphosis method. In this way, a much simpler description is obtained within a two-dimensional Arnold-Liouville integrable system. 2024-01-01T00:00:00Z http://hdl.handle.net/11089/54444 Wykorzystanie spektroskopii Ramana w badaniach materiałów niskowymiarowych Piskorski, Michał The presented dissertation focuses on the application of Raman spectroscopy in the study of low-dimensional systems. The main objectives included the integration of the Raman spectrometer with systems operating under controlled conditions, such as a glovebox with an inert gas atmosphere and an ultrahigh vacuum low-temperature scanning tunneling microscope system, as well as conducting investigations of low-dimensional materials using the developed system. The dissertation consists of five chapters, the last of which is a summary. Chapter 1 discusses research motivations, study objectives, and the theoretical foundations of the Raman effect, along with technical aspects of Raman spectroscopy. Chapter 2 details the design of a mapping Raman spectrometer integrated with a glovebox for argon-atmosphere measurements. Only essential components are placed inside. Subchapter 2.4 highlights the benefits of a protective atmosphere using hygroscopic Re₂O₇. Chapter 3 explores low-dimensional TMDC flakes of various polytypes. Data analysis enabled determining absorption coefficients and flake thickness. Anomalous Raman intensity dependence was examined, while tellurium-based flakes revealed unexpected metallic tellurium, prompting further studies. Chapter 4 discusses ultrahigh vacuum and low-temperature measurements, as well as the spectrometer’s integration with the vacuum system. A low-intensity silicon reference spectrum was obtained. Angle-dependent optical studies clarified results. Future work will expand the system for Tip-Enhanced Raman Spectroscopy mapping. 2024-01-01T00:00:00Z http://hdl.handle.net/11089/52945 Developing low-energy data analysis methods for Large-Sized Telescopes and observations of Flat-Spectrum Radio Quasars with Cherenkov telescopes Gliwny, Paweł My doctoral thesis is focused on the exciting field of gamma-ray astrophysics, which deals with the study of the highest-energy part of the electromagnetic spectrum. Ground-based observations via Cherenkov telescopes are the primary tool used for investigation in this area. My research endeavors to contribute to this field in two ways. Firstly, I have made a number of contributions to the standard analysis chain of LST-1 data. The new analysis methods that I developed involve low-level calibration techniques such as raw signal correction to reduce noise and time calibration to improve time resolution. I have also developed special cleaning methods that account for noise from calibration runs to improve the accuracy of my analysis further. Secondly, I have undertaken a detailed study of FSRQs (Flat Spectrum Radio Quasars) using MAGIC telescopes. 2024-01-01T00:00:00Z http://hdl.handle.net/11089/49410 Relativistic reflection from accretion disks in Seyfert galaxies and black-hole binaries: black hole spin and geometrical parameters of the X-ray source and the disk Klepczarek, Łukasz In the last few decades, the development of observational techniques and the continuous improvement of measuring instruments have enabled a deeper understanding of the nature of compact objects. As a result of the systematisation of knowledge from numerous observational data, different classes of such objects, their different spectral states (soft, hard, transient), and the occurrence of various forms of accretion flows in their surroundings have been distinguished. The most advanced tool for studying the vicinity of strong gravitational fields is reflection spectroscopy. In this thesis, reflection models have been used to describe X-ray sources in a more physical way. In particular, the effects of finite extent, rotation and vertical motion of the source were considered. Section 2 contains a discussion of the first two effects and a new analysis of the size of the corona is presented, which can be accurately approximated by a point-like source, as is typically assumed in the lamp-post models. Section 3 presents the results of the application of the reflection model with an outflowing corona to the hard state observation of Cyg X-1 source by the Suzaku and NuSTAR telescopes. The aim of this analysis was to impose constraints on the parameters of the X-ray source and the accretion disk. In section 4, an extended corona model is considered for the 1H 0707–495 source. The results presented are for the full range of the XMM detector, i.e. 0.3-10 keV. The aim of this analysis was to impose constraints on the source parameters. 2023-01-01T00:00:00Z