This dissertation is devoted to study of complex systems in human physiology particularly heartbeats and brain dynamics. We have studied the dynamics of heartbeats that has been a subject of investigation of two independent groups. The first group emphasized the multifractal nature of the heartbeat dynamics of healthy subjects, whereas the second group had established a close connection between healthy subjects and the occurrence of crucial events. We have analyzed the same set of data and established that in fact the heartbeats are characterized by the occurrence of crucial and Poisson events. An increase in the percentage of crucial events makes the multifractal spectrum broader, thereby bridging the results of the former group with the results of the latter group. The crucial events are characterized by a power index that signals the occurrence of 1/f noise for complex systems in the best physiological condition. These results led us to focus our analysis on the statistical properties of crucial events. We have adopted the same statistical analysis to study the statistical properties of the heartbeat dynamics of subjects practicing meditation. The heartbeats of people doing meditation are known to produce coherent fluctuations. In addition to this effect, we made the surprising discovery that meditation makes the heartbeat depart from the ideal condition of 1/f noise. We also discussed how to combine the wave-like nature of the dynamics of the brain with the existence of crucial events that are responsible for the 1/f noise. We showed that the anomalous scaling generated by the crucial events could be established by means of a direct analysis of raw data. The efficiency of the direct analysis procedure is made possible by the fact that periodicity and crucial events is the product of a spontaneous process of self-organization. We argue that the results of this study can be used to shed light into the nature of this process of self-organization.

No description available.

Ziel der vorliegenden Arbeit ist es, das Preisach-Modell bezüglich stochastischer äußerer Felder und temperaturbezogener Aspekte zu untersuchen. Das phänomenologische Preisach-Modell wird oft erfolgreich angewendet, um Systeme mit Hysterese zu beschreiben. Im ersten Teil der Arbeit wird die Antwort des Preisach-Modells auf stochastische äußere Felder untersucht. Hier liegt das Augenmerk hauptsächlich auf der Autokorrelation; sie dient dazu den Einfluss des hysteretischen Gedächtnisses zu quantifizieren. Mit analytischen Methoden wird gezeigt, dass sich ein Langzeitgedächtnis, sichtbar in der Autokorrelation der Systemantwort, entwickeln kann, selbst wenn das treibende Feld unkorreliert ist. Im Anschluss werden diese Resultate, m.H. von Simulationen, auf äußere Felder ausgeweitet, die selbst Korrelationen aufweisen können. Der zweite Teil der Arbeit befasst sich mit dem Einfluss einer endlichen Temperatur auf das Preisach-Modell. Es werden unterschiedliche Methoden besprochen, wie das Nichtgleichgewichtsmodell in seiner mikromagnetischen Interpretation mit Temperatur als Gleichgewichtseigenschaft verknüpft werden kann. Eine Formulierung wird genutzt, um die Magnetisierung von Nickelnanopartikeln in einer Fullerenmatrix zu simulieren und mit Experimenten zu vergleichen. Des Weiteren wird die Relaxationsdynamik des Gedächtnisses des Preisach-Modells bei endlichen Temperaturen untersucht. / The aim of this thesis is to investigate the Preisach model in regard to stochastically driving and temperature-related aspects. The Preisach model is a phenomenological model for systems with hysteresis which is often successfully applied. Hysteresis is a widespread phenomenon which is observed in nature and the key feature of certain technological applications. Further, it contributes to phenomena of interest in social science and economics as well. Prominent examples are the magnetization of ferromagnetic materials in an external magnetic field or the adsorption-desorption hysteresis observed in porous media. Hysteresis involves the development of a hysteresis memory, and multistability in the interrelations between external driving fields and system response. In the first part, we mainly investigate the response of Preisach hysteresis models driven by stochastic input processes with regard to autocorrelation functions to quantify the influence of the system’s memory. Using rigorous methods, it is shown that the development of a hysteresis memory is reflected in the possibility of long-time tails in the autocorrelation functions, even for uncorrelated driving fields. In the case of uncorrelated driving, these long-time tails in the autocorrelations of the system’s response are determined only by the tails of the involved densities. They will be observed if there are broad Preisach densities assigning a high weight to elementary loops of large width and narrow input densities such that rare extreme events of the input time series contribute significantly to the output for a long period of time. Afterwards, these results are extended by simulations to driving fields which themselves show correlations. It is shown that the autocorrelation of the output does not decay faster than the autocorrelation of the input process. Further, there is a possibility that long-term memory in the hysteretic response is more pronounced in the case of uncorrelated driving than in the case of correlated driving. The behavior of the output probability distribution at the saturation values is quite universal. It is not affected by the presence of correlations and allows conclusions whether the input density is much more narrow than the Preisach density or not. Moreover, the existence of effective Preisach densities is shown which define equivalence classes of systems of input and Preisach densities which lead to realizations of the same output variable. The asymptotic behavior of an effective Preisach density determines the asymptotic correlation decay of the system’s response in the case of uncorrelated driving. In the second part, temperature-related effects are considered. It is reviewed how the non-equilibrium Preisach model in its micromagnetic picture can be related to temperature within the framework of extended irreversible thermodynamics. The irreversible response of a ferromagnetic material, namely, Nickel nanoparticles in a fullerene matrix, is simulated. The model includes superparamagnetism where ferromagnetism breaks down at temperatures lower than the Curie temperature and the results are compared to experimental data. Furthermore, we adapt known results for the thermal relaxation of the system’s memory in the form of a front propagation in the Preisach plane derived basically from solving a master equation and by the use of a contradictory assumption. A closer look is taken at short time scales which dissolves the contradiction and shows that the known results apply, taking into account the fact that the dividing line propagation starts with an additional delay time depending on the front coordinates in the Preisach plane. Additionally, it is outlined how thermal relaxation behavior in the Preisach model of hysteresis can be studied using a Fokker-Planck equation. The latter is solved analytically in the non-hysteretic limit using eigenfunction methods. The results indicate a change in the relaxation behavior, especially on short time scales.

Ziel der vorliegenden Arbeit ist es, das Preisach-Modell bezüglich stochastischer äußerer Felder und temperaturbezogener Aspekte zu untersuchen. Das phänomenologische Preisach-Modell wird oft erfolgreich angewendet, um Systeme mit Hysterese zu beschreiben. Im ersten Teil der Arbeit wird die Antwort des Preisach-Modells auf stochastische äußere Felder untersucht. Hier liegt das Augenmerk hauptsächlich auf der Autokorrelation; sie dient dazu den Einfluss des hysteretischen Gedächtnisses zu quantifizieren. Mit analytischen Methoden wird gezeigt, dass sich ein Langzeitgedächtnis, sichtbar in der Autokorrelation der Systemantwort, entwickeln kann, selbst wenn das treibende Feld unkorreliert ist. Im Anschluss werden diese Resultate, m.H. von Simulationen, auf äußere Felder ausgeweitet, die selbst Korrelationen aufweisen können. Der zweite Teil der Arbeit befasst sich mit dem Einfluss einer endlichen Temperatur auf das Preisach-Modell. Es werden unterschiedliche Methoden besprochen, wie das Nichtgleichgewichtsmodell in seiner mikromagnetischen Interpretation mit Temperatur als Gleichgewichtseigenschaft verknüpft werden kann. Eine Formulierung wird genutzt, um die Magnetisierung von Nickelnanopartikeln in einer Fullerenmatrix zu simulieren und mit Experimenten zu vergleichen. Des Weiteren wird die Relaxationsdynamik des Gedächtnisses des Preisach-Modells bei endlichen Temperaturen untersucht. / The aim of this thesis is to investigate the Preisach model in regard to stochastically driving and temperature-related aspects. The Preisach model is a phenomenological model for systems with hysteresis which is often successfully applied. Hysteresis is a widespread phenomenon which is observed in nature and the key feature of certain technological applications. Further, it contributes to phenomena of interest in social science and economics as well. Prominent examples are the magnetization of ferromagnetic materials in an external magnetic field or the adsorption-desorption hysteresis observed in porous media. Hysteresis involves the development of a hysteresis memory, and multistability in the interrelations between external driving fields and system response. In the first part, we mainly investigate the response of Preisach hysteresis models driven by stochastic input processes with regard to autocorrelation functions to quantify the influence of the system’s memory. Using rigorous methods, it is shown that the development of a hysteresis memory is reflected in the possibility of long-time tails in the autocorrelation functions, even for uncorrelated driving fields. In the case of uncorrelated driving, these long-time tails in the autocorrelations of the system’s response are determined only by the tails of the involved densities. They will be observed if there are broad Preisach densities assigning a high weight to elementary loops of large width and narrow input densities such that rare extreme events of the input time series contribute significantly to the output for a long period of time. Afterwards, these results are extended by simulations to driving fields which themselves show correlations. It is shown that the autocorrelation of the output does not decay faster than the autocorrelation of the input process. Further, there is a possibility that long-term memory in the hysteretic response is more pronounced in the case of uncorrelated driving than in the case of correlated driving. The behavior of the output probability distribution at the saturation values is quite universal. It is not affected by the presence of correlations and allows conclusions whether the input density is much more narrow than the Preisach density or not. Moreover, the existence of effective Preisach densities is shown which define equivalence classes of systems of input and Preisach densities which lead to realizations of the same output variable. The asymptotic behavior of an effective Preisach density determines the asymptotic correlation decay of the system’s response in the case of uncorrelated driving. In the second part, temperature-related effects are considered. It is reviewed how the non-equilibrium Preisach model in its micromagnetic picture can be related to temperature within the framework of extended irreversible thermodynamics. The irreversible response of a ferromagnetic material, namely, Nickel nanoparticles in a fullerene matrix, is simulated. The model includes superparamagnetism where ferromagnetism breaks down at temperatures lower than the Curie temperature and the results are compared to experimental data. Furthermore, we adapt known results for the thermal relaxation of the system’s memory in the form of a front propagation in the Preisach plane derived basically from solving a master equation and by the use of a contradictory assumption. A closer look is taken at short time scales which dissolves the contradiction and shows that the known results apply, taking into account the fact that the dividing line propagation starts with an additional delay time depending on the front coordinates in the Preisach plane. Additionally, it is outlined how thermal relaxation behavior in the Preisach model of hysteresis can be studied using a Fokker-Planck equation. The latter is solved analytically in the non-hysteretic limit using eigenfunction methods. The results indicate a change in the relaxation behavior, especially on short time scales.

Kadmium telurid je velmi důležitý materiál jak základního, tak i aplikovaného výzkumu. Je to dáno zejména jeho výhodnými elektronickými, optickými a strukturními vlastnostmi, které ho předurčují pro náročné technické aplikace. Dnes se hlavně používá pro jeho vysoké rozlišení k detekci a X-záření. Hlavní výhodou detektorů na bázi CdTe je, že nepotřebují chlazení a mohou spolehlivě fungovat i při pokojové teplotě. To způsobuje efektivnější interakce fotonů než je tomu u Si nebo jiných polovodičových materiálů. Obsahem této práce byla analýza a interpretace výsledků získaných studiem šumových a transportních charakteristik CdTe vzorků. Měření ukázaly že odpor homogenní části CdTe krystalů mírně klesá při připojení elektrického pole na vzorku. Při změně teploty navíc dochází k odlišné reakci u CdTe typu p a n. Právě těmto efektům je v práci věnována pozornost. Pomocí šumové spektroskopie bylo zjištěno, že při nízkých frekvencích je u vzorků dominantní šum typu 1/f, zatímco při vyšších frekvencích je sledován generačně-rekombinační šum a tepelný šum. Všechny měřené vzorky vykazovaly mnohem vyšší hodnotu šumu na nízkých frekvencích než udává Hoogeova rovnice. Byly nalezeny a popsány zdroje nadbytečného šumu.

No description available.

The purpose of this thesis is to introduce a musical work of one of the world's most favorite composers of the 20th century - Sergej Prokofiev. Even though I would like to address all his pieces, given the extensiveness of his work and my profession as a pianist and a pedagogue, I decided to focus only on the pieces for solo piano. I detail each piano piece in a catalogue organized by opus number. My analysis focuses on compositions, eventually on cycles, which can be somehow beneficial to us. Beneficial, in this sense means exposure to pieces with variety of character, use of melody and eventually pieces from a various work periods. Another condition during a selection of pieces for my dissertation was various levels of difficulty. The majority of my thesis is dedicated to the piano sonatas. Although they are not very long, they belong to the piano masterpieces forever. Further, I mention less performed Etudes, Op. 2 and Visions fugitives, Op. 22, and on the other hand well known Suit from Romeo and Juliet, Op. 75. The music for children is represented in my analysis by one piece only - Children's Songs, Op. 65. Prokofiev wrote nearly 40 opuses for piano, which makes up almost a third of his work. That is a remarkable number and these pieces are worth interest.