Pilot Induced Oscillations (PIO) are described as pilot-aircraft dynamic couplings which can lead to instability in an otherwise stable system. Previous and ongoing research has attempted to explain, predict, and avoid such oscillations. In contrast to other research, this effort backs away from pilot models and PIO avoidance and focuses on the characteristics of the pilot before, during, and after a PIO. Often, PIO''s can be explained by limit cycles occurring in a non-linear system where the non-linearities cause a sustained, constant amplitude oscillation. The primary instigators in such a PIO are usually a non-linear element (i.e. rate limit saturation) and a trigger event (i.e. pilot mode switching or increased pilot gain). By performing analysis in the frequency domain, determining such oscillations becomes easier. Using spectrograms and power spectral density functions, the frequency content of a signal in the pilot-aircraft system can also be investigated. An F-14 flight test was recently performed where the hydraulic system was modified to determine the feasibility of trying to recover the aircraft (land on carrier) during such an extreme hydraulic failure. During testing, a severe PIO occurred because of the tight tracking task used during aerial refueling. While performing spectrograms and power spectral analysis, an increase in power concentration at the PIO frequency was observed. With a linear approximation of the F-14 aircraft dynamics, a closed-loop system containing the aircraft, actuator, and pilot dynamics is developed so that limit cycle analysis can be performed. With stable limit cycle solutions found possible, a pilot-in-the-loop simulation is performed to verify the pilot model used in limit cycle analysis. Using the flight test data, limit cycle analysis, and pilot-in-the-loop simulation, a connection between variation in pilot behavior and PIO predicted by the increase in power concentration is investigated. The resulting connection showed that an increase in pilot gain along with a transition from observing pitch attitude to pitch rate are the possible trigger events causing the PIO. The use of spectrograms as a PIO predictor is shown to be possible, provided the necessary calculations can be completed in real-time. / Master of Science

Complex processes whose evolution in time rests on the occurrence of a large and random number of intermittent events are the systems under study. The mean time distance between two consecutive events is infinite, thereby violating the ergodic condition and activating at the same time a stochastic central limit theorem that explains why the Mittag-Leffler function is a universal property of nature. The time evolution of these complex systems is properly generated by means of fractional differential equations, thus leading to the interpretation of fractional trajectories as the average over many random trajectories, each of which fits the stochastic central limit theorem and the condition for the Mittag-Leffler universality. Additionally, the effect of noise on the generation of the Mittag-Leffler function is discussed. Fluctuations of relatively weak intensity can conceal the asymptotic inverse power law behavior of the Mittag-Leffler function, providing a reason why stretched exponentials are frequently found in nature. These results afford a more unified picture of complexity resting on the Mittag-Leffler function and encompassing the standard inverse power law definition.

Passage of the Volstead Act in 1920 expanded the mission of the U.S. Coast Guard. Law enforcement directives required officers to use "all necessary force" should a liquor smuggling vessel refuse the order to stop. On March 22, 1929, the Coast Guard Cutter Dexter sank the Canadian-flagged rum runner I'm Alone in the Gulf of Mexico, triggering an international incident that centered on "hot pursuit" and treaty jurisdiction. International encounters occurred frequently during Prohibition. The I'm Alone incident was the first sinking of a foreign flagged vessel that cost the life of a foreign national. The I'm Alone affair reflected the barriers any federal law enforcement agency faced in making Prohibition effective. The rum runner captain became a celebrity in Canada, while the Coast Guard was vilified. The Coast Guard amended boarding procedures after the incident cautioning officers about the possibility of accidental deaths.

A interligação dos sistemas elétricos de potência (SEPs) resultou em um aumento na complexidade dos mesmos. Além disso, devido a pressões econômicas e ambientais, os sistemas têm operado mais próximos aos seus limites de transmissão, o que aumenta a relevância de análises de segurança no contexto de estabilidade de tensão. Neste cenário, problemas associados à capacidade de transmissão do SEP, como a bifurcação induzida por limite (BIL), tornam-se mais importantes, criando a necessidade de ferramentas de análise apropriadas. Um dos objetivos deste projeto de mestrado é estudar mais profundamente as BILs para que se possa tratar melhor o fenômeno no contexto de estabilidade de tensão. Outro objetivo é o desenvolvimento de técnicas para avaliação da margem de estabilidade de tensão (MET) considerando a possibilidade de ocorrência de BIL. Finalmente, dada a grande importância e ampla utilização da análise de sensibilidade da MET devido à bifurcação sela-nó (BSN) em estudos de estabilidade de tensão, o equacionamento do problema de análise de sensibilidade da MET devido à BIL é o terceiro objetivo deste trabalho. A análise de sensibilidade é importante pois, não só fornece mais informações sobre o fenômeno de instabilidade e seus mecanismos, mas também auxilia na análise de segurança de SEPs, fornecendo informações sobre quais ações de controle serão mais eficazes na manutenção da MET e quais contingências serão mais severas. Isto é, quais mudanças no sistema mais afetam a MET. No entanto, este tipo de análise só foi realizado para o caso em que a MET é determinada por um ponto de BSN, não para o caso da BIL. Com o intuito de possibilitar que ferramentas de seleção de controles preventivos tratem o fenômeno da BIL, realizou-se uma análise de sensibilidade do ponto de BIL similar à análise usual baseada na BSN. Outra contribuição deste trabalho é uma formulação suave de limites complementares que foi aplicada ao problema de limites de injeção de potência reativa de unidades geradoras. A formulação proposta transforma, pelo menos numericamente, a BIL em uma BSN que pode ser detectada através de métodos já consolidados na literatura. / The interconnection of electric power systems (EPSs) led to an increase in security assessment complexity. Besides, due to economical and environmental inuences, EPSs have been operating closer to their transmission limits, which raises the relevance of security assessment in the context of voltage stability. In this scenario, problems related to EPS power transmission capacity, such as the limit induced bifurcation (LIB), become more important and bring the need of appropriate analysis tools. One of the goals of this project is to study the LIB problem more deeply, so it can be better understood in the context of voltage stability. Another objective is the development of methods for evaluating the load margin (LM) considering the possible occurrence of LIBs. Finally, since the LM sensitivity analysis due to saddle-node bifurcation (SNB) plays a highly important role in voltage stability studies, developing a method for LM sensitivity analysis due to LIB is our third objective. The sensitivity analysis is important not only because it provides information on the instability phenomenon and its mechanisms, but it is also useful for EPS security assessment, since it may provide knowledge on which control actions will be more eective in increasing the LM and which contingencies may be more severe. However, this analysis has been performed only for the case in which the LM is determined by a SNB point, not for the LIB case. With the intention of enabling pre-existing preventive control selection tools to treat the LIB phenomenon, a sensitivity analysis was performed at the LIB point similarly to what was developed for the SNB. Another contribution of this work is a smoothing formulation for complementary limits that was applied to the problem of limited reactive power injection of generating units. The proposed formulation transforms, at least numerically, the LIB in a SNB, which may be detected through methods already established in literature.

A interligação dos sistemas elétricos de potência (SEPs) resultou em um aumento na complexidade dos mesmos. Além disso, devido a pressões econômicas e ambientais, os sistemas têm operado mais próximos aos seus limites de transmissão, o que aumenta a relevância de análises de segurança no contexto de estabilidade de tensão. Neste cenário, problemas associados à capacidade de transmissão do SEP, como a bifurcação induzida por limite (BIL), tornam-se mais importantes, criando a necessidade de ferramentas de análise apropriadas. Um dos objetivos deste projeto de mestrado é estudar mais profundamente as BILs para que se possa tratar melhor o fenômeno no contexto de estabilidade de tensão. Outro objetivo é o desenvolvimento de técnicas para avaliação da margem de estabilidade de tensão (MET) considerando a possibilidade de ocorrência de BIL. Finalmente, dada a grande importância e ampla utilização da análise de sensibilidade da MET devido à bifurcação sela-nó (BSN) em estudos de estabilidade de tensão, o equacionamento do problema de análise de sensibilidade da MET devido à BIL é o terceiro objetivo deste trabalho. A análise de sensibilidade é importante pois, não só fornece mais informações sobre o fenômeno de instabilidade e seus mecanismos, mas também auxilia na análise de segurança de SEPs, fornecendo informações sobre quais ações de controle serão mais eficazes na manutenção da MET e quais contingências serão mais severas. Isto é, quais mudanças no sistema mais afetam a MET. No entanto, este tipo de análise só foi realizado para o caso em que a MET é determinada por um ponto de BSN, não para o caso da BIL. Com o intuito de possibilitar que ferramentas de seleção de controles preventivos tratem o fenômeno da BIL, realizou-se uma análise de sensibilidade do ponto de BIL similar à análise usual baseada na BSN. Outra contribuição deste trabalho é uma formulação suave de limites complementares que foi aplicada ao problema de limites de injeção de potência reativa de unidades geradoras. A formulação proposta transforma, pelo menos numericamente, a BIL em uma BSN que pode ser detectada através de métodos já consolidados na literatura. / The interconnection of electric power systems (EPSs) led to an increase in security assessment complexity. Besides, due to economical and environmental inuences, EPSs have been operating closer to their transmission limits, which raises the relevance of security assessment in the context of voltage stability. In this scenario, problems related to EPS power transmission capacity, such as the limit induced bifurcation (LIB), become more important and bring the need of appropriate analysis tools. One of the goals of this project is to study the LIB problem more deeply, so it can be better understood in the context of voltage stability. Another objective is the development of methods for evaluating the load margin (LM) considering the possible occurrence of LIBs. Finally, since the LM sensitivity analysis due to saddle-node bifurcation (SNB) plays a highly important role in voltage stability studies, developing a method for LM sensitivity analysis due to LIB is our third objective. The sensitivity analysis is important not only because it provides information on the instability phenomenon and its mechanisms, but it is also useful for EPS security assessment, since it may provide knowledge on which control actions will be more eective in increasing the LM and which contingencies may be more severe. However, this analysis has been performed only for the case in which the LM is determined by a SNB point, not for the LIB case. With the intention of enabling pre-existing preventive control selection tools to treat the LIB phenomenon, a sensitivity analysis was performed at the LIB point similarly to what was developed for the SNB. Another contribution of this work is a smoothing formulation for complementary limits that was applied to the problem of limited reactive power injection of generating units. The proposed formulation transforms, at least numerically, the LIB in a SNB, which may be detected through methods already established in literature.

This thesis consists of two papers devoted to the asymptotics of random matrix ensembles and measure valued stochastic processes which can be considered as generalizations of the Gaussian unitary ensemble (GUE) of Hermitian matrices H=A+A†, where the entries of A are independent identically distributed (iid) centered complex Gaussian random variables. In the first paper, a system of interacting diffusing particles on the real line is studied; special cases include the eigenvalue dynamics of matrix-valued Ornstein-Uhlenbeck processes (Dyson's Brownian motion). It is known that the empirical measure process converges weakly to a deterministic measure-valued function and that the appropriately rescaled fluctuations around this limit converge weakly to a Gaussian distribution-valued process. For a large class of analytic test functions, explicit formulae are derived for the mean and covariance functionals of this fluctuation process. The second paper concerns a family of random matrix ensembles interpolating between the GUE and the Ginibre ensemble of n x n matrices with iid centered complex Gaussian entries. The asymptotic spectral distribution in these models is uniform in an ellipse in the complex plane, which collapses to an interval of the real line as the degree of non-Hermiticity diminishes. Scaling limit theorems are proven for the eigenvalue point process at the rightmost edge of the spectrum, and it is shown that a non-trivial transition occurs between Poisson and Airy point process statistics when the ratio of the axes of the supporting ellipse is of order n -1/3. / Denna avhandling består av två vetenskapliga artiklar som handlar om gränsvärdessatser för slumpmatriser och måttvärda stokastiska processer. De modeller som studeras kan betraktas som generaliseringar av den gaussiska unitära ensembeln (GUE) av hermiteska n x n-matriser H=A+A†, där A är en matris vars element är oberoende, likafördelade, centrerade, komplexa normalfördelade stokastiska variabler. I artikel I betraktas ett system av växelverkande diffunderande partiklar på reella linjen, vissa specialfall av denna modell kan tolkas som egenvärdesdynamiken för matrisvärda Ornstein-Uhlenbeck-processer (Dysons brownska rörelse). Sedan tidigare är det känt att den empiriska måttprocessen konvergerar svagt mot en deterministisk måttvärd funktion och att fluktuationerna runt denna gräns, i lämplig skalning, konvergerer svagt mot en distributionsvärd gaussisk process. För en stor klass av analytiska testfunktioner härleds explicita formler för medelvärdes- och kovariansfunktionalerna för denna fluktuationsprocess. Artikel II behandlar en familj av slumpmatrisensembler som interpolerar mellan GUE och Ginibre-ensembeln, bestående av matriser A som ovan. För denna modell är egenvärdena komplexa och asymptotiskt likformigt fördelade i en ellips i komplexa planet. Skalningsgränsvärdessatser för egenvärdet med maximal realdel och för egenvärdespunktprocessen kring detta visas för ett allmänt val av interpolationsparametern i modellen. Då förhållandet mellan axlarna i den asymptotiska ellipsen är av storleksordning n-1/3 uppträder en övergångsfas mellan Airypunktprocess- och Poissonprocessbeteendena, typiska för GUE respektive Ginibre-ensembeln. / QC 20100705

The concept of the limit of a function is undoubtedly the key to higher mathematics. With a view to very fine mathematical essence of the notion mathematics educators permanently deliberate what didactic method to take in order to reach relatively satisfactory level of its understanding. The paper presents an approach based on the aid of hypothesis that is put forward by means of calculator support.

This diploma thesis deals with design of roof structure of the church in Brno Lesná. It is arched shell, which is symmetrical only by one axis. The roof is clamped by bond beam at supports of roof structure, which sits on a reinforced concrete walls, which transfers load to foundations. This structure is checked for the Ultimate Limit State and Service Limit State. Text part of design contains report, where is described structural system and technological proces. The structural design report contains assessment proces of designed structure.

The subject of this diploma thesis is the design and analysis of a bridge at the R48 bypass over the Ostravica River. For this purpose, three variants of the supporting structure solution were developed from which a variant of additionally prestressed chamber girder with perpendicular walls was selected. The main task is to assess the construction for phased construction. The static calculation was drawn up according to European

Vena contracta width (VCW) and effective regurgitant orifice area (EROA) are well established methods for evaluating mitral regurgitation using transesophageal echocardiography (TEE). For color-flow Doppler (CF) measurements Nyquist limit of 50–60 cm/s is recommended. Aim of the study was to investigate the effectiveness of a baseline shift of the Nyquist limit for these measurements. After a comprehensive 2-dimensional (2D) TEE examination, the mitral regurgitation jet was acquired with a Nyquist limit of 50 cm/s (NL50) along with a baseline shift to 37.5 cm/s (NL37.5) using CF. Moreover a real time 3-dimensional (RT 3D) color complete volume dataset was stored with a Nyquist limit of 50 cm/s (NL50) and 37.5 cm/s (NL37.5). Vena contracta width (VCW) as well as Proximal Isovelocity Surface Area (PISA) derived EROA were measured based on 2D TEE and compared to RT 3D echo measurements for vena contracta area (VCA) using planimetry method. Correlation between VCA 3D NL50 and VCW NL50 was 0.29 (p<0.05) compared to 0.6 (p<0.05) using NL37.5. Correlation between VCA 3D NL50 and EROA 2D NL50 was 0.46 (p<0.05) vs. 0.6 (p<0.05) EROA 2D NL37.5. Correlation between VCA 3D NL37.5 and VCW NL50 was 0.45 (p<0.05) compared to 0.65 (p<0.05) using VCW NL37.5. Correlation between VCA 3D NL37.5 and EROA 2D NL50 was 0.41 (p<0.05) vs. 0.53 (p<0.05) using EROA 2D NL37.5. Baseline shift of the NL to 37.5 cm/s improves the correlation for VCW and EROA when compared to RT 3D NL50 planimetry of the vena contracta area. Baseline shift in RT 3D to a NL of 37.5 cm/s shows similar results like NL50.