Orientador: Amir Ordacgi Caldeira / Dissertação (mestrado) - Universidade Estadual de Campinas, Instituto de Física Gleb Wataghin / Made available in DSpace on 2018-08-27T17:13:50Z (GMT). No. of bitstreams: 1 Durao_LisanMarcosMarques_M.pdf: 1224728 bytes, checksum: b2631019a5882f7a0fca6cb609bfff9f (MD5) Previous issue date: 2015 / Resumo: Sistemas quânticos abertos, ou não isolados, podem ser caracterizados a partir de uma entropia estatística. A entropia é um conceito fundamental na física e usualmente é interpretada como falta de informação a respeito do estado do sistema. O programa usual da física estatística para sistemas não isolados é propor um Hamiltoniano para o "Universo", descrito por uma distribuição de Gibbs e aplicando uma abordagem do tipo "Sistema + Reservatório", de onde podemos avaliar o operador densidade reduzido do sistema através de um processo de traço parcial. Outra maneira de obter o operador densidade seria obter a entropia de Von Neumann do sistema completo e a partir dela o operador densidade total pelo princípio de máxima entropia para então tomar o traço parcial com respeito as coordenadas do reservatório. Por outro lado, podemos tentar obter esse operador densidade e as propriedades termodinâmicas do sistema diretamente do princípio de máxima entropia Tal tarefa pode exigir o uso de outras formas de entropia não necessariamente extensivas. Partindo de uma abordagem do tipo sistema + reservatório, estudamos a entropia de uma partícula Browniana acoplada com um reservatório harmônico. Usando isso como o ponto de partida para a maximização de entropias dependentes de um parâmetro, busca-se uma correspondência entre as constantes emergentes do nosso modelo e os parâmetros ajustáveis de algumas bem conhecidas entropias generalizadas a fim de determinar qual ansatz é mais apropriado para nosso sistema / Abstract: The main goal of our project is the characterization of open quantum systems by means of a statistical entropy. Entropy is a fundamental physical quantity and is usually interpreted as the lack of knowledge about the state of the system, which means it is an informational metric. The statistical mechanical program for non-isolated quantum systems consists in creating a Hamiltonian for the "universe" within the so-called system-plus-reservoir approach from which one can evaluate the reduced density operator of the system of interest through the partial trace of the full density operator with respect to the reservoir coordinates. Notice that, in so doing we are tacitly assuming that the equilibrium state of the whole universe can be described by a Gibbsian distribution. Alternatively one can evaluate the Von Neumman entropy for the whole universe from which the above mentioned full density operator can be obtained via the maximum entropy priciple, and then, by the same partial tracing procedure, obtain the desired reduced density operator. Now we can ask ourselves what happens if one insists in obtaining a density operator and the thermodynamical properties for the system of interest directly from a maximum entropy principle. Such a task can require the use of other forms of entropy not necessarily extensive. Starting from the system-plus-reservoir approach we study the entropy and mean values of a Brownian particle coupled to a harmonic reservoir. Using this as the starting point to the maximization of non-extensive "parameter depending" entropies, we aim at finding a correspondence between the constants arising from our model and the adjustable parameters of some well-known generalized entropies which may turn out to be more appropriate to our needs / Mestrado / Física / Mestre em Física

This thesis examines the utility of mathematical complexity measures for the analysis of stratospheric dynamics. Through theoretical considerations and tests with artificial data sets, e.g., the iteration of the logistic map, suitable parameters are determined for the application of the statistical entropy measures sample entropy (SE) and Rényi entropy (RE) to methane (a long-lived stratospheric tracer) data from simulations of the SOCOL chemistry-climate model. The SE is shown to be useful for quantifying the variability of recurring patterns in a time series and is able to identify tropical patterns similar to those reported by previous studies of the ``tropical pipe'' region. However, the SE is found to be unsuitable for use in polar regions, due to the non-stationarity of the methane data at extra-tropical latitudes. It is concluded that the SE cannot be used to analyse climate complexity on a global scale. The focus is turned to the RE, which is a complexity measure of probability distribution functions (PDFs). Using the second order RE and a normalisation factor, zonal PDFs of ten consecutive days of methane data are created with a Bayesian optimal binning technique. From these, the RE is calculated for every day (moving 10-day window). The results indicate that the RE is a promising tool for identifying stratospheric mixing barriers. In Southern Hemisphere winter and early spring, RE produces patterns similar to those found in other studies of stratospheric mixing. High values of RE are found to be indicative of the strong fluctuations in tracer distributions associated with relatively unmixed air in general, and with gradients in the vicinity of mixing barriers, in particular. Lower values suggest more thoroughly mixed air masses. The analysis is extended to eleven years of model data. Realistic inter-annual variability of some of the RE structures is observed, particularly in the Southern Hemisphere. By calculating a climatological mean of the RE for this period, additional mixing patterns are identified in the Northern Hemisphere. The validity of the RE analysis and its interpretation is underlined by showing that qualitatively similar patterns can be seen when using observational satellite data of a different tracer. Compared to previous techniques, the RE has the advantage that it requires significantly less computational effort, as it can be used to derive dynamical information from model or measurement tracer data without relying on any additional input such as wind fields. The results presented in this thesis strongly suggest that the RE is a useful new metric for analysing stratospheric mixing and its variability from climate model data. Furthermore, it is shown that the RE measure is very robust with respect to data gaps, which makes it ideal for application to observations. Hence, using the RE for comparing observations of tracer distributions with those from model simulations potentially presents a novel approach for analysing mixing in the stratosphere.

This thesis examines the utility of mathematical complexity measures for the analysis of stratospheric dynamics. Through theoretical considerations and tests with artificial data sets, e.g., the iteration of the logistic map, suitable parameters are determined for the application of the statistical entropy measures sample entropy (SE) and Rényi entropy (RE) to methane (a long-lived stratospheric tracer) data from simulations of the SOCOL chemistry-climate model. The SE is shown to be useful for quantifying the variability of recurring patterns in a time series and is able to identify tropical patterns similar to those reported by previous studies of the ``tropical pipe'' region. However, the SE is found to be unsuitable for use in polar regions, due to the non-stationarity of the methane data at extra-tropical latitudes. It is concluded that the SE cannot be used to analyse climate complexity on a global scale. The focus is turned to the RE, which is a complexity measure of probability distribution functions (PDFs). Using the second order RE and a normalisation factor, zonal PDFs of ten consecutive days of methane data are created with a Bayesian optimal binning technique. From these, the RE is calculated for every day (moving 10-day window). The results indicate that the RE is a promising tool for identifying stratospheric mixing barriers. In Southern Hemisphere winter and early spring, RE produces patterns similar to those found in other studies of stratospheric mixing. High values of RE are found to be indicative of the strong fluctuations in tracer distributions associated with relatively unmixed air in general, and with gradients in the vicinity of mixing barriers, in particular. Lower values suggest more thoroughly mixed air masses. The analysis is extended to eleven years of model data. Realistic inter-annual variability of some of the RE structures is observed, particularly in the Southern Hemisphere. By calculating a climatological mean of the RE for this period, additional mixing patterns are identified in the Northern Hemisphere. The validity of the RE analysis and its interpretation is underlined by showing that qualitatively similar patterns can be seen when using observational satellite data of a different tracer. Compared to previous techniques, the RE has the advantage that it requires significantly less computational effort, as it can be used to derive dynamical information from model or measurement tracer data without relying on any additional input such as wind fields. The results presented in this thesis strongly suggest that the RE is a useful new metric for analysing stratospheric mixing and its variability from climate model data. Furthermore, it is shown that the RE measure is very robust with respect to data gaps, which makes it ideal for application to observations. Hence, using the RE for comparing observations of tracer distributions with those from model simulations potentially presents a novel approach for analysing mixing in the stratosphere.

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Este trabalho consiste no desenvolvimento de uma metodologia de otimização multidisciplinar de projeto conceitual de aeronaves. O conceito de aeronave otimizada tem como base o estudo evolutivo de características das categorias imediatas àquela que se propõe. Como estudo de caso, foi otimizada uma aeronave de treinamento militar que faça a correta transição entre as fases de treinamento básico e avançado. Para o estabelecimento dos parâmetros conceituais esse trabalho integra técnicas de entropia estatística, desdobramento da função de qualidade (QFD), aritmética fuzzy e algoritmo genético (GA) à aplicação de otimização multidisciplinar ponderada de projeto (OMPP) como metodologia de projeto conceitual de aeronaves. Essa metodologia reduz o tempo e o custo de projeto quando comparada com as técnicas tradicionais existentes. / This work is concerned with the development of a methodology for multidisciplinary optimization of the aircraft conceptual design. The aircraft conceptual design optimization was based on the evolutionary simulation of the aircraft characteristics outlined by a QFD/Fuzzy arithmetic approach where the candidates in the Pareto front are selected within categories close to the target proposed. As a test case a military trainer aircraft was designed target to perform the proper transition from basic to advanced training. The methodology for conceptual aircraft design optimization implemented in this work consisted on the integration of techniques such statistical entropy, quality function deployment (QFD), arithmetic fuzzy and genetic algorithm (GA) to the weighted multidisciplinary design optimization (WMDO). This methodology proved to be objective and well balanced when compared with traditional design techniques.

Este trabalho consiste no desenvolvimento de uma metodologia de otimização multidisciplinar de projeto conceitual de aeronaves. O conceito de aeronave otimizada tem como base o estudo evolutivo de características das categorias imediatas àquela que se propõe. Como estudo de caso, foi otimizada uma aeronave de treinamento militar que faça a correta transição entre as fases de treinamento básico e avançado. Para o estabelecimento dos parâmetros conceituais esse trabalho integra técnicas de entropia estatística, desdobramento da função de qualidade (QFD), aritmética fuzzy e algoritmo genético (GA) à aplicação de otimização multidisciplinar ponderada de projeto (OMPP) como metodologia de projeto conceitual de aeronaves. Essa metodologia reduz o tempo e o custo de projeto quando comparada com as técnicas tradicionais existentes. / This work is concerned with the development of a methodology for multidisciplinary optimization of the aircraft conceptual design. The aircraft conceptual design optimization was based on the evolutionary simulation of the aircraft characteristics outlined by a QFD/Fuzzy arithmetic approach where the candidates in the Pareto front are selected within categories close to the target proposed. As a test case a military trainer aircraft was designed target to perform the proper transition from basic to advanced training. The methodology for conceptual aircraft design optimization implemented in this work consisted on the integration of techniques such statistical entropy, quality function deployment (QFD), arithmetic fuzzy and genetic algorithm (GA) to the weighted multidisciplinary design optimization (WMDO). This methodology proved to be objective and well balanced when compared with traditional design techniques.

Um método para avaliação do uso de ganho adequado em ensaios de verificação de PIO (Pilot Induced Oscillations) é apresentado. As tarefas de manobra sintética (Synthetic Tracking Task) são utilizadas para demonstração. A teoria é baseada no conceito de entropia estatística proveniente da teoria da informação e no modelo estrutural do piloto humano. O método é apresentado para manobras executadas no eixo lateral e oferece uma medida do ganho humano utilizado durante a sua execução em malha-fechada. Para a modelagem da planta é utilizado modelo black-box com equacionamento de espaço de estados e identificação de parâmetros. Dados de ensaios em voo provenientes de uma aeronave de transporte certificada FAR-25 são utilizados para medir a razão entre o tempo gasto pelo piloto humano em uma malha fechada em posição versus o tempo em uma malha de derivada da posição (roll vs. roll rate). Esta medida é proposta como validadora da execução correta do ensaio. / A method is proposed to verify losed-loop adequate flight test piloting gain in PIO aircraft certification. The synthetic tracking task PIO flight test is used. The theory is based on the entropy concept from information theory and on the structural pilot model of the human pilot. The method is presented for single axis pilot tracking maneuvers and offers a measure of the human pilot gain employed during its execution. A black-box, state-space, parameter-identified model is used for the plant. Flight test data from a FAR-25 transport aircraft is used to verify the theory of how to determine a measure of the ratio between time spent by the human pilot in the error loop versus in the error rate loop to control the aircraft. This measure is proposed as a test point validation method for PIO flight testing.

Um método para avaliação do uso de ganho adequado em ensaios de verificação de PIO (Pilot Induced Oscillations) é apresentado. As tarefas de manobra sintética (Synthetic Tracking Task) são utilizadas para demonstração. A teoria é baseada no conceito de entropia estatística proveniente da teoria da informação e no modelo estrutural do piloto humano. O método é apresentado para manobras executadas no eixo lateral e oferece uma medida do ganho humano utilizado durante a sua execução em malha-fechada. Para a modelagem da planta é utilizado modelo black-box com equacionamento de espaço de estados e identificação de parâmetros. Dados de ensaios em voo provenientes de uma aeronave de transporte certificada FAR-25 são utilizados para medir a razão entre o tempo gasto pelo piloto humano em uma malha fechada em posição versus o tempo em uma malha de derivada da posição (roll vs. roll rate). Esta medida é proposta como validadora da execução correta do ensaio. / A method is proposed to verify losed-loop adequate flight test piloting gain in PIO aircraft certification. The synthetic tracking task PIO flight test is used. The theory is based on the entropy concept from information theory and on the structural pilot model of the human pilot. The method is presented for single axis pilot tracking maneuvers and offers a measure of the human pilot gain employed during its execution. A black-box, state-space, parameter-identified model is used for the plant. Flight test data from a FAR-25 transport aircraft is used to verify the theory of how to determine a measure of the ratio between time spent by the human pilot in the error loop versus in the error rate loop to control the aircraft. This measure is proposed as a test point validation method for PIO flight testing.