[pt] Sistemas dinâmicos não-lineares são comuns em engenharia. Este tipo de problema é resolvido por integração numérica das equações de movimento ou por métodos analíticos aproximados (métodos de perturbação) ou semi- analíticos como o método do Balanço Harmônico. A integração numérica é um processo lento e oneroso em análises paramétricas. Já os outros métodos aproximados são extremamente rápidos, mas são menos precisos e em pro- blemas com certos tipos de não-linearidade, tais como expoentes fracionários, são de difícil, ou impossível, aplicação. Neste trabalho, são apresentados dois métodos alternativos, baseados nas séries de Taylor, para a análise de sistemas não-lineares. No primeiro método, a resposta é escrita em série de Taylor e propriedades de simetria do sistema no espaço de fase são utilizadas para se determinar a relação freqüência-amplitude ou pontos fixos da resposta. No segundo método a solução é escrita em série de Fourier e as amplitudes dos harmônicos são determinadas da mesma forma que os coeficientes da série de Taylor. A simetria do sistema agora fica implícita na solução em série de Fourier, e a relação freqüência- amplitude ou os pontos fixos da resposta são obtidos utilizando equações suplementares. Através de comparações com outros métodos, mostra-se que os métodos desenvolvidos são de fácil implementação e precisos. Estes possuem as vantagens de serem aplicados a problemas com diversos tipos de não-linearidade e de fornecerem uma resposta em série de Fourier onde as amplitudes são determinadas analiticamente resolvendo-se um sistema de equações algébricas lineares. / [en] Nonlinear dynamical systems are rather common in engineering. This class of problems is usually solved by numerical integration or through the use of ap- proximate analytical methods (perturbation methods) or semi-analytical meth- ods such as the harmonic balance method. The numerical integration is a slow and cumbersome process in parametric analyses. The other methods are usu- ally extremely fast but they are less precise and their application to problems involving certain types of non-linearity, such as fractional power non-linearities, are difficult or even impossible. In this work two alternative methodologies for the analysis of non-linear dynamical systems, based on Taylor series expan- sions, are proposed. In the first method, the solution of the initial value prob- lem is obtained by expanding the response in Taylor series and the symmetries of the response in phase space are used to obtain the frequency-amplitude rela- tion or the fixed points of the steady-state response. In the second method the response is written as a Fourier series and the modal amplitudes are obtained using the same methodology used in the previous method for the determina- tion of the coefficients of the Taylor expansion. The symmetries of the response are implicit in the Fourier series, and supplementary equations are proposed for the determination of the frequency-amplitude relation and the fixed points of the response. Comparisons with other existing methods show that the two proposed methods are precise and can be easily applied to the analysis of sev- eral dynamical systems. The main advantages of the proposed methods are that they can be applied to several types of non-linearities and that analytic expression for the Fourier coefficients can be obtained by the solution of a system of linear algebraic equations.

The topic of the thesis is Search (approximate) methods for detecting alcohol in the human body. The aim of the thesis was to evaluate and compare methods and technical means that are used to detect alcohol in the human body for forensic purposes, self-control, corporate control and other purposes. The theoretical part is focused on the description of the chemical properties of alcohol, its physiological effect, metabolism and occurrence in breath. The theoretical part includes also an overview of methods which are used to detect alcohol in the human body. The practical part of the thesis deals with the availability of detection tools and their basic sorting. On the basis of used methodology, which included a survey of domestic and foreign sources and targeted interview, all gained knowledge were thoroughly evaluated and systematically described. The thesis is structured in a way that it can be used as an overview of this issue for the general public, national institutions, companies and other organizations that try to prevent alcohol addiction and abuse of minors. The thesis could also be beneficial for education as a study material.

Title: Study of dark energy and modified gravity and their influence on the cosmological parameters of the universe Author: Michal Vraštil Institute: Institute of Physics of the Czech Academy of Sciences Supervisor: RNDr. Michael Prouza, Ph.D., Institute of Physics of the Czech Academy of Sciences Abstract: Discovery of the accelerated expansion of the Universe poses a major theoretical puzzle. Although the assumption of a non-zero cosmological constant provides a minimal extension of general relativity that is consistent with observational data, many theories of modified gravity have been suggested as possible alternatives due to serious problems connected with the cosmological constant. Numerical predictions of structure formation for these models in the fully non-linear regime are very expensive and it is difficult, if not impossible, to explore such a huge space of models and parameters using high-resolution N-body simulations. Even in the mildly nonlinear regime, perturbative methods can become extremely complex. We explore whether simplified dynamical approximations, applicable for a certain set of cosmological probes, can be used to investigate models of modified gravity with acceptable accuracy in the latter instance. For the case of chameleon gravity, we found that it is screened away on scales...

Made available in DSpace on 2016-06-02T20:16:43Z (GMT). No. of bitstreams: 1 2389.pdf: 676894 bytes, checksum: 7c529b06a0e41de3d113cccbae2281c9 (MD5) Previous issue date: 2009-02-18 / Universidade Federal de Sao Carlos / In the Quantum Optics area, the construction of effective hamiltonian is a matter of great importance, since from them we can generate and manipulate quantum states and logical operations. In this work we discuss 3 approximate methods for obtaining such effective hamiltonians: i) adiabatic elimination, ii) method of effective dynamics for oscillating hamiltonians and iii) nonlinear small rotations. Here we analyze the regime of validity of these techniques, their disadvantages and advantages. We note that, although adiabatic elimination is the most used and known, it has inconsistencies and can provide incorrect effective hamiltonians. The method of effective dynamics, although a very simple technique, also has inconsistencies and is not applicable to dissipative systems. Moreover, the method of nonlinear small rotations, which appears as the most accurate, is rarely used in the literature. / Em Óptica Quântica a construção de hamiltonianos efetivos é um assunto de suma importância, visto que a partir deles podemos manipular e gerar estados quânticos e operações lógicas. Nesta dissertação discutimos 3 métodos aproximativos para a obtenção de hamiltonianos efetivos: i) a eliminação adiabática, ii) o métodos de dinâmicas efetivas para hamiltonianos oscilantes e iii) o método de pequenas rotações não-lineares, de forma a analisar o regime de validade destas técnicas, desvantagens e vantagens. Notamos que, embora a eliminação adiabática seja a mais utilizada e divulgada, apresenta inconsistências e prevê hamiltonianos efetivos incorretos. O método de dinâmicas efetivas, embora seja uma técnica simples e muito operacional, também apresenta inconsistência e não se aplica a sistemas dissipativos. Por outro lado, o método de pequenas rotações não-lineares, que aparece como o mais preciso, é muito pouco utilizado na literatura.

La majeure partie des travaux sur les problèmes d’ordonnancement se placent dans le contexte où les ressources sont disponibles en permanence. Ce qui en réalité n’est pas toujours le cas. Nous nous plaçons dans le contexte d’indisponibilités connues ; nous nous intéressons plus particulièrement aux problèmes de type job shop avec des périodes d’indisponibilité flexibles et des tâches pouvant éventuellement être interrompues par les périodes d’indisponibilité. L’intégration de ces contraintes rend les problèmes d’ordonnancement nettement plus difficiles à résoudre. La flexibilité que nous considérons peut être relative à au moins l’un des points suivants : déplacement de la période d’indisponibilité dans une fenêtre de temps, modification de la durée de la période d’indisponibilité, interruption d’une tâche par une période d’indisponibilité, ensuite reprise avec une éventuelle pénalité.Dans cette thèse, nous avons proposé des modèles mathématiques pour le problème. En plus de la résolution des problèmes considérés, le but de ces modélisations est de permettre d’analyser l'impact des différentes contraintes et d'évaluer la qualité des méthodes approchées que nous proposons. Ces dernières permettent de construire très rapidement un ordonnancement en se basant sur des règles de priorité. Les solutions sont aussi utilisées pour notre approche basée sur la génération de colonnes. Cette approche s’adapte bien à différents fonctions objectif et permet d'intégrer relativement facilement plusieurs contraintes. De nombreuses expérimentations ont été menées pour valider les méthodes proposées. / In most of the machine scheduling literature, resources are assumed to be continuously available which is not always true. We deal with the context of unavailability known a priori; we are particularly interested in job-shop scheduling problems with flexible unavailability periods and tasks that can eventually be interrupted by unavailability periods. Integrating these constraints increase the complexity of the scheduling problems. We deal with flexibility that is related to at least one of the following points: moving the unavailability period in a time window, modification of the duration of the unavailability period, interruption of a task by an unavailability period, then resumed with a possible penalty.In this thesis, we propose mathematical models for the problem. In addition to the resolution of the considered problems, the aim of this modeling is to allow for the analysis of the impact of different constraints and evaluation of the quality of the approximate methods and the column generation approach we develop. The approximate methods construct in very short time a schedule based on priority rules. The solutions are also used in our column generation approach. This approach adapts well to various objective functions and allows relatively easily for the integration of several constraints. Many experiments have been performed to validate the designed methods.