L'étude des Hydrocarbures Aromatiques Polycycliques (PAH) a connu un intérêt croissant depuis une trentaine d'années, en raison notamment de leur possible présence dans le milieu interstellaire qui expliquerait l'observation des bandes d'émission IR encore non attribuées. Dans ce travail de thèse, la dynamique de refroidissement du cation naphtalène C10H8+, la plus petite molécule de la famille des PAH, est étudiée dans un anneau de stockage électrostatique, le Mini-Ring. La distribution en énergie interne des ions stockés est sondée en induisant la photo dissociation d'une fraction des ions par une excitation laser à la longueur d'onde 532 nm. La dynamique de refroidissement des cations photo-excités est observée en mesurant en fonction du temps le nombre de neutres émis par dissociation. La courbe de déclin du signal de neutres est directement reliée à la distribution en énergie interne des ions à l'instant de l'excitation laser. Cette distribution en énergie interne peut alors être déterminée à différents temps de stockage en analysant les courbes de déclin à l'aide d'un programme numérique développé pendant la thèse. L'évolution temporelle de la distribution met en évidence un processus de refroidissement rapide caractérisé par un taux de refroidissement compris entre 70 et 90 s−1 pour des énergies internes de 5.9 et 6.8 eV. Ce refroidissement rapide ne peut être expliqué par l'émission de photons infrarouges. Il est attribué à la "fluorescence de Poincaré" caractérisée par un processus de conversion interne inverse suivie de l'émission d'un photon dans le domaine du visible. Cette fluorescence de Poincaré ou fluorescence récurrente a été prédite il y a plus de 20 ans mais n'a jamais été mesurée directement à ce jour. Les taux de refroidissement mesurés lors de ce travail de thèse apportent une évidence indirecte de ce processus / The study of Polycyclic Aromatic Hydrocarbons (PAH) has been of increasing interest during the last thirty years: their possible presence in the interstellar medium is commonly invoked to explain the observation of still unassigned IR emission bands. In this thesis, the cooling dynamics of the naphthalene cations C10H8 +, the smallest molecule of the PAH family, is studied in an electrostatic storage ring, the Mini-Ring. Particularly, we consider the two main cooling processes for naphthalene cation, the dissociation and photon emission. Naphthalene molecules are ionized in an electron cyclotron resonance source (ECR), accelerated to 12 keV and then injected and stored in the Mini-Ring for several milliseconds. The internal energy distribution of the stored ions is probed by laser induced dissociation using an excitation wavelength at 532 nm. The cooling dynamics of the photo-excited cations is observed by measuring the number of emitted neutrals as a function of time. The decay curve of the neutral signal is directly related to the internal energy distribution of the ions at the excitation time. This internal energy distribution can then be determined at various storage times by analyzing the decay curves using a code developed during this thesis. The time evolution of the internal energy distribution shows a fast cooling process characterized by a cooling rate increasing from 70 to 90 s−1 for internal energies from 5.9 to 6.8 eV. This fast cooling process can’t be explained by infrared photons emission. It is attributed to the "Poincaré fluorescence " which involves an inverse internal conversion process followed by the emission of a visible photon. This fluorescence from thermally excited electron or recurrent fluorescence was predicted more than 20 years ago, but has never been measured directly up to now. The measured cooling rates in this thesis provide indirect evidence of this process

The thesis deals with the measurement of tolerance zone and the influence of birefringence on the activity of polarization multiplex. The theoretical part deals with polarization of light, mathematical description using Stokes and Jones vectors and its representation by Poincaré sphere. It also deals with optical transmission and channel merging. The final part describes the designed measuring workplace and the measurement itself.

Tato diplomová práce se zabývá matematickými modely kráčejících robotů. Dva z těchto modelů jsou vybrány a analyzovány. Pasivní model "rimless wheel" , který slouží jako základ pro další, složitější modely, je podrobně analyzován. "Compass gait" model dvounohého robota je v práci analyzován a numericky simulován v programovacím jazyce Python. Metoda pro nalezení podmínek pro pasivní chůzi robota je rovněž implementována.

The aim of this master’s thesis is to analyze ways of propagation light in optical fiber with two polarization planes. Theoretical part is focused to to the issue of polarized light, its mathematical description using Stokes and Jones vectors, the state of polarization on Poincare sphere and polarization multiplex. In the practicle part are first measured several laboratory measurements to verify the theoretical assumptions from the previous chapters. At the end of the thesis was constructed a functional polarization multiplex for wavelength 1550 nm.

The irrational rotation algebra A_θ is known to be Poincaré self-dual in the KK-theoretic sense. The spectral triple representing the required K-homology fundamental class was constructed by Connes out of the Dolbeault operator on the 2-torus, but so far, there has not been an explicit description of the dual element. We geometrically construct, for certain elements g of the modular group, a finitely generated projective module L_g over A_θ ⊗ A_θ out of a pair of transverse Kronecker flows on the 2-torus. For upper triangular g, we find an unbounded cycle representing the dual of said module under Kasparov product with Connes' class, and prove that this cycle is invertible in KK(A_θ,A_θ), allowing us to 'untwist' L_g to an unbounded cycle representing the unit for the self-duality of A_θ. / Graduate

The lattice point problem in dynamical systems investigates the distribution of certain objects with some length property in the space that the dynamics is defined. This problem in different contexts can be interpreted differently. In the context of symbolic dynamical systems, we are trying to investigate the growth of N(T), the number of finite words subject to a specific ergodic length T, as T tends to infinity. This problem has been investigated by Pollicott and Urbański to a great extent. We try to investigate it further, by relaxing a condition in the context of deterministic dynamical systems. Moreover, we investigate this problem in the context of random dynamical systems. The method for us is considering the Fourier-Stieltjes transform of N(T) and expressing it via a Poincaré series for which the spectral gap property of the transfer operator, enables us to apply some appropriate Tauberian theorems to understand asymptotic growth of N(T). For counting in the random dynamics, we use some results from probability theory.

Completely locked-in state (CLIS) patients are unable to speak and have lost all muscle movement. From the external view, the internal brain activity of such patients cannot be easily perceived, but CLIS patients are considered to still be conscious and cognitively active. Detecting the current state of consciousness of CLIS patients is non-trivial, and it is difficult to ascertain whether CLIS patients are conscious or not. Thus, it is important to find alternative ways to re-establish communication with these patients during periods of awareness, and one such alternative is through a brain–computer interface (BCI). In this study, multiscale-based methods (multiscale sample entropy, multiscale permutation entropy and multiscale Poincaré plots) were applied to analyze electrocorticogram signals from a CLIS patient to detect the underlying consciousness level. Results from these different methods converge to a specific period of awareness of the CLIS patient in question, coinciding with the period during which the CLIS patient is recorded to have communicated with an experimenter. The aim of the investigation is to propose a methodology that could be used to create reliable communication with CLIS patients.

In the study of the weighted p-Laplace equation, it is often important to acquire good estimates of capacities. One useful tool for finding such estimates in metric spaces is exponent sets, which are sets describing the local dimensionality of the measure associated with the space. In this thesis, we limit ourselves to the weighted Rn space, where we investigate the relationship between exponent sets and Muckenhoupt Ap-weights - a certain class of well behaved functions. Additionally, we restrict our scope to radial weights, that is, weights w(x) that only depend on |x|. First, we determine conditions on α such that |x|α ∈ Ap(μ) for doubling measures μ on Rn. From those results, we develop weight exponent sets - a tool for making Ap-classifications of general radial weights, under certain conditions. Finally, we apply our techniques to the weight |x|α(log 1/|x|)β. We find that the weight belongs to Ap(μ) if α ∈ (-q, (p-1)q), where q = sup Q(μ) is a constant associated with the dimensionality of μ. The Ap-conditions in this thesis are found to be sharp.

Mémoire numérisé par la Division de la gestion de documents et des archives de l'Université de Montréal.

Les travaux récents en fondements de la théorie quantique (des champs) et en information quantique relativiste tentent de mieux comprendre les effets des contraintes de causalité imposées aux opérations physiques sur la structure des corrélations quantiques. Le premier chapitre de cette thèse est consacré à l'étude des implications conceptuelles de la non-localité quantique, notion qui englobe celle d'intrication dans un sens précis. Nous détaillons comment les récentes approches informationnelles tentent de saisir la structure des corrélations non-locales, ainsi que les questions que ces dernières soulèvent concernant la capacité d'un observateur localisé à isoler un système de son environnement. Le second chapitre détaille les effets de l'invariance de Poincaré sur la détection et la quantification de l'intrication. Cette invariance impose que tous les systèmes soient modélisés en dernière instance dans le cadre de la théorie des champs, ce qui implique qu'aucun système à énergie finie ne puisse être localisé, ainsi que la divergence de toute mesure d'intrication pour des observateurs localisés. Nous fournissons une solution à ces deux problèmes en démontrant l'équivalence générique qui existe entre une résolution spatiale finie des appareils de mesure et l'exclusion des degrés de liberté de haute énergie de la définition du système observé. Cette équivalence permet une interprétation épistémique du formalisme quantique standard décrivant les systèmes localisés non-relativistes et leurs corrélations, clarifiant ainsi l'origine des mesures finies d'intrication pour de tels systèmes. Le dernier chapitre explore un cadre théorique récemment introduit qui prédit l'existence de corrélations quantiques sans ordre causal défini. Procédant par analogie avec le cas des corrélations non-locales, nous présentons quelques principes informationnels contraignant la structure de ces corrélations dans le but de mieux en comprendre l'origine physique. / Recent works in foundations of quantum (field) theory and relativistic quantum information try to better grasp the interplay between the structure of quantum correlations and the constraints imposed by causality on physical operations. Chapter 1 is dedicated to the study of the conceptual implications of quantum nonlocality, a concept that subsumes that of entanglement in a certain way. We detail the recent information-theoretic approaches to understanding the structure of nonlocal correlations, and the issues the latter raise concerning the ability of local observers to isolate a system from its environment. Chapter 2 reviews in what sense imposing Poincaré invariance affects entanglement detection and quantification procedures. This invariance ultimately forces a description of all quantum systems within the framework of quantum field theory, which leads to the impossibility of localized finite-energy states and to the divergence of all entanglement measures for local observers. We provide a solution to these two problems by showing that there exists a generic equivalence between a finite spatial resolution of the measurement apparatus and the exclusion of high-energy degrees of freedom from the definition of the observed system. This equivalence allows for an epistemic interpretation of the standard quantum formalism describing nonrelativistic localized systems and their correlations, hence a clarification of the origin of the finite measures of entanglement between such systems. Chapter 3 presents a recent theoretical framework that predicts the existence of correlations with indefinite causal order. In analogy to the information-theoretic approaches to nonlocal correlations, we introduce some principles that constrain the structure of such correlations, which is a first step toward a clear understanding of their physical origin.