Investigaremos algumas propriedades dinâmicas e de transporte para um conjunto de partículas clássicas não interagentes em diversos sistemas físicos. Os sistemas descritos aqui, em sua maioria, apresentam estrutura mista no espaço de fase no sentido de que curvas invariantes do tipo spanning, mares de caos e ilhas periódicas estão presentes. A descrição de cada sistema será feita utilizando mapeamentos discretos não lineares. Detalharemos a forma de obter os mapeamentos assim como discutiremos algumas de suas propriedades dinâmicas. Expoentes de Lyapunov serão utilizados para caracterizar a região de caos nos sistemas. Hipóteses de escala são usadas para provar que certos observáveis, por exemplo a energia média ao longo de mares de caos, são invariantes de escala. Consideraremos também que quando uma partícula, ou de forma equivalente um conjunto delas atinge uma determinada altura no espaço de fases, ela pode escapar. Ao estudar o escape de partículas, vemos que o histograma do número de partículas que atingem uma certa altura (ou energia) h no espaço de fases em uma dada iterada n, ao qual observamos ser invariante de escala, cresce rapidamente até atingir um máximo e então tende à zero para n grande. Quando a altura h varia proporcionalmente a posição da primeira curva invariante spanning, podemos confirmar uma invariância de escala do histograma de frequências. O mesmo ocorre para a probabilidade de sobrevivência da partícula à dinâmica. Neste contexto, abordaremos os seguintes problemas: (1) Um guia de ondas senoidalmente corrugado; (2) Uma família de mapas Hamiltonianos bidimensionais que recupera diversos modelos; (3) Partículas confinadas em uma caixa com potenciais infinitos nas bordas e contendo em seu interior um poço de potencial dependente periodicamente do tempo; (4) Analisaremos um bilhar ovóide com dependência temporal introduzida através de giro, onde para certas condições observamos que este não apresenta um aparente crescimento ilimitado de energia (aceleração de Fermi), desta forma sendo um possível contra-exemplo da conjectura LRA. Esta tese é um resumo de 8 artigos que foram publicados em revistas internacionais. / We investigate some dynamical and transport properties for a set of non-interacting classical particles. The systems here described, for the most part, present mixed structure in the phase space in the sense that invariant spanning curves, chaotic seas and periodic islands are present. The dynamics of each model is described by using non-linear mappings. We show all the details to construct the mappings and discuss some of their dynamical properties including fixed points stability among others. Lyapunov exponents will be obtained to characterize the chaotic dynamics observed in the phase space. Moreover some scaling hypotheses are used to prove that certain observables, including the average energy, are scaling invariant. We consider also that when a particle or an ensemble of them reach a certain portion of the phase space, they can escape. When studying the escape, we see that the histogram for the number of particles that reach certain height (or energy) h in the phase space for the iteration n, for which we observe to be scaling invariant, grows quickly until reaching a maximum and then goes towards zero for large enough n. When changing the height h proportionally to the position of the first invariant spanning curve, we can confirm the scaling invariance. The same happens for the survival probability for a particle in the chaotic dynamics. In this way, we will discuss the following problems: (1) A corrugated waveguide; (2) A family of two-dimensional Hamiltonian mappings which can reproduce different scaling exponents; (3) Particles confined to bounce in the interior of a time-dependent potential well; (4) We will analyse a rotating oval billiard, where for certain conditions we observed that this system does not present the unbounded energy growth (Fermi acceleration), in this way it is a possible counterexample of the LRA conjecture. This thesis is as summary of eight papers already published.

Investigaremos algumas propriedades dinâmicas e de transporte para um conjunto de partículas clássicas não interagentes em diversos sistemas físicos. Os sistemas descritos aqui, em sua maioria, apresentam estrutura mista no espaço de fase no sentido de que curvas invariantes do tipo spanning, mares de caos e ilhas periódicas estão presentes. A descrição de cada sistema será feita utilizando mapeamentos discretos não lineares. Detalharemos a forma de obter os mapeamentos assim como discutiremos algumas de suas propriedades dinâmicas. Expoentes de Lyapunov serão utilizados para caracterizar a região de caos nos sistemas. Hipóteses de escala são usadas para provar que certos observáveis, por exemplo a energia média ao longo de mares de caos, são invariantes de escala. Consideraremos também que quando uma partícula, ou de forma equivalente um conjunto delas atinge uma determinada altura no espaço de fases, ela pode escapar. Ao estudar o escape de partículas, vemos que o histograma do número de partículas que atingem uma certa altura (ou energia) h no espaço de fases em uma dada iterada n, ao qual observamos ser invariante de escala, cresce rapidamente até atingir um máximo e então tende à zero para n grande. Quando a altura h varia proporcionalmente a posição da primeira curva invariante spanning, podemos confirmar uma invariância de escala do histograma de frequências. O mesmo ocorre para a probabilidade de sobrevivência da partícula à dinâmica. Neste contexto, abordaremos os seguintes problemas: (1) Um guia de ondas senoidalmente corrugado; (2) Uma família de mapas Hamiltonianos bidimensionais que recupera diversos modelos; (3) Partículas confinadas em uma caixa com potenciais infinitos nas bordas e contendo em seu interior um poço de potencial dependente periodicamente do tempo; (4) Analisaremos um bilhar ovóide com dependência temporal introduzida através de giro, onde para certas condições observamos que este não apresenta um aparente crescimento ilimitado de energia (aceleração de Fermi), desta forma sendo um possível contra-exemplo da conjectura LRA. Esta tese é um resumo de 8 artigos que foram publicados em revistas internacionais. / We investigate some dynamical and transport properties for a set of non-interacting classical particles. The systems here described, for the most part, present mixed structure in the phase space in the sense that invariant spanning curves, chaotic seas and periodic islands are present. The dynamics of each model is described by using non-linear mappings. We show all the details to construct the mappings and discuss some of their dynamical properties including fixed points stability among others. Lyapunov exponents will be obtained to characterize the chaotic dynamics observed in the phase space. Moreover some scaling hypotheses are used to prove that certain observables, including the average energy, are scaling invariant. We consider also that when a particle or an ensemble of them reach a certain portion of the phase space, they can escape. When studying the escape, we see that the histogram for the number of particles that reach certain height (or energy) h in the phase space for the iteration n, for which we observe to be scaling invariant, grows quickly until reaching a maximum and then goes towards zero for large enough n. When changing the height h proportionally to the position of the first invariant spanning curve, we can confirm the scaling invariance. The same happens for the survival probability for a particle in the chaotic dynamics. In this way, we will discuss the following problems: (1) A corrugated waveguide; (2) A family of two-dimensional Hamiltonian mappings which can reproduce different scaling exponents; (3) Particles confined to bounce in the interior of a time-dependent potential well; (4) We will analyse a rotating oval billiard, where for certain conditions we observed that this system does not present the unbounded energy growth (Fermi acceleration), in this way it is a possible counterexample of the LRA conjecture. This thesis is as summary of eight papers already published.

The main topic of this thesis is analysis of an unidentified Galactic TeV gamma-ray source, MGRO J1908+06, discovered by Milagro instrument in 2007. We analyzed 54 hours of observational data from the Very Energetic Radiation Imaging Telescope Array System (VERITAS), a ground-based gamma-ray observatory in southern Arizona comprised of an array of four Cherenkov Telescopes that reconstructs the energy and direction of astrophysical gamma-rays by imaging Cherenkov light emitted by energetic particles in air showers produced by the primary gamma-rays. MGRO J1908+06 is located between a supernova remnant SNR G40.5-0.5 and a young, energetic pulsar PSR J1907+0602. We studied the energy dependent morphology of the TeV emission from the source and measured the source extent and spectrum. The source extends well past the boundary of the SNR and is not correlated with strong radio continuum or molecular line emission which likely excludes an origin for the emission as solely due to the SNR. While emission in the 0.5-1.25 TeV band was centered around the pulsar, higher energy emission was observed near the supernova remnant. This morphology is opposite that observed in other pulsar wind nebulae. We proposed two models for the high energy emission located well away from the pulsar but close to the SNR: (1) shock acceleration at the shock front created by an interaction between the pulsar wind and the dense gas at the edge of the SNR or (2) molecular clouds around the SNR provides seed photons with energies higher than those from Cosmic Microwave Backgrounds for inverse Compton scattering. The former model can be tested by looking for molecular emission lines that trace shocks and by measuring the pulsar velocity. In addition, we investigated the gamma-ray emission from the nova explosion of V407 Cygni that occurred in March 2010. The Fermi-LAT observed this event in the energy range of E >100 MeV. The origins of the gamma-ray emission that the Fermi-LAT team proposed are either protons (hadronic model) or electrons (leptonic model), both of which were accelerated at the nova shock via the Fermi acceleration mechanism. We did not consider their leptonic model because no TeV gamma-ray emission is predicted. Their hadronic model can generate TeV gamma-rays with the modeled parameters. We found no evidence for TeV emission. We showed that with the flux upper limit calculated using the VERITAS data imposes constraints on the extension of the proton spectrum at high energies.

Made available in DSpace on 2014-06-11T19:25:32Z (GMT). No. of bitstreams: 0 Previous issue date: 2011-02-16Bitstream added on 2014-06-13T18:28:57Z : No. of bitstreams: 1 livorati_alp_me_rcla.pdf: 934954 bytes, checksum: 1373f1521e1656d8b2c2126db694e3f5 (MD5) / Neste trabalho investigamos a dinâmica de uma partícula confinada dentro de um bilhar stadium-like. Em uma primeira aproximação, consideramos as fronteiras do bilhar estáticas, encontramos um mapeamento bidimensional não linear que preserva a área no espaço de fases e que descreve a dinâmica de uma partícula clássica sofrendo reflexões especulares com a fronteira. Variando os parâmetros geométricos da fronteira, pudemos observar uma transição de caos global para caos misto, quando os pontos fixos perdem sua estabilidade. Tal transição é caracterizada pelo mecanismo desfocalizador do bilhar, pela análise estatística do desvio do ângulo médio ψ e pela invariância de escala do expoente de Lyapunov máximo. Baseado nesses itens, descrevemos o bilhar através de um mapeamento genérico que apresenta transição semelhante. Introduzimos uma perturbação temporal na fronteira e consideremos a dinâmica de duas maneiras distintas; (i) onde a partícula pode sofrer colisões sucessivas com a mesma componente e (ii) colisões indiretas. Através da linearização do mapeamento obtido na versão estática, encontramos um valor crítico de velociade de ressonância, onde velocidades iniciais com valores menores do que esse valor crítico, sofrem um decréscimo em sua velocidade devido ao fenômeno de stickiness. Contudo, se a velocidade inicial é maior do que a velocidade crítica de ressonância, temos um comportamento típico de aceleração de Fermi, onde conseguimos descrever esse crescimento ilimitado de energia da partícula através de hipóteses de escala. Quando a disipação é introduzida via colisões inelásticas da partícula com a fronteira móvel, observamos... / In this work we consider the dynamics of a point particle confined inside a stadium-like billiard. In a first approximation, and considering static boundaries, we construct a two-dimensional nonlinear area preserving mapping. Ranging the control parameters, we observed a transition from partial chaos to global, when the fixed points loose their stability. This transition is characterized by the defocusing mechanism. A statistical analysis of the deviation of the average angle ψ, and the scaling invariance of the maximal Lyapunov exponent, give support to this transition. We also introduced a perturbation to the boundaries. Linearizing the unperturbed mapping, we found a critical value for the resonant velocity. For initial velocities smaller than the critical one, we observe a decreasing of the particle’s velocity caused by a stickiness phenomenum. However, when initial velocity is larger than the resonant one, we observe a typical behavior of Fermi acceleration, where we describe this unlimited energy growth by using scaling arguments. When dissipation is introduced via inelastic collisions, we observe a... (Complete abstract click electronic access below)

Stochastic differential equations are becoming a popular tool for modeling the transport and acceleration of cosmic rays in the heliosphere. In diffusive shock acceleration, cosmic rays diffuse across a region of discontinuity where the up- stream diffusion coefficient abruptly changes to the downstream value. Because the method of stochastic integration has not yet been developed to handle these types of discontinuities, I utilize methods and ideas from probability theory to develop a conceptual framework for the treatment of such discontinuities. Using this framework, I then produce some simple numerical algorithms that allow one to incorporate and simulate a variety of discontinuities (or boundary conditions) using stochastic integration. These algorithms were then modified to create a new algorithm which incorporates the discontinuous change in diffusion coefficient found in shock acceleration (known as Skew Brownian Motion). The originality of this algorithm lies in the fact that it is the first of its kind to be statistically exact, so that one obtains accuracy without the use of approximations (other than the machine precision error). I then apply this algorithm to model the problem of diffusive shock acceleration, modifying it to incorporate the additional effect of the discontinuous flow speed profile found at the shock. A steady-state solution is obtained that accurately simulates this phenomenon. This result represents a significant improvement over previous approximation algorithms, and will be useful for the simulation of discontinuous diffusion processes in other fields, such as biology and finance.

Made available in DSpace on 2014-06-11T19:25:31Z (GMT). No. of bitstreams: 0 Previous issue date: 2010-02-19Bitstream added on 2014-06-13T20:53:31Z : No. of bitstreams: 1 abud_cv_me_rcla.pdf: 2091525 bytes, checksum: f8a3b24150a2a718ad53ff294a3c6844 (MD5) / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES) / Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP) / Procuramos nesta dissertação, entender e desenvolver estudos relacionados com o movimento de trajetórias caóticas num sistema dinâmico não linear. Esses estudos, envolvem uma abordagem sobre a quantificação de recorrências de trajetórias a uma região e sobre o transporte no espaço de fases. Nós escolhemos como modelo o bilhar anular em duas configurações: primeiramente com as fronteiras estáticas e posteriormente, uma dependência temporal (pulsante) e introduzida. Inicialmente reproduzimos os resultados sobre aprisionamentos para caso do bilhar estático, existentes na literatura, a fim de ganharmos experiência para estudar o sistema pulsante. Nesse caso, a topologia dos dois planos de fases possíveis constituídos de variáveis canônicas, apesar de bastante complexas, apresentaram resultados interessantes. Os principais resultados obtidos foram: a observação de regiões de aprisionamentos nos dois planos de fases conectadas entre si; a aceleração de Fermi caracterizada por vários regimes anômalos; ( uma explicação para a diferença desses regimes e dada por aprisionamentos no plano do bilhar) e a evolução do espaço de fases, dito geométrico, que tende a se recuperar conforme a velocidade relativa partícula-fronteira aumenta. Estudamos ainda os efeitos de dissipação no sistema pulsante através de colisões inelásticas. Os resultados indicam que qualquer dissipação desse tipo, independente da magnitude, é suficiente para saturar o crescimento de energia. Porém, em situações especiais essa mesma dissipação pode ser usada para que na média o sistema ganhe energia. / We reach in this dissertation, understand and develop studies related to the motion of the chaotic trajectories in a non-linear dynamical system. These studies require an approach on the quanti cation of the recurrences of trajectories to a region and on the transport in the phase space. We choose as a model the annular billiard with two con gurations: rstly with the static boundaries and next, a time-dependent (pulsating)is introduced. Initially we reproduced some results about stickiness in the static case in order to gain experience to study the pulsating system. In such case the topology of the two possible phase space of canonical variables, showed interesting results. The main results were: the observation of sticky regions in both connected phase spaces; the Fermi acceleration characterized by di erent anomalous regimes ( an explanation to this diferent regimes is given by the stickiness on the billiard plane) and the evolution of the phase space, called geometric, which tends to be recovered as the relative velocity particle-boundary increases. We also studied the e ects of dissipation in the pulsating system through inelastic collisions. The results show that this kind of dissipation, regardless of its magnitude, is enough to saturate the energy growth. However, in special situations the mean average of the system can increase with the introduction of inelastic collisions.

Les preuves pour l'existence de la matière noire (MN), sous forme d'une particule inconnue qui rempli les halos galactiques, sont issues d'observations astrophysiques et cosmologiques: son effet gravitationnel est visible dans les rotations des galaxies, des amas de galaxies et dans la formation des grandes structures de l'univers. Une manifestation non-gravitationnelle de sa présence n'a pas encore été découverte. L'une des techniques les plus prometteuse est la détection indirecte de la MN, consistant à identifier des excès dans les flux de rayons cosmiques pouvant provenir de l'annihilation ou la désintégration de la MN dans le halo de la Voie Lactée. Les efforts expérimentaux actuels se focalisent principalement sur une gamme d'énergie de l'ordre du GeV au TeV, où un signal de WIMP (Weakly Interacting Massive Particles) est attendu. L'analyse des mesures récentes et inédites des rayons cosmiques chargés (antiprotons, électrons et positrons) et leurs émissions secondaires et les améliorations des modèles astrophysiques sont présentées.Les données de PAMELA sur les antiprotons contraignent l'annihilation et la désintégration de la MN de manière similaire (et même légèrement meilleurs) que les contraintes les plus fortes venant des rayons gamma, même dans le cas où les énergies cinétiques inférieures à 10 GeV sont écartées. En choisissant des paramètres astrophysiques différents (modèles de propagation et profils de MN), les contraintes peuvent changer d'un à deux ordres de grandeur. Pour exploiter la totalité de la capacité des antiprotons à contraindre la MN, des effets précédemment négligés sont incorporés et se révèlent être importants dans l'analyse des données inédites de AMS-02 : ajouter les pertes d'énergie, la diffusion dans l'espace des moments et la modulation solaire peut modifier les contraintes, même à de hautes masses. Une mauvaise interprétation des données peut survenir si ces effets ne sont pas pris en compte. Avec les flux de protons et d'hélium exposé par AMS-02, le fond astrophysique et ces incertitudes du ratio antiprotons sur protons sont réévalués et comparés aux données inédites de AMS-02. Aucune indication pour un excès n'est trouvé. Une préférence pour un halo confinant plus large et une dépendance en énergie du coefficient de diffusion plus plate apparaissent. De nouvelles contraintes sur l'annihilation et la désintégration de la MN sont ainsi dérivés.Les émissions secondaires des électrons et des positrons peuvent aussi contraindre l'annihilation et la désintégration de la MN dans le halo galactique : le signal radio dû à la radiation synchrotron des électrons et positrons dans le champs magnétique galactique, les rayons gamma des processus de bremsstrahlung avec le gas galactique et de Compton Inverse avec le champs radiatif interstellaire sont considérés. Différentes configurations de champs magnétique galactique et de modèles de propagation et des cartes de gas et de champs radiatif interstellaire améliorés sont utilisées pour obtenir des outils permettant le calculs des émissions synchrotrons et bremsstrahlung venant de MN de type WIMP. Tous les résultats numériques sont incorporés dans la dernière version du Poor Particle Physicist Coookbook for DM Indirect Detection (PPPC4DMID).Une interprétation d'un possible excès dans les données de rayons gamma de Fermi-LAT au centre galactique comme étant dû à l'annihilation de MN en canaux hadronique et leptonique est analysée. Dans une approche de messagers multiples, le calcul des émissions secondaires est amélioré et se révèle être important pour la détermination du spectre pour le canal leptonique. Ensuite, les limites provenant des antiprotons sur l'annihilation en canal hadronique contraignent sévèrement l'interprétation de cet excès comme étant dû à la MN, dans le cas de paramètres de propagation et de modulation solaire standards. Avec un choix plus conservatif de ces paramètres elles s'assouplissent considérablement. / Overwhelming evidence for the existence of Dark Matter (DM), in the form of an unknownparticle filling the galactic halos, originates from many observations in astrophysics and cosmology: its gravitational effects are apparent on galactic rotations, in galaxy clusters and in shaping the large scale structure of the Universe. On the other hand, a non-gravitational manifestation of its presence is yet to be unveiled. One of the most promising techniques is the one of indirect detection, aimed at identifying excesses in cosmic ray fluxes which could possibly be produced by DM annihilations or decays in the Milky Way halo. The current experimental efforts mainly focus in the GeV to TeV energy range, which is also where signals from WIMPs (Weakly Interacting Massive Particles) are expected. Focussing on charged cosmic rays, in particular antiprotons, electrons and positrons, as well as their secondary emissions, an analysis of current and forseen cosmic ray measurements and improvements on astrophysical models are presented. Antiproton data from PAMELA imposes contraints on annihilating and decaying DM which are similar to (or even slightly stronger than) the most stringent bounds from gamma ray experiments, even when kinetic energies below 10 GeV are discarded. However, choosing different sets of astrophysical parameters, in the form of propagation models and halo profiles, allows the contraints to span over one or two orders of magnitude. In order to exploit fully the power of antiprotons to constrain or discover DM, effects which were previously perceived as subleading turn out to be relevant especially for the analysis of the newly released AMS-02 data. In fact, including energy losses, diffusive reaccelleration and solar modulation can somewhat modify the current bounds, even at large DM masses. A wrong interpretation of the data may arise if they are not taken into account. Finally, using the updated proton and helium fluxes just released by the AMS-02 experiment, the astrophysical antiproton to proton ratio and its uncertainties are reevaluated and compared to the preliminarly reported AMS-02 measurements. No unambiguous evidence for a significant excess with respect to expectations is found. Yet, some preference for thicker halos and a flatter energy dependence of the diffusion coefficient starts to emerge. New stringed constraints on DM annihilation and decay are derived. Secondary emissions from electrons and positrons can also be used to constrain DM annihilation or decay in the galactic halo. The radio signal due to synchrotron radiation of electrons and positrons on the galactic magnetic field, gamma rays from bremsstrahlung processes on the galactic gas densities and from Inverse Compton scattering processes on the interstellar radiation field are considered. With several magnetic field configurations, propagation scenarios and improved gas density maps and interstellar radiation field, state-of-art tools allowing the computaion of synchrotron and bremssttrahlung radiation for any WIMP DM model are provided. All numerical results for DM are incorporated in the release of the Poor Particle Physicist Coookbook for DM Indirect Detection (PPPC4DMID). Finally, the possible GeV gamma-ray excess identified in the Fermi-LAT data from the Galactic Center in terms of DM annihilation, either in hadronic or leptonic channels is studied. In order to test this tantalizing interprestation, a multi-messenger approach is used: first, the computation of secondary emisison from DM with respect to previous works confirms it to be relevant for determining the DM spectrum in leptonic channels. Second, limits from antiprotons severely constrain the DM interpretation of the excess in the hadronic channel, for standard assumptions on the Galactic propagation parameters and solar modulation. However, they considerably relax if more conservative choices are adopted.