Utilizando um laser de corante pulsado sintonizado em 5460.7 R excitamos seletivamente os níveis rovibrônicos v=25 j=34, v=25 J=28, v=27 J=108 e v=28 J=45 do estado eletrônico B 3110+da mo fécula de iodo. A partir destes níveis, utilizando um segundo laser de corante sintonizãvel na região de 4130-4400 R e sincronizado com o primeiro, estudamos as transições para os estados eletrônicos com energia acima de 41000 cm-1 que normalmente são inacessíveis por absorção de um único fóton a partir d.o estado fundamental. As séries de transições observadas podem ser identificadas como ab sorção para um único estado eletrônico de simetria 0g + e caráter iônico. / With a pulsed dye laser tuned in 5460.7 R we selectively excite the rovibronic leveis v=25 J=34, v=25 J=28, v=27 J=108 and v=28 J=45 of the 12 B 3110 + electronic state. With a second dye laser, tunable in the range 4130-4400 R and synchronized with the first, we search for transitions from the leveis populated in the B 3116 +state to leveis of the electronic states with energy above 41000 cm 1, that normally are inaccessible by single absorbtion from the ground state. The observed transitions can be assigned to a single ion-pair state with 0g + symmetry.

Executantes habilidosos desenvolvem uma capacidade de perceber e processar uma vasta quantidade de informações com velocidade e precisão, bem como o de realizar ajustes eficientes quando necessário (Schmidt e Wrisberg 2001). Corticalmente, para obter esse controle mais refinado, a integração sensoriomotora é fundamental. Essa integração consiste no contínuo processamento, pelo sistema motor, das aferências sensoriais que preparam para o ato motor e melhoram a execução de atividades de controle motor fino (Minc et al., 2010). Atividades físicas que diferem exatamente em relação a como seus praticantes necessitam processar as informações sensoriais para gerar o movimento, devem resultar em integrações sensoriomotoras distintas. Este estudo tem como objetivo analisar a atividade eletroencefálica de indivíduos com habilidades percepto-motoras distintas (indivíduos altamente habilidosos com treinamento em dança/TD e treinamento em vôlei/TV), evocados por tarefas de simulação de ação. A amostra do presente estudo foi intencional e composta por 14 participantes destros, cada grupo foi constituído por 07 mulheres com idade entre 18 anos e 29 anos. Através de EEG, foram extraídos os parâmetros de média de energia (processamento cortical ao longo do tempo), amplitude (número de elementos neuronais envolvidos na tarefa) e frequência (ritmo oscilatório predominante) na banda alfa e gama do sinal cerebral nos pontos C3, C4, Cz (córtex motor primário), F3 (área motora suplementar esquerda), F7 (córtex pré-motor esquerdo), P3, P4 e Pz (córtex parietal), evocados por tarefas envolvendo a observação e imaginação de gestos específicos dos dois treinamentos e gestos considerados como neutros. Os principais resultados encontrados forneceram evidências de que o grupo TD apresentou, nas tarefas de dança, um maior processamento cortical ao longo do tempo nos pontos referentes ao córtex motor primário (Minc et al., 2010), córtex pré-motor (Freund e Hummelsheim, 1984) e área motora suplementar (Serrien et al.,2002) esquerdos; maior número de elementos neuronais envolvidos na tarefa no ponto referente ao córtex motor primário esquerdo; diferenças na principal componente da frequência no ritmo alfa no córtex motor primário esquerdo; e diferenças na principal componente da frequência no ritmo gama no córtex motor primário direito. Nas tarefas referentes ao treinamento em vôlei, o grupo TV apresentou menor processamento ao longo do tempo nos pontos parietal (Wolpert et al., 1998); menor número de elementos neuronais envolvidos na tarefa nos pontos referentes aos córtices motor primário e pré-motor esquerdos e diferença na principal componente da frequência no ritmo gama no córtex motor primário esquerdo. Nas tarefas consideradas como neutras foram encontradas diferenças entre os grupos no córtex motor primário direito no ritmo alfa e no córtex parietal direito no ritmo gama. Os resultados encontrados no presente estudo nos parâmetros que representam o processamento cortical, que refletem o número de elementos neuronais envolvidos na tarefa e que representam o ritmo oscilatório predominante demonstraram claramente que as regiões corticais envolvidas na integração sensoriomotora apresentaram diferenças na forma como os dois grupos processaram a informação sensorial e prepararam o gesto motor. Tomados em conjunto, esses resultados demonstram que cada grupo apresentou um padrão constante de processamento sensoriomotor, independente da tarefa. Essas evidências nos permitem concluir que indivíduos com diferentes habilidades percepto-motoras apresentam integrações sensoriomotoras distintas. / Skilled performers develop an ability to perceive and process a vast amount of information with speed and accuracy, as well as to perform efficient adjustments when necessary (Schmidt and Wrisberg 2001). Cortically to achieve this finer control, sensorimotor integration is the key. This integration consists in continuous processing, by the motor system, the sensory afferents that prepare for the motor act and improve the performance of activities for fine motor control (Minc et al., 2010). Physical activities that differ over exactly how its practitioners need to process sensory information to generate movement should result in distinct sensorimotor integration. This study aims to analyze the electroencephalography activity of individuals with perceptual-motor skills (highly skilled individuals with training in dance/TD and training in volleyball/TV) evoked by action simulation tasks. The study sample was intentional and composed of 14 right-handed participants; each group consisted of 07 women aged between 18 and 29 years. Through EEG were extracted parameters mean energy (cortical processing over time), amplitude (number of neural elements involved in the task) and frequency (oscillating rhythm predominant) in alpha and gamma bands in the brain signal points C3, C4, Cz (primary motor cortex), F3 (left supplementary motor area), F7 (left premotor cortex), P3, P4 and Pz (parietal cortex), evoked by tasks involving observation and imagination of specific gestures of both training and gestures considered neutral. The main results provided evidence that the TD group presented the tasks of dance, a higher cortical processing over time in points for the primary motor cortex (Minc et al., 2010), left premotor cortex (Freund and Hummelsheim, 1984) and left supplementary motor area (Serrien et al. 2002); greater number of neural elements involved in the task at point for the left primary motor cortex; differences in the main frequency component of the alpha rhythm in the left primary motor cortex , and differences in the main component of the frequency gamma in the right primary motor cortex. In tasks relating to training volleyball, VT group showed lower processing over time at parietal points (Wolpert et al. 1998); smaller number of neural elements involved in the task at points related to left primary motor cortex and left premotor and main component difference in the frequency gamma in the left primary motor cortex. In the tasks considered neutral differences were found between groups in the right primary motor cortex in the alpha rhythm and in the right parietal cortex in the gamma rhythm. The results found in this study at the parameters that represent the cortical processing, that reflect the number of neuronal elements involved in the task and which represent the predominant rhythm oscillatory clearly demonstrated that cortical regions involved in sensorimotor integration showed differences in how the two groups processed sensory information and prepared the gesture motor. Taken together, these results demonstrate that each group had a consistent pattern of sensorimotor processing, regardless of the task. This evidence allows us to conclude that individuals with different perceptual-motor skills have distinct sensorimotor integration.

Submitted by Danielle Karla Martins Silva (danielle.martins@ufpe.br) on 2015-03-12T15:00:27Z No. of bitstreams: 2 license_rdf: 1232 bytes, checksum: 66e71c371cc565284e70f40736c94386 (MD5) TESE Milrian da Silva Mendes.pdf: 9715367 bytes, checksum: d2f422f9ea59e0b5381776bcfc1de025 (MD5) / Made available in DSpace on 2015-03-12T15:00:27Z (GMT). No. of bitstreams: 2 license_rdf: 1232 bytes, checksum: 66e71c371cc565284e70f40736c94386 (MD5) TESE Milrian da Silva Mendes.pdf: 9715367 bytes, checksum: d2f422f9ea59e0b5381776bcfc1de025 (MD5) Previous issue date: 2013 / Nesta tese estudamos o mecanismo de extração da informação armazenada em uma memória quântica constituída de um ensemble de átomos de césio aprisionados e resfriados em uma armadilha magneto-ótica. Consideramos memórias contendo uma única excitação de um estado atômico coletivo, mapeada em um único fóton durante o processo de leitura. Os processos de geração, deteção, e caracterização dos fótons no sistema experimental são detalhados. Observamos correlações não clássicas entre os campos óticos gerados no sistema. Resultados são obtidos na presença e na ausência dos campos magnéticos da armadilha. Além disso, apresentamos uma teoria para o pacote de onda do fóton extraído, conduzindo a uma expressão analítica que depende dos parâmetros principais do problema. Comparamos a teoria com uma série de situações experimentais e um acordo quantitativo satisfatório é obtido. Desta forma, estudamos sistematicamente a saturação e o espectro do processo de leitura, elucidando ainda o papel da superradiância no sistema. Utilizando uma alta profundidade ótica, observamos a formação da condição de transparência eletromagneticamente induzida no meio através do desaparecimento de uma estrutura característica no espectro de leitura. Tal estrutura é representada pela diminuição da probabilidade de extração do fóton em torno da ressonância, desaparecendo para altas potências de leitura. Estudamos ainda o comportamento da probabilidade condicional de geração de um par de fótons variando a profundidade ótica do meio e, consequentemente, a própria condição de superradiância.

O estudo da envoltória de novas clássicas permite diagnosticar com precisão aceitável as condições físicas nos estágios avançados do fenômeno de nova. A Nova Velorum 1999, foi a mais brilhante em 24 anos, sendo um ótimo caso para este estudo. Trata-se de uma nova de neônio, formada em um sistema onde se acredita que a primária seja uma anã branca massiva de O-Ne-Mg. Neste trabalho seguimos a evolução espectral deste objeto nos primeiros três anos após sua erupção verificando um aumento da ionização aproximadamente 200 dias após o máximo visual. A partir de 565 dias após o máximo observamos um aumento do continuo azul que provavelmente reflete o restabelecimento do disco de acréscimo. Derivamos uma velocidade de ejeção do envelope da ordem de aproximadamente 1600 km/s e a escala de tempo de amortecimento no meio interestelar (aproximadamente 10 anos). Os principais resultados desta análise sugerem uma envoltória heterogênea sem simetria esférica. Estimamos também a densidade e temperatura eletrônica da envoltória bem como a evolução da temperatura da fonte central. Com estes dados estimamos limites inferiores para as abundâncias numéricas de He, N, O, Ne, S, Ar e Fe, confirmando ser uma nova de neônio. As abundâncias de oxigênio e neônio foram relativamente baixas se comparadas a outras novas de neônio, embora a abundância numérica deste último tenha sido a maior entre os elementos pesados desta nova. Outro fato relevante foi encontrar uma abundância de ferro bastante alta se comparada com o valor solar. / The study of the classical novae shells allows to diagnosis with accuracy the physical conditions of the advanced phases in nova phenomenum. Nova Velorum 1999 (V382 Vel) was the brightest nova in the last 24 years being a good candidate to this study. This object probably is a neon nova wich is formed in a system where, according to theoretical models, there is an O-Ne-Mg white dwarf primary. In this work we present the spectral evolution of Nova Velorum 1999 shell during the first 3 years after the visual maximum. We verified an increase in ionization about 200 days after the outburst. In addition, 565 days after the outburst an increase in the blue continuum was observed, which is probably due to the reestablishment of the accretion disk. A shell ejection velocity of 1600 km/s and a damping time-scale of about 10 years were observed. The main results suggested that the shell is inomogeneous and non-spherical. We also estimated shell eletronic temperatures and densities as well as the central source temperature. With these data we estimated lower limits to He, N, O, Ne, S, Ar and Fe numerical abundances. The results confirmed that this nova is a neon nova. The oxygen and neon abundance limits were relatively low when compared to other neon nova, but the neon abundances in this nova were high when compared with other heavy element abundances in this object. It was also found that iron is enhanced in the shell, when compared to solar value.

Submitted by Rosivalda Pereira (mrs.pereira@ufma.br) on 2017-06-07T18:20:05Z No. of bitstreams: 1 PauloPinheiro.pdf: 740954 bytes, checksum: 7a586404eb9969daad1f2c29dbbf0b42 (MD5) / Made available in DSpace on 2017-06-07T18:20:05Z (GMT). No. of bitstreams: 1 PauloPinheiro.pdf: 740954 bytes, checksum: 7a586404eb9969daad1f2c29dbbf0b42 (MD5) Previous issue date: 2009-07-06 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES) / Fundação de Amparo à Pesquisa e ao Desenvolvimento Científico e Tecnológico do Maranhão (FAPEMA) / The possibility of spontaneous breaking of Lorentz symmetry in the context of string theory appeared in 1990´s as an element capable to direct new ways for developing physics at Planck scale. Possible breaking of Lorentz invariance is seen as a characteristic of the physics beyond the usual Model Standard, that forbids such breaking in its structure. The observation of Lorentz breaking (LV) at lower energies can be seen as an evidence of occurrence of Lorentz spontaneous breaking at Planck scale, with important consequence for the development of the quantum gravitation theory. This work aims at studying the LV effects in a regime of low energies, more necessarily in the context of the Maxwell electrodynamics, in the presence of the CPT-even term (W∝υρφF∝υFρφ) of the standard model extension. In the first part of the work, we deal with the electrodynamics stemming from the parity-odd sector of the tensor W∝υρφ, where the electric and magnetic sectors are connected by the breaking parameter (violating vector k). The method of Green is then used to yield the classic solutions for this electrodynamics. It is observed that Lorentz-violating coefficients contribute in first order for the electric and magnetic sectors. An experiment of feasible accomplishment in laboratory is considered for stipulating an upper bound for the background magnitude (k < 10−16). In the sequel we deal with the electrodynamics stemming from the parity-even sector of the tensor W∝υρφ. The solutions for the electric and magnetic sector are attained similarly by the Green method. With such solutions, we are able to impose an upper bound on the parameters: (eκe−)ib < 2.9 × 10−20. Finally, we evaluate the gauge propagator of this theory, both for the parity-even and the parity-odd sectors. We then use it to analyze the stability, causality and unitary of this model. Keywords: Maxwell electrodynamics, Lorentz symmetry, Classical solutions, / A possibilidade de violação espontanea da simetria de Lorentz no contexto da teoria das cordas surgiu nos anos 90 como um elemento capaz de direcionar novos caminhos para a fısica na escala de Planck. Possíveis violações da invariância de Lorentz são vistas como uma caracterıstica da fısica além do Modelo Padrão usual, que proíbe tal violação em sua estrutura. A observação da violação de Lorentz (VL) em mais baixas energias pode ser vista como uma evidência da ocorrência do mecanismo de quebra espontanea na escala de Planck, com importantes consequências para o desenvolvimento da teoria da gravitação quantica. Este trabalho propõe-se a estudar efeitos da VL em um regime de baixas energias, mais precisamente no contexto da eletrodinâmica de Maxwell modificada pelo termo CPT-par (W∝υρφF∝υFρφ) do Modelo Padrão Estendido. Na primeira parte do trabalho, tratamos a eletrodinamica resultante do setor de paridade ímpar do tensor W∝υρφ, em que os setores elétrico e magnético são acoplados pelo parâmetro de quebra (vetor violador k). Usa-se então o método de Green para obter as soluções clássicas desta eletrodinâmica. Observa-se que os coeficientes violadores de Lorentz contribuem em primeira ordem para os setores elétrico e magnético. Propõe-se um experimento de factível realização em laboratório, para estipular um limite superior para a magnitude do ”background”(k < 10−16). Tratamos em seguida a eletrodinâmica advinda do setor de paridade par. As soluções para o setor elétrico e magnético são obtidas similarmente pelo método de Green. Com tais soluções, conseguimos impor um limite superior sobre os parâmetros: (eκe−)ib < 2.9 × 10−20. Por fim, calculamos o propagador desta teoria, tanto para o setor paridade-par quanto para o setor paridade ímpar, e usamo-lo para obter informações sobre a causalidade, estabilidade e unitariedade do modelo.

Der Energietransfer von elektronischer Energie in Schwingungs- und Rotationsenergie ist einer der elementarsten nichtadiabatischen Prozesse. Obwohl diese Prozesse seit langen untersucht werden, sind sie nicht im Detail verstanden. Das StoBsystem Na+H2 hat dabei Modellcharakter. Natrium ist ein Wasserstoffãhnliches Atom mit einem s-Elektron auf der auBersten Schale, und H2 ist das einfachste Molekül überhaupt. Ab initio Potentialflachen- Berechnungen sind deshalb mit guter Genauigkeit moglich und auch durchgef iihrt worden. Die elektronische Energie des Na-Atoms von 2,1eV wird dabei durch einen nichtadiabatischen Stoi3 in Schwingungs- und Rotationsenergie des H2-Moleküls iibertragen; ein Vorgang der auch als "Quenchen" bekannt ist. Von essentieller Bedeutung ist es, welche Schwingungs- und Rotationszustãnde besetzt werden. Es gab bisher keine experimentelle Untersuchung, bei der die interne Energieverteilung des H2-Moleküls direkt untersucht wurde. Der Grund dafür ist der, daB konventionelle Techniken zum Nachweis von H2 nicht geeignet sind. Aufgabe der vorliegenden Arbeit war es, erstmals CARS (Kohirente Antistokes-Raman-Streuung) für die oben genannten StoBprozesse einzusetzen und nachzuprüfen, wie gut sich diese Technik anwenden IãBt. CARS ist seit vielen Jahren bekannt, hat jedoch erst in der letzten Zeit durch die Entwicklung von intensiven gepulsten Laser mit geringer Bandbreite sehr an Bedeutung gewonnen. Insbesonders CARS an Wasserstoff wurde intensiv untersucht, nicht jedoch mit Beimischung von Natrium. Im vorliegenden Gasgemisch aus Natrium und H2 erzeugt Natrium durch seine energetisch sehr niedrigen elektronischen Zustãnde einen nichtresonanten Untergrund, der die Nachweis-Wahrscheinlichkeit so stark reduzieren kann, daí3 eine sinnvolle Anwendung nicht mehr mõglich sein konnte. Es ist gelungen zu zeigen, dali trotz eines enormen nichtresonanten Untergrundes eine sehr hohe Nachweiswahrscheinlichkeit mit CARS erzielt werden kann. Sie betrãgt für H2 mit Na im Grundzustand 1012 Teilchen pro cm3 und Quantenzustand und in Gegenwart von angeregtem Natrium 1013 Teilchen pro cm 3 und Quantenzustand. Mit der neu gebauten CARS-Apparatur wurde eine Reihe von neuen Experimenten durchgef a) Es konnte erstmals direkt die Schwingungsverteilung von H2 nach dem Quenchprozel3 bestimmt werden. Es konnte die absolute Besetzung der Schwingungszustãnde v=3,2 und 1 bestimmt werden. Eine Besetzung bei v=4 wurde nicht beobachtet. b) Mit einer zeitabhãngigen CARS-Messung konnte erstmalig die Schwingungsrelaxation der genannten Schwingungszustãnde gemessen und mit einem Ratengleichungsmodell die Ratenkonstanten mit sehr guter Obereinstimmung bestimmt werden. c) Aus der Besetzung der Schwingungszustãnde laBt sich ein absoluter Querschnitt für den Quenchprozei bestimmen. In Vergleich zu den klassischen Fluoreszenzmethoden wird dabei nicht die Abnahme der Fluoreszenz durch den StoBgasdruck bestimmt, sondern die direkte Besetzung des Quenchers nachgewiesen. Diese Methode wird erstmalig vorgestellt. Sie ist viel weniger empfindlich auf Verunreinigungen. Der erhaltene Wert für den Quenchquerschnitt betragt aq=12A2. d) Es laBt sich auch eine Aussage Uber die Rotationsbesetzung nach dem QuenchprozeB machen. Sie konnte bestimmt werden und ist nahezu thermisch, d.h. sie hat dieselbe Temperatur wie die Zelle. Dieses Ergebnis ist in übereinstimmung mit theoretische Modellen und bestãtigt die Vorstellung, dali das p-Orbital des angeregten Natriums sich bei Annãherung an das H2-Molekül ausrichtet und der QuenchprozeB vorwiegend in C2v -Symmetrie ablauft. Es ist gelungen zu zeigen, daB CARS sich erfolgreich für Untersuchungen an nichtadiabatischen StoBprozessen einsetzen laBt. Dadurch wurde erstmals erzielt. / Nonadiabatic collisions between atoms and molecules have drawn a large amount of attention in theoretical and experimental studies. In particular, the transfer of electronic energy of an atom to the vibrational, rotational and translational energy of a diatomic molecule (also called electronic quenching) can be considered an important fundamental process of this type and is thus extensively investigated. We study the Na + 112 as a model collision system for experimental and theoretical reasons since ab initio potential surfaces are currently available, enabling comparison of experimental results with theoretical calculations. We apply a new experimental technique in the field of nonadiabatic processes to obtain a more detailed understanding of these energy transfer processes. We use Coherent Anti-Stokes Raman Spectroscopy (CARS) to measure directly the internai energy distribution of H2 molecules produced by quenching of Na in the first excited state (3 2P112). Although CARS has been used to detect 112 among other species, it has never been applied to gaseous mixtures with H2 and atomic or molecular sodium. Sodium with its low lying electronic states produces a strong nonresonant background that strongly reduces the sensitivity of CARS. With a new constructed apparatus a sensitivity for H2 of 1012 particles per cm3 and quantum state in the presence of ground state sodium was achieved and 1013 particles per cm3 and quantum state with excited sodium. The following results were obtained: 1. The absolute population of vibrational leveis up to v=3 has been obtained and was found to be extremly nonthermal. The state distribution is, however, in good agreement with the available theoretical predictions. 2. With a time resolved CARS experiment we monitored the vibrational relaxation of these states. For this experiment we use excited sodium as an effective way to produce vibrationally hot hydrogen. With a simple model, we determined for the first time the vibrational relaxation time for v=3, 2 and 1 to be 2.4ps, 3.4ps and 31ps respectively. 3. From the measured absolute populations of the vibrational states of hydrogen the absolute cross section for the quenching process can be determined. This novel technique is not sensitive to impurities that also quench the electronic states of sodium very effectively. Our method involves only processes that produce vibrationally excited hydrogen. Due to the large vibrational spacing only H2 molecules that have undergone a quenching process are vibrationally excited. The cross section we determinei! is 12 cA'2, and is smaller than literature values due to the effect described. 4. We also measured the rotational distribution for different vibrational leveis. At the sensitivity limit of our apparatus the rotational distribution was estimated to be nearly thermal. This fact is also in good agreement with theoretical models for the collision process. It has heen shown that CARS is a very usefull spectroscopic technique with sufficient sensitivity to be applied to the study of nonadiabatic collision processes. CARS was used for the first time to investigate these processes and gave the new interesting results shown above.

Submitted by Santos Davilene (davilenes@ufba.br) on 2017-05-30T22:02:04Z No. of bitstreams: 1 Tese - Versão definitiva- Luiz Alberto Oliveira.pdf: 1176212 bytes, checksum: 682151271cf115f6a5ac0fea44cd999a (MD5) / Approved for entry into archive by Vanessa Reis (vanessa.jamile@ufba.br) on 2017-06-01T12:55:33Z (GMT) No. of bitstreams: 1 Tese - Versão definitiva- Luiz Alberto Oliveira.pdf: 1176212 bytes, checksum: 682151271cf115f6a5ac0fea44cd999a (MD5) / Made available in DSpace on 2017-06-01T12:55:33Z (GMT). No. of bitstreams: 1 Tese - Versão definitiva- Luiz Alberto Oliveira.pdf: 1176212 bytes, checksum: 682151271cf115f6a5ac0fea44cd999a (MD5) / Este trabalho fornece algumas contribuições originais para o estudo geométrico de equações evolutivas que descrevem superfícies pseudo-esféricas (equações PEs). Por definição, uma equação PE para funções z = z(x; t) _e equivalente _as equações de estrutura d!1 = !3 ^ !2, d!2 = !1 ^ !3, d!3 =!1 ^ !2 de uma variedade Riemanniana 2-dimensional com curvatura Gaussiana K = 􀀀1, com 1-formas !i = fi1 dx+fi2 dt, i = 1; 2; 3, satisfazendo a condições de não-degeneração !1 ^ !2 6= 0 e com fij funções suaves de x, t, z e suas derivadas com respeito a x e t. Usando a noções de representação a curvatura nula (RCN), pode-se dizer que toda equação PE admite uma RCN a valores em sl (2;R). / A primeira contribui¸c˜ao deste trabalho diz respeito a uma classifica¸c˜ao completa e explícita de equações PEs evolutivas de segunda ordem da forma zt = A(x, t, z)z2 + B(x, t, z, z1), com z = z (x, t) e zi = ∂ i z ∂xi , sob as hip´oteses que fij = fij (x, t, z, z1, z2) e f21 = η. De acordo com a classifica¸c˜ao dada, estas equações subdividem-se em trˆes classes principais (chamadas de Tipos I-III) juntamente com os correspondentes sistemas de 1-formas {ω1, ω2, ω3} que, em virtude da hipótese f21 = η, definem para cada tipo uma fam´ılia a 1-parˆametro de RCNs associadas. Nesta classe de equações PEs encontram-se em particular algumas equações já conhecidas, dentre as quais as equações integráveis classificadas por Svinolupov e Sokolov, a equa¸c˜ao de Boltzmann, e equa¸c˜oes de rea¸c˜ao e difus˜ao como a equa¸c˜ao de Murray. Ulteriores novos exemplos explicitos s˜ao tamb´em apresentados. A segunda contribuição ´e relativa ao problema de existência de imersões isométricas locais, no espaço Euclidiano 3-dimensional E3 , para as fam´ılias de superf´ıcies pseudo-esf´ericas descritas pelas equa¸c˜oes PEs da classifica¸c˜ao acima. O resultado principal obtido neste caso ´e que estas imers˜oes existem somente para as equa¸c˜oes do Tipo I, que possuem forma de lei de conserva¸c˜ao, e isso levou `a uma extens˜ao natural deste resultado ao caso das equa¸c˜oes evolutivas de ordem k da forma Dt (f(x, t, z)) = Dx (Ω(x, t, z, z1, . . . , zk)). No ˆambito da literatura existente sobre este problema, todos os resultados obtidos nesta parte do trabalho s˜ao novos; em particular al´em de equa¸c˜oes de segunda ordem, como por exemplo as equa¸c˜oes de Boltzmann, Murray e as equa¸c˜oes de Svinolupov e Sokolov, entre os exemplos de equa¸c˜oes PEs que admitem este tipo de imers˜ao isom´etrica h´a tamb´em equa¸c˜oes de ordem superior como as equa¸c˜oes de Kuramoto-Sivashinsky, Sawada-Kotera, Kaup-Kupershmidt e inteiras hierarquias de equa¸c˜oes integr´aveis como as de Burgers, mKdV e KdV. Finalmente, n´os consideramos o problema de construir fam´ılias a 1-parˆametro n˜ao-triviais de RCNs para equações PEs. Este problema ´e de interesse especial para as aplicações da teoria das RCNs, por exemplo no calculo de soluções exatas e hierarquias infinitas de leis de conserva¸c˜ao, e tem sido resolvido no caso mais geral de RCNs a valores em g, com g uma sub-´álgebra de gl(n, R) ou gl(n, C), usando a teoria de simetrias clássicas de equacões diferenciais.

Orientador: Prof. Dr Roberto Menezes Serra / Dissertação (mestrado) - Universidade Federal do ABC, Programa de Pós-Graduação em Física, 2014.

Der Energietransfer von elektronischer Energie in Schwingungs- und Rotationsenergie ist einer der elementarsten nichtadiabatischen Prozesse. Obwohl diese Prozesse seit langen untersucht werden, sind sie nicht im Detail verstanden. Das StoBsystem Na+H2 hat dabei Modellcharakter. Natrium ist ein Wasserstoffãhnliches Atom mit einem s-Elektron auf der auBersten Schale, und H2 ist das einfachste Molekül überhaupt. Ab initio Potentialflachen- Berechnungen sind deshalb mit guter Genauigkeit moglich und auch durchgef iihrt worden. Die elektronische Energie des Na-Atoms von 2,1eV wird dabei durch einen nichtadiabatischen Stoi3 in Schwingungs- und Rotationsenergie des H2-Moleküls iibertragen; ein Vorgang der auch als "Quenchen" bekannt ist. Von essentieller Bedeutung ist es, welche Schwingungs- und Rotationszustãnde besetzt werden. Es gab bisher keine experimentelle Untersuchung, bei der die interne Energieverteilung des H2-Moleküls direkt untersucht wurde. Der Grund dafür ist der, daB konventionelle Techniken zum Nachweis von H2 nicht geeignet sind. Aufgabe der vorliegenden Arbeit war es, erstmals CARS (Kohirente Antistokes-Raman-Streuung) für die oben genannten StoBprozesse einzusetzen und nachzuprüfen, wie gut sich diese Technik anwenden IãBt. CARS ist seit vielen Jahren bekannt, hat jedoch erst in der letzten Zeit durch die Entwicklung von intensiven gepulsten Laser mit geringer Bandbreite sehr an Bedeutung gewonnen. Insbesonders CARS an Wasserstoff wurde intensiv untersucht, nicht jedoch mit Beimischung von Natrium. Im vorliegenden Gasgemisch aus Natrium und H2 erzeugt Natrium durch seine energetisch sehr niedrigen elektronischen Zustãnde einen nichtresonanten Untergrund, der die Nachweis-Wahrscheinlichkeit so stark reduzieren kann, daí3 eine sinnvolle Anwendung nicht mehr mõglich sein konnte. Es ist gelungen zu zeigen, dali trotz eines enormen nichtresonanten Untergrundes eine sehr hohe Nachweiswahrscheinlichkeit mit CARS erzielt werden kann. Sie betrãgt für H2 mit Na im Grundzustand 1012 Teilchen pro cm3 und Quantenzustand und in Gegenwart von angeregtem Natrium 1013 Teilchen pro cm 3 und Quantenzustand. Mit der neu gebauten CARS-Apparatur wurde eine Reihe von neuen Experimenten durchgef a) Es konnte erstmals direkt die Schwingungsverteilung von H2 nach dem Quenchprozel3 bestimmt werden. Es konnte die absolute Besetzung der Schwingungszustãnde v=3,2 und 1 bestimmt werden. Eine Besetzung bei v=4 wurde nicht beobachtet. b) Mit einer zeitabhãngigen CARS-Messung konnte erstmalig die Schwingungsrelaxation der genannten Schwingungszustãnde gemessen und mit einem Ratengleichungsmodell die Ratenkonstanten mit sehr guter Obereinstimmung bestimmt werden. c) Aus der Besetzung der Schwingungszustãnde laBt sich ein absoluter Querschnitt für den Quenchprozei bestimmen. In Vergleich zu den klassischen Fluoreszenzmethoden wird dabei nicht die Abnahme der Fluoreszenz durch den StoBgasdruck bestimmt, sondern die direkte Besetzung des Quenchers nachgewiesen. Diese Methode wird erstmalig vorgestellt. Sie ist viel weniger empfindlich auf Verunreinigungen. Der erhaltene Wert für den Quenchquerschnitt betragt aq=12A2. d) Es laBt sich auch eine Aussage Uber die Rotationsbesetzung nach dem QuenchprozeB machen. Sie konnte bestimmt werden und ist nahezu thermisch, d.h. sie hat dieselbe Temperatur wie die Zelle. Dieses Ergebnis ist in übereinstimmung mit theoretische Modellen und bestãtigt die Vorstellung, dali das p-Orbital des angeregten Natriums sich bei Annãherung an das H2-Molekül ausrichtet und der QuenchprozeB vorwiegend in C2v -Symmetrie ablauft. Es ist gelungen zu zeigen, daB CARS sich erfolgreich für Untersuchungen an nichtadiabatischen StoBprozessen einsetzen laBt. Dadurch wurde erstmals erzielt. / Nonadiabatic collisions between atoms and molecules have drawn a large amount of attention in theoretical and experimental studies. In particular, the transfer of electronic energy of an atom to the vibrational, rotational and translational energy of a diatomic molecule (also called electronic quenching) can be considered an important fundamental process of this type and is thus extensively investigated. We study the Na + 112 as a model collision system for experimental and theoretical reasons since ab initio potential surfaces are currently available, enabling comparison of experimental results with theoretical calculations. We apply a new experimental technique in the field of nonadiabatic processes to obtain a more detailed understanding of these energy transfer processes. We use Coherent Anti-Stokes Raman Spectroscopy (CARS) to measure directly the internai energy distribution of H2 molecules produced by quenching of Na in the first excited state (3 2P112). Although CARS has been used to detect 112 among other species, it has never been applied to gaseous mixtures with H2 and atomic or molecular sodium. Sodium with its low lying electronic states produces a strong nonresonant background that strongly reduces the sensitivity of CARS. With a new constructed apparatus a sensitivity for H2 of 1012 particles per cm3 and quantum state in the presence of ground state sodium was achieved and 1013 particles per cm3 and quantum state with excited sodium. The following results were obtained: 1. The absolute population of vibrational leveis up to v=3 has been obtained and was found to be extremly nonthermal. The state distribution is, however, in good agreement with the available theoretical predictions. 2. With a time resolved CARS experiment we monitored the vibrational relaxation of these states. For this experiment we use excited sodium as an effective way to produce vibrationally hot hydrogen. With a simple model, we determined for the first time the vibrational relaxation time for v=3, 2 and 1 to be 2.4ps, 3.4ps and 31ps respectively. 3. From the measured absolute populations of the vibrational states of hydrogen the absolute cross section for the quenching process can be determined. This novel technique is not sensitive to impurities that also quench the electronic states of sodium very effectively. Our method involves only processes that produce vibrationally excited hydrogen. Due to the large vibrational spacing only H2 molecules that have undergone a quenching process are vibrationally excited. The cross section we determinei! is 12 cA'2, and is smaller than literature values due to the effect described. 4. We also measured the rotational distribution for different vibrational leveis. At the sensitivity limit of our apparatus the rotational distribution was estimated to be nearly thermal. This fact is also in good agreement with theoretical models for the collision process. It has heen shown that CARS is a very usefull spectroscopic technique with sufficient sensitivity to be applied to the study of nonadiabatic collision processes. CARS was used for the first time to investigate these processes and gave the new interesting results shown above.

Der Energietransfer von elektronischer Energie in Schwingungs- und Rotationsenergie ist einer der elementarsten nichtadiabatischen Prozesse. Obwohl diese Prozesse seit langen untersucht werden, sind sie nicht im Detail verstanden. Das StoBsystem Na+H2 hat dabei Modellcharakter. Natrium ist ein Wasserstoffãhnliches Atom mit einem s-Elektron auf der auBersten Schale, und H2 ist das einfachste Molekül überhaupt. Ab initio Potentialflachen- Berechnungen sind deshalb mit guter Genauigkeit moglich und auch durchgef iihrt worden. Die elektronische Energie des Na-Atoms von 2,1eV wird dabei durch einen nichtadiabatischen Stoi3 in Schwingungs- und Rotationsenergie des H2-Moleküls iibertragen; ein Vorgang der auch als "Quenchen" bekannt ist. Von essentieller Bedeutung ist es, welche Schwingungs- und Rotationszustãnde besetzt werden. Es gab bisher keine experimentelle Untersuchung, bei der die interne Energieverteilung des H2-Moleküls direkt untersucht wurde. Der Grund dafür ist der, daB konventionelle Techniken zum Nachweis von H2 nicht geeignet sind. Aufgabe der vorliegenden Arbeit war es, erstmals CARS (Kohirente Antistokes-Raman-Streuung) für die oben genannten StoBprozesse einzusetzen und nachzuprüfen, wie gut sich diese Technik anwenden IãBt. CARS ist seit vielen Jahren bekannt, hat jedoch erst in der letzten Zeit durch die Entwicklung von intensiven gepulsten Laser mit geringer Bandbreite sehr an Bedeutung gewonnen. Insbesonders CARS an Wasserstoff wurde intensiv untersucht, nicht jedoch mit Beimischung von Natrium. Im vorliegenden Gasgemisch aus Natrium und H2 erzeugt Natrium durch seine energetisch sehr niedrigen elektronischen Zustãnde einen nichtresonanten Untergrund, der die Nachweis-Wahrscheinlichkeit so stark reduzieren kann, daí3 eine sinnvolle Anwendung nicht mehr mõglich sein konnte. Es ist gelungen zu zeigen, dali trotz eines enormen nichtresonanten Untergrundes eine sehr hohe Nachweiswahrscheinlichkeit mit CARS erzielt werden kann. Sie betrãgt für H2 mit Na im Grundzustand 1012 Teilchen pro cm3 und Quantenzustand und in Gegenwart von angeregtem Natrium 1013 Teilchen pro cm 3 und Quantenzustand. Mit der neu gebauten CARS-Apparatur wurde eine Reihe von neuen Experimenten durchgef a) Es konnte erstmals direkt die Schwingungsverteilung von H2 nach dem Quenchprozel3 bestimmt werden. Es konnte die absolute Besetzung der Schwingungszustãnde v=3,2 und 1 bestimmt werden. Eine Besetzung bei v=4 wurde nicht beobachtet. b) Mit einer zeitabhãngigen CARS-Messung konnte erstmalig die Schwingungsrelaxation der genannten Schwingungszustãnde gemessen und mit einem Ratengleichungsmodell die Ratenkonstanten mit sehr guter Obereinstimmung bestimmt werden. c) Aus der Besetzung der Schwingungszustãnde laBt sich ein absoluter Querschnitt für den Quenchprozei bestimmen. In Vergleich zu den klassischen Fluoreszenzmethoden wird dabei nicht die Abnahme der Fluoreszenz durch den StoBgasdruck bestimmt, sondern die direkte Besetzung des Quenchers nachgewiesen. Diese Methode wird erstmalig vorgestellt. Sie ist viel weniger empfindlich auf Verunreinigungen. Der erhaltene Wert für den Quenchquerschnitt betragt aq=12A2. d) Es laBt sich auch eine Aussage Uber die Rotationsbesetzung nach dem QuenchprozeB machen. Sie konnte bestimmt werden und ist nahezu thermisch, d.h. sie hat dieselbe Temperatur wie die Zelle. Dieses Ergebnis ist in übereinstimmung mit theoretische Modellen und bestãtigt die Vorstellung, dali das p-Orbital des angeregten Natriums sich bei Annãherung an das H2-Molekül ausrichtet und der QuenchprozeB vorwiegend in C2v -Symmetrie ablauft. Es ist gelungen zu zeigen, daB CARS sich erfolgreich für Untersuchungen an nichtadiabatischen StoBprozessen einsetzen laBt. Dadurch wurde erstmals erzielt. / Nonadiabatic collisions between atoms and molecules have drawn a large amount of attention in theoretical and experimental studies. In particular, the transfer of electronic energy of an atom to the vibrational, rotational and translational energy of a diatomic molecule (also called electronic quenching) can be considered an important fundamental process of this type and is thus extensively investigated. We study the Na + 112 as a model collision system for experimental and theoretical reasons since ab initio potential surfaces are currently available, enabling comparison of experimental results with theoretical calculations. We apply a new experimental technique in the field of nonadiabatic processes to obtain a more detailed understanding of these energy transfer processes. We use Coherent Anti-Stokes Raman Spectroscopy (CARS) to measure directly the internai energy distribution of H2 molecules produced by quenching of Na in the first excited state (3 2P112). Although CARS has been used to detect 112 among other species, it has never been applied to gaseous mixtures with H2 and atomic or molecular sodium. Sodium with its low lying electronic states produces a strong nonresonant background that strongly reduces the sensitivity of CARS. With a new constructed apparatus a sensitivity for H2 of 1012 particles per cm3 and quantum state in the presence of ground state sodium was achieved and 1013 particles per cm3 and quantum state with excited sodium. The following results were obtained: 1. The absolute population of vibrational leveis up to v=3 has been obtained and was found to be extremly nonthermal. The state distribution is, however, in good agreement with the available theoretical predictions. 2. With a time resolved CARS experiment we monitored the vibrational relaxation of these states. For this experiment we use excited sodium as an effective way to produce vibrationally hot hydrogen. With a simple model, we determined for the first time the vibrational relaxation time for v=3, 2 and 1 to be 2.4ps, 3.4ps and 31ps respectively. 3. From the measured absolute populations of the vibrational states of hydrogen the absolute cross section for the quenching process can be determined. This novel technique is not sensitive to impurities that also quench the electronic states of sodium very effectively. Our method involves only processes that produce vibrationally excited hydrogen. Due to the large vibrational spacing only H2 molecules that have undergone a quenching process are vibrationally excited. The cross section we determinei! is 12 cA'2, and is smaller than literature values due to the effect described. 4. We also measured the rotational distribution for different vibrational leveis. At the sensitivity limit of our apparatus the rotational distribution was estimated to be nearly thermal. This fact is also in good agreement with theoretical models for the collision process. It has heen shown that CARS is a very usefull spectroscopic technique with sufficient sensitivity to be applied to the study of nonadiabatic collision processes. CARS was used for the first time to investigate these processes and gave the new interesting results shown above.