Thesis (Ph. D.)--University of Missouri-Columbia, 1997. / Typescript. Vita. Includes bibliographical references (leaves 223-229). Also available on the Internet.

Thesis (Ph. D.)--University of Texas at Austin, 2009. / Title from PDF title page (University of Texas Digital Repository, viewed on Sept. 9, 2009). Vita. Includes bibliographical references.

<strong>Chapter 1</strong> introduces the concept of spin, how spins interact, and how the spin state in a radical pair can affect the outcome of a chemical reaction between the unpaired electrons. The computational methodology for simulating such radical pairs is also discussed. <strong>Chapter 2</strong> discusses anisotropy in the singlet recombination yield of a radical pair in a carotenoid-porphyrin-fullerene triad, containing many hyperfine couplings. The singlet yield was calculated as a function of the direction of an applied magnetic field, using symmetry in the molecule to reduce the size of the problem. The symmetry reduction was partially successful, however it was not possible to include all the hyperfine couplings in the molecule. <strong>Chapter 3</strong> introduces a radical pair located on a flavin ligand and a tryptophan residue in the protein cryptochrome, and discusses the spin-relaxation mechanism of singlet-triplet dephasing. Magnetic field effect curves, describing the formation of a secondary radical pair as a function of applied magnetic field, were found to be broader in longer-lived radical pairs, due to dephasing caused by spin-selective recombination to the singlet ground state. Additional singlet-triplet dephasing may occur due to hopping of one of the unpaired electrons, between a zone of strong exchange interaction and a zone of negligible exchange interaction, although this is an incomplete description of the spin-relaxation. <strong>Chapter 4</strong> discusses the effect of rotational tumbling on spin-relaxation in the flavin-tryptophan radical pair in cryptochrome. Simulations indicated that the resulting modulation of anisotropic hyperfine couplings contributed modestly to spinrelaxation during transient absorption measurements, but was insufficient to explain the lack of an experimental low-field effect, or to explain the width of the experimental magnetic field effect curves as a function of magnetic field strength. <strong>Chapter 5</strong> discusses magnetic field effects on the mutual annihilation of a pair of triplet excitons in tetracene and anthracene crystals. The experimental singlet recombination yield was found, for the first time, to be modulated as a function of the direction of a applied magnetic field as weak as 2 mT. Simulations indicated that this anisotropy arose due to the zero field splitting of the electronic state in each triplet exciton. The direction of the external magnetic field altered the singlet component of the eigenstates of the Hamiltonian, and therefore altered the timeaverage of the singlet probability of a triplet exciton pair. This is different to the already established mechanism under a strong magnetic field, where the anisotropy arises from level crossings of eigenstates.

Made available in DSpace on 2015-12-10T14:24:29Z (GMT). No. of bitstreams: 0 Previous issue date: 2015-07-29. Added 1 bitstream(s) on 2015-12-10T14:30:41Z : No. of bitstreams: 1 000852038.pdf: 6705690 bytes, checksum: fed6b575fb58363e4d0342e0e54a1385 (MD5) / Realizamos dois diferentes estudos envolvendo o acoplamento spin-_orbita. Um deles foi sobre a origem da obliquidade de Urano, que ainda permanece desconhecida. Algumas teorias de formação foram publicadas nas ultimas décadas, sendo que as duas mais citadas: por meio de uma colisão (Urano sofreu uma grande colisão tangencial); e por meio de um efeito ressonante entre a rotação de Urano e um satélite. Focamos nosso estudo no modelo de ressonância. Baseado num artigo de Boué & Laskar (2010), no qual os autores estudam a origem da obliquidade de Urano por meio de uma ressonância que só ocorre na presença de um satélite de grande porte (Satélite X). Fizemos um estudo numérico do problema em questão. Utilizando _orbitas já integradas do Modelo de Nice, estudamos a possibilidade de obter a atual obliquidade de Urano devido a perturbações dos planetas gigantes, Sol e o Satélite X. Nossos resultados mostram que o Satélite X ocasiona crescimento na obliquidade de Urano, podendo assim ser o responsável pela atual configuração do eixo de rotação de Urano, onde esse crescimento da obliquidade ocorre somente para determinadas configurações de semi-eixo maior e massa do Satélite X, sendo máximo quando o ângulo ressonante ( _) (longitude do equador de Urano menos a longitude do nodo ascendente do Satélite X) é zero e mínima quando é 180 graus. Porém, assim como no estudo anterior, só foi possível reproduzir a atual obliquidade de Urano com Satélite X com massas excessivamente grandes, da ordem de 0; 01 da massa de Urano. As simulações mostraram também que o Satélite X causa instabilidade no sistema de satélites internos desestabilizando-os a ponto de extingui-los. Outro estudo realizado foi sobre a origem de sistemas binários de asteroides por meio de ruptura rotacional. O processo de fissão rotacional de asteroides ... (Resumo completo, clicar acesso eletrônico abaixo) / We conducted two different studies about the spin-orbit coupling. One of them was about the origin of Uranus obliquity, that still remains unknown. Some theories of formations have been published in the last decades, the two most cited is: by collision (Uranus suffered a great tangential collision) and by a resonance between Uranus rotation and a satellite. We focused our study on the resonance model. Based on article of Boué & Laskar (2010), in which the authors study the origin of Uranus obliquity by a resonance that occurs only in the presence of a large satellite (Satellite X). We did a numerical study of this problem. Using orbits previously integrated by Nice Model, we studied the possibility of obtaining the current Uranus obliquity due to disturbances of the giant planets, the Sun and the Satellite X. Our results show that the Satellite X causes growth in Uranus obliquity and so may be the responsible for the current configuration of the Uranus rotation axis. And this growth of obliquity occurs only for certain configurations of semi-major axis and mass of the Satellite X, and maximum when the resonant angle ( _) (Uranus's equator longitude less the longitude of the ascending node of the Satellite X) is zero and minimal when it is 180 degrees. However, as in the previous study, it was only possible to reproduce the current Uranus obliquity with Satellite X with excessively large masses, about 0:01 mass of Uranus. The simulations also showed that Satellite X causes instability in the satellite with internal orbits until extinguishing them. Another study was about the origin of binary asteroid systems through rotational fission. The process of rotational fission of asteroids has been studied theoretically Scheeres (2007) and numerically Jacobson & Scheeres (2011) with simplified models restricted to planar motion. However, the observed physical configuration of contact ... (Complete abstract click electronic access below)

Resumo: Este trabalho tem por objetivo analisar a estabilidade do movimento rotacional de satélites arti…ciais simétricos (com dois momentos principais de inércia iguais), em órbita circular, sob a in‡uência do torque de gradiente de gravidade, usando as variáveis de Andoyer. O método utilizado neste trabalho para analisar a estabilidade é o teorema de Kovalev e Savchenko,o qual requer a redução da Hamiltoniana na forma normal até quarta ordem, por meio de transformações canônicas em torno dos pontos de equilíbrio. Os coe…cientes da Hamiltoniana normal são indispensáveis no estudo da estabilidade não linear de seus pontos de equilíbrio, de acordo com as três condições estabelecidas no teorema. Aplicações foram realizadas para satélites de médio e pequeno porte, com dados similares a satélites reais, utilizando o software MATHEMATICA. Diversos pontos de equilíbrio estáveis foram encontrados e regiões de equilíbrio ao redor destes pontos foram estabelecidas através de variações na inclinação orbital e nos momentos principais de inércia do satélite. Em comparação com trabalhos anteriores os resultados mostram um maior número de pontos de equilíbrio e uma otimização no algoritmo de determinação da forma normal e na análise de estabilidade, devido a possibilidade de inclusão de cálculo analítico dos coe…cientes da Hamiltoniana normal de 4a ordem. Assim, a utilização das variáveis de Andoyer se mostra adequada para a análise da estabilidade do movimento rotacional, podendo ser útil em análises de missões espaciais. Salienta-se que o lançamento do satélite em regiões de estabilidade pode contribuir para a manutenção da atitude do satélite, podendo gerar uma economia de combustível através de um menor número de manobras de atitude para manter a atitude desejada da missão / Abstract: This work aims to analyze the stability of the rotational motion of symmetrical arti…cial satellite (with two principal moments of inertia equal), in circular orbit with the in‡uence of gravity gradient torque, using the variables of Andoyer. The used method in this paper to analyze stability is the Kovalev-Savchenko theorem, which requires the reduction of the Hamiltonian in its normal form up to fourth order by means of canonical transformations around equilibrium points. The coe¢ cients of the normal Hamiltonian are indispensable in the study of nonlinear stability of its equilibrium points according the three established conditions in the theorem studied. The applications were made to satellites of medium and small size, with data similar to real satellites, using the software MATHEMATICA. Several stable equilibrium points were determined and regions around these equilibrium points have been established by variations in orbital inclination and the principal moments of inertia of the satellite. In comparison with previous results show a larger number of equilibrium points and an optimization in algorithm determining the normal form in the stability analysis, due the possibility of inclusion of analytical calculation of the coe¢ cients of the normal Hamiltonian of 4th order. Thus, the uses of variables Andoyer are adequate for the stability analysis of rotational motion, which can be useful for the analysis of space missions. Stresses those, the launch of the satellite regions of stability can contribute to the maintenance of the satellite attitude, which can generate a fuel economy through lower number of attitude maneuvers to maintain desired attitude of the mission / Orientador: Maria Cecília Franca de Paula Santos Zanardi / Coorientador: Jorge Kennety Silva Formiga / Banca: Ernesto Vieira / Banca: Mário Cesar Ricci / Mestre

MSc (Mathematics) / Department of Mathematics and Applied Mathematics / See the attached abstract below

Rotating machines such as motors, generators, turbines, etc. are crucial mechanical components of modern industrial and power generation facilities. For proper functioning of these facilities during and after an earthquake, it is essential that the rotating machines in these facilities also function as desired. The dynamics of a rotating machine is quite complex. It is further complicated by the presence of earthquake induced base motions. The response spectrum methods, which are now commonly used for calculating seismic design response of civil structures, cannot be used as such for calculating the design response of rotating machines. In this thesis, a response spectrum method which can be applied to the rotating machines is developed. To develop the response spectrum approach, a generalized modal superposition method is utilized. The random vibration analysis is applied to incorporate the stochastic characteristics of the seismic inputs. The applicability of the proposed response spectrum approach is verified by a simulation study where fifty sets of acceleration time histories are used. The proposed method considers the fact that earthquake induced base motions have several components, including rotational inputs. To define the correlation between the rotational and translational input components of the excitation, the correlation matrix and a travelling seismic wave approaches are used. The numerical results are obtained to evaluate the effect of rotational input components on the response of a rotating machine. It is observed that the rotational components are important only when they are very strong. In actual practice, such strong rotational inputs are not expected to excite rotors which are either directly placed on ground or are placed in common buildings. In the proposed spectrum approach, nevertheless, the effect of rotational input components can be easily incorporated if the correlation between various excitation components is specified. / Master of Science

Halo currents (HCs) in post-disruption plasmas can be large enough to exert significant electromagnetic loads on structures surrounding the plasma. These currents have axisymmetric and non-axisymmetric components, both of which pose threats to the vacuum vessel and other components. However, the non-axisymmetric forces can rotate, amplifying the displacements they cause when the rotation is close to the structures’ resonant frequencies. A new physically motivated scaling law has been developed that describes the rotation frequencies of these HCs and has been validated against measurements on HBT-EP, Alcator C-Mod, and other tokamaks. This scaling law can describe the time-evolution of the asymmetric HC rotation throughout disruptions on HBT-EP as well as the time-averaged rotation on C-Mod. The scaling law can also be modified to include the edge safety factor at the onset of rotation (𝒒_𝑜𝑛𝑠𝑒𝑡), which significantly improves its validity when applied to machines like C-Mod, where 𝒒_𝑜𝑛𝑠𝑒𝑡 changes frequently. The 𝒒_𝑜𝑛𝑠𝑒𝑡 dependence is explained by the relationship between the poloidal structure of the HC asymmetries and the MHD instabilities that drive them, which has been observed experimentally for the first time using a novel set of current sensing limiter tiles installed on HBT-EP. The 1/𝑎² and 𝒒_𝑜𝑛𝑠𝑒𝑡-dependence of the rotation suggest that the HCs predominantly rotate poloidally. This remains consistent with the toroidal rotation observed on HBT-EP and other tokamaks through the “Barber Pole Illusion” and the direction of rotation’s dependence on the direction of 𝐼_𝑝. This scaling law is used to make projections for next generation tokamaks like ITER and SPARC, which predicts that rotation will be resonant on ITER. However, resonant effects can still be avoided if the duration of the disruption is kept short enough to prevent two rotations from being completed.

The heterogeneous dynamics exhibited by supercooled liquids near the glass transition temperature (𝑇_𝑔) has been a topic of much research over the past several decades. In particular, the advent of single molecule (𝖲𝖬) methods has permitted great insight into the extent of both spatial and temporal heterogeneities in these systems, information which is either difficult or impossible to access via ensemble approaches. Despite this, the related phenomenon of rotational-translation decoupling, whereby the translational motion observed in supercooled systems is enhanced relative to Debye-Stokes-Einstein predictions, is difficult to study with 𝖲𝖬 approaches. This is due to the very low localization uncertainty required to accurately report the extremely slow translational motion in supercooled systems near 𝑇_𝑔. In this thesis, a new approach for quantifying rotational dynamics in supercooled liquids is introduced which leverages fluorescence intensity fluctuations due to out-of-plane fluorophore rotations. Unlike linear dichroism (LD) measurements, the most common experiment used to access rotational dynamics, this technique does not require a polarizing optical element, thus improving localization precision in the acquired images. This intensity fluctuation-based approach is shown to report comparable rotational correlation timescales (𝝉_𝘤) and information on dynamic heterogeneity to that typically extracted via LD measurements. On a probe-by-probe basis, rotational correlation times obtained from simultaneous measurement of LD (𝝉_𝘤,𝘓𝘋) and intensity fluctuations (𝝉_𝘤,𝘐 ) are found to be only moderately well-correlated. We postulate that this is a consequence of dynamic heterogeneity due to temporal dynamic exchange, the process in which a probe (and its surroundings) undergoes sudden changes in dynamics. This hypothesis is explored through simulations, which reveal that the Pearson R correlation coefficients associated comparing log 𝝉_𝘤,𝘐 and log 𝝉_𝘤,𝘓𝘋 increases as the time between dynamic exchange increases. The information obtained from such simulations is then used to estimate the exchange timescales from experimental data. When examined in concert with experimentally measured degrees of relaxation non-exponentiality - generally considered a metric of heterogeneity in an interrogated supercooled liquid – this permits access to previously inaccessible information regarding the breadth of the distribution of underlying timescales experienced by these supercooled systems. In addition to this work focused on rotational dynamics, we also aim to further clarify information contained in 𝖲𝖬 experiments characterizing translational dynamics, towards the goal of full understanding of rotational-translational decoupling. Here, two widefield fluorescence imaging setups are optimized to minimize localization uncertainty, and differences in how localization uncertainties manifest in perceived translational motion near 𝑇_𝑔 are examined. The setup with greater localization uncertainty reports faster translational dynamics compared to the other optical setup, suggesting significant influence of the localization noise floor on perceived dynamics and highlighting the importance of maximizing the signal to noise ratio of 𝖲𝖬 experiments aiming to study the underlying cause of rotational-translational decoupling.

The development of Magnaquench in 1985 by the Delco-Remy laboratories, increased the research of applications of permanent magnets for use in automobiles. However the application of permanent magnet machines for cranking purposes has not been investigated much. Difficult operating conditions, like, a maximum current density of 35A/mm², and the ability to withstand demagnetizing armature currents up to 250% of the stall current require a new design approach to be developed. Commutation in the permanent magnet machine is obtained by a three phase full wave inverter. The machine - inverter model was simulated by a standard method (SPICE), and an second analytical method we developed. A permanent magnet brushless motor and a drive for cranking purposes is designed and simulated as a part of this thesis. / Master of Science