Thesis: S.B., Massachusetts Institute of Technology, Department of Electrical Engineering, 1965 / "September 1965." / Includes bibliographical references (leaf 65). / by Eduardo Jose Barragan Schenone. / S.B. / S.B. Massachusetts Institute of Technology, Department of Electrical Engineering

Finite element analysis is versatile and used widely in a range of engineering andscientific disciplines. As time passes, the problems that engineers and designers areexpected to solve are becoming more computationally demanding. Often theproblems involve the interplay of two or more processes which are physically andtherefore mathematically coupled. Although parallel computers have been availablefor about twenty years to satisfy this demand, finite element analysis is still largelyexecuted on serial machines. Parallelisation appears to be difficult, even for thespecialist. Parallel machines, programming languages, libraries and tools are used toparallelise old serial programs with mixed success. In some cases the serialalgorithm is not naturally suitable for parallel computing. Some argue that rewritingthe programs from scratch, using an entirely different solution strategy is a betterapproach. Taking this point of view, using MPI for portability, a mesh free elementby element method for simple data distribution and the appropriate iterative solvers,a general parallel strategy for finite element analysis is developed and assessed.

A fossil magnetic field embedded in the radiative core of the Sun has been thought possible for some time now. However, such a fossil magnetic field has, a priori, not been considered a visible phenomenon due to the effects of turbulence in the solar convection zone. Since a well developed theory (referred to herein as magnetohydrodynamic dynamo theory) exists for describing the regeneration of magnetic fields in astrophysical objects like the Sun, it is possible to quantitatively evaluate the interaction of a fossil magnetic field with the magnetohydrodynamic dynamo operating in the solar convection zone. In this work, after a brief description of the basic dynamo equations, a spherical model calculation of the solar dynamo is introduced. First, we calculate the interaction of a fossil magnetic field with a dynamo in which the regeneration mechanisms of cyclonic convection and large-scale, nonuniform rotation are confined to spherical shells. It is argued that the amount of amplification or suppression of a fossil magnetic field will be smallest for a uniform distribution of cyclonic convection and nonuniform rotation, as expected in the Sun. Secondly, we calculate the interaction of a fossil magnetic field with a dynamo having a uniform distribution of cyclonic convection and large-scale, nonuniform rotation. We find that the dipole or quadrupole moments of a fossil magnetic field are suppressed by factors of -0.35 and -0.37, respectively. The dynamo modified fossil field, superimposed on the theoretically calculated magnetic fields of the solar magnetic cycle, are compared with the actual sunspot cycle and solar magnetic fields as observed by others, indicating that a fossil magnetic field may be responsible for asymmetries in the sunspot cycle and an observed solar magnetic quadrupole moment. Further observations and reduction of the data are required before the presence of a fossil magnetic field can be established. A discussion is given of the implications for the Sun if a fossil magnetic field is observed and identified. It is considered most likely that a fossil magnetic field would be a remnant of the possible Hayashi phase of a fully convective, protosun. Other possibilities also exist.

No description available.

Jatos e discos de acreção associados a objetos galácticos e extragalácticos tais como, microquasares (i.e., buracos negros de massa estelar presentes em alguns sistemas binários estelares), núcleos ativos de galáxias (NAGs) e objetos estelares jovens (OEJs), frequentemente exibem eventos de ejeção de matéria quase periódicos que podem fornecer importantes informações sobre os processos físicos que ocorrem nas suas regiões mais internas. Entre essas classes de objetos, os microquasares com emissão transiente em raios-X vêm sendo identificados em nossa Galáxia desde a última década, e tal como os NAGs e quasares distantes, alguns desses sistemas também produzem jatos colimados com velocidades aparentemente superluminais, não deixando dúvidas de que se tratam de um gás ejetado com velocidades relativísticas. Um exemplo amplamente observado em comprimentos de onda do rádio aos raios-X é o microquasar GRS 1915+105 (e.g., Dhawan et al.,2000), que foi o primeiro objeto galáctico a exibir evidências de um jato com movimento aparentemente superluminal (Mirabel e Rodríguez, 1998, 1994). Um modelo para explicar a origem dessas ejeções superluminais, bem como a emissão rádio sincrotrônica em flares não muito diferentes dos que ocorrem na coroa solar, foi desenvolvido por de Gouveia Dal Pino e Lazarian (2005), onde é invocado um processo de reconexão magnética violenta entre as linhas de campo magnético que se erguem do disco de acreção e as linhas da magnetosfera da fonte central. Em episódios de acreção onde a razão entre a pressão efetiva do disco e a pressão magnética diminui para valores menores ou da ordem de 1 e as taxas de acreção se aproximam da taxa crítica de Eddington, a reconexão pode tornar-se violenta e libera grandes quantidades de energia magnética em pouco tempo. Parte dessa energia aquece o gás, tanto da coroa quanto do disco, e parte acelera as partículas a velocidades relativísticas por um processo de Fermi de primeira ordem, pela primeira vez estudado em zonas de reconexão magnética por esses autores, produzindo um espectro sincrotrônico de lei de potência com índice espectral comparável às observações. Neste trabalho realizamos um estudo complementar, iniciado por Piovezan (2009), no qual generalizamos o modelo acima descrito para o caso dos NAGs. Nesse estudo, constatamos que a atividade de reconexão magnética na região coronal, na base de lançamento do jato, pode explicar a origem das ejeções relativísticas, dos microquasares aos NAGs de baixa luminosidade (tais como galáxias Seyfert e LINERS). A potência liberada em eventos de reconexão magnética em função das massas dos buracos negros dessas fontes, de 5 massas solares a 10^10 massas solares, obedece a uma correlação que se mantém por todo esse intervalo, abrangendo 10^9 ordens de magnitude. Essa correlação implica em uma dependência quase linear (em um diagrama log-log), aproximadamente independente das características físicas locais dos discos de acreção dessas fontes. Além do mais, ela é compatível com o chamado plano fundamental, obtido empiricamente, que correlaciona a emissão rádio e raios-X dos microquasares e NAGs às massas dos seus buracos negros (veja Merloni et al., 2003). Assim, o modelo de de Gouveia Dal Pino e Lazarian (2005), oferece uma interpretação física simples para a existência dessa correlação empírica, como devida à atividade magnética coronal nessas fontes. Já os quasares e NAGs mais luminosos não satisfazem à mesma correlação, possivelmente porque a densidade ao redor da região coronal nessas fontes é tão alta que mascara a emissão devida à atividade magnética. A emissão rádio nesses casos deve-se, possivelmente, a regiões mais externas do jato supersônico, onde ele já expandiu o suficiente para tornar-se opticamente fino e visível, e onde os elétrons relativísticos são possivelmente produzidos em choques (veja também de Gouveia Dal Pino et al., 2010a,b). Paralelamente, investigamos a formação de eventos de reconexão magnética através de simulações magnetohidrodinâmicas axissimétricas (2.5D-MHD), da interação entre o campo magnético poloidal ancorado no disco de acreção viscoso (satisfazendo ao modelo padrão de Shakura e Sunyaev, 1973) e a magnetosfera dipolar da fonte central em rotação. Para esse fim, consideramos condições iniciais semelhantes às dos OEJs. Nos testes preliminares aqui realizados, a reconexão magnética das linhas ocorre em presença de uma resistividade numérica, que não é intensa o bastante para determinar um processo de reconexão a taxas da ordem da velocidade de Alfvén, ou seja, ela é essencialmente lenta. Ainda assim, pudemos identificar alguns dos efeitos previstos pelo modelo de reconexão magnética rápida aqui estudado. Por exemplo, verificamos que a frequência e a intensidade com que eventos de reconexão magnética podem ocorrer é sensível tanto à topologia inicial do campo magnético do sistema quanto às taxas de acreção do disco (como previsto pelo modelo de de Gouveia Dal Pino e Lazarian, 2005), de modo que tais eventos ocorrem de forma mais eficiente em regimes de alta taxa de acreção. Finalmente, além da investigação sobre o desenvolvimento de eventos de reconexão magnética, pudemos também examinar a partir das simulações a formação natural de funis de acreção, os quais são colunas de acreção que conduzem gás do disco para a superfície da fonte central através das linhas do campo magnético. Os resultados desse estudo foram comparados com as observações de funis de acreção de objetos estelares jovens. / Jets and accretion disks associated with galactic and extragalactic objects such as microquasars (i.e., stellar-mass black holes occurring in some binary stellar systems), active galactic nuclei (AGNs) and young stellar objects (YSOs), often exhibit quasi-periodic ejections of matter that may offer important clues about the physical processes that occur in their inner regions. Among these classes of objects, microquasars with transient emission in X-rays have been identified in our Galaxy since the last decade and like AGNs and distant quasars, some of them also produce collimated jets with apparent superluminal speeds, leaving no doubt that we are also dealing with ejected gas with relativistic velocities. One example widely investigated from radio wavelengths to X-rays is the microquasar GRS 1915+105 (e.g., Dhawan et al.,2000), which was the first Galactic object to show evidence of a jet with apparent superluminal motion (Mirabel e Rodríguez, 1998, 1994). A model to explain the origin of the superluminal ejections and the synchrotron radio emission in flares which are not very different from those occurring in the solar corona, was developed by de Gouveia Dal Pino e Lazarian (2005), where they invoked a process of violent magnetic reconnection between the magnetic field lines that arise from the accretion disk and the lines of the magnetosphere of the central source. In accretion episodes where the ratio between the effective disk pressure and magnetic pressure decreases to values smaller than the unity and the accretion rate approaches the critical Eddington rate, the reconnection may become violent and releases large amounts of magnetic energy in a short time. Part of this energy heats the coronal and the disk gas and part accelerates particles to relativistic velocities through a first-order Fermi-like process, which was investigated for the first time in magnetic reconnection by these authors and results a synchrotron radio power-law spectrum that is compatible to the observations. In the present work we conducted a complementary study, initiated by Piovezan (2009), which generalize the model described above for the case of AGNs. We found that the activity due to magnetic reconnection in the coronal region, at the base of the launching jet, can explain the origin of relativistic ejections from microquasars to low luminous AGNs (LLAGNs, such as Seyfert galaxies and LINERs). The power released by magnetic reconnection events as a function of the black hole masses of these sources, between 5 solar mass and 10^10 solar mass, obeys a correlation that is maintained throughout this interval, spanning 10^9 orders of magnitude. This correlation implies an almost linear dependence (in a log-log diagram), which is approximately independent of the physical properties of the accretion disks of these sources. Moreover, it is compatible with the so-called fundamental plan obtained empirically, which correlates the radio and X-rays emission of microquasars and AGNs with the masses of their black holes (see Merloni et al., 2003). Thus, the model of de Gouveia Dal Pino e Lazarian (2005) provides a simple physical interpretation for the existence of this empirical correlation as due to coronal magnetic activity in these sources. More luminous AGNs and quasars do not seem to obey the same correlation, possibly because the density around the coronal region in these sources is so high that it \"masks\" the emission due to the magnetic activity. The radio emission in these cases is possibly due regions further out of the supersonic jet, where it has already expanded enough to become optically thin and visible and where the relativistic electrons are probably accelerated in shocks (see also de Gouveia Dal Pino et al., 2010a,b). In addition, we investigated the development of magnetic reconnection events through axisymmetric magnetohydrodynamic simulations (2.5D-MHD) of the interaction between the poloidal magnetic field that arises from the viscous accretion disk (which satisfies the standard model of Shakura e Sunyaev, 1973) and the dipolar magnetosphere of the rotating central source. To this aim, we considered initial conditions which are compatible to those of YSOs. In the preliminary tests conducted here, magnetic reconnection occurs in the presence of numerical resistivity only, which is not intense enough to determine a process of reconnection with rates of the order of the Alfvén speed, i.e., it is essentially slow. Nevertheless, we were able to identify some of the effects predicted by the model of fast magnetic reconnection studied here. For example, we found that the frequency and strength with which events of magnetic reconnection can occur is sensitive to both the initial topology of the magnetic field of the system and the accretion disk rates (as predicted by the model of de Gouveia Dal Pino e Lazarian, 2005), so that such events occur more efficiently under high accretion rates. Finally, besides the investigation of the development of magnetic reconnection events, we could also examine in our numerical studies the natural formation of funnel flows which are accretion columns that transport gas from the accretion disk to the surface of the central source along the magnetic field lines. The results of these studies were compared with the observations of funnel flows in young stellar objects.

Investigamos o efeito da rotação de equilíbrio nos fluxos zonais (ZF) e modos acústicos geodésicos (GAM) em tokamaks da secção circular. Estes modos, ZF e GAM, ocorrem em sistemas toroidais como uma resposta do plasma à curvatura geodésica das linhas de campo magnético e devido ao movimento de deriva do fluido ( plasma). Este movimento de deriva é causado pela resposta de partículas carregadas ao campo elétrico e magnético e, para ambas as espécies de cargas, isto é, íons positivo e elétrons, o movimento é na mesma direção. Ao fazer uso de basicamente três aproximações tokamaks de alta razão de aspecto, princípio de quase-neutralidade e baixos valores de (aproximação eletrostática) e ao perturbar as equações da magnetohidrodinâmica ideal até primeira ordem, constatamos que a rotação de equilíbrio, de fato, afeta a freqüência dos ZF e dos GAM. No equilíbrio com rotação toroidal, já investigado por W. Shaojie, os ZF se tornam instáveis e a freqüência dos GAM se altera com a rotação no caso de condutividade de calor finita; entretanto, quando a condutividade de calor tende a infinito, a rotação não influencia na freqüência dos ZF e GAM. Esta observação e os valores das freqüências dos ZF e GAM diferem da publicação original e portanto, se estivermos corretos, nosso trabalho poderá ajudar a resolver o problema dos ZF e dos GAM, que são questões ainda não completamente entendidas. A rotação causada por um campo eletrostático que surge devido à difusão ambipolar, ainda não investigada anteriormente, é descrita neste trabalho, Vimos que não há instabilidades neste caso, porém esse tipo de rotação também afeta a freqüência dos ZF e dos GAM. A freqüência dos ZF, que na ausência de rotação é nula, é proporcional à intensidade do fluxo de rotação. Interpretamos este resultado como uma conseqüência do efeito doppler. A freqüência dos GAM, por outro lado, se anula quando a rotação atinge um certo valor, que está relacionado com o fator de segurança e a razão do aspecto do tokamak. Considerando de ordem um fluxo de rotação, obtivemos altas freqüências, as quais não são aceitáveis em nosso modelo devido à aproximação de quase-neutralidade, de forma que nosso modelo é válido apenas para fluxos cuja ordem equivalem à razão de aspecto inversa. Entretanto, mesmo neste regime, a rotação tem grande impacto na freqüência dos ZF e dos GAM. Este é o principal resultado obtido. / We investigate the efect of equilibrium rotation on zonal flows (ZF) and geodesic acoustic modes (GAM) in tokamaks of circular cross section. These models, ZF and GAM, occur in toroidal systems as a response of the plasma to the geodesic curvature of the magnetic field lines and due to the drift motion of the fluid (plasma). This drift motions is caused by the response of charged particles to the electric and magnetic field and, for both species of charges, i. e., positive ions and negative electrons, the motion is in the same direction. By making use of basically three approximations, high aspect ratio tokamkas, the quasi-neutrality principle and low values (electrostatic approximation), and pertubing the ideal magnetohydrodynamics equations to first order, we find that the equilibrium rotation does affects the ZF and GAM frequencies. In the equilibrium toroidal rotation flow, which had already been studied by W. Shaojie, the ZF becomes unstable and the GAM frequency is changed by rotation for finity heat conductivity; but when the heat conductivity goes to infinity, the rotation has no influence on the ZF and GAM frequencies. This assertion and also the ZF and GAM frequencies values differ from the original publication and therefore, if we are correct, our work may help to solve the ZF and GAM problem, which is not yet a completely understood subject. The rotation caused by an equilibrium electrostatic field created by ambipolar diffusion, which has not been dealt is also investigate. We find no instability in this case, but the rotation also affects the ZF and GAM frequencies. The ZF frequency, which is usually null, becomes proportional to the equilibrium rotation flow. We interptret this result as a consequency of the doppler effect. The GAM frequency, on the other hand, becomes zero when the rotation reaches a certain value, which is related to the safety factor and the aspect ratio of the tokamak. Consideration of equilibrium flows scaling to order one leads to high frequencies, which is not accepted by contrasting the quasi-neutrality approximation and so, our model is valid only for small equilibrium electric field that scale to the inverse aspect ratio. But even in this regime, we find that the rotation has great impact on the ZF and GAM frequencies, which is the main result we obtain.

The concept of using Magnetohydrodynamics to provide thrust has been around for decades. However little work has been carried out in one of the fundamental aspects that allows for these systems to operate in seawater. Therefore a series of tests were carried out to determine how the electrochemical reactions occurring at the electrodes affect the seawater system. These tests were used to determine the effects magnetic fields have on seawater conductivity, the pH changes around the electrodes, and consider the double layer capacitance model as a means to decrease the amount of gas bubbles created at the electrodes. As a result significant increases in resistivity in seawater were observed when the magnetic field was introduced, pH changes were seen on both the cathode and anode, and pulsing of the applied potential may stimulate further work to be considered. / by Juan E. Moreno. / Thesis (M.S.C.S.)--Florida Atlantic University, 2011. / Includes bibliography. / Electronic reproduction. Boca Raton, Fla., 2011. Mode of access: World Wide Web.

When a ferromagnet is heated, it loses its magnetism. Stars and planets have magnetic fields, as does the Earth. But it is known that the center of the Earth is very hot. Therefore, to sustain the large magnetic field of a planet, we cannot look to simple ferromagnetism like that of a bar magnet, but we have to look at the movement of electric charges within the Earth’s molten core to generate magnetic field. This magnetic field sustainment against ohmic dissipation by turbulent flow is referred to as the turbulent dynamo effect. Theoretical research into the mechanisms that create the dynamo has been actively pursued for several decades, culminating recently in massive computer simulations of the Earth’s core. Most of these studies have employed the equations of magnetohydrodynamics (MHD), a nonlinear theory of electrically conducting fluids. The EDQNM (Eddy-Damped Quasi-Normal Markovian) closure is a statistical model designed so that the turbulence equations derived from Navier-Stokes dynamics can be closed and satisfy the realizability condition of positivity of the kinetic energy spectrum. In case of MHD turbulence, realizability requires more work. We have proved in an earlier work that equations analogous to those expected of the EDQNM closure for MHD without mean fields satisfy the appropriate realizability conditions (Turner and Pratt 1999). In this work, we discuss requirements needed to make the MHD equations realizable with mean fields, extending those of neutral fluid turbulence by Turner [1]. Finally, we discuss direct numerical simulations and the correspondence of the statistical theories with simulation results.

Based on a Sc.D. thesis in the Dept. of Electrical Engineering, 1965. / Bibliography: p.98-99.

Donald M. Dix. / "Submitted to the Department of Mechanical Engineering, M.I.T., August 25, 1961, in partial fulfillment of the requirements for the degree of Doctor of Science." "July 9, 1962." / Bibliography: p. 127-128. / Army Signal Corps Contract DA 36-039-sc-78108. Dept. of the Army Task 3-99-20-001 and Project 3-99-00-000. Army Signal Corps Contract No. DA-SIG-36-039-61-G14. National Science Foundation Grant G-9330.