Thesis (M.A.)--Ball State University, 2009. / Title from PDF t.p. (viewed on July 12, 2010). Research paper (M.A.), 3 hrs. Includes bibliographical references (p. 42-43).

Indiana University-Purdue University Indianapolis (IUPUI) / We introduce the quantum toroidal superalgebra E(m|n) associated with the Lie superalgebra gl(m|n) and initiate its study. For each choice of parity "s" of gl(m|n), a corresponding quantum toroidal superalgebra E(s) is defined. To show that all such superalgebras are isomorphic, an action of the toroidal braid group is constructed. The superalgebra E(s) contains two distinguished subalgebras, both isomorphic to the quantum affine superalgebra Uq sl̂(m|n) with parity "s", called vertical and horizontal subalgebras. We show the existence of Miki automorphism of E(s), which exchanges the vertical and horizontal subalgebras. If m and n are different and "s" is standard, we give a construction of level 1 E(m|n)-modules through vertex operators. We also construct an evaluation map from E(m|n)(q1,q2,q3) to the quantum affine algebra Uq gl̂(m|n) at level c=q3^(m-n)/2.

<p> Inflatable structures have attracted much interest in space applications. The three main components of inflatable satellites are inflatable struts, an inflatable torus as the structural support component, and some sort of lens, aperture, or array housed inside the boundary of the torus. This project is devoted towards understanding the dynamic characteristics of an inflated torus with a focus on the self-rigidizing torus, SRT, developed by United Applied Technologies.</p> <p> The self-rigidizing torus is manufactured from flat sheets of Kapton® that are formed into curved films with the regular pattern of hexagonal domes. The inflated torus can support its structural shape even when there is no internal pressure.</p> <p> Modal testing is used to determine the dynamic properties of the structure for comparison with the numerical model. The feasibility of using a non-contact in-house fabricated electromagnetic excitation is investigated. The first four, in-plane and out-of-plane, damped natural frequencies and their corresponding damping ratios and modes shapes are extracted and compared with prior experimental studies. A preliminary finite element modal analysis is carried out for a torus made of flat film and the results are compared with prior studies. Kapton 300JP®'s frequency-dependent modulus of elasticity is determined.</p> <p> Owing to the large number of hexagonal domes in the self-rigidizing torus, a simplified sub-structuring technique is used. Each hexagonal dome is replaced with a statically equivalent flat hexagon with the same mass and stiffness as the hexagonal dome. Then the finite element modal analysis of the self-rigidizing torus is carried out for an equivalent torus made of flat film. The geometric nonlinearity and the effect of the follower load on the stiffness are included in this analysis. The methodology is verified through the correlation between the analytical and modal test results of the self-rigidizing torus.</p> / Thesis / Doctor of Philosophy (PhD)

Ion traps can easily be miniaturized to become portable mass spectrometers. Trapped ions can be ejected by adjusting voltage settings of the radiofrequency (RF) signal applied to the electrodes. Several ion trap designs include the quadrupole ion trap (QIT), cylindrical ion trap (CIT), linear ion trap (LIT), rectilinear ion trap (RIT), toroidal ion trap, and cylindrical toroidal ion trap. Although toroidal ion traps are being used more widely in miniaturized mass spectrometers, there is a lack of fundamental understanding of how the toroidal electric field affects ion motion, and therefore, the ion trap's performance as a mass analyzer. Simulation programs can be used to discover how traps with toroidal geometry can be optimized. Potential mapping, field calculations, and simulations of ion motion were used to compare three types of toroidal ion traps: a symmetric and an asymmetric trap made using hyperbolic electrodes, and a simplified trap made using cylindrical electrodes. Toroidal harmonics, which represent solutions to the Laplace equation in a toroidal coordinate system, may be useful to understand toroidal ion traps. Ion trapping and ion motion simulations were performed in a time-varying electric potential representing the symmetric, second-order toroidal harmonic of the second kind—the solution most analogous to the conventional, Cartesian quadrupole. This potential distribution, which we call the toroidal quadrupole, demonstrated non-ideal features in the stability diagram of the toroidal quadrupole which were similar to that for conventional ion traps with higher-order field contributions. To eliminate or reduce these non-ideal features, other solutions to the Laplace equation can be added to the toroidal quadrupole, namely the toroidal dipole, toroidal hexapole, toroidal octopole, and toroidal decapole. The addition of a toroidal hexapole component to the toroidal quadrupole provides improvement in ion trapping, and is expected to play an important role in optimizing the performance of all types of toroidal ion trap mass spectrometers.The cylindrical toroidal ion trap has been miniaturized for a portable mass spectrometer. The first miniaturized version (r0 and z0 reduced by 1/3) used the same central electrode and alignment sleeve as the original design, but it had too high of capacitance for the desired RF frequency. The second miniaturized version (R, r0, and z0 reduced by 1/3) was designed with much less capacitance, but several issues including electrode alignment and sample pressure control caused the mass spectra to have poor resolution. The third miniaturized design used a different alignment method, and its efficiency still needs to be improved.

S.Skryabin demonstrou que qualquer álgebra de Lie simples de dimensão finita sobre um corpo de característica 2 possui posto toroidal 2. Duas 2- álgebras de Lie de dimensão 31 foram estudadas. Neste trabalho, mostramos que a primeira delas contem uma base toroidal absoluta de dimensão três, assim como a segunda, que foi estudada por Grishkov e Guerreiro anteriormente. Utilizando uma decomposicão de Cartan, exibimos um isomorfismo entre as duas 2- álgebras de Lie de dimensão 31. Este resultado foi sugerido depois de encontrar uma sub álgebra de dimensão 12 n ao solúvel e 7 isomorfas 2-sub álgebras de Lie de dimensão 7 nas duas álgebras. Finalmente, exploramos uma 2- álgebra de Lie de dimensão 34 como o fim de encontrar base toroidal absoluta de dimensão 4. Apoiamos os cálculos com algumas códigos no linguajem de MATLAB que permitiram optimizar e acelerar a pesquisa. / S.Skryabin showed that any finite dimensional simple Lie algebra over a field of characteristic 2 has absolute toral rank 2. Two 31-dimensional 2-algebras were known. In this work, we show that the first of these algebras, contains a 3-dimensional maximal toral subalgebra, as the second one, which was studied by Grishkov e Guerreiro previously. Using a Cartan decomposition we establish an isomorphism between the two 31-dimensional 2-algebras. This result was suggested after finding a 12-dimensional not soluble subalgebra and seven 7-dimensional isomorphic 2-subalgebras in both algebras. Finally, a 34-dimensional 2-Lie algebra was studied in order to find 4-dimensional maximal toral subalgebras. Some computations in this work were performed with help of MATLAB.

Submitted by Lucienne Costa (lucienneferreira@ufcg.edu.br) on 2018-04-24T17:01:07Z No. of bitstreams: 1 THAÍS LUANA VIDAL DE NEGREIROS DA SILVA – DISSERTAÇÃO (PPGEE) 2016.pdf: 1884666 bytes, checksum: afeda21236f3e2ea365c427c256b6865 (MD5) / Made available in DSpace on 2018-04-24T17:01:07Z (GMT). No. of bitstreams: 1 THAÍS LUANA VIDAL DE NEGREIROS DA SILVA – DISSERTAÇÃO (PPGEE) 2016.pdf: 1884666 bytes, checksum: afeda21236f3e2ea365c427c256b6865 (MD5) Previous issue date: 2016-10-17 / Capes / Neste trabalho são apresentados estudos analíticos e simulações computacionais sobre transformadores de corrente (TC) com núcleo toroidal de material magneticamente mole como recuperadores de energia eletromagnética. A fundamentação teórica parte das leis fundamentais do eletromagnetismo derivadas das equações de Maxwell. Na obtenção dos circuitos magnéticos equivalentes foram levados em conta as forças magnetomotrizes, relutâncias e os fluxos magnéticos. Como estudo de caso, foi utilizada uma simulação computacional baseada no método dos elementos finitos para a obtenção da distribuição de indução magnética dentro do núcleo toroidal. Tal como previsto pelas expressões analíticas, verificou-se que a indução magnética distribui-se de maneira não uniforme na direção radial do núcleo. Partindo dos circuitos magnéticos, circuitos elétricos equivalentes foram deduzidos, nos quais foram representadas as resistências e as reatâncias. Simulou-se o comportamento do TC como recuperador de energia e verificou-se que o rendimento do sistema de recuperação depende do material do núcleo, da carga acoplada ao secundário do TC, do coeficiente de acoplamento entre primário e secundário e da existência ou não de entreferro no núcleo magnético. / In this work an analytic and computational analysis of current transformers (CT) with soft magnetic material toroidal core used as energy harvester is presented. The theoretical approach is based on the fundamental laws of electromagnetism presented in Maxwell's equations. Magnetomotive forces, reluctance and magnetic flux were taken into account in order to obtain equivalent magnetic circuits. Using a 2D simulation tool based on finite element method, computational simulations were performed in order obtain the distribution of magnetic induction in radial direction of the toroidal core. As predicted by the analytical expressions, the magnetic induction is distributed nonuniformly in the radial direction of the core. Based on the magnetic circuits, equivalent electrical circuits were deducted, in which the resistance and reactance were represented. Based on computational simulations, it was possible to conclude that the efficiency of the TC as energy harvester varies according to the core material, to the load at its secondary terminal, to the coupling coefficient between primary and secondary and to the existence of air gap in the magnetic core.

The objective of the proposed research is to design, fabricate, characterize and test silicon-embedded magnetic components for on-chip integrated power applications. Driven by the trend towards continued system multi-functionality and miniaturization, MEMS technology can be used to enable fabrication of three-dimensional (3-D) functional devices into the silicon bulk, taking advantage of the 'dead volume' in the substrate and achieving a greater level of miniaturization and integration. As an example, one of the challenges in realizing ultra-compact high-frequency power converters lies in the integration of magnetic components due to their relatively large volume. Embedding 3-D magnetic components within the wafer volume and implementing high-power, through-wafer interconnect for connection to circuitry on the wafer surface is a promising solution for achieving ultra-compact power converters, in which digital control circuitry and power switches are located on the wafer surface, and suitable magnetic components are embedded within the silicon substrate. In order to do this, key tasks in the following areas have been accomplished: development of new fabrication technologies for silicon embedding and 3-D structure realization; creation of high-current, through-wafer interconnects for connection of the device to circuitry; ability to incorporate a variety of magnetic materials when performance enhancement of the device is needed; exploration of a new design space for the devices due to ultra-compactness and silicon interaction; understanding of the complicated loss mechanisms in the embedded devices; and demonstration of device performance and in-circuit operation.

We study log varieties, over a field of characteristic zero, which are generically logarithmically smooth and fs in the Kummer normally log étale topology. As an application, we prove an analog of Abramovich-Temkin-Wlodarczyk’s log resolution of singularities of fs log schemes in the Kummer fs setting.<br>

The effect of changing edge safety factor on the toroidal flow of the STOR-M plasma has been investigated during the application of both resonant magnetic perturbation (RMP) and compact torus injection (CTI). The edge safety factor was varied by varying the plasma current while keeping the toroidal field constant. A Czyner-Turner spectrometer was used to collect the spectral data from which the velocity of specific impurity ions was diagnosed. Time resolved velocity measurements were inferred from the Doppler wavelength shift of the emission lines. Impurity emission lines at different ionization stages are located at different radial locations within the STOR-M plasma. Properties of these impurity ions are assumed to be closely related the hydrogen ion (main working gas) due to the strong interaction among the ion species. Changing the edge safety factor has a similar effect on the toroidal flow of STOR-M plasma during discharges with both RMP and CTI. A velocity shear was discovered for different impurity ions. The toroidal flow is enhanced for edge ions while a reversal of flow is observed for core ions. As the edge safety factor reduces, the emission location for the core ions is located with q=2 surface and RMP has a significant impact on their toroidal flow velocity. It was also observed that CT injection has a significant effect on the toroidal velocity of the core ions compared to that of the edge ions. In addition, high plasma current (low safety factor) induced large change in the toroidal flow velocity of the STOR-M plasma.

Dissertation (Ph.D.)--Auburn University, 2008. / Abstract.