An investigation is carried out to determine whether or not on the basis of theory one expects axial asymmetry in heavy nuclei. The average one-body potential well is taken as an anisotropic harmonic oscillator, modified by the usual ℓ ∙ s and ℓ² forces. The method of matrix diagonalisation is used to find the eigenvalues. Residual interaction between nucleons is also treated in the pairing approximation. The calculations show that prolate axial symmetry is favoured in each of the nuclei considered. It is possible to indicate the underlying physical reasons for this result. Assuming equilibrium prolate axial symmetry an attempt is made to understand the collective excited levels in the transition region, i.e. the region between spherical nuclei and permanently deformed nuclei. A model calculation is done to show how the levels can be obtained. / Thesis / Doctor of Philosophy (PhD)

In this dissertation, we utilize the discrete Fourier analysis on axially symmetric data generation and nonparametric estimation. We first represent the axially symmetric process as Fourier series on circles with the Fourier random coefficients expressed as circularlysymmetric complex random vectors. We develop an algorithm to generate the axially symmetric data that follow the given covariance function. Our simulation study demonstrates that our approach performs comparable with the classical approach using the given axially symmetric covariance function directly, while at the same time significantly reducing computational costs. For the second contribution of this dissertation, we apply the discrete Fourier transform to provide the nonparametric estimation on the covariance function of the above circularly-symmetric complex random vectors under gridded data structure. Our results show that these estimates has closely related to the simultaneous diagonalization of circulant matrices. The simulation study shows that our proposed estimates match well with their theoretical counterparts. Finally through the Fourier transform of the original gridded data, the covariance estimator of an axially symmetric process based on the method of moments can be represented as a quadratic form of transformed data that is associated with a rotation matrix.

No description available.

My thesis is focused on using ICT (Information and Communication Technology) for teaching about percentage and axial symmetry. Specifically I am using an interactive whiteboard to support my teaching. The thesis is divided into two parts, a theoretical and a practical part. The first part is looking into various teaching methods, use of ICT and the interactive whiteboard in teaching in general. The second part of my thesis contains a workbook I have prepared to support my teaching on the interactive whiteboard and the application of the workbook during lessons for the students on secondary school. I have concluded my thesis with evaluation of my teaching methods and reflective practice.

Made available in DSpace on 2014-10-09T12:42:21Z (GMT). No. of bitstreams: 0 / Made available in DSpace on 2014-10-09T14:02:11Z (GMT). No. of bitstreams: 0 / Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP) / Tese (Doutoramento) / IPEN/T / Instituto de Pesquisas Energeticas e Nucleares - IPEN-CNEN/SP / FAPESP:09/13764-3

Made available in DSpace on 2014-10-09T12:42:21Z (GMT). No. of bitstreams: 0 / Made available in DSpace on 2014-10-09T14:02:11Z (GMT). No. of bitstreams: 0 / Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP) / Tomografia por Coerência Óptica, ou simplesmente OCT (acrônimo do inglês: Optical Coherence Tomography), é uma técnica para geração de imagens de seções transversais de meios espalhadores ao comprimento de onda utilizado. A OCT é baseada em interferometria óptica e gera imagens comumente correlacionadas às imagens geradas exames histológicos com a vantagem de ser indolor, não invasiva e não utilizar radiação ionizante. Este estudo dividiu-se em dois objetivos distintos, um refere-se à aplicação de sinais interferométricos de autocorrelação para a formação de imagens de amostras com estruturas complexas. O segundo objetivo foi o estudo das estruturas denominadas de harmônicos e sua aplicação no aumento da resolução axial de um sistema OCT. Com relação à primeira parte, constatou-se que o sinal interferométrico de autocorrelação é muitas vezes ignorado ou descartado pela OCT tradicional. Análises mais profundas da teoria de interferometria, juntamente com alguns estudos anteriores, apontaram para a possibilidade de gerar imagens de maior complexidade morfológica utilizando o sinal de autocorrelação, com a vantagem de se utilizar um arranjo óptico mais simples e também possibilitar imagens estáticas de amostras em movimento axial. Para testar os benefícios e as limitações da técnica de autocorrelação (Au-OCT) foi montado em laboratório e foram realizadas imagens de amostras no repouso e em movimento e confrontadas com imagens geradas no sistema OCT convencional. O sistema de Au-OCT foi capaz de gerar imagens de estruturas diversas (dentes, filmes plásticos entre outros), e apesar de possuir uma qualidade de imagem inferior à OCT, ela apresentou vantagens quando a amostra sofre deslocamentos axiais. Já em relação as características harmônicas, que se apresentam em amostras de alta refletividade óptica como falsas estruturas em imagens OCT, todo um estudo para o entendimento do fenômeno foi desenvolvido. Demonstrou-se também a possibilidade de utilização dessas estruturas para aprimorar a resolução axial diferencial (entre estruturas da própria amostra) através de um estudo numérico e experimental. Para isso padrões dimensionais do tipo degrau foram mensurados e os resultados tratados de acordo com procedimentos metrológicos, mostrando que os harmônicos podem ser utilizados para promover o aumento de resolução axial de um fator de aproximadamente dois. Por fim uma análise crítica sobre os resultados e uma discussão sobre perspectivas dos temas abordados, foram realizada. / Tese (Doutoramento) / IPEN/T / Instituto de Pesquisas Energeticas e Nucleares - IPEN-CNEN/SP / FAPESP:09/13764-3

No description available.

This thesis presents axially symmetric equivalents of three-dimensional rf ion traps. Miniaturization in mass spectrometry has focused on miniaturizing mass analyzers. Decrease in mass analyzer size facilitates reduction of the size of other components of a mass spectrometer, especially the radio frequency electronics and vacuum system. Miniaturized mass analyzers are made using advanced microfabrication techniques. Due to micromachining limitations, it is not possible to fabricate ion traps with exact axial symmetry. The motivation for this thesis is to investigate newer three-dimensional geometries which do not possess axial symmetry, but are equivalent in performance to axially symmetric ion traps. We introduce a 3D geometry called square ion trap(SIT) having a ring electrode made off our square shaped planar surfaces and square shaped endcap electrodes resembling a cuboid. Initially, a SIT geometry is taken and it will be investigated if this unknown 3D geometry can be made equivalent to a well characterized, axially symmetric ion trap like the CIT. The purpose of showing equivalence will be to understand the ion dynamics and fields inside the new 3D SIT. This thesis consists of five chapters. In Chapter 1, we present the necessary background information required to understand the operation of a mass spectrometer. The Paul trap geometry is introduced followed by the derivation of equation of ion motion inside the Paul trap. The Mathieu stability plot and the modes of operation of a mass spectrometer are briefly discussed. The chapter ends by outlining scope of the thesis. Chapter 2 describes the computational methods employed by us in the thesis. First, the geometry of square ion trap is introduced. Then the boundary element method(BEM) which is used to compute the charge distribution on the electrode surfaces is discussed. This is followed by the three-dimensional Green’s function which should be employed for non-axially symmetric structures. The method to calculate potential and field inside the ion trap from charge distribution is shown. Calculation of multipole coefficients for non-axially symmetric traps using charge distribution is shown. The methods used to generate ion trajectory and stability plot are discussed. The Nelder-Mead simplex method used for optimization is also presented. To verify our numerical methods of charge calculation, we have taken standard textbook problems and compared our results with those presented therein. The multipoles calculation, field and ion trajectory was verified by comparing the results for the Paul trap and cylindrical ion traps. Chapter 3 presents the results for axially symmetric equivalents of 3D rf ion traps. SIT geometry of dimensions equivalent to the CIT0 are taken and field and multipoles are studied in it. Then optimization is applied to create a CIT geometry equivalent to the SIT under study. Axial field and ion trajectory was compared and observed to be matching. Finally, stability plot was generated for both SIT and its equivalent CIT and was found to present a close match. Chapter 4 presents the numerical results obtained for three-dimensional rf ion trap equivalent of CIT. In this chapter, we have considered two standard geometries, the CIT0 and the CITopt. Optimization was applied to create SIT geometries equivalent to the CIT0 and the CITopt respectively. Comparison of fields and ion trajectory confirmed the fact that non-axially symmetric traps can be created equivalent to any axially symmetric ion trap. We have also considered another case of axially symmetric circular planar ion trap which has an annular ring electrode and two planar endcap electrodes. Square equivalent of circular planar trap was created by the optimizer and its equivalent was verified by ion trajectory comparison. Chapter 5 summarizes the thesis with a few concluding remarks.

The thesis is aimed on the mathematical knowledge and skills development in leisure time activities. The theoretical part of the thesis is dedicated to leisure time, pedagogy of leisure time, out-of-school education - its content, functions and requirements for realization of out-of-school education. This part of the thesis is also dedicated to the motivation and its use in leisure time activities and development of mathematical knowledge in leisure activities. Based on this information and on my own experience, I worked out and introduced the prin- ciples for preparing leisure time activities developing mathematical knowledge and skills. Following is a compilation of leisure time activities that develop knowledge and skills in geometry, arithmetic, algebra, logical thinking, or geometric imagination. The compilation contains activities suitable for relaxing, recreational and hobby activities. The practical part includes a case study of the Textile Applications activity, which deals with consolidation and development of knowledge in axial symmetry within the leisure time sewing ring. The case study verified if participants in this activity developed knowledge in axial symmetry, if the activity respects the requirements for out-of-school education and if it improves belief in the applicability of...

O objetivo deste trabalho é apresentar um novo tipo de sistema de levitação baseado na força de interação magnética entre uma bobina de núcleo não-magnético e um imã permanente, em casos de simetria axial entre os dispositivos, nos moldes do problema 23 proposto no TEAM Workshop. Este tema é bastante atual e vários métodos têm sido estudados e propostos em razão da complexidade na determinação precisa das forças sobre os imãs permanentes imersos em um campo magnético em um circuito magnético aberto. O primeiro grande desafio deste trabalho é obter uma expressão analítica para esta força de interação magnética em casos de simetria axial usando o método de cargas magnéticas ligadas. Para tal, algumas hipóteses simplificadoras foram adotadas como considerar o campo magnético gerado pela bobina aproximadamente uniforme em toda a face do imã permanente e assumir que a magnetização do imã é constante e independente da variação de sua distância para a bobina. Pretende-se aproveitar o sistema implementado neste trabalho como bancada experimental no Laboratório de Controle da Universidade de São Paulo. Foi projetado um controlador PID através de ferramentas gráficas obedecendo a alguns critérios de desempenho, tanto no domínio do tempo como no domínio da freqüência. Uma vez sintonizado, foi utilizado o toolbox Real-Time Windows Target do Simulink e a placa de aquisição PCI 6221 (da National Instruments) para controlar em tempo real a planta de levitação em malha fechada. Os resultados experimentais foram muito satisfatórios de modo que o modelo analítico foi considerado válido. O sistema apresentou boas características como, por exemplo, um bom acompanhamento do sinal de referência, mesmo em grandes excursões, erro de regime nulo, levitação estável em distâncias relativamente grandes e uma boa estabilidade radial. O uso de dois sensores Hall mostrou-se eficiente na determinação da posição do imã permanente. / The objective of this work is to present a new kind of levitation system based on the interaction force between a non-magnetic core coil and a permanent magnet, in the case of axial symmetry between devices, as proposed by TEAM Workshop problem 23. This theme is very current and various methods have been studied and proposed in face of the complexity in determining precisely the force over permanent magnets immersed in a magnetic field in an open magnetic circuit. The first big challenge of this work is to obtain an analytical expression for this interaction magnetic force in the case of axial symmetry using the equivalent magnetic charge method. For this, some simplifying hypothesis have been adopted like considering the magnetic field created by the coil approximately uniform over all the permanent magnets face and assuming that magnets magnetization is constant and independent of the variation of its distance to the coil. The system implemented in this work is intended to be used as an experimental bench for the Laboratory of Control of Sao Paulo University. A PID controller was projected by means of graphical tools according to some criteria for performance, both in the field of time as in the frequency domain. Once tuned, the toolbox Real-Time Windows Target of Simulink and the PCI-6221 acquisition board (of National Instruments) were used to control in real time the levitation plant in closed loop. The experimental results were very satisfactory so that the analytical model was considered valid. The system showed good characteristics as, for instance, a good tracking of reference signal, even in large excursions of it, null stationary error, stable levitation at relatively big gaps and a good radial stability. The use of two Hall-effect sensors proved to be efficient in the determination of permanent magnets position.