Thesis. 1978. Elec.E.--Massachusetts Institute of Technology. Dept. of Electrical Engineering and Computer Science. / MICROFICHE COPY AVAILABLE IN ARCHIVES AND ENGINEERING. / Includes bibliographical references. / Elec.E.

Thesis (Ph.D.)--M.I.T, Dept. of Physics, 1981. / MICROFICHE COPY AVAILABLE IN ARCHIVES AND SCIENCE. / Includes bibliographical references. / by Cyrus Reza Safinya. / Ph.D.

Mott insulators are materials in which strong correlations among the electrons induce an unconventional insulating state. Rich interplay between the structural, magnetic, and electronic degrees of freedom resulting from the electron correlation can lead to unusual complexity of Mott materials on the atomic scale, such as microscopically heterogeneous phases or local structural correlations that deviate significantly from the average structure. Such behavior must be studied by suitable experimental techniques, i.e. "local probes", that are sensitive to this local behavior rather than just the bulk, average properties. In this thesis, I will present results from our studies of multiple families of Mott insulators using two such local probes: muon spin relaxation (muSR), a probe of local magnetism; and pair distribution function (PDF) analysis of x-ray and neutron total scattering, a probe of local atomic structure. In addition, I will present the development of magnetic pair distribution function analysis, a novel method for studying local magnetic correlations that is highly complementary to the muSR and atomic PDF techniques. We used muSR to study the phase transition from Mott insulator to metal in two archetypal Mott insulating systems: RENiO₃ (RE = rare earth element) and V₂O₃. In both of these systems, the Mott insulating state can be suppressed by tuning a nonthermal parameter, resulting in a "quantum" phase transition at zero temperature from the Mott insulating state to a metallic state. In RENiO₃, this occurs through variation of the rare-earth element in the chemical composition; in V₂O₃, through the application of hydrostatic pressure. Our results show that the metallic and Mott insulating states unexpectedly coexist in phase-separated regions across a large portion of parameter space near the Mott quantum phase transition and that the magnitude of the ordered antiferromagnetic moment remains constant across the phase diagram until it is abruptly destroyed at the quantum phase transition. Taken together, these findings point unambiguously to a first-order quantum phase transition in these systems. We also conducted x-ray and neutron PDF experiments, which suggest that the distinct atomic structures associated with the insulating and metallic phases similarly coexist near the quantum phase transition. These results have significant implications for our understanding of the Mott metal-insulator quantum phase transition in real materials. The second part of this thesis centers on the derivation and development of the magnetic pair distribution function (mPDF) technique and its application to the antiferromagnetic Mott insulator MnO. The atomic PDF method involves Fourier transforming the x-ray or neutron total scattering intensity from reciprocal space into real space to directly reveal the local atomic correlations in a material, which may deviate significantly from the average crystallographic structure of that material. Likewise, the mPDF method involves Fourier transforming the magnetic neutron total scattering intensity to probe the local correlations of magnetic moments in the material, which may exist on short length scales even when the material has no long-range magnetic order. After deriving the fundamental mPDF equations and providing a proof-of-principle by recovering the known magnetic structure of antiferromagnetic MnO, we used this technique to investigate the short-range magnetic correlations that persist well into the paramagnetic phase of MnO. By combining the mPDF measurements with ab initio calculations of the spin-spin correlation function in paramagnetic MnO, we were able to quantitatively account for the observed mPDF. We also used the mPDF data to evaluate competing ab initio theories, thereby resolving some longstanding questions about the magnetic exchange interactions in MnO.

As variáveis de processo determinam as propriedades dos produtos resultantes dos processos de fundição ou de soldagem, que são função da sua macro e microestrutura bruta de solidificação. Um dos parâmetros importantes para se determinar as propriedades de um produto é a posição da transição colunarequiaxial (CET) e, por este motivo, o entendimento dos fenômenos físicos que causam esta transição é essencial. Com o intuito de se prever a formação da CET, surgiram os métodos empíricos e os modelos matemáticos, que são divididos em dois grandes grupos: modelos determinísticos e modelos estocásticos. Estes dois grupos foram bem estudados, porém nunca foram comparados entre si, particularmente em relação à previsão da posição da CET. O presente trabalho tem como um primeiro objetivo preencher esta lacuna através da comparação entre estes modelos. No entanto, o objetivo principal é apresentar, implementar e validar um novo modelo matemático, denominado de híbrido estocástico-determinístico (CADE -\"Cellular Automaton Deterministic\"), que combine características importantes e vantajosas de cada um dos dois grupos de modelos. Inicialmente, um modelo representante do grupo dos modelos estocásticos foi implementado e validado frente a resultados disponíveis na literatura. Durante esta validação, foi necessária a elaboração de um critério baseado na razão de aspecto dos grãos para a identificação da CET nas macroestruturas calculadas pelo modelo. Estes resultados foram então comparados com os resultados de modelos determinísticos para, após cuidadosa discussão, possibilitar a proposta e implementação do modelo híbrido. Os modelos determinísticos que utilizam o critério mecânico para prever o bloqueio de grãos colunares e a ocorrência da CET mostram regiões colunares em geral maiores que as previstas pelo modelo estocástico. Por outro lado, os modelos determinísticos que utilizam um critério de bloqueio a partir da interação do campo de concentração de soluto ao redor dos grãos prevêem uma CET em posições semelhantes às calculadas pelos modelos estocásticos. O modelo implementado no presente trabalho é capaz de prever a macroestrutura bruta de solidificação e ainda utilizar as equações tradicionalmente empregadas nos modelos determinísticos, sem a necessidade de qualquer método extra para prever a posição da frente de crescimento colunar ou o seu bloqueio por grãos equiaxiais. / The processing variables determine many properties of the products obtained by casting and welding processes and these properties, on the other hand, are strongly affected by the as-cast micro and macrostructure. Particularly the position of the columnar-to-equiaxed transition (CET), which determines the amount of columnar and equiaxed grains in the macrostructure, has an important effect on the properties of as-cast parts. Therefore, understanding the important physical phenomena that cause and affect the formation of the CET plays a crucial role in predicting the ascast macrostructure. To predict the CET formation, empirical methods and mathematical models have been developed. These models are frequently divided into two main groups: deterministic and stochastic. Both groups have been thoroughly studied, but a comparison between them was never attempted, especially regarding the prediction of the CET position. One of the main objectives of the present work is to fulfill this gap by carefully comparing these models. Nevertheless, the most important objective is to propose, implement, and validate a hybrid stochastic-deterministic model, referred to as CADE (Cellular Automaton Deterministic), that combines some important and well-known features of each model. Initially, a model from the stochastic group was implemented and validated using results available in the literature and then used to analyze the effects of some processing variables on the CET prediction. To carry out this analyzes, a criteria based on the aspect ratio of the grains was proposed and developed to identify the CET region from macrostructure images calculated by the model. The results were compared with those obtained by deterministic models and finally led to the development of the new proposed model. This new model has some characteristics from each group of mathematical models and, for this reason, was denoted as hybrid. A deterministic model based on a mechanical blocking criterion to block columnar grains and define the CET position showed, for the most part, larger columnar regions than those predicted by the stochastic model. A deterministic model with a solutal blocking criterion to predict the CET showed results similar to those calculated with the stochastic model. The model proposed in the present work (CADE) was able to predict the as-cast macrostructure using the well-established deterministic equations, without the need for a new method to track columnar grains or predict their blocking by equiaxed grains.

Yuen Yung Hui. / Thesis (Ph.D.)--Chinese University of Hong Kong, 2002. / Electronic reproduction. Hong Kong : Chinese University of Hong Kong, [2012] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Electronic reproduction. Ann Arbor, MI : ProQuest Information and Learning Company, [200-] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Mode of access: World Wide Web. / Abstracts in English and Chinese. / Yuen Yung Hui.

by Zhou ping. / Thesis (Ph.D.)--Chinese University of Hong Kong, 1997. / Includes bibliographical references (p. 160-170). / Electronic reproduction. Hong Kong : Chinese University of Hong Kong, [2012] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Mode of access: World Wide Web.

Esta dissertação apresenta uma experiência de abordagem do conceito de congruência de figuras planas, no Ensino Fundamental, por meio de estudo das transformações isométricas. O estudo foi realizado com uma turma de alunos do nono ano do Ensino Fundamental de uma escola pública municipal de Parobé, no Rio Grande do Sul. Sob a inspiração do modelo de cooperação investigativa de Ole Skovsmose, foram desenvolvidas atividades de natureza exploratória e investigativa com questões abertas ao diálogo entre os participantes da pesquisa e uso de materiais manipulativos e de um software de geometria dinâmica. As soluções propostas pelos alunos e as discussões realizadas durante o desenvolvimento das atividades foram registradas por meio das produções escritas dos alunos, de gravações em áudio e vídeo e de arquivos elaborados no ambiente do software GeoGebra. As análises desses registros permitiram concluir que os alunos compreenderam o conceito de congruência de figuras planas por meio da exploração e da discussão sobre as transformações isométricas. / This work presents an experience of an approach of the concept of plane figures, in elementary school, through the study of isometric transformations. This study was conducted with a ninth grade group of students of a public elementary school in the city of Parobé, Rio Grande do Sul. Under the inspiration of the investigative cooperation model of Ole Skovsmose, exploratory and investigative nature activities were developed and open questions were proposed in order to establish a dialogue between the participants in the research. The use of manipulative materials and a dynamic geometry software has also been applied. The solutions proposed by the students and the discussion conducted during the activities development were recorded through written papers, audio and video recordings and files created with GeoGebra software environment. Through the analysis of these records, the conclusion was that the students understood the concept of congruence of plane figures through the exploration and the discussion around the isometric transformations.

by Man-Ching Auyeung. / Thesis (M.Phil.)--Chinese University of Hong Kong, 1997. / Includes bibliographical references (leaves 86-93). / Chapter 1 --- Introduction --- p.1 / Chapter 1.1 --- Transform coding and the JPEG scheme --- p.2 / Chapter 1.2 --- Motivation --- p.5 / Chapter 1.3 --- Thesis outline --- p.6 / Chapter 2 --- MED and DC Coefficient Restoration scheme --- p.8 / Chapter 2.1 --- Introduction --- p.8 / Chapter 2.2 --- MED and DC Coefficient Restoration scheme --- p.10 / Chapter 2.2.1 --- Definition --- p.10 / Chapter 2.2.2 --- Existing schemes --- p.11 / Chapter 2.3 --- DC Coefficient Restoration scheme using block selection scheme --- p.14 / Chapter 2.4 --- Joint optimization technique --- p.16 / Chapter 2.4.1 --- Lagrange multiplier method --- p.17 / Chapter 2.4.2 --- Algorithm description --- p.18 / Chapter 2.5 --- Experimental results --- p.20 / Chapter 2.6 --- Summary --- p.32 / Chapter 3 --- Low Frequency Walsh Transform Coefficient Restoration scheme --- p.34 / Chapter 3.1 --- Introduction --- p.34 / Chapter 3.2 --- Restoration of low frequency coefficient using Walsh transform --- p.35 / Chapter 3.3 --- Selection of quantization table optimized for Walsh transform --- p.37 / Chapter 3.3.1 --- Image model used --- p.39 / Chapter 3.3.2 --- Infinite uniform quantization --- p.40 / Chapter 3.3.3 --- Search for an optimized quantization matrix --- p.42 / Chapter 3.4 --- Walsh transform-based LFCR scheme --- p.44 / Chapter 3.5 --- Experimental results --- p.46 / Chapter 3.6 --- Summary --- p.56 / Chapter 4 --- Low Frequency DCT Coefficient Prediction --- p.57 / Chapter 4.1 --- Introduction --- p.57 / Chapter 4.2 --- Low Frequency Coefficient Prediction scheme with negligible side information --- p.58 / Chapter 4.2.1 --- Selection of threshold --- p.63 / Chapter 4.2.2 --- Representation of the AC component --- p.63 / Chapter 4.3 --- Experimental results --- p.67 / Chapter 4.4 --- Summary --- p.84 / Chapter 5 --- Conclusions --- p.86 / Appendix A --- p.89 / Bibliography --- p.90

by Tse, Fu Wing. / Thesis (M.Phil.)--Chinese University of Hong Kong, 1996. / Includes bibliographical references (leaves 155-[63]). / Acknowledgment --- p.iii / Abstract --- p.iv / Contents --- p.vi / List of Tables --- p.x / List of Figures --- p.xii / Notations --- p.xvii / Chapter 1 --- Introduction --- p.1 / Chapter 1.1 --- DC coefficient restoration --- p.1 / Chapter 1.2 --- Model based image compression --- p.5 / Chapter 1.3 --- The minimum edge difference criterion and the existing estima- tion schemes --- p.7 / Chapter 1.3.1 --- Fundamental definitions --- p.8 / Chapter 1.3.2 --- The minimum edge difference criterion --- p.9 / Chapter 1.3.3 --- The existing estimation schemes --- p.10 / Chapter 1.4 --- Thesis outline --- p.14 / Chapter 2 --- A mathematical description of the DC coefficient restoration problem --- p.17 / Chapter 2.1 --- Introduction --- p.17 / Chapter 2.2 --- Mathematical formulation --- p.18 / Chapter 2.3 --- Properties of H --- p.22 / Chapter 2.4 --- Analysis of the DC coefficient restoration problem --- p.22 / Chapter 2.5 --- The MED criterion as an image model --- p.25 / Chapter 2.6 --- Summary --- p.27 / Chapter 3 --- The global estimation scheme --- p.29 / Chapter 3.1 --- Introduction --- p.29 / Chapter 3.2 --- the global estimation scheme --- p.30 / Chapter 3.3 --- Theory of successive over-relaxation --- p.34 / Chapter 3.3.1 --- Introduction --- p.34 / Chapter 3.3.2 --- Gauss-Seidel iteration --- p.35 / Chapter 3.3.3 --- Theory of successive over-relaxation --- p.38 / Chapter 3.3.4 --- Estimation of optimal relaxation parameter --- p.41 / Chapter 3.4 --- Using successive over-relaxation in the global estimation scheme --- p.43 / Chapter 3.5 --- Experiments --- p.48 / Chapter 3.6 --- Summary --- p.49 / Chapter 4 --- The block selection scheme --- p.52 / Chapter 4.1 --- Introduction --- p.52 / Chapter 4.2 --- Failure of the minimum edge difference criterion --- p.53 / Chapter 4.3 --- The block selection scheme --- p.55 / Chapter 4.4 --- Using successive over-relaxation with the block selection scheme --- p.57 / Chapter 4.5 --- Practical considerations --- p.58 / Chapter 4.6 --- Experiments --- p.60 / Chapter 4.7 --- Summary --- p.61 / Chapter 5 --- The edge selection scheme --- p.65 / Chapter 5.1 --- Introduction --- p.65 / Chapter 5.2 --- Edge information and the MED criterion --- p.66 / Chapter 5.3 --- Mathematical formulation --- p.70 / Chapter 5.4 --- Practical Considerations --- p.74 / Chapter 5.5 --- Experiments --- p.76 / Chapter 5.6 --- Discussion of edge selection scheme --- p.78 / Chapter 5.7 --- Summary --- p.79 / Chapter 6 --- Performance Analysis --- p.81 / Chapter 6.1 --- Introduction --- p.81 / Chapter 6.2 --- Mathematical derivations --- p.82 / Chapter 6.3 --- Simulation results --- p.92 / Chapter 6.4 --- Summary --- p.96 / Chapter 7 --- The DC coefficient restoration scheme with baseline JPEG --- p.97 / Chapter 7.1 --- Introduction --- p.97 / Chapter 7.2 --- General specifications --- p.97 / Chapter 7.3 --- Simulation results --- p.101 / Chapter 7.3.1 --- The global estimation scheme with the block selection scheme --- p.101 / Chapter 7.3.2 --- The global estimation scheme with the edge selection scheme --- p.113 / Chapter 7.3.3 --- Performance comparison at the same bit rate --- p.121 / Chapter 7.4 --- Computation overhead using the DC coefficient restoration scheme --- p.134 / Chapter 7.5 --- Summary --- p.134 / Chapter 8 --- Conclusions and Discussions --- p.136 / Chapter A --- Fundamental definitions --- p.144 / Chapter B --- Irreducibility by associated directed graph --- p.146 / Chapter B.1 --- Irreducibility and associated directed graph --- p.146 / Chapter B.2 --- Derivation of irreducibility --- p.147 / Chapter B.3 --- Multiple blocks selection --- p.149 / Chapter B.4 --- Irreducibility with edge selection --- p.151 / Chapter C --- Sample images --- p.153 / Bibliography --- p.155

Submitted by WELTON FRANCISCO DE OLIVEIRA null (welton.oliveira3@etec.sp.gov.br) on 2017-03-16T16:03:13Z No. of bitstreams: 1 Uma proposta para ampliar a perspectiva de professores e alunos no estudo de matrizes.pdf: 12604887 bytes, checksum: cb8a97167b40fc0fe963439e55c0a0ff (MD5) / Approved for entry into archive by Juliano Benedito Ferreira (julianoferreira@reitoria.unesp.br) on 2017-03-21T18:00:34Z (GMT) No. of bitstreams: 1 oliveira_wf_me_sjrp.pdf: 12604887 bytes, checksum: cb8a97167b40fc0fe963439e55c0a0ff (MD5) / Made available in DSpace on 2017-03-21T18:00:34Z (GMT). No. of bitstreams: 1 oliveira_wf_me_sjrp.pdf: 12604887 bytes, checksum: cb8a97167b40fc0fe963439e55c0a0ff (MD5) Previous issue date: 2017-02-24 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES) / As matrizes são objeto de estudo na Educação Básica e na Educação Superior, porém, apesar de estarem relacionadas a diversas aplicações na Matemática, Engenharia, Computação Gráfica, e Economia, por exemplo, no Ensino Médio são abordadas de maneira superficial, mecânica e subjetiva. Em 2008, a proposta curricular do Estado de São Paulo tentou alterar esse panorama associando o estudo de matrizes a codificações e transformações geométricas. No entanto, como professor de matemática da rede estadual de ensino de São Paulo desde 2005, entendo nos diálogos com os colegas professores de Matemática e nos resultados das avaliações, sejam internas ou externas, que a estrutura do material oferecido ainda deixa lacunas que dificultam o ensino de matrizes. O presente trabalho pretende utilizar o software GeoGebra como principal agregador de teoria e prática, com foco no estudo de transformações geométricas. Além disso, serão apresentadas aplicações de matrizes na computação gráfica e imagens digitais. Outro ponto relevante é a proposta diferenciada de resolução de situações de aprendizagem contidas no material de apoio ao currículo do Estado de São Paulo. Também serão elaboradas atividades sobre transformações geométricas. Essas atividades serão aplicadas como pesquisa a um grupo de alunos do Ensino Médio. Dessa forma, pretende-se não descartar o material didático existente, mas sim enriquecer e aprimorar as práticas pedagógicas em sala de aula, transformando um material muitas vezes rejeitado em uma poderosa fonte de conhecimento que oferece aos professores e alunos do ensino médio uma alternativa que amplia a perspectiva de Matriz de forma eficiente e significativa. / The matrices are object of study in Basic Education and Higher Education, but, although they are related to several applications in Mathematics, Engineering, Computer Graphics, and Economics, for example, in High School are approached superficially, mechanically and subjectively. In 2008, the curricular proposal of the State of São Paulo tried to change this scenario by associating the study of matrices with geometric codifications and transformations. However, as a professor of mathematics at the São Paulo state education network since 2005, I understand in the dialogues with my fellow mathematics teachers and in the results of the evaluations, whether internal or external, that the structure of the material offered still leaves gaps that make it difficult to Teaching of matrices. The present work intends to use GeoGebra software as the main aggregator of theory and practice, focusing on the study of geometric transformations. In addition, matrix applications will be presented in computer graphics and digital images. Another relevant point is the differentiated proposal for solving learning situations contained in the curriculum support material of the State of São Paulo. Also will be elaborated activities on geometric transformations. These activities will be applied as research to a group of high school students. Thus, it is intended not to discard existing teaching material, but rather to enrich and improve pedagogical practices in the classroom, transforming an often rejected material into a powerful source of knowledge that offers teachers and high school students an alternative that Extends the matrix perspective efficiently and significantly.