Dissertations / Theses: 'Geometric and numerical sequences'

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TITONELI, LUANA MIRANDA BALTAZAR. "THE PATTERN OBSERVATION: MATHEMATICAL MODELING THROUGH NUMERICAL SEQUENCES AND GEOMETRIC OBJECTS." PONTIFÍCIA UNIVERSIDADE CATÓLICA DO RIO DE JANEIRO, 2017. http://www.maxwell.vrac.puc-rio.br/Busca_etds.php?strSecao=resultado&nrSeq=33077@1.

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PONTIFÍCIA UNIVERSIDADE CATÓLICA DO RIO DE JANEIRO
COORDENAÇÃO DE APERFEIÇOAMENTO DO PESSOAL DE ENSINO SUPERIOR
PROGRAMA DE MESTRADO PROFISSIONAL EM MATEMÁTICA EM REDE NACIONAL
Este trabalho é uma análise de padrões que são modelados matematicamente através de conceitos que envolvem as sequências numéricas bem como aspectos geométricos. São consideradas algumas aplicações práticas de conteúdos trabalhados na educação básica, muitas vezes estudados de forma mecânica através de fórmulas que tornam a Matemática enfadonha e até sem sentido para os discentes. O objetivo é mostrar que a Matemática transpõe os limites das salas de aula e que sua beleza pode ser vista em áreas diversas. As ideias e conceitos que envolvem as Progressões Aritméticas e Geométricas, por exemplo, são úteis na resolução de várias situações. A arte musical que está envolta em conhecimentos matemáticos desde os primórdios de seu desenvolvimento. Os estudos desenvolvidos com a sequência de Fibonacci e como está relacionada com a razão áurea e com fenômenos naturais que aparentemente nada teriam em comum. Além disso, a presença tão marcante na natureza das características dos fractais que traçam um padrão de formação para certos elementos naturais. É possível fazer com que o processo ensino- aprendizagem de Matemática torne-se efetivo através da abordagem dos conteúdos de forma prática, o que desperta no aluno o desejo de compreender o que é proposto. Este trabalho é inspirado na frase de Pitágoras: A Matemática é o alfabeto com o qual Deus escreveu o Universo e o que pretende-se é mostrar que esta ciência de fato está em toda a parte e que seu aprendizado pode ser significativo e interessante.
This work is an analysis of patterns that are modeled mathematically through concepts involving numerical sequences as well as geometric aspects. Some practical applications of content worked in basic education are considered, often mechanically studied through formulas that make Mathematics boring and even meaningless to students. The goal is to show that Mathematics transposes the boundaries of classrooms and that its beauty can be seen in several areas. The ideas and concepts that involve Arithmetic and Geometric Progressions, for example, are useful in solving various situations. The musical art that is shrouded in mathematical knowledge from the beginnings of its development. The studies developed with the Fibonacci sequence and how it is related to the golden ratio and with natural phenomena that apparently would have nothing in common. In addition, the presence so striking in the nature of the characteristics of the fractals that lay out a pattern of formation for certain natural elements. It is possible to make the teaching-learning process of Mathematics become effective by approaching the contents in a practical way, which awakens in the student the desire to understand what is proposed. This work is inspired by the phrase of Pythagoras: Mathematics is the alphabet with which God wrote the Universe and what is intended is to show that this science is indeed everywhere and that its learning can be meaningful and interesting.

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Batista, Bárbara Regina da Silveira. "SEQUÊNCIAS NUMÉRICAS A PARTIR DA GEOMETRIA FRACTAL PARA LICENCIANDOS EM MATEMÁTICA Santa Maria 2017." Centro Universitário Franciscano, 2017. http://www.tede.universidadefranciscana.edu.br:8080/handle/UFN-BDTD/595.

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This dissertation is a result of a mathematic investigation carried out in an university, located in Santa Maria/RS, that had as objective investigate which contributions of Fractal Geometry, when was used to introduce the content of numerical sequences, to Mathematics students. This is a mathematical investigation, as a research methodology, for systematization of teaching, complemented by the qualitative approach. Fractal Geometry allows the integration of many Mathematic fields and others sciences and, when inserted in teaching process, can develop the experimental side of students and understand as a facilitator to apropration of numerical sequences concepts. The data collect was by means of photographical register, notes, material made by participants and constructions and performed registered activities in a field journal, during two horas in each workshop. Previously, the application was developed in a pilot Project, with a activities sequence, involving three licenced Mathematics professor, belonging at the institution that the researcher acts and they had experience with calculation, Statistics, discrete mathematics, analytical geometry and linear algebra subjects. Such professors never had worked with fractal geometry, even though they had some superficial knowledge about the subject, without however using it in their activities. Workshop application with professor allowed a reflexion of the referrals given by the researcher and provided the correction of ways to posterior reapplication with the graduates.in a first meeting, the researcher made a survey about the students framing on a logical sequence of graduation, concluding every graduates had finished some calculation subject. At the same meeting, explored a fractal construction by materials resources as ruler and compass, recovering some contents, forgetted by them. In the second meeting, was resumed the Snowflake fractal, builded at first meeting, to obtain sequences, involving perimeters and áreas. In a survey, applied to participants, was verified the relevance of project to recover knowledges of numerical sequences convergence, that the same indicated possibilities of using in a future professional practic, since the application was made in Mathematic Analysis and the focus in the workshop had given a new sight about the contente in a direction of teaching, main object of professor training.
Esta dissertação é resultante de uma investigação matemática realizada em uma Instituição de Ensino Superior no Município de Santa Maria/RS, a qual teve como objetivo investigar quais as contribuições da Geometria Fractal quando utilizada para introdução do conteúdo de sequências numéricas para licenciandos em Matemática. Trata-se da Investigação Matemática, como metodologia de pesquisa, para a sistematização do ensino, complementando-se por meio de uma abordagem qualitativa. A Geometria Fractal permite a integração de vários campos da Matemática e de outras ciências e, quando inserida no ensino, pode desenvolver o lado experimental dos alunos e entender Geometria como facilitadora para apropriação de conceitos de sequências numéricas. A coleta de dados deu-se por meio de registro fotográfico, anotações, material confeccionado pelos participantes e as construções e atividades realizadas e registradas em diário de campo durante dois encontros de 2 horas cada em uma oficina. Anteriormente à aplicação com os estudantes foi desenvolvido um projeto piloto com a sequência de atividades, envolvendo três professores com Licenciatura em Matemática, pertencentes à instituição em que a pesquisadora atua e que já tinham experiência com as disciplinas de Cálculo, Estatística, Matemática Discreta, Geometria Analítica e Álgebra Linear. Tais professores nunca haviam trabalhado com Geometria Fractal, muito embora tivessem algum conhecimento superficial da mesma, sem, entretanto, a utilizarem em suas atividades. A aplicação da oficina com os professores permitiu reflexão sobre os encaminhamentos dados pela pesquisadora e proporcionou correção de rumos para replicação posterior com os licenciandos. Num primeiro encontro a pesquisadora fez um levantamento sobre o enquadramento dos estudantes no quadro de sequência lógica do curso, tendo concluído que todos já haviam cursado alguma disciplina de Cálculo. No mesmo encontro explorou a construção de um fractal por meio de recursos materiais como régua e compasso, resgatando alguns conteúdos já esquecidos por eles. No segundo encontro, foi retomado o fractal Floco de Neve, construído no primeiro encontro, para obtenção de sequências envolvendo perímetros e áreas. Num questionário aplicado aos participantes foi constatada a relevância do projeto para resgatar conhecimentos de convergência de sequência numéricas, sendo que os mesmos indicaram possibilidades de utilização na prática profissional futura, uma vez que a aplicação foi realizada na disciplina de Análise Matemática e o foco dado na oficina proporcionou um novo olhar sobre o conteúdo voltado ao ensino, objeto principal da formação de professores.

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Brum, Maria Gorete Nascimento. "ATIVIDADES INVESTIGATIVAS PARA O ENSINO DE MATEMÁTICA PARA ALUNOS DE 5º SÉRIE DO ENSINO FUNDAMENTAL." Universidade Franciscana, 2012. http://tede.universidadefranciscana.edu.br:8080/handle/UFN-BDTD/128.

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Coordenação de Aperfeiçoamento de Pessoal de Nível Superior
The present research investigated the contributions of the use of investigative activities in the exploration of standards and regularities in numerical and geometric sequences as elements that become easy the learning of the pupils of 5º series of Basic Education. This work was carried through with a group of 5º degree with 30 pupils of the State school of Basic Education Marechal Rondon in the periphery of the city of Santa Maria, RS. The date of the research, qualitative matrix, had been gotten of the direct action teacher s in the classroom with the pupils by means of the observation and the registers in its diary beyond the analysis of the pupils, work and the presentations to the great group. It can be inferred that the objectives considered in the sessions as explore the standard concept, to recognize, to describe standards, to continue the drawing of the sequence was reached. The objectives to generalize, to explore the notion and properties of the numbers pairs, uneven and multiple, as well as the involution of natural numbers and to work the concept of area and perimeter of plain figures, partially had been reached. The results presented for the pupils it can be concluded that the investigative activities worked with the pupils of 5ª degree, had propitiated the increase of interest, the motivation in the accomplishment of the activities proposals in classroom and as consequence had an improvement in the learning.
A presente pesquisa investigou as contribuições da utilização de atividades investigativas na exploração de padrões e regularidades em sequências numéricas e geométricas como elementos facilitadores da aprendizagem dos alunos de 5º série do Ensino Fundamental. Este trabalho foi realizado com uma turma de 5º série com 30 alunos da escola Estadual de Ensino Fundamental Marechal Rondon na periferia de Santa Maria R.S. Os dados da pesquisa, de cunho qualitativo, foram obtidos da ação direta do professor na sala de aula com os alunos por meio da observação e dos registros no seu diário de campo, além da análise dos trabalhos dos alunos e de suas apresentações ao grande grupo. Pode-se inferir que os objetivos propostos nas sessões como explorar o conceito de padrões, reconhecer, descrever padrões, continuar o desenho da sequência foram plenamente atingidos. Os objetivos de generalizar, explorar a noção e propriedade dos números pares, ímpares e múltiplos, bem como a potenciação de números naturais e trabalhar o conceito de área e perímetro de figuras planas, foram parcialmente atingidos. Dos resultados apresentados pelos alunos pode-se concluir que as atividades investigativas trabalhadas com os alunos de 5º série, propiciaram o aumento de interesse, a motivação na realização das atividades propostas em sala de aula e como consequência houve uma melhoria na aprendizagem.

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Kaneko, Hajime. "LIMIT POINTS OF FRACTIONAL PARTS OF GEOMETRIC SEQUENCES." 京都大学 (Kyoto University), 2010. http://hdl.handle.net/2433/120624.

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Palmacci, Matthew Stephen. "Escher's problem and numerical sequences." Link to electronic thesis, 2006. http://www.wpi.edu/Pubs/ETD/Available/etd-042706-133106/.

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Lawver, Jordan D. "Robust Feature Tracking in Image Sequences Using View Geometric Constraints." The Ohio State University, 2013. http://rave.ohiolink.edu/etdc/view?acc_num=osu1365611706.

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Alsallami, Shami Ali M. "Discrete integrable systems and geometric numerical integration." Thesis, University of Leeds, 2018. http://etheses.whiterose.ac.uk/22291/.

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This thesis deals with discrete integrable systems theory and modified Hamiltonian equations in the field of geometric numerical integration. Modified Hamiltonians are used to show that symplectic schemes for Hamiltonian systems are accurate over long times. However, for nonlinear systems the series defining the modified Hamiltonian equation usually diverges. The first part of the thesis demonstrates that there are nonlinear systems where the modified Hamiltonian has a closed-form expression and hence converges. These systems arise from the theory of discrete integrable systems. Specifically, they arise as reductions of a lattice version of the Korteweg-de Vries (KdV) partial differential equation. We present cases of one and two degrees of freedom symplectic mappings, for which the modified Hamiltonian equations can be computed as a closed form expression using techniques of action-angle variables, separation of variables and finite-gap integration. These modified Hamiltonians are also given as power series in the time step by Yoshida's method based on the Baker-Campbell-Hausdorff series. Another example is a system of an implicit dependence on the time step, which is obtained by dimensional reduction of a lattice version of the modified KdV equation. The second part of the thesis contains a different class of discrete-time system, namely the Boussinesq type, which can be considered as a higher-order counterpart of the KdV type. The development and analysis of this class by means of the B{\"a}cklund transformation, staircase reductions and Dubrovin equations forms one of the major parts of the thesis. First, we present a new derivation of the main equation, which is a nine-point lattice Boussinesq equation, from the B{\"a}cklund transformation for the continuous Boussinesq equation. Second, we focus on periodic reductions of the lattice equation and derive all necessary ingredients of the corresponding finite-dimensional models. Using the corresponding monodromy matrix and applying techniques from Lax pair and $r$-matrix structure analysis to the Boussinesq mappings, we study the dynamics in terms of the so-called Dubrovin equations for the separated variables.

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San, Juan Camilo Andrés Méndez. "Texts, numerical sequences and patterns in my recent music." Thesis, Royal College of Music, 2015. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.691366.

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Radvar-Esfahlan, Hassan. "Fixtureless geometric inspection of nonrigid parts using "generalized numerical inspection fixture"." Mémoire, École de technologie supérieure, 2014. http://espace.etsmtl.ca/1294/1/RADVAR_ESFAHLAN_Hassan.pdf.

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Aujourd’hui les pièces mécaniques de forme libre et qui sont souples (non rigides) sont fréquentes dans les industries automobile et aéronautique. Ces pièces possèdent des formes significativement différentes à l'état libre que leurs formes nominales, telles que définies dans un modeleur numérique, en raison de leurs variations dimensionnelles et géométriques, l’effet de la gravité et les contraintes résiduelles induites par le procédé de fabrication. Pour l'inspection géométrique de ces pièces flexibles, des appareils d'inspection spécialisés tel que les gabarits de conformation, en combinaison avec les machines à mesure tridimensionnelle (MMT) et/ou des dispositifs d'acquisition de données optiques (scanners) sont utilisés. Ce qui se traduit immanquablement par des coûts et des délais additionnels qui se traduisent par une carence de compétitivité pour l’industrie. L'objectif de cette thèse est de faciliter l'inspection dimensionnelle et géométrique des composants flexibles à partir d'un nuage de points sans l'aide d’un gabarit ou autre opération de conformation secondaire. Plus précisément, nous visons à développer une méthodologie pour localiser et quantifier les défauts de profil dans le cas des coques minces qui sont typiques pour les industries aéronautique et automobile. La méthodologie présentée est basée sur le fait que la distance géodésique entre deux points d'une forme demeure invariante au cours d'une déformation isométrique (absence d’étirement, stretch). Cette étude développe donc la théorie générale, les méthodes et outils pour une métrologie des pièces non rigides en se basant sur l’hypothèse d’une déformation isométrique. Nous avons ainsi développé une méthode originale que nous avons nommée ‘Gabarit d'Inspection Numérique Généralisée (GNIF)’. C’est une méthodologie robuste qui utilise les découvertes et technologies récemment développées en géométrie métrique et algorithmique. Les techniques de réduction dimensionnelle non linéaire sont employées pour identifier les meilleures correspondances entre deux sets de points (CAD et nuage mesuré). Finalement, la méthode des éléments finis est employée en post-traitement pour ‘caler’ les deux nuages de points et produire un état numérique ‘virtuel’ d’une opération de conformation pour atteindre le but du projet qui est de développer une approche générale de l'inspection géométrique sans gabarit pour les pièces non rigides. La validation et l’exploration des performances métrologiques de notre approche sont réalisées sur des composants typiques de l’industrie.

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Fasi, Massimiliano. "Weighted geometric mean of large-scale matrices: numerical analysis and algorithms." Master's thesis, Alma Mater Studiorum - Università di Bologna, 2015. http://amslaurea.unibo.it/8274/.

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Computing the weighted geometric mean of large sparse matrices is an operation that tends to become rapidly intractable, when the size of the matrices involved grows. However, if we are not interested in the computation of the matrix function itself, but just in that of its product times a vector, the problem turns simpler and there is a chance to solve it even when the matrix mean would actually be impossible to compute. Our interest is motivated by the fact that this calculation has some practical applications, related to the preconditioning of some operators arising in domain decomposition of elliptic problems. In this thesis, we explore how such a computation can be efficiently performed. First, we exploit the properties of the weighted geometric mean and find several equivalent ways to express it through real powers of a matrix. Hence, we focus our attention on matrix powers and examine how well-known techniques can be adapted to the solution of the problem at hand. In particular, we consider two broad families of approaches for the computation of f(A) v, namely quadrature formulae and Krylov subspace methods, and generalize them to the pencil case f(A\B) v. Finally, we provide an extensive experimental evaluation of the proposed algorithms and also try to assess how convergence speed and execution time are influenced by some characteristics of the input matrices. Our results suggest that a few elements have some bearing on the performance and that, although there is no best choice in general, knowing the conditioning and the sparsity of the arguments beforehand can considerably help in choosing the best strategy to tackle the problem.

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SOUSA, RAFAEL ARAUJO DE. "GEOMETRIC AND NUMERICAL ADAPTATIVITY OF 2D AND 3D FINITE ELEMENT MESHES." PONTIFÍCIA UNIVERSIDADE CATÓLICA DO RIO DE JANEIRO, 2007. http://www.maxwell.vrac.puc-rio.br/Busca_etds.php?strSecao=resultado&nrSeq=10376@1.

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COORDENAÇÃO DE APERFEIÇOAMENTO DO PESSOAL DE ENSINO SUPERIOR
TECNOLOGIA EM COMPUTAÇÃO GRÁFICA
Este trabalho apresenta uma metodologia para geração de malhas adaptativas de elementos finitos 2D e 3D usando modeladores geométricos com multi-regiões e superfícies paramétricas. A estratégia adaptativa adotada é fundamentada no refinamento independente das curvas, superfícies e sólidos. Inicialmente as curvas são refinadas, no seu espaço paramétrico, usando uma técnica de partição binária da curva (binary-tree). A discretização das curvas é usada como dado de entrada para o refinamento das superfícies. A discretização destas é realizada no seu espaço paramétrico e utiliza uma técnica de avanço de fronteira combinada com uma estrutura de dados do tipo quadtree para gerar uma malha não estruturada de superfície. Essas malhas de superfícies são usadas como dado de entrada para o refinamento dos domínios volumétricos. A discretização volumétrica combina uma estrutura de dados do tipo octree juntamente com a técnica de avanço de fronteira para gerar uma malha sólida não estruturada de elementos tetraédricos. As estruturas de dados auxiliares dos tipos binary-tree, quadtree e octree são utilizadas para armazenar os tamanhos característicos dos elementos gerados no refinamento das curvas, superfícies e regiões volumétricas. Estes tamanhos característicos são definidos pela estimativa de erro numérico associado à malha global do passo anterior do processo adaptativo. A estratégia adaptativa é implementada em dois modeladores: o MTOOL (2D) e o MG (3D), que são responsáveis pela criação de um modelo geométrico, podendo ter, multi-regiões, onde no caso 3D as curvas e superfícies são representadas por NURBS.
This work presents a methodology for adaptive generation of 2D and 3D finite-element meshes using geometric modeling with multi- regions and parametric surfaces. The adaptive strategy adopted in this methodology is based on independent refinements of curves, surfaces and solids. Initially, the model´s curves are refined using a binary-partition algorithm in parametric space. The discratizetion of these curves is used as input for the refinement of adjacent surfaces. Surface discretization is also performed in parametric space and employs a quadtree-based refinement coupled to an advancing-front technique for the generation of an unstructured triangulation. These surface meshes are used as input for the refinement adjacent volumetric domains. Volume discretization combines an octree refinement with an advancing-front technique to generate an unstructural mesh of tetrahedral elements. In all stages of the adaptive strategy, the refinement of curves, surface meshes and solid meshes is based on estimated numerical errors associated to the mesh of the previous step in the adaptive process. In addition, curve and surface refinement takes into account metric distortions between parametric and Cartesian spaces and high curvatures of the model´s geometric entities. The adaptive strategies are implemented in two different modelers: MTOOL (2D) and MG (3D), which are responsible for the creation of a geometric model with multi-regions, where for case 3D the curves and surfaces are represented by NURBS, and for the interactive and automatic finite-element mesh generation associated to surfaces and solid regions. Numerical examples of the simulation of engineering problems are presented in order to validate the methodology proposed in this work.

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Ross, David M. "Hopf bifurcations in ecological models : algebraic, geometric and numerical methods of analysis." Thesis, University of Stirling, 2002. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.275981.

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Westlund, Arvid. "Image analysis tool for geometric variations of the jugular veins in ultrasonic sequences : Development and evaluation." Thesis, Uppsala universitet, Avdelningen för visuell information och interaktion, 2018. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-348336.

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The aim of this project is to develop and perform a first evaluation of a software, based on the active contour, which automatically computes the cross-section area of the internal jugular veins through a sequence of 90 ultrasound images. The software is intended to be useful in future research in the field of intra cranial pressure and its associated diseases. The biomechanics of the internal jugular veins and its relationship to the intra cranial pressure is studied with ultrasound. It generates data in the form of ultrasound sequences shot in seven different body positions, supine to upright. Vein movements in cross section over the cardiac cycle are recorded for all body positions. From these films, it is interesting to know how the cross-section area varies over the cardiac cycle and between body positions, in order to estimate the pressure. The software created was semi-automatic, where the operator loads each individual sequence and sets the initial contour on the first frame. It was evaluated in a test by comparing its computed areas with manually estimated areas. The test showed that the software was able to track and compute the area with a satisfactory accuracy for a variety of sequences. It is also faster and more consistent than manual measurements. The most difficult sequences to track were small vessels with narrow geometries, fast moving walls, and blurry edges. Further development is required to correct a few bugs in the algorithm. Also, the improved algorithm should be evaluated on a larger sample of sequences before using it in research.

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Bader, Philipp Karl-Heinz. "Geometric Integrators for Schrödinger Equations." Doctoral thesis, Universitat Politècnica de València, 2014. http://hdl.handle.net/10251/38716.

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The celebrated Schrödinger equation is the key to understanding the dynamics of quantum mechanical particles and comes in a variety of forms. Its numerical solution poses numerous challenges, some of which are addressed in this work. Arguably the most important problem in quantum mechanics is the so-called harmonic oscillator due to its good approximation properties for trapping potentials. In Chapter 2, an algebraic correspondence-technique is introduced and applied to construct efficient splitting algorithms, based solely on fast Fourier transforms, which solve quadratic potentials in any number of dimensions exactly - including the important case of rotating particles and non-autonomous trappings after averaging by Magnus expansions. The results are shown to transfer smoothly to the Gross-Pitaevskii equation in Chapter 3. Additionally, the notion of modified nonlinear potentials is introduced and it is shown how to efficiently compute them using Fourier transforms. It is shown how to apply complex coefficient splittings to this nonlinear equation and numerical results corroborate the findings. In the semiclassical limit, the evolution operator becomes highly oscillatory and standard splitting methods suffer from exponentially increasing complexity when raising the order of the method. Algorithms with only quadratic order-dependence of the computational cost are found using the Zassenhaus algorithm. In contrast to classical splittings, special commutators are allowed to appear in the exponents. By construction, they are rapidly decreasing in size with the semiclassical parameter and can be exponentiated using only a few Lanczos iterations. For completeness, an alternative technique based on Hagedorn wavepackets is revisited and interpreted in the light of Magnus expansions and minor improvements are suggested. In the presence of explicit time-dependencies in the semiclassical Hamiltonian, the Zassenhaus algorithm requires a special initiation step. Distinguishing the case of smooth and fast frequencies, it is shown how to adapt the mechanism to obtain an efficiently computable decomposition of an effective Hamiltonian that has been obtained after Magnus expansion, without having to resolve the oscillations by taking a prohibitively small time-step. Chapter 5 considers the Schrödinger eigenvalue problem which can be formulated as an initial value problem after a Wick-rotating the Schrödinger equation to imaginary time. The elliptic nature of the evolution operator restricts standard splittings to low order, ¿ < 3, because of the unavoidable appearance of negative fractional timesteps that correspond to the ill-posed integration backwards in time. The inclusion of modified potentials lifts the order barrier up to ¿ < 5. Both restrictions can be circumvented using complex fractional time-steps with positive real part and sixthorder methods optimized for near-integrable Hamiltonians are presented. Conclusions and pointers to further research are detailed in Chapter 6, with a special focus on optimal quantum control.
Bader, PK. (2014). Geometric Integrators for Schrödinger Equations [Tesis doctoral no publicada]. Universitat Politècnica de València. https://doi.org/10.4995/Thesis/10251/38716
TESIS
Premiado

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Johnson, Scott M. (Scott Matthew) 1978. "Investigation of efficient geometric shape algorithms for numerical simulation of discrete particle systems." Thesis, Massachusetts Institute of Technology, 2003. http://hdl.handle.net/1721.1/8037.

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Thesis (S.M.)--Massachusetts Institute of Technology, Dept. of Civil and Environmental Engineering, 2003.
Includes bibliographical references (leaves 46-49).
The efficiency of a discrete particle simulation implementation relies on several factors, including the geometric representation, contact resolution, and neighbor-sorting algorithm used. The focus here is on the first two of this list: the geometric representation and the corresponding contact resolution. An argument is developed to advocate the use of geometric representations with inconstant radius based on results of a numerical study of angles of repose for deposited grains. The equivalent spheres method is then developed as a potential cure for the problems arising from constant radius geometric representations. A coherent approach to utilizing this geometry in discrete element modeling is developed. This includes the proposal of an accurate, robust contact resolution algorithm and explicit functions to describe moments of inertia. Considerations for numerical modeling are also addressed, including numerical integration, formulation of rotation transformations, and resolution of forces and motions in the context of rigid body motions. The details of a generalized computational implementation of the representation are also given, and empirical convergence properties are compared with a different method for detecting contact between ellipsoidal approximations.
by Scott M. Johnson.
S.M.

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Torberntsson, Kim, and Vidar Stiernström. "A High Order Finite Difference Method for Simulating Earthquake Sequences in a Poroelastic Medium." Thesis, Uppsala universitet, Avdelningen för beräkningsvetenskap, 2016. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-298414.

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Induced seismicity (earthquakes caused by injection or extraction of fluids in Earth's subsurface) is a major, new hazard in the United States, the Netherlands, and other countries, with vast economic consequences if not properly managed. Addressing this problem requires development of predictive simulations of how fluid-saturated solids containing frictional faults respond to fluid injection/extraction. Here we present a numerical method for linear poroelasticity with rate-and-state friction faults. A numerical method for approximating the fully coupled linear poroelastic equations is derived using the summation-by-parts-simultaneous-approximation-term (SBP-SAT) framework. Well-posedness is shown for a set of physical boundary conditions in 1D and in 2D. The SBP-SAT technique is used to discretize the governing equations and show semi-discrete stability and the correctness of the implementation is verified by rigorous convergence tests using the method of manufactured solutions, which shows that the expected convergence rates are obtained for a problem with spatially variable material parameters. Mandel's problem and a line source problem are studied, where simulation results and convergence studies show satisfactory numerical properties. Furthermore, two problem setups involving fault dynamics and slip on faults triggered by fluid injection are studied, where the simulation results show that fluid injection can trigger earthquakes, having implications for induced seismicity. In addition, the results show that the scheme used for solving the fully coupled problem, captures dynamics that would not be seen in an uncoupled model. Future improvements involve imposing Dirichlet boundary conditions using a different technique, extending the scheme to handle curvilinear coordinates and three spatial dimensions, as well as improving the high-performance code and extending the study of the fault dynamics.

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Sharma, Harsh Apurva. "Structure-preserving Numerical Methods for Engineering Applications." Diss., Virginia Tech, 2020. http://hdl.handle.net/10919/99912.

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This dissertation develops a variety of structure-preserving algorithms for mechanical systems with external forcing and also extends those methods to systems that evolve on non-Euclidean manifolds. The dissertation is focused on numerical schemes derived from variational principles – schemes that are general enough to apply to a large class of engineering problems. A theoretical framework that encapsulates variational integration for mechanical systems with external forcing and time-dependence and which supports the extension of these methods to systems that evolve on non-Euclidean manifolds is developed. An adaptive time step, energy-preserving variational integrator is developed for mechanical systems with external forcing. It is shown that these methods track the change in energy more accurately than their fixed time step counterparts. This approach is also extended to rigid body systems evolving on Lie groups where the resulting algorithms preserve the geometry of the configuration space in addition to being symplectic as well as energy and momentum-preserving. The advantages of structure-preservation in the numerical simulation are illustrated by various representative examples from engineering applications, which include limit cycle oscillations of an aeroelastic system, dynamics of a neutrally buoyant underwater vehicle, and optimization for spherical shape correlation and matching.
Doctor of Philosophy
Accurate numerical simulation of dynamical systems over long time horizons is essential in applications ranging from particle physics to geophysical fluid flow to space hazard analysis. In many of these applications, the governing physical equations derive from a variational principle and their solutions exhibit physically meaningful invariants such as momentum, energy, or vorticity. Unfortunately, most traditional numerical methods do not account for the underlying geometric structure of the physical system, leading to simulation results that may suggest nonphysical behavior. In this dissertation, tools from geometric mechanics and computational methods are used to develop numerical integrators that respect the qualitative features of the physical system. The research presented here focuses on numerical schemes derived from variational principles– schemes that are general enough to apply to a large class of engineering problems. Energy-preserving algorithms are developed for mechanical systems by exploiting the underlying geometric properties. Numerical performance comparisons demonstrate that these algorithms provide almost exact energy preservation and lead to more accurate prediction. The advantages of these methods in the numerical simulation are illustrated by various representative examples from engineering applications, which include limit cycle oscillations of an aeroelastic system, dynamics of a neutrally buoyant underwater vehicle, and optimization for spherical shape correlation and matching.

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18

Hocking, Laird Robert. "Shell-based geometric image and video inpainting." Thesis, University of Cambridge, 2018. https://www.repository.cam.ac.uk/handle/1810/281805.

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The subject of this thesis is a class of fast inpainting methods (image or video) based on the idea of filling the inpainting domain in successive shells from its boundary inwards. Image pixels (or video voxels) are filled by assigning them a color equal to a weighted average of either their already filled neighbors (the ``direct'' form of the method) or those neighbors plus additional neighbors within the current shell (the ``semi-implicit'' form). In the direct form, pixels (voxels) in the current shell may be filled independently, but in the semi-implicit form they are filled simultaneously by solving a linear system. We focus in this thesis mainly on the image inpainting case, where the literature contains several methods corresponding to the {\em direct} form of the method - the semi-implicit form is introduced for the first time here. These methods effectively differ only in the order in which pixels (voxels) are filled, the weights used for averaging, and the neighborhood that is averaged over. All of them are very fast, but at the same time all of them leave undesirable artifacts such as ``kinking'' (bending) or blurring of extrapolated isophotes. This thesis has two main goals. First, we introduce new algorithms within this class, which are aimed at reducing or eliminating these artifacts, and also target a specific application - the 3D conversion of images and film. The first part of this thesis will be concerned with introducing 3D conversion as well as Guidefill, a method in the above class adapted to the inpainting problems arising in 3D conversion. However, the second and more significant goal of this thesis is to study these algorithms as a class. In particular, we develop a mathematical theory aimed at understanding the origins of artifacts mentioned. Through this, we seek is to understand which artifacts can be eliminated (and how), and which artifacts are inevitable (and why). Most of the thesis is occupied with this second goal. Our theory is based on two separate limits - the first is a {\em continuum} limit, in which the pixel width →0, and in which the algorithm converges to a partial differential equation. The second is an asymptotic limit in which h is very small but non-zero. This latter limit, which is based on a connection to random walks, relates the inpainted solution to a type of discrete convolution. The former is useful for studying kinking artifacts, while the latter is useful for studying blur. Although all the theoretical work has been done in the context of image inpainting, experimental evidence is presented suggesting a simple generalization to video. Finally, in the last part of the thesis we explore shell-based video inpainting. In particular, we introduce spacetime transport, which is a natural generalization of the ideas of Guidefill and its predecessor, coherence transport, to three dimensions (two spatial dimensions plus one time dimension). Spacetime transport is shown to have much in common with shell-based image inpainting methods. In particular, kinking and blur artifacts persist, and the former of these may be alleviated in exactly the same way as in two dimensions. At the same time, spacetime transport is shown to be related to optical flow based video inpainting. In particular, a connection is derived between spacetime transport and a generalized Lucas-Kanade optical flow that does not distinguish between time and space.

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19

Nkonkobe, Sithembele. "A study of barred preferential arrangements with applications to numerical approximation in electric circuits." Thesis, Rhodes University, 2016. http://hdl.handle.net/10962/d1020394.

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In 1854 Cayley proposed an interesting sequence 1,1,3,13,75,541,... in connection with analytical forms called trees. Since then there has been various combinatorial interpretations of the sequence. The sequence has been interpreted as the number of preferential arrangements of members of a set with n elements. Alternatively the sequence has been interpreted as the number of ordered partitions; the outcomes in races in which ties are allowed or geometrically the number of vertices, edges and faces of simplicial objects. An interesting application of the sequence is found in combination locks. The idea of a preferential arrangement has been extended to a wider combinatorial object called barred preferential arrangement with multiple bars. In this thesis we study barred preferential arrangements combinatorially with application to resistance of certain electrical circuits. In the process we derive some results on cyclic properties of the last digit of the number of barred preferential arrangements. An algorithm in python has been developed to find the number of barred preferential arrangements.

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20

Angoshtari, Arzhang. "Geometric discretization schemes and differential complexes for elasticity." Diss., Georgia Institute of Technology, 2013. http://hdl.handle.net/1853/49026.

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In this research, we study two different geometric approaches, namely, the discrete exterior calculus and differential complexes, for developing numerical schemes for linear and nonlinear elasticity. Using some ideas from discrete exterior calculus (DEC), we present a geometric discretization scheme for incompressible linearized elasticity. After characterizing the configuration manifold of volume- preserving discrete deformations, we use Hamilton’s principle on this configuration manifold. The discrete Euler-Lagrange equations are obtained without using Lagrange multipliers. The main difference between our approach and the mixed finite element formulations is that we simultaneously use three different discrete spaces for the displacement field. We test the efficiency and robustness of this geometric scheme using some numerical examples. In particular, we do not see any volume locking and/or checkerboarding of pressure in our numerical examples. This suggests that our choice of discrete solution spaces is compatible. On the other hand, it has been observed that the linear elastostatics complex can be used to find very efficient numerical schemes. We use some geometric techniques to obtain differential complexes for nonlinear elastostatics. In particular, by introducing stress functions for the Cauchy and the second Piola-Kirchhoff stress tensors, we show that 2D and 3D nonlinear elastostatics admit separate kinematic and kinetic complexes. We show that stress functions corresponding to the first Piola-Kirchhoff stress tensor allow us to write a complex for 3D nonlinear elastostatics that similar to the complex of 3D linear elastostatics contains both the kinematics an kinetics of motion. We study linear and nonlinear compatibility equations for curved ambient spaces and motions of surfaces in R3. We also study the relationship between the linear elastostatics complex and the de Rham complex. The geometric approach presented in this research is crucial for understanding connections between linear and nonlinear elastostatics and the Hodge Laplacian, which can enable one to convert numerical schemes of the Hodge Laplacian to those for linear and possibly nonlinear elastostatics.

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21

Minzé, Sérgio da Silva. "Séries geométricas no Ensino Fundamental." Universidade Estadual da Paraíba, 2015. http://tede.bc.uepb.edu.br/tede/jspui/handle/tede/2393.

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Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - CAPES
This work aims to develop a didatic sequence for the student can learn inductively the notion of convergent geometric series. The proposal was applied and developed in a class of 9th grade ofelementary school and the results obtainedwere very satisfactory. The work also contains a historical review of the concepts of sequences and geometric series.
Este trabalho tem como objetivo desenvolver uma sequência didática para que o aluno consiga aprender de forma indutiva a noção de série geométrica convergente. A o proposta foi aplicada e desenvolvida em uma turma do 9 ano do ensino fundamental e os resultados obtidos foram muito satisfatórios. O trabalho também contém uma resenha histórica dos conceitos de sequências e séries geométricas.

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22

Filchev, Ivan. "Buckling and geometric nonlinear FE analysis of pitched large-spanroof structure of wood." Thesis, Linnéuniversitetet, Institutionen för byggteknik (BY), 2016. http://urn.kb.se/resolve?urn=urn:nbn:se:lnu:diva-54324.

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An arched structure provides an effective load carrying system for large span structures. When it comes to long span roof structures, timber arches are one of the best solutions from both structural and aesthetical point of view. Glulam arched structures are often designed using slender elements due to economic consideration. Such slender cross-section shape increases the risk of instability. Instability analysis of straight members such as beam and column are explicitly defined in Eurocode. However, for instability of curved members no analytical approach is provided in the code, thus some numerical method is required. Nonetheless, an approximation is frequently used to obtain the effective buckling length for the arched structures in the plane of arches. In this master thesis a linear buckling analysis is carried out in Abaqus to obtain an optimal effective buckling length both in-plane and out-of-plane for circular glulam arched structures. The elastic springs are used to simulate the overall stiffness of the bracing system. The results obtained by the FE simulations are compared with a simple approximation method. Besides, the forces acting on the bracings system is obtained based on 3D geometric nonlinear stress analysis of the timber trusses. Our findings conclude that the approximation method overestimates the effective buckling length for the circular glulam arched structures. In addition, the study indicates that the position of the lateral supports along the length of the arch is an important design aspect for buckling behaviour of the arched structures. Moreover, in order to acquire an effective structure lateral supports are needed both in extrados and intrados. Furthermore, instead of using elastic spring elements to simulate the overall stiffness of the bracing system, a full 3D simulation of two parallel arches was performed. It was shown that the springs are stronger than the real bracing system for the studied arch.

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23

Sensi, Mattia. "A Geometric Singular Perturbation approach to epidemic compartmental models." Doctoral thesis, Università degli studi di Trento, 2021. http://hdl.handle.net/11572/286191.

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We study fast-slow versions of the SIR, SIRS and SIRWS epidemiological models, and of the SIRS epidemiological model on homogeneous graphs, obtained through the application of the moment closure method. The multiple time scale behavior is introduced to account for large differences between some of the rates of the epidemiological pathways. Our main purpose is to show that the fast-slow models, even though in nonstandard form, can be studied by means of Geometric Singular Perturbation Theory (GSPT). In particular, without using Lyapunov's method, we are able to not only analyze the stability of the endemic equilibria of the SIR and SIRS models, but also to show that in the remaining models limit cycles arise. We show that the proposed approach is particularly useful in more complicated (higher dimensional) models such as the SIRWS model and the SIRS on homogeneous graphs, for which we provide a detailed description of their dynamics by combining analytic and numerical techniques. In particular, for the latter we show that the model can give rise to periodic solutions, differently from the corresponding model based on homogeneous mixing.

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24

Ramos, Gabriel Lauffer. "Evolutionary sequences for H and He atmosphere massive white dwarf stars." reponame:Biblioteca Digital de Teses e Dissertações da UFRGS, 2018. http://hdl.handle.net/10183/181005.

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White dwarf stars are the most common final stage of stellar evolution, corresponding to 99% of all stars in the Galaxy. White dwarf models can be used to obtain the age of stellar populations, to build an initial to final mass relation to understand the connection between the properties of white dwarfs and their progenitors, determine the upper mass limit that separates white dwarfs progenitors from Type II supernovae, enhance the comprehension of the physical properties of high density matter and derive ages and masses for observed white dwarfs from the cooling tracks. The literature is populated with low mass and intermediate mass white dwarf models, however the massive white dwarfs are often forgotten and the evolutionary sequences are incomplete. In this dissertation, we compute full evolutionary sequences for massive white dwarfs, exploring the evolution of hydrogen-rich and hydrogen-deficient white dwarfs stars with masses between 1.012 and 1.307 M , and initial metallicity of Z = 0.02. These sequences are the result of main sequence stars with masses between 8.8 and 11.8 M . The simulations were performed with the Modules for Experiments in Stellar Astrophysics - MESA code, starting at the zero-age main sequence, through thermally pulsing and mass-loss phases, ending as the white dwarfs at the cooling sequence. Our simulations are full evolutionary, in which we consider the entire evolutionary history of the progenitors. We present reliable nuclear chemical profiles for the whole mass range considered, covering the different expected central compositions, i.e. C/O, O/Ne and Ne/O/Mg, and their dependence with the stellar mass. In addition, we present detailed chemical profiles of hybrid C/O-O/Ne core white dwarfs, found in the mass range between 1.024 and 1.150 M . We present the initial-to-final mass relation, mass-radius relation, and cooling times with improved crystallization limits, considering the effects of atmosphere and core composition.

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25

Stancil, Maurice Marcus. "Creation and Experimental Validation of a Numerical Model of a Michelson Interferometer." Thesis, Virginia Tech, 2017. http://hdl.handle.net/10919/74957.

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The study whose results are presented here was carried out in support of an ongoing larger effort to investigate and understand the impact of coherence and polarization on the performance of instruments intended to monitor the Earth's radiant energy budget. The visibility of fringes produced by a Michelson interferometer is known to be sensitive to the degree to which the incident light beam is monochromatic. Therefore, the Michelson interferometer has significant potential as a tool for quantifying the degree of temporal coherence of a quasi-monochromatic light beam. Simulation of the performance of an optical instrument using the Monte-Carlo ray-trace (MCRT) method has been shown to be an efficient method for transferring knowledge of the coherence state of a beam of light from one instrument to another. The goal of the effort reported here is to create and experimentally validate an MCRT model for the optical performance of a Michelson interferometer. The effort is motivated by the need to consolidate the knowledge and skills of the investigator in the realm of physical optics, and by the need to make a useful analytical tool available to other investigators in the larger effort.
Master of Science

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26

Chen, Yujia. "Geometric multigrid and closest point methods for surfaces and general domains." Thesis, University of Oxford, 2015. http://ora.ox.ac.uk/objects/uuid:56a3bf12-ff09-4ea5-b406-9d77054770e2.

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This thesis concerns the analytical and practical aspects of applying the Closest Point Method to solve elliptic partial differential equations (PDEs) on smooth surfaces and domains with smooth boundaries. A new numerical scheme is proposed to solve surface elliptic PDEs and a novel geometric multigrid solver is constructed to solve the resulting linear system. The method is also applied to coupled bulk-surface problems. A new embedding equation in a narrow band surrounding the surface is formulated so that it agrees with the original surface PDE on the surface and has a unique solution which is constant along the normals to the surface. The embedding equation is then discretized using standard finite difference scheme and barycentric Lagrange interpolation. The resulting scheme has 2nd-order accuracy in practice and is provably 2nd-order convergent for curves without boundary embedded in ℝ². To apply the method to solve elliptic equations on surfaces and domains with boundaries, the "ghost" point approach is adopted to handle Dirichlet, Neumann and Robin boundary conditions. A systematic method is proposed to represent values of ghost points by values of interior points according to boundary conditions. A novel geometric multigrid method based on the closest point representation of the surface is constructed to solve the resulting large sparse linear systems. Multigrid solvers are designed for surfaces with or without boundaries and domains with smooth boundaries. Numerical results indicate that the convergence rate of the multigrid solver stays roughly the same as we refine the mesh, as is desired of a multigrid algorithm. Finally the above methods are combined to solve coupled bulk-surface PDEs with some applications to biology.

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27

Aydin, Ayhan. "Geometric Integrators For Coupled Nonlinear Schrodinger Equation." Phd thesis, METU, 2005. http://etd.lib.metu.edu.tr/upload/12605773/index.pdf.

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Multisymplectic integrators like Preissman and six-point schemes and a semi-explicit symplectic method are applied to the coupled nonlinear Schrö
dinger equations (CNLSE). Energy, momentum and additional conserved quantities are preserved by the multisymplectic integrators, which are shown using modified equations. The multisymplectic schemes are backward stable and non-dissipative. A semi-explicit method which is symplectic in the space variable and based on linear-nonlinear, even-odd splitting in time is derived. These methods are applied to the CNLSE with plane wave and soliton solutions for various combinations of the parameters of the equation. The numerical results confirm the excellent long time behavior of the conserved quantities and preservation of the shape of the soliton solutions in space and time.

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28

Kopylov, Nikita. "Magnus-based geometric integrators for dynamical systems with time-dependent potentials." Doctoral thesis, Universitat Politècnica de València, 2019. http://hdl.handle.net/10251/118798.

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[ES] Esta tesis trata sobre la integración numérica de sistemas hamiltonianos con potenciales explícitamente dependientes del tiempo. Los problemas de este tipo son comunes en la física matemática, porque provienen de la mecánica cuántica, clásica y celestial. La meta de la tesis es construir integradores para unos problemas relevantes no autónomos: la ecuación de Schrödinger, que es el fundamento de la mecánica cuántica; las ecuaciones de Hill y de onda, que describen sistemas oscilatorios; el problema de Kepler con la masa variante en el tiempo. El Capítulo 1 describe la motivación y los objetivos de la obra en el contexto histórico de la integración numérica. En el Capítulo 2 se introducen los conceptos esenciales y unas herramientas fundamentales utilizadas a lo largo de la tesis. El diseño de los integradores propuestos se basa en los métodos de composición y escisión y en el desarrollo de Magnus. En el Capítulo 3 se describe el primero. Su idea principal consta de una recombinación de unos integradores sencillos para obtener la solución del problema. El concepto importante de las condiciones de orden se describe en ese capítulo. En el Capítulo 4 se hace un resumen de las álgebras de Lie y del desarrollo de Magnus que son las herramientas algebraicas que permiten expresar la solución de ecuaciones diferenciales dependientes del tiempo. La ecuación lineal de Schrödinger con potencial dependiente del tiempo está examinada en el Capítulo 5. Dado su estructura particular, nuevos métodos casi sin conmutadores, basados en el desarrollo de Magnus, son construidos. Su eficiencia es demostrada en unos experimentos numéricos con el modelo de Walker-Preston de una molécula dentro de un campo electromagnético. En el Capítulo 6, se diseñan los métodos de Magnus-escisión para las ecuaciones de onda y de Hill. Su eficiencia está demostrada en los experimentos numéricos con varios sistemas oscilatorios: con la ecuación de Mathieu, la ec. de Hill matricial, las ecuaciones de onda y de Klein-Gordon-Fock. El Capítulo 7 explica cómo el enfoque algebraico y el desarrollo de Magnus pueden generalizarse a los problemas no lineales. El ejemplo utilizado es el problema de Kepler con masa decreciente. El Capítulo 8 concluye la tesis, reseña los resultados y traza las posibles direcciones de la investigación futura.
[CAT] Aquesta tesi tracta de la integració numèrica de sistemes hamiltonians amb potencials explícitament dependents del temps. Els problemes d'aquest tipus són comuns en la física matemàtica, perquè provenen de la mecànica quàntica, clàssica i celest. L'objectiu de la tesi és construir integradors per a uns problemes rellevants no autònoms: l'equació de Schrödinger, que és el fonament de la mecànica quàntica; les equacions de Hill i d'ona, que descriuen sistemes oscil·latoris; el problema de Kepler amb la massa variant en el temps. El Capítol 1 descriu la motivació i els objectius de l'obra en el context històric de la integració numèrica. En Capítol 2 s'introdueixen els conceptes essencials i unes ferramentes fonamentals utilitzades al llarg de la tesi. El disseny dels integradors proposats es basa en els mètodes de composició i escissió i en el desenvolupament de Magnus. En el Capítol 3, es descriu el primer. La seua idea principal consta d'una recombinació d'uns integradors senzills per a obtenir la solució del problema. El concepte important de les condicions d'orde es descriu en eixe capítol. El Capítol 4 fa un resum de les àlgebres de Lie i del desenvolupament de Magnus que són les ferramentes algebraiques que permeten expressar la solució d'equacions diferencials dependents del temps. L'equació lineal de Schrödinger amb potencial dependent del temps està examinada en el Capítol 5. Donat la seua estructura particular, nous mètodes quasi sense commutadors, basats en el desenvolupament de Magnus, són construïts. La seua eficiència és demostrada en uns experiments numèrics amb el model de Walker-Preston d'una molècula dins d'un camp electromagnètic. En el Capítol 6 es dissenyen els mètodes de Magnus-escissió per a les equacions d'onda i de Hill. El seu rendiment està demostrat en els experiments numèrics amb diversos sistemes oscil·latoris: amb l'equació de Mathieu, l'ec. de Hill matricial, les equacions d'onda i de Klein-Gordon-Fock. El Capítol 7 explica com l'enfocament algebraic i el desenvolupament de Magnus poden generalitzar-se als problemes no lineals. L'exemple utilitzat és el problema de Kepler amb massa decreixent. El Capítol 8 conclou la tesi, ressenya els resultats i traça les possibles direccions de la investigació futura.
[EN] The present thesis addresses the numerical integration of Hamiltonian systems with explicitly time-dependent potentials. These problems are common in mathematical physics because they come from quantum, classical and celestial mechanics. The goal of the thesis is to construct integrators for several import ant non-autonomous problems: the Schrödinger equation, which is the cornerstone of quantum mechanics; the Hill and the wave equations, that describe oscillating systems; the Kepler problem with time-variant mass. Chapter 1 describes the motivation and the aims of the work in the historical context of numerical integration. In Chapter 2 essential concepts and some fundamental tools used throughout the thesis are introduced. The design of the proposed integrators is based on the composition and splitting methods and the Magnus expansion. In Chapter 3, the former is described. Their main idea is to recombine some simpler integrators to obtain the solution. The salient concept of order conditions is described in that chapter. Chapter 4 summarises Lie algebras and the Magnus expansion ¿ algebraic tools that help to express the solution of time-dependent differential equations. The linear Schrödinger equation with time-dependent potential is considered in Chapter 5. Given its particular structure, new, Magnus-based quasi-commutator-free integrators are build. Their efficiency is shown in numerical experiments with the Walker-Preston model of a molecule in an electromagnetic field. In Chapter 6, Magnus-splitting methods for the wave and the Hill equations are designed. Their performance is demonstrated in numerical experiments with various oscillatory systems: the Mathieu equation, the matrix Hill eq., the wave and the Klein-Gordon-Fock eq. Chapter 7 shows how the algebraic approach and the Magnus expansion can be generalised to non-linear problems. The example used is the Kepler problem with decreasing mass. The thesis is concluded by Chapter 8, in which the results are reviewed and possible directions of future work are outlined.
Kopylov, N. (2019). Magnus-based geometric integrators for dynamical systems with time-dependent potentials [Tesis doctoral no publicada]. Universitat Politècnica de València. https://doi.org/10.4995/Thesis/10251/118798
TESIS

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29

Samadi, Reza. "Particle-Based Geometric and Mechanical Modelling of Woven Technical Textiles and Reinforcements for Composites." Thèse, Université d'Ottawa / University of Ottawa, 2013. http://hdl.handle.net/10393/26241.

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Technical textiles are increasingly being engineered and used in challenging applications, in areas such as safety, biomedical devices, architecture and others, where they must meet stringent demands including excellent and predictable load bearing capabilities. They also form the bases for one of the most widespread group of composite materials, fibre reinforced polymer-matrix composites (PMCs), which comprise materials made of stiff and strong fibres generally available in textile form and selected for their structural potential, combined with a polymer matrix that gives parts their shape. Manufacturing processes for PMCs and technical textiles, as well as parts and advanced textile structures must be engineered, ideally through simulation, and therefore diverse properties of the textiles, textile reinforcements and PMC materials must be available for predictive simulation. Knowing the detailed geometry of technical textiles is essential to predicting accurately the processing and performance properties of textiles and PMC parts. In turn, the geometry taken by a textile or a reinforcement textile is linked in an intricate manner to its constitutive behaviour. This thesis proposes, investigates and validates a general numerical tool for the integrated and comprehensive analysis of textile geometry and constitutive behaviour as required toward engineering applications featuring technical textiles and textile reinforcements. The tool shall be general with regards to the textiles modelled and the loading cases applied. Specifically, the work aims at fulfilling the following objectives: 1) developing and implementing dedicated simulation software for modelling textiles subjected to various load cases; 2) providing, through simulation, geometric descriptions for different textiles subjected to different load cases namely compaction, relaxation and shear; 3) predicting the constitutive behaviour of the textiles undergoing said load cases; 4) identifying parameters affecting the textile geometry and constitutive behaviour under evolving loading; 5) validating simulation results with experimental trials; and 6) demonstrating the applicability of the simulation procedure to textile reinforcements featuring large numbers of small fibres as used in PMCs. As a starting point, the effects of reinforcement configuration on the in-plane permeability of textile reinforcements, through-thickness thermal conductivity of PMCs and in-plane stiffness of unidirectional and bidirectional PMCs were quantified systematically and correlated with specific geometric parameters. Variability was quantified for each property at a constant fibre volume fraction. It was observed that variability differed strongly between properties; as such, the simulated behaviour can be related to variability levels seen in experimental measurements. The effects of the geometry of textile reinforcements on the aforementioned processing and performance properties of the textiles and PMCs made from these textiles was demonstrated and validated, but only for simple cases as thorough and credible geometric models were not available at the onset of this work. Outcomes of this work were published in a peer-reviewed journal [101]. Through this thesis it was demonstrated that predicting changes in textile geometry prior and during loading is feasible using the proposed particle-based modelling method. The particle-based modelling method relies on discrete mechanics and offers an alternative to more traditional methods based on continuum mechanics. Specifically it alleviates issues caused by large strains and management of intricate, evolving contact present in finite element simulations. The particle-based modelling method enables credible, intricate modelling of the geometry of textiles at the mesoscopic scale as well as faithful mechanical modelling under load. Changes to textile geometry and configuration due to the normal compaction pressure, stress relaxation, in-plane shear and other types of loads were successfully predicted. During simulation, particles were moved randomly until a stable state of minimum strain energy in the system was reached; as particles moved upon iteration, the configuration of fibres in the textile changed under constant boundary conditions. Then boundary conditions were altered corresponding to strains imposed on the textile, and the system was iterated again towards a new state of minimum strain energy. The Metropolis algorithm of the Monte Carlo method was adopted in this specific implementation. The method relies on a statistical approach implemented in computational algorithms. In addition to geometrical modelling, the proposed particle-based modelling method enables the prediction of major elements of the constitutive behaviour of textiles and textile reinforcements. In fact, prediction of the constitutive behaviour is integral to the prediction of the meso-scale geometry. Simulation results obtained from the proposed particle-based modelling method were validated experimentally for yarns, single-layer textiles and multi-layer textiles undergoing compaction. Validation work showed that the particle-based modelling method replicates reality very faithfully, and it also showed the suitability of including Gutowski's function along with Hertz' function for representing lateral compaction of yarns. The procedure and results were accepted in final form for publication in a peer reviewed journal [104]. The capability of the proposed particle-based modelling method towards replicating the time-dependent relaxation and reconfiguration of woven textiles subjected to compaction loading was investigated. The capability, which was demonstrated for single and double-layers of plain woven textiles, is intrinsic to the modelling method. The method is unique in the fact that in contrary to work previously reported in the literature, it models the compaction and the relaxation seamlessly in the same simulations and environment. This work is being finalised towards submission for publication in a peer reviewed journal [103]. The proposed particle-based modelling method was also used for modelling in-plane shear in woven textiles. Simulation results were validated experimentally for a single-layer plain woven textile. Validation work showed that the particle-based modelling method reproduces experimental data and published trends very well. A novel algorithm for modelling friction was introduced, leading to results being obtained from a significantly less computationally demanding procedure in these simulations. This work was submitted for publication in a peer reviewed journal [102]. Finally the thesis discusses early work towards the application of the method to carbon fibre fabrics through the description of expansion algorithm (EA) to be used in modelling textiles made of yarns featuring very large numbers of fibres. Furthermore, additional modelling work is presented towards further manufacturing process involving technical textiles, namely textile bending and punching. The latter part is presented as early steps towards future work.

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30

Fan, Ang-Xiao. "Geometric and numerical modeling of facial mimics derived from Magnetic Resonance Imaging (MRI) using Finite Element Method (FEM)." Thesis, Compiègne, 2016. http://www.theses.fr/2016COMP2307.

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Le visage humain joue un rôle important dans la communication interpersonnelle. La dysfonction du visage ou le défigurement due aux traumatismes ou pathologies peuvent entraver les activités sociales normales. Le traitement chirurgical est souvent nécessaire. De nos jours, le résultat du traitement chirurgical et l’état d’établissement ne sont estimé qu’avec les méthodes qualitatives telles que l’observation visuelle et la palpation. Dans l’attente de fournir des critères quantitatifs, cette thèse a pour l’objectif de modéliser la mimique faciale utilisant MEF (Méthode d’Éléments Finis) sur la base des données d’IRM (Imagerie par Résonance Magnétique). Un modèle sujet-spécifique du visage a été construit sur la base de la segmentation des données IRM ; il contient des parties osseuses, muscles de la mimique (p.ex. le muscle grand zygomatique), les tissues mous sous-cutanées et la peau. L’identification des tissus mous biologiques a été réalisée via des essais de traction bi-axiale et la modélisation numérique. Ensuite, le modèle géométrique a été maillé pour effectuer des calculs EF simulant trois mouvements mimiques du visage (sourire, prononciation du son « Pou » et « O »). Les muscles ont été modélisés comme un matériau quasi-incompressible, transversalement isotrope et hyperélastique, avec la capacité d’activation. Des informations pertinentes (p.ex. l’amplitude de contraction du muscle) utilisées dans la simulation ont été extraites de la mesure des données d’IRM. Il est à noter que les mêmes données expérimentales d’IRM telles qu’ils ont utilisées dans la modélisation ont été prises comme une référence de validation pour les résultats de simulation. Cette étude peut être appliquée cliniquement dans l’évaluation du traitement faciale et le rétablissement postopérative
Human face plays an important role interpersonal communication. Facial dysfunction or disfigurement due to trauma or pathologies may impede normal social activities. Surgical treatment is often necessary. Nowadays, treatment outcome and rehabilitation condition are estimated only by qualitative methods, such as visual observation and palpation. In expectation of providing quantitative criteria, this thesis proposes to model facial mimics using FEM (Finite Element Method) on the basis of MRI (Magnetic Resonance Imaging) data. A subject-specific face model was reconstructed based on segmentation of MRI data; it contains bony parts, mimic muscles (e.g. zygomaticus major muscle), subcutaneous soft tissues and skin. Identification of biological soft tissues was conducted through bi-axial tension tests and numerical modeling. Then the geometric model was meshed to conduct FE calculations simulating three facial mimic movements (smile, pronunciation of sound “Pou” and “O”). Muscle was modeled as quasi-incompressible, transversely-isotropic, hyperelastic material, with activation ability. Relevant information (e.g. contraction amplitude of muscle) used in simulation was extracted from measurement of MRI data. It is to be noted that the same experimental MRI data as used in modeling was taken as validation reference for simulation results. This study can be applied clinically in evaluation of facial treatment andpostoperative recovery

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31

Asadi, Keivan. "Experimental, Theoretical, and Numerical Study of Nonlinear Resonances in Non-prismatic Micromechanical Resonators." The Ohio State University, 2019. http://rave.ohiolink.edu/etdc/view?acc_num=osu156614403113873.

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32

Joubert, Retief. "Influence of geometric and environmental parameters on air-cooled steam condenser performance." Thesis, Stellenbosch : University of Stellenbosch, 2010. http://hdl.handle.net/10019.1/4153.

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Thesis (MScEng (Mechanical and Mechatronic Engineering))--University of Stellenbosch, 2010.
ENGLISH ABSTRACT: Air-cooled steam condensers (ACSCs) are used in the power generation industry to directly condense turbine exhaust steam in areas where cooling water is expensive or unavailable. Large axial flow fans force ambient air through A-frame heat exchanger bundles made up of a number of rows of finned tubes through which the steam is ducted and consequently condensed during the heat transfer process to the air. The heat rejection rate or performance of an ACSC is proportional to the air mass flow rate, determined by fan volumetric performance, and the temperature difference between the finned tubes and the air. The air flow through a 30 fan ACSC (termed the generic ACSC) operating under windy conditions is solved using the commercial computational fluid dynamics (CFD) code FLUENT and the required data is extracted from the solution to calculate performance trends. It is found that fan performance is reduced due to a combination of factors. The first is additional upstream flow losses caused by separated flow occurring primarily at the leading edge of the ACSC and secondarily at the fan bellmouth inlets. The second factor leading to reduced fan performance is the presence of distorted flow conditions at the fan inlets. Hot plume air recirculation is responsible for decreased ACSC thermal performance due to increased fan inlet air temperatures. It is found that reduced fan performance is the greater contributor to reduced ACSC performance. The performance effects of varying two geometrical parameters of the generic ACSC, namely the fan platform height and the windwall height, are investigated under windy conditions. It is found that each parameter is linked to a specific mechanism of performance reduction with the fan platform height affecting fan performance and the windwall height affecting recirculation. The respective platform and windwall heights specified for the generic ACSC are found to provide acceptable performance results. To mitigate wind induced performance reductions a number of modification and additions to the ACSC are investigated. These primarily aim at improving fan performance and included the addition of walkways or skirts, the addition of wind screens beneath the fan platform, removing the bellmouth fan inlets, using different types of fans and increasing fan power. The addition of a periphery walkway and windscreens is considered to be the most practical methods of improving ACSC performance under windy conditions. The generic ACSC is modified to include both modifications and under high wind conditions the performance is found to increase measurably. The modifications also resulted in the ACSC performance being less sensitive to wind direction effects.
AFRIKAANSE OPSOMMING: Lugverkoelde kondensators word in die kragopwekkings industrie gebruik om turbine uitlaatstoom te kondenseer, veral in gebiede waar verkoelingwater duur of onbeskikbaar is. Aksiaalvloei-waaiers forseer omgewingslug deur A-raam warmteuitruiler bondels wat bestaan uit verskeie rye vinbuise. Die uitlaatstoom vloei in die vinbuise en kondenseer as gevolg van die warmteoordrag na die lug. Die warmteoordragkapasiteit van die lugverkoelde stoom kondensator is eweredig aan die massavloei-tempo van die lug, wat bepaal word deur die waaierwerkverigting, en die temperatuur verskil tussen die vinbuise en die lug. Die lugvloei deur 'n 30 waaier lugverkoelde stoom kondensator (genoem die generiese lugverkoelde stoom kondensator) onderworpe aan winderige toestande word opgelos deur die gebruik van die kommersiële vloeidinamika-pakket, FLUENT. Die nodige data is onttrek uit die oplossing en werkverrigting neigings is bereken. Dit is gevind dat waaierwerkverigting verminder as gevolg van 'n kombinasie van faktore. Die eerste is bykomende vloeiverliese wat veroorsaak word deur vloeiwegbreking wat plaasvind primêr by die voorste rand van die lugverkoelde stoom kondensator asook by die klokvormige waaier-inlate. 'n Tweede faktor wat lei tot vermindere waaierwerkverigting is die teenwoordigheid van lugvloeiversteurings by die waaier-inlate. Hersirkulering van warm pluim lug is ook verantwoordelik vir verminderde lugverkoelde stoom kondensator werkverrigting. Daar word bevind dat die vermindering in waaierwerkverrigting die grootste bydraende faktor tot vermindere lugverkoelde stoom kondensator werkverrigting is. Die effek van verandering van twee geometriese lugverkoelde stoom kondensator parameters, naamlik die waaierplatformhoogte en die windwandhoogte is ondersoek onder winderige toestande. Daar word bevind dat elk van die parameters gekoppel is aan 'n spesifieke meganisme van vermindere lugverkoelde stoom kondensator verrigting: Die waaierplatformhoogte beïnvloed waaierverrigting terwyl die windwandhoogte hersirkulering beinvloed. Daar word ook bevind dat die onderskeie waaierplatform- and windwandhoogtes van die generiese lugverkoelde stoom kondensator, van so 'n aard is dat dit aanvaarbare werkverrigting tot gevolg het. Om verlaging in werksverrigting in winderige toestande te verminder is verskeie modifikasies en byvoegings tot die lugverkoelde stoom kondensator ondersoek wat primêr gemik is op verbetering in waaierwerkverigting. Die ondersoek dek die byvoeging van 'n loopvlak, die byvoeging van windskerms onder die waaierplatform, verwydering van die klokvormige waaier-inlate, die gebruik van verskillende waaiers en die verhoging van waaierdrywing. Daar was besluit dat die byvoeging van 'n loopvlak rondom die rand van die lugverkoelde stoom kondensator en die byvoeging van windskerms die mees praktiese manier was om die lugverkoelde stoom kondensator verigting te verbeter. Die generiese lugverkoelde stoom kondensator was aangepas om beide veranderings in te sluit en meetbare verbetering in werkrigting was verkry. Die veranderings het ook meegebring dat die lugverkoelde stoom kondensator minder sensitief is vir windrigting effekte.

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33

Gilliam, Trey D. "NUMERICAL MODELING OF THE DYNAMIC RESPONSE OF A MULTI-BILINEAR-SPRING SUPPORT SYSTEM." UKnowledge, 2010. http://uknowledge.uky.edu/gradschool_theses/137.

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The Alpha Magnetic Spectrometer is an International Space Station Experiment that features a unique nonlinear support system with no previous flight heritage. The experiment consists of multiple straps with piecewise-linear stiffness curves that support a cryogenic magnet in three-dimensional space inside of a vacuum chamber. The stiffness curves for each strap are essentially bilinear and switch between two distinct slopes at a specified displacement. This highly nonlinear support system poses many questions in regards to feasible computational methods of analysis and possible response behavior. This thesis develops a numerical model for a multi-bilinear-spring support system motivated by the Alpha Magnetic Spectrometer design. Methods of analysis applied to the single bilinear oscillator served as the foundation of the model developed in this thesis. The model is developed using MATLAB and proves to be more computationally efficient than ANSYS finite element software. Numerical simulations contained herein demonstrate the variety of response behaviors possible in a multi-bilinear-spring support system, thus aiding future endeavors which may use a support system similar to the Alpha Magnetic Spectrometer. Classic nonlinear responses, such as subharmonic and chaotic, were found to exist.

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34

Sampath, Rahul Srinivasan. "A parallel geometric multigrid method for finite elements on octree meshes applied to elastic image registration." Diss., Atlanta, Ga. : Georgia Institute of Technology, 2009. http://hdl.handle.net/1853/29702.

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Thesis (Ph.D)--Computing, Georgia Institute of Technology, 2009.
Committee Chair: Vuduc, Richard; Committee Member: Biros, George; Committee Member: Davatzikos, Christos; Committee Member: Tannenbaum, Allen; Committee Member: Zhou, Hao Min. Part of the SMARTech Electronic Thesis and Dissertation Collection.

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35

Shepherd, David. "Numerical methods for dynamic micromagnetics." Thesis, University of Manchester, 2015. https://www.research.manchester.ac.uk/portal/en/theses/numerical-methods-for-dynamic-micromagnetics(e8c5549b-7cf7-44af-8191-5244a491d690).html.

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Micromagnetics is a continuum mechanics theory of magnetic materials widely used in industry and academia. In this thesis we describe a complete numerical method, with a number of novel components, for the computational solution of dynamic micromagnetic problems by solving the Landau-Lifshitz-Gilbert (LLG) equation. In particular we focus on the use of the implicit midpoint rule (IMR), a time integration scheme which conserves several important properties of the LLG equation. We use the finite element method for spatial discretisation, and use nodal quadrature schemes to retain the conservation properties of IMR despite the weak-form approach. We introduce a novel, generally-applicable adaptive time step selection algorithm for the IMR. The resulting scheme selects error-appropriate time steps for a variety of problems, including the semi-discretised LLG equation. We also show that it retains the conservation properties of the fixed step IMR for the LLG equation. We demonstrate how hybrid FEM/BEM magnetostatic calculations can be coupled to the LLG equation in a monolithic manner. This allows the coupled solver to maintain all properties of the standard time integration scheme, in particular stability properties and the energy conservation property of IMR. We also develop a preconditioned Krylov solver for the coupled system which can efficiently solve the monolithic system provided that an effective preconditioner for the LLG sub-problem is available. Finally we investigate the effect of the spatial discretisation on the comparative effectiveness of implicit and explicit time integration schemes (i.e. the stiffness). We find that explicit methods are more efficient for simple problems, but for the fine spatial discretisations required in a number of more complex cases implicit schemes become orders of magnitude more efficient.

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36

Londani, Mukhethwa. "Numerical Methods for Mathematical Models on Warrant Pricing." University of the Western Cape, 2010. http://hdl.handle.net/11394/8210.

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>Magister Scientiae - MSc
Warrant pricing has become very crucial in the present market scenario. See, for example, M. Hanke and K. Potzelberger, Consistent pricing of warrants and traded options, Review Financial Economics 11(1) (2002) 63-77 where the authors indicate that warrants issuance affects the stock price process of the issuing company. This change in the stock price process leads to subsequent changes in the prices of options written on the issuing company's stocks. Another notable work is W.G. Zhang, W.L. Xiao and C.X. He, Equity warrant pricing model under Fractional Brownian motion and an empirical study, Expert System with Applications 36(2) (2009) 3056-3065 where the authors construct equity warrants pricing model under Fractional Brownian motion and deduce the European options pricing formula with a simple method. We study this paper in details in this mini-thesis. We also study some of the mathematical models on warrant pricing using the Black-Scholes framework. The relationship between the price of the warrants and the price of the call accounts for the dilution effect is also studied mathematically. Finally we do some numerical simulations to derive the value of warrants.

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37

Gu, Hongmei. "Structure Based, Two-dimensional, Anisotropic, Transient Heat Conduction model for Wood." Diss., Virginia Tech, 2001. http://hdl.handle.net/10919/28938.

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The importance of precise values for the parameters used in heat and mass transfer models has been demonstrated by many research studies. Thermal conductivity values used in previous models are usually empirical and fluctuate. Theoretical analysis and estimations of wood thermal conductivities in the radial and tangential directions were conducted with the geometric models built up from the macro- and micro-structure observations. Theoretically, thermal conductivity in the radial direction is about 1.5 to 2.5 times of the tangential direction for softwood species with moisture content (MC) below Fiber Saturation Point (FSP). When MC is over the FSP, tangential radial thermal conductivity both increase dramatically and are linear function of MC. The two thermal conductivity values are close with a ratio of near one estimated by the model for MC above the FPS. In hardwood species, radial thermal conductivity estimated by the model is 1.5 times of the tangential thermal conductivity. Validation tests for model estimations of thermal conductivities in the radial and tangential directions for three wood species showed the reliability of the geometric models developed in this project. Correlations between the wood thermal conductivity and structure parameters, such as latewood percentage and cell wall percentage, were examined. Linear relationships for the thermal conductivity and average temperature in wood were established in both radial and tangential directions of three wood species. A two-dimensional transient heat conduction model was developed utilizing thermal conductivity values derived from geometric models. The anisotropic material property affect on heat transport in radial and tangential directions was discussed using an assumed situation. The simulation run showed slightly faster heat flow in the radial direction than in the tangential direction due to higher thermal conductivity in the radial direction. Validation tests on practical wood blocks showed the 2D model with the use of theoretical thermal conductivity values can predict good temperature distribution in wood during the heating process. However, in the practical wood samples with curved rings on the cross section, no significant difference was found in the two transverse directions. Mathematica software was introduced in this study for the intense and complicated math calculations and model programming. Mathematica was found to be a powerful technique for solving sophisticated math problems. It had abundant and flexible plotting options for providing optimized presentations for the results. These advantages make Mathematica popular for engineering modeling research.
Ph. D.

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Lindman, Mattias. "Physics of Aftershocks in the South Iceland Seismic Zone : Insights into the earthquake process from statistics and numerical modelling of aftershock sequences." Doctoral thesis, Uppsala universitet, Geofysik, 2009. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-9531.

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In seismology, an important goal is to attain a better understanding of the earthquake process. In this study of the physics of aftershock generation, I couple statistical analysis with modelling of physical processes in the postseismic period. I present a theoretical formulation for the distribution of interevent times for aftershock sequences obeying the empirically well established Omori law. As opposed to claims by other authors, this work demonstrates that the duration of the time interval between two successive earthquakes cannot be used to identify whether or not they belong to the same aftershock sequence or occur as a result of the same underlying process. This implies that a proper understanding of earthquake interevent time distributions is necessary before conclusions regarding the physics of the earthquake process are drawn. In a discussion of self-organised criticality (SOC) in relation to empirical laws in seismology, I find that Omori's law for aftershocks cannot be used as evidence for the theory of SOC. Instead, I consider that the occurrence of aftershocks in accordance with Omori's law is a result of a physical process that can be modelled and understood. I analyse characteristic features in the spatiotemporal distribution of aftershocks in the south Iceland seismic zone, following the two M6.5 June 2000 earthquakes and a M4.5 earthquake in September, 1999. These features include an initially constant aftershock rate, whose duration is larger following a larger main shock, and a subsequent power law decay that is interrupted by distinct and temporary deviations in terms of rate increases and decreases. Based on pore pressure diffusion modelling, I interpret these features in terms of main shock initiated diffusion processes. I conclude that thorough data analysis and physics-based modelling are essential components in attempts to improve our understanding of processes governing the occurrence of earthquakes.

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Wang, Dongtao. "Equilibrium temperature analysis and fill pattern reasoning for die casting process." Connect to this title online, 2004. http://rave.ohiolink.edu/etdc/view?acc%5Fnum=osu1095171663.

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Thesis (Ph. D.)--Ohio State University, 2004.
Title from first page of PDF file. Document formatted into pages; contains xx, 199 p.; also includes graphics. Includes bibliographical references (p. 196-199).

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40

Bulman-Fleming, Neil. "Numerical simulations of stent-based local drug delivery : 2D geometric investigations and the evaluation of 3D designs on the basis of local delivery effectiveness." Thesis, McGill University, 2003. http://digitool.Library.McGill.CA:80/R/?func=dbin-jump-full&object_id=80000.

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Drug-eluting coronary stents have been identified as a promising means of treating in-stent restenosis. Animal models used to investigate these devices can deliver results for restenosis rates, but cannot provide accurate dose delivery information which would be very useful for refining stent geometries and apposition techniques to optimize dose delivery. In this study, a two-dimensional numerical model is constructed to explore geometrical situations of interest following stent implantation. Metallic stents with a polymer coating and biodegradable solid polymeric stents represent two different vehicles for local delivery. A comparison between these stent types is carried out through the variation of geometric parameters of interest. An investigation of solid polymeric stent struts in a curved vessel is then done through a comparison of dose delivery characteristics on inner and outer walls. Dose delivery success is measured using three quantities: the dose homogeneity in a defined therapeutic region, the percentage of mass remaining in that therapeutic region after a defined therapeutic duration, and the amount of contact between the stent and the vascular wall. The appropriateness of a quasi-stationary hypothesis is then justified in two dimensions through analysis of flow and diffusion parameters. This simplification is applied to stent geometries in three dimensions and a single local delivery effectiveness score based on the three dose delivery parameters is calculated. This tool for evaluating stent designs on the basis of local delivery effectiveness provides a starting point for similar, more sophisticated methods that could eventually be applied to a larger sample of existing stent geometries. Ultimately, the output of such a tool could be used to optimize drug-eluting stent designs.

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41

Corno, Jacopo [Verfasser], Schöps [Akademischer Betreuer] Sebastian, and de Falco [Akademischer Betreuer] Carlo. "Numerical Methods for the Estimation of the Impact of Geometric Uncertainties on the Performance of Electromagnetic Devices / Jacopo Corno ; Schöps Sebastian, de Falco Carlo." Darmstadt : Universitäts- und Landesbibliothek Darmstadt, 2017. http://d-nb.info/1149252553/34.

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42

Tsener, Inna. "Numerical methods for analyzing nonstationary dynamic economic models and their applications." Doctoral thesis, Universidad de Alicante, 2015. http://hdl.handle.net/10045/50216.

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43

Temperley, Neil Colin Mechanical &amp Manufacturing Engineering Faculty of Engineering UNSW. "Optimisation of an Ultrasonic Flow Meter Based on Experimental and Numerical Investigation of Flow and Ultrasound Propagation." Awarded by:University of New South Wales. School of Mechanical and Manufacturing Engineering, 2002. http://handle.unsw.edu.au/1959.4/22044.

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This thesis presents a procedure to optimise the shape of a coaxial transducer ultrasonic flow meter. The technique uses separate numerical simulations of the fluid flow and the ultrasound propagation within a meter duct. A new flow meter geometry has been developed, having a significantly improved (smooth and monotonic) calibration curve. In this work the complex fluid flow field and its influence on the propagation of ultrasound in a cylindrical flow meter duct is investigated. A geometric acoustics (ray tracing) propagation model is applied to a flow field calculated by a commercial Computational Fluid Dynamics (CFD) package. The simulation results are compared to measured calibration curves for a variety of meter geometries having varying lengths and duct diameters. The modelling shows reasonable agreement to the calibration characteristics for several meter geometries over a Reynolds number range of 100...100000 (based on bulk velocity and meter duct diameter). Various CFD simulations are validated against flow visualisation measurements, Laser Doppler Velocimetry measurements or published results. The thesis includes software to calculate the acoustic ray propagation and also to calculate the optimal shape for the annular gap around the transducer housings in order to achieve desired flow acceleration. A dimensionless number is proposed to characterise the mean deflection of an acoustic beam due to interaction with a fluid flow profile (or acoustic velocity gradient). For flow in a cylindrical duct, the 'acoustic beam deflection number' is defined as M g* (L/D)^2, where: M is the Mach Number of the bulk velocity; g* is the average non-dimensionalised velocity gradient insonified by the acoustic beam (g* is a function of transducer diameter - typically g* = 0.5...4.5); L is the transducer separation; and D is the duct diameter. Large values of this number indicate considerable beam deflection that may lead to undesirable wall reflections and diffraction effects. For a single path coaxial transducer ultrasonic flow meter, there are practical limits to the length of a flow meter and to the maximum size of a transducer for a given duct diameter. The 'acoustic beam deflection number' characterises the effect of these parameters.

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44

Costanzo, Caetano Pontes 1984. "Análise de incerteza de cenários de bombeamento e tratamento em áreas contaminadas." [s.n.], 2014. http://repositorio.unicamp.br/jspui/handle/REPOSIP/286636.

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Orientador: Alexandre Campane Vidal
Dissertação (mestrado) - Universidade Estadual de Campinas, Instituto de Geociências
Made available in DSpace on 2018-08-24T10:58:04Z (GMT). No. of bitstreams: 1 Costanzo_CaetanoPontes_M.pdf: 3384236 bytes, checksum: 7b4516eef162c87ff3e03f0d56f08215 (MD5) Previous issue date: 2014
Resumo: Em face da crescente demanda de execução de projetos de remediação de aquíferos contaminados, a técnica de bombeamento e tratamento está sendo utilizada de forma significativa. Esta ferramenta de recuperação ambiental consiste no bombeamento da água subterrânea em pontos estrategicamente posicionados de maneira a gerar uma barreira hidráulica que impeça o avanço da extensão de uma pluma de contaminação. Em áreas com alta heterogeneidade litológica, a organização espacial dos valores de condutividade hidráulica (K) em subsuperfície apresenta incertezas associadas à variabilidade na distribuição das fácies. No presente estudo foram analisadas estas incertezas por meio de métodos geoestatísticos (krigagem da indicatriz e simulações estocásticas) e também a partir de simulações numéricas de fluxo e transporte de contaminantes. Estas ferramentas permitiram a análise das possibilidades de deslocamentos espaciais das plumas de contaminação, bem como possíveis cenários de bombeamento e tratamento numa área contaminada, em função de distintos campos aleatórios de condutividade locais, devido à complexidade geológica. A partir da krigagem da indicatriz foi possível elaborar um modelo geoestatístico de fácies que foi utilizado como ferramenta para validar o uso da condutividade hidráulica em função de cada litologia, definindo assim os possíveis grupos de hidrofácies presentes na área. Por meio das simulações estocásticas foram gerados vinte campos distintos de condutividade hidráulica, os quais configuraram distintas distribuições espaciais das áreas das plumas de contaminação, como também cenários otimista, intermediário e pessimista para o deslocamento das mesmas. Foram simulados três cenários de bombeamento e tratamento resultando nove situações desta técnica de remediação. Dessa forma, os efeitos da heterogeneidade atrelada à condutividade hidráulica evidenciaram que, para a execução de um projeto de remediação por bombeamento e tratamento em áreas com certa heterogeneidade geológica, é necessária a análise de incertezas atreladas ao diagnostico hidrogeológico. Ao considerar modelos com homogeneidade na condutividade e mais simplistas, o projeto de remediação pode vir a ser ineficiente aumentando o tempo para a recuperação ambiental local e consequentemente aumentando os custos
Abstract: Due to the growing demand for project execution remediation of contaminated aquifers, the pump-and-treat is being used significantly. This remediation technique consists in groundwater pumping in strategically placed at points to generate a hydraulic barrier to prevent the advance of a contamination plume. In areas with high lithological heterogeneity, the spatial organization of the hydraulic conductivity (K) values in the subsurface introduces uncertainties associated with the variability in the distribution of facies. In this study these uncertainties were evaluated using geostatistical methods (indicator kriging and stochastic simulations) and also from numerical simulations of flow and contaminant transport. These tools enable the analysis of the contamination plumes areas, as well as scenarios for pump-and-treat, due to different random fields of local conductivity according to the geological complexity. By indicator kriging, was possible to provide a geostatistical facies model which was used as a tool to validate the hydraulic conductivity as a function of each lithology, thus defining the possible hydrofacies groups in the area. The stochastic simulations generated twenty distinct hydraulic conductivity fields, which represented different spatial distributions of contamination plumes, as well as scenarios optimistic, intermediate and pessimistic to offset these. Three scenarios for pump-and-treat were simulated resulting nine situations of this remediation technique. Therefore the effects of heterogeneity associated with hydraulic conductivity showed that, for the remediation design in areas with certain geological heterogeneity, the analysis of uncertainties linked to hydrogeological studies is needed. When considering models with homogeneous conductivity and most simplistic, the remediation project may prove to be inefficient increasing the time to the project and consequently increasing costs
Mestrado
Geologia e Recursos Naturais
Mestre em Geociências

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Godineau, Kévin. "Optimisation du pilotage de chaînes opto-mécaniques pour l'exécution de trajectoires en fabrication additive par fusion laser sur lit de poudre." Thesis, Université Paris-Saclay (ComUE), 2019. http://www.theses.fr/2019SACLN019.

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En fabrication additive métallique par fusion laser sur lit de poudre, la géométrie et les caractéristiques mécaniques des pièces produites sont générées au cours de la fabrication. Ces deux aspects sont grandement influencés par les trajectoires du spot laser et par la maîtrise de l'énergie apportée à la poudre localement. La commande numérique dont le rôle est de générer les consignes à envoyer aux actionneurs a donc un impact conséquent sur la qualité des pièces produites.Ces travaux proposent d'étudier l'impact des traitements effectués dans la commande numérique sur les trajectoires réalisées et sur l'énergie apportée à la matière. Dans la littérature, peu de travaux traitent de ces aspects en fabrication additive. C'est pourquoi une plateforme expérimentale est mise en œuvre et utilisée afin d'analyser et de mieux comprendre les opérations actuellement implémentées dans les commandes numériques industrielles.Un modèle mathématique représentatif de la géométrie de la machine est d'abord établi. Ce modèle permet de convertir les trajectoires du spot laser en consigne pour les actionneurs. Le modèle développé est utilisé afin d'améliorer l'étape de calibration des machines. Une fois le système calibré, les consignes envoyées aux actionneurs sont étudiées. Les différents traitements effectués dans la commande numérique industrielle sont analysés, des limitations sont mises en évidence et plusieurs propositions d'améliorations sont implémentées. Tous ces développements sont ensuite utilisés afin de maîtriser finement l'énergie apportée à la matière dans le cas de certaines trajectoires adaptées au procédé. Les développements scientifiques proposés dans ces travaux sont tous validés expérimentalement sur une machine de fabrication additive ou sur le banc d'essai développé. Les travaux effectués permettent d'envisager de nombreuses perspectives concernant l'amélioration des traitements réalisés dans la commande numérique en fabrication additive
In metal additive manufacturing by laser powder bed fusion, the geometry and mechanical characteristics of the produced parts are generated during the manufacturing process. These two aspects are greatly influenced by the laser spot trajectories, and by the control of the energy provided to the powder locally. The numerical control system, whose purpose is to generate instructions to be sent to actuators, has therefore a significant impact on the quality of the parts produced.This work proposes to study the local impact of the operations carried out in the numerical control on both the trajectories executed and the energy provided to the material. In the literature, few studies have addressed these aspects in additive manufacturing. For this reason, an experimental platform is implemented and used to analyze and better understand the operations currently implemented in industrial numerical controls.First, a mathematical model representative of the machine geometry is established. This model converts the laser spot trajectories into instructions for actuators. The model developed is used to improve the calibration step of the machines. Once the system is calibrated, the instructions sent to the actuators are studied. The various processes carried out in the industrial numerical control are analysed, limitations are highlighted and several proposals for improvements are implemented. All these developments are then used to precisely control the energy supplied to the material in the case of certain trajectories adapted to the process. The scientific developments proposed in these works are all validated experimentally on an additive manufacturing machine or on the test bench developed. The work carried out makes it possible to envisage many perspectives concerning the improvement of the treatments carried out inside the numerical control in additive manufacturing

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Lopes, Fernando Henrique [UNESP]. "O ensino de progressão geométrica de segunda ordem no ensino médio." Universidade Estadual Paulista (UNESP), 2017. http://hdl.handle.net/11449/151716.

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O presente trabalho tem como objetivo principal apresentar a definição e propriedades de progressões geométricas de 2º grau, geralmente não trabalhadas no estudo de sequências numéricas, que é iniciado no 1º Ano do Ensino Médio. Para isto, é realizado um estudo de casos gerais para sequências e séries de números reais, para posteriormente, exibir aplicações do conceito no Ensino Médio. Inicialmente é apresentado ao aluno as definições e propriedades de sequências e séries, que requer um estudo mais aprofundado uma vez que é um assunto de maior complexidade para aplicação em turmas de ensino médio. Tais propriedades são utilizadas como ferramentas para o desenvolvimento posterior de progressões aritméticas e geométricas, tanto de 1ª como de 2ª ordem. Uma vez definidas as progressões, atividades sobre o assunto são aplicadas aos alunos para que os mesmos dissertem sobre suas facilidades e dificuldades encontradas na resolução.
The present work has as main objective to present the definition and properties of geometric progressions of 2nd degree, usually not worked in the study of numerical sequences, that is initiated in the 1st Year of High School. For this, a study of general cases for sequences and series of real numbers is carried out, later, to show applications of the concept in High School. Initially the definitions and properties of sequences and series are presented to the student, which requires a more in-depth study since it is a subject of greater complexity for application in high school classes. These properties are used as tools for the later development of arithmetic and geometric progressions, both 1st and 2nd order. Once the progressions are defined, activities on the subject are applied to the students so that they tell about their facilities and difficulties found in the resolution.

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Elsheikh, Sara Mohamed Ahmed Suleiman. "Analysis and implementation of robust numerical methods to solve mathematical models of HIV and Malaria co-infection." Thesis, University of the Western Cape, 2011. http://etd.uwc.ac.za/index.php?module=etd&action=viewtitle&id=gen8Srv25Nme4_2221_1319804516.

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There is a growing interest in the dynamics of the co-infection of these two diseases. In this thesis, firstly we focus on studying the effect of a distributed delay representing the incubation period for the malaria parasite in the mosquito vector to possibly reduce the initial transmission and prevalence of malaria. This model can be regarded as a generalization of SEI models (with a class for the latently infected mosquitoes) and SI models with a discrete delay for the incubation period in mosquitoes. We study the possibility of occurrence of backward bifurcation. We then extend these ideas to study a full model of HIV and malaria co-infection. To get further inside into the dynamics of the model, we use the geometric singular perturbation theory to couple the fast and slow models from the full model. Finally, since the governing models are very complex, they cannot be solved analytically and hence we develop and analyze a special class of numerical methods to solve them.

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Oliveira, Rubia Mara de. "Algoritmos de busca global para problemas de otimização geometricos e multiplicativos." [s.n.], 2005. http://repositorio.unicamp.br/jspui/handle/REPOSIP/260215.

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Orientador: Paulo Augusto Valente Ferreira
Tese (doutorado) - Universidade Estadual de Campinas, Faculdade de Engenharia Eletrica e de Computação
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Resumo: Nesta tese são propostos novos algoritmos de otimização baseados na busca global para duas importantes classes de problemas de programação não-linear: problemas geométricos, nos quais as funções envolvidas são descritas por somas de polinômios generalizados, e problemas de programação multiplicativa convexa, os quais, por sua vez, apresentam funções objetivos e/ou restrições expressas como produtos de funções convexas. Uma abordagem multiobjetivo para problemas geométricos posinomiais, que admitem reformulações convexas, é apresentada. Para problemas geométricos signomiais, que não possuem reformulações convexas conhecidas, propõe-se incorporar um procedimento de busca local a um algoritmo branch-and-bound, visando acelerar a convergência deste tipo de algoritmo. Elementos de análise convexa e programação multiobjetivo são usados para abordar problemas de programação multiplicativa quando estes apresentam produtos e somas de produtos de funções convexas positivas nas suas funções objetivos. Um mínimo global para o primeiro caso é obtido como o limite das soluções de uma seqüência de minimizações quase-côncavas sobre politopos, resolvidas eficientemente por meio de enumeração de vértices. Um mínimo global para o segundo caso é obtido como o limite das soluções de uma seqüência de problemas quadráticos indefinidos com características especiais, resolvidos por enumeração de restrições. O desempenho computacional dos algoritmos propostos nesta tese é avaliado por meio de problemas-testes e comparado com algoritmos alternativos existentes na literatura
Abstract: In this thesis new optimization algorithms based on global search are proposed for two important classes of nonlinear programming problems: geometric problems, in which the functions involved are described by a sum of generalized polynomials, and convex multiplicative problems, in which, in turn, objective functions and/or constraints are expressed as a product of convex functions. A multiobjective approach for posinomial geometric problems, which admit convex reformulations, is presented. As convex reformulations for signomial geometric problems are unknown, a local search procedure with the purpose of speeding up the convergence of branchand-bound algorithms is proposed. Elements of convex analysis and multiobjective programming are used for dealing with multiplicative programming problems presenting products and sums of products of positive convex functions in their objective functions. A global minimum in the first case is obtained as the limit of a sequence of quasi-concave minimizations on polytopes, efficiently solved by vertex enumeration. A global minimum for the second case is obtained as the limit of a sequence of special indefinite quadratic problems, solved by constraint enumeration. The computational performance of the algorithms proposed in this thesis has been evaluated by means of test problems and compared with alternate algorithms from the literature
Doutorado
Automação
Doutor em Engenharia Elétrica

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Steinhilber, Jan [Verfasser], and Gerhard [Akademischer Betreuer] Dziuk. "Numerical analysis for harmonic maps between hypersurfaces and grid improvement for computational parametric geometric flows = Numerische Analysis für harmonische Abbildungen zwischen Hyperflächen und Gitterverbesserung für parametrische geometrische Flüsse in der Numerik." Freiburg : Universität, 2014. http://d-nb.info/1123480117/34.

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Hu, Hao. "Detection and treatment of inconsistent or locally over-constrained configurations during the manipulation of 3D geometric models made of free-form surfaces." Thesis, Paris, ENSAM, 2018. http://www.theses.fr/2018ENAM0002/document.

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Trois modules seront développés: Le module de détection a produit une analyse des problématiques figurations con, à savoir un ensemble de domaines où soit quelques nouveaux DDL ou des changements locaux dans les contraintes sont obligatoires. Le module de traitement permettra à la défi nition des mécanismes pour aider la décision sur modi cations. Le module de prédiction dire le degré de déformation en pré-analyser les caractéristiques des configurations de NURBS
Three modules will be developed: The detection module has produced an analysis of problematic con figurations, i.e. a set of areas where either some new DOFs or some local changes in the constraints are mandatory. The treatment module will enable the defi nition of mechanisms to help the decision on modi cations. The prediction module will tell the degree of deformation by pre-analyzing the features of NURBS configurations

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Dissertations / Theses on the topic 'Geometric and numerical sequences'

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