Dissertations / Theses on the topic 'Topology (Applied)'
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Ortiz, Marcos A. "Convex decomposition techniques applied to handlebodies." Diss., University of Iowa, 2015. https://ir.uiowa.edu/etd/1713.
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Contact structures on 3-manifolds are 2-plane fields satisfying a set of conditions. The study of contact structures can be traced back for over two-hundred years, and has been of interest to mathematicians such as Hamilton, Jacobi, Cartan, and Darboux. In the late 1900's, the study of these structures gained momentum as the work of Eliashberg and Bennequin described subtleties in these structures that could be used to find new invariants. In particular, it was discovered that contact structures fell into two classes: tight and overtwisted. While overtwisted contact structures are relatively well understood, tight contact structures remain an area of active research. One area of active study, in particular, is the classification of tight contact structures on 3-manifolds. This began with Eliashberg, who showed that the standard contact structure in real three-dimensional space is unique, and it has been expanded on since. Some major advancements and new techniques were introduced by Kanda, Honda, Etnyre, Kazez, Matić, and others. Convex decomposition theory was one product of these explorations. This technique involves cutting a manifold along convex surfaces (i.e. surfaces arranged in a particular way in relation to the contact structure) and investigating a particular set on these cutting surfaces to say something about the original contact structure. In the cases where the cutting surfaces are fairly nice, in some sense, Honda established a correspondence between information on the cutting surfaces and the tight contact structures supported by the original manifold.
In this thesis, convex surface theory is applied to the case of handlebodies with a restricted class of dividing sets. For some cases, classification is achieved, and for others, some interesting patterns arise and are investigated.
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Naidoo, Inderasan. "Nearness and convergence in pointfree topology." Doctoral thesis, University of Cape Town, 2004. http://hdl.handle.net/11427/5962.
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Bibliography: leaves 99-106.We introduce and investigate the concept of a nearness structure on a σ-frame. Analogues of the Samuel Compactification, Uniform Coreflection and Completion in the nearness σ-frame setting are obtained. Convergence in uniform frames is also a subject of this thesis integrating compactness, precompactness and paracompactness. Finally, the notion of uniform paracompactness is introduced and its relation with convergence is investigated.
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Grimaud, Lou. "Magnetic shielding topology applied to low power Hall thrusters." Thesis, Orléans, 2018. http://www.theses.fr/2018ORLE2046/document.
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Les propulseurs de Hall sont l’une des techniques de propulsion fusée par plasma les plus utilisés. Ils possèdent une impulsion spécifique moyenne et un haut rapport poussé sur puissance qui les rend idéal pour une grande partie des applications commerciales et scientifiques. Une de leurs limitations principales est l’érosion des parois du propulseur par le plasma qui réduit leur durée de vie. La topologie dite “d’écrantage magnétique” est une solution proposée pour prolonger cette durée de vie. Elle est ici appliquée à un petit propulseur de Hall de 200W. Dans cette thèse les règles de mise à l’échelle pour les propulseurs de Hall de la gamme de 100 à 200W sont testées expérimentalement. Un propulseur écranté de 200W est comparé avec un propulseur standard similaire. Le comportement des ions dans ces deux moteurs est extrêmement différent. Des mesures de performance ont été réalisées avec des parois en BN-SiO2 et graphite. Le courant de décharge augmente de 25% avec le graphite dans le propulseur non-écranté. Le résultat et un rendement maximum de 38% avec le nitrure de bore mais de seulement 31% pour le graphite. Le propulseur écranté quant à lui n’atteint que 25% de rendement quel que soit le matériau.Cette baisse de performance dans les petits moteurs écrantés peut être attribuée à un mauvais rendement d’utilisation de l’ergol. Analyses des résultats expérimentaux ainsi que la conduite de simulations suggèrent que cela est dû au fait que la zone d’ionisation ne couvre pas l’ensemble du canal de décharge. Un nouveau design pour un petit propulseur de Hall écranté est proposéHall thrusters are one of the most used rocket electric propulsion technology. They combine moderate specific impulse with high thrust to power ratio which makes them ideal for a wide range of practical commercial and scientific applications. One of their limitations is the erosion of the thruster walls which reduces their lifespan.The magnetic shielding topology is a proposed solution to prolong the lifespan. It is implemented on a small200W Hall thruster.In this thesis the scaling of classical unshielded Hall thrusters down to 200 and 100W is discussed. A 200W low power magnetically shielded Hall thruster is compared with an identically sized unshielded one. The ion behavior inside the thruster is measured and significant differences are found across the discharge channel.Both thrusters are tested with classical BN-SiO2 and graphite walls. The magnetically shielded thruster is not sensitive to the material change while the discharge current increase by 25% in the unshielded one. The result is a maximum efficiency of 38% for boron nitride in the unshielded thruster but only 31% with graphite.The shielded thruster achieves a significantly lower efficiency with only 25% efficiency with both materials.Analysis of the experimental results as well as simulations of the thrusters reveal that the performance difference is mostly caused by low propellant utilization. This low propellant utilization comes from the fact that the ionization region doesn’t cover all of the discharge channel. A new magnetically shielded thruster is designed to solve this issue
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Holmberg, Erik. "Topology optimization considering stress, fatigue and load uncertainties." Doctoral thesis, Linköpings universitet, Mekanik och hållfasthetslära, 2016. http://urn.kb.se/resolve?urn=urn:nbn:se:liu:diva-123008.
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This dissertation concerns structural topology optimization in conceptual design stages. The objective of the project has been to identify and solve problems that prevent structural topology optimization from being used in a broader sense in the avionic industry; therefore the main focus has been on stress and fatigue constraints and robustness with respect to load uncertainties. The thesis consists of two parts. The first part gives an introduction to topology optimization, describes the new contributions developed within this project and motivates why these are important. The second part includes five papers. The first paper deals with stress constraints and a clustered approach is presented where stress constraints are applied to stress clusters, instead of being defined for each point of the structure. Different approaches for how to create and update the clusters, such that sufficiently accurate representations of the local stresses are obtained at a reasonable computational cost, are developed and evaluated. High-cycle fatigue constraints are developed in the second paper, where loads described by a variable-amplitude load spectrum and material data from fatigue tests are used to determine a limit stress, for which below fatigue failure is not expected. A clustered approach is then used to constrain the tensile principal stresses below this limit. The third paper introduces load uncertainties and stiffness optimization considering the worst possible loading is then formulated as a semi-definite programming problem, which is solved very efficiently. The load is due to acceleration of point masses attached to the structure and the mass of the structure itself, and the uncertainty concerns the direction of the acceleration. The fourth paper introduces an extension to the formulated semi-definite programming problem such that both fixed and uncertain loads can be optimized for simultaneously. Game theory is used in the fifth paper to formulate a general framework, allowing essentially any differentiable objective and constraint functions, for topology optimization under load uncertainty. Two players, one controlling the structure and one the loads, are in conflict such that a solution to the game, a Nash equilibrium, is a design optimized for the worst possible load.
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Sá, Luís Fernando Nogueira de. "Topology optimization method applied to laminar flow machine rotor design." Universidade de São Paulo, 2016. http://www.teses.usp.br/teses/disponiveis/3/3152/tde-16032017-103709/.
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Flow machines are very important to industry, being widely used on various processes. Performance improvements are relevant factors and can be achieved by using optimization methods, such as topology optimization. Thus, this work aims to develop a method to design radial flow machine rotors operating on laminar regime, by implementing a topology optimization formulation based on density model. The design of a rotor involves firstly modelling the fluid flow by using the Navier-Stokes equations on a rotating reference frame and using the Finite Element Method for solving the differential equations. To determine the material distribution on the domain, a porous flow model based on the Darcy equation is employed by using an inverse permeability that interpolates between fluid and solid. In the optimization phase, it is defined a multi-objective function that aims to minimize the viscous energy dissipation, vorticity and power. The optimization problem is implemented using the FEniCS environment and the libraries dolfin-adjoint and pyIpopt. The optimized topologies are verified with the ANSYS software. The resulting topologies are post-processed and a CAD model is created. The rotors are manufactured by using a 3D printer, the complete prototype is built by coupling an electric brushless motor and an experimental characterization is performed by measuring fluid flow and pressure head given by the pumps. Experimental and computational results are compared and the improvement is verified.Máquinas de fluxo são muito importantes para a indústria, sendo utilizadas em diversos processos. Assim, melhorias de desempenho são fatores relevantes e podem ser alcançadas com a utilização de métodos de otimização, como a otimização topológica. Este trabalho visa desenvolver uma metodologia para projetar rotores de máquinas de fluxo radiais que operam em escoamento laminar implementando-se a formulação de otimização topológica baseada no modelo de densidades. O projeto de rotores envolve, primeiramente, a modelagem do escoamento utilizando-se as equações de Navier-Stokes em um referencial rotativo e a utilização do Método de Elementos Finitos para a resolução das equações diferenciais. A distribuição de material no domínio é feita empregando-se um modelo de escoamento em meio poroso baseado nas equações de Darcy, utilizando-se a permeabilidade inversa que interpola o elemento entre sólido e fluido. Na fase de otimização é definida uma função multi-objetivo, que visa minimizar dissipação de energia viscosa, a vorticidade e a potência. O problema de otimização é implementado utilizando-se o ambiente FEniCS para a resolução do sistema de elementos finitos e as bibliotecas dolfin-adjoint e pyIpopt para o algorithmo de otimização. As topologias otimizadas são verificadas com o software ANSYS. As topologias resultantes são pós-processadas para a criação de um modelo CAD dos rotores. Os rotores são construídos utilizando-se a impressão 3D, o protótipo completo é montado acoplando-se um motor elétrico sem escovas e a caracterização experimental é feita medindo-se a vazão e o ganho de pressão dados pelas bombas. Por fim, os resultados experimentais e computacionais são comparados e uma melhoria de desempenho é observada.
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Suresh, Shyam. "Topology Optimization for Additive Manufacturing Involving High-Cycle Fatigue." Licentiate thesis, Linköpings universitet, Mekanik och hållfasthetslära, 2020. http://urn.kb.se/resolve?urn=urn:nbn:se:liu:diva-165503.
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Additive Manufacturing (AM) is gaining popularity in aerospace and automotive industries. This is a versatile manufacturing process, where highly complex structures are fabricated and together with topology optimization, a powerful design tool, it shares the property of providing a very large freedom in geometrical form. The main focus of this work is to introduce new developments of Topology Optimization (TO) for metal AM. The thesis consists of two parts. The first part introduces background and theory, where TO and adjoint sensitivity analysis are described. Furthermore, methodology used to identify surface layer and high-cycle fatigue are introduced. In the second part, three papers are appended, where the first paper presents the treatment of surface layer effects, while the second and third papers provide high-cycle fatigue constraint formulations. In Paper I, a TO method is introduced to account for surface layer effects, where different material properties are assigned to bulk and surface regions. In metal AM, the fabricated components in as-built surface conditions significantly affect mechanical properties, particularly fatigue properties. Furthermore, the components are generally in-homogeneous and have different microstructures in bulk regions compared to surface regions. We implement two density filters to account for surface effects, where the width of the surface layer is controlled by the second filter radius. 2-D and 3-D numerical examples are treated, where the structural stiffness is maximized for a limited mass. For Papers II and III, a high-cycle fatigue constraint is implemented in TO. A continuous-time approach is used to predict fatigue-damage. The model uses a moving endurance surface and the development of damage occurs only if the stress state lies outside the endurance surface. The model is applicable not only for isotropic materials (Paper II) but also for transversely isotropic material properties (Paper III). It is capable of handling arbitrary load histories, including non-proportional loads. The anisotropic model is applicable for additive manufacturing processes, where transverse isotropic properties are manifested not only in constitutive elastic response but also in fatigue properties. Two optimization problems are solved: In the first problem the structural mass is minimized subject to a fatigue constraint while the second problem deals with stiffness maximization subjected to a fatigue constraint and mass constraint. Several numerical examples are tested with arbitrary load histories.
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Bavuma, Yanga. "Some combinatorial aspects in algebraic topology and geometric group theory." Master's thesis, University of Cape Town, 2018. http://hdl.handle.net/11427/29763.
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The present Msc thesis deals with classical topics of topology and it has been written, referring to [C. Kosniowski, Introduction to Algebraic Topology, Cambridge University Press, 1980, Cambridge], which is a well known textbook of algebraic topology. It has been selected a list of main exercises from this reference, whose solutions were not directly available, or subject to differerent methods. In fact combinatorial methods have been preferred and the result is a self-contained dissertation on the theory of the fundamental group and of the coverings. Finally, there are some recent problems in geometric group theory which are related to the presence of finitely presented groups which appear naturally as fundamental groups.
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Gonzalez, Lorenzo Aldo. "Computational homology applied to discrete objects." Thesis, Aix-Marseille, 2016. http://www.theses.fr/2016AIXM4073/document.
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La théorie de l'homologie formalise la notion de trou dans un espace. Pour un sous-ensemble de l'espace Euclidien, on définit une séquence de groupes d'homologie, dont leurs rangs sont interprétés comme le nombre de trous de chaque dimension. Ces groupes sont calculables quand l'espace est décrit d'une façon combinatoire, comme c'est le cas pour les complexes simpliciaux ou cubiques. À partir d'un objet discret (un ensemble de pixels, voxels ou leur analogue en dimension supérieure) nous pouvons construire un complexe cubique et donc calculer ses groupes d'homologie.Cette thèse étudie trois approches relatives au calcul de l'homologie sur des objets discrets. En premier lieu, nous introduisons le champ de vecteurs discret homologique, une structure combinatoire généralisant les champs de vecteurs gradients discrets, qui permet de calculer les groupes d'homologie. Cette notion permet de voir la relation entre plusieurs méthodes existantes pour le calcul de l'homologie et révèle également des notions subtiles associés. Nous présentons ensuite un algorithme linéaire pour calculer les nombres de Betti dans un complexe cubique 3D, ce qui peut être utilisé pour les volumes binaires. Enfin, nous présentons deux mesures (l'épaisseur et l'ampleur) associés aux trous d'un objet discret, ce qui permet d'obtenir une signature topologique et géométrique plus intéressante que les simples nombres de Betti. Cette approche fournit aussi quelques heuristiques permettant de localiser les trous, d'obtenir des générateurs d'homologie ou de cohomologie minimaux, d'ouvrir et de fermer les trousHomology theory formalizes the concept of hole in a space. For a given subspace of the Euclidean space, we define a sequence of homology groups, whose ranks are considered as the number of holes of each dimension. Hence, b0, the rank of the 0-dimensional homology group, is the number of connected components, b1 is the number of tunnels or handles and b2 is the number of cavities. These groups are computable when the space is described in a combinatorial way, as simplicial or cubical complexes are. Given a discrete object (a set of pixels, voxels or their analog in higher dimension) we can build a cubical complex and thus compute its homology groups.This thesis studies three approaches regarding the homology computation of discrete objects. First, we introduce the homological discrete vector field, a combinatorial structure which generalizes the discrete gradient vector field and allows to compute the homology groups. This notion allows to see the relation between different existing methods for computing homology. Next, we present a linear algorithm for computing the Betti numbers of a 3D cubical complex, which can be used for binary volumes. Finally, we introduce two measures (the thickness and the breadth) associated to the holes in a discrete object, which provide a topological and geometric signature more interesting than only the Betti numbers. This approach provides also some heuristics for localizing holes, obtaining minimal homology or cohomology generators, opening and closing holes
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Kian, Jacqueline de Miranda. "Topology optimization method applied to design channels considering non-newtonian fluid flow." Universidade de São Paulo, 2017. http://www.teses.usp.br/teses/disponiveis/3/3152/tde-05012018-084558/.
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The study of non-Newtonian flow is presents itself as relevant in bioengineering field, specially for design of devices that conduct blood, as arterial bypass grafts. Improvements in reducing energy dissipation and blood cell damage caused by artificial flows can be achieved by using numerical simulation and optimization methods. Thus, the present work proposes the study of design channels for steady, incompressible non-Newtonian flow, by using Topology Optimization Method based on the density method. The fluid flow is modeled with the Navier-Stokes equations coupled with Carreau-Yasuda constitutive equation for the dynamic viscosity to take into account the effects of the non-Newtonian blood properties. The Topology Optimization Method distributes regions of solid and fluid, given a volume constraint, within a specified domain in order to obtain a geometry and layout that minimizes energy dissipation, shear stress and vorticity by using the material pseudo-density as design variable. To apply this method to fluidic systems design, a fictional porous media based on Darcy equation is introduced. The flow model is implemented in its discrete form by using the Finite Element Method through the OpenSource platform FEniCS, applied to automate the solution of mathematical models based on differential equations. The optimization problem is solved by using the library DOLFIN-adjoint and IPOpt optimizer. Optimized topologies of channels for blood flow, focusing in arterial bypass grafts, are presented to illustrate the proposed method.O estudo de escoamento de fluidos não-Newtonianos apresenta-se relevante no campo de bioengenharia, em especial no projeto de dispositivos para condução de sangue, como bypass arterial. Melhorias na redução de dissipação de energia e no dano às células sanguíneas causados por fluxos artificiais podem ser obtidas através do uso de técnicas de simulação e otimização numéricas. Deste modo, este trabalho propõe o estudo do projeto de canais para escoamentos incompressíveis em regime permanente de fluidos não-Newtonianos através do Método de Otimização Topológica baseado no método de densidade. O escoamento é modelado com as equações de Navier-Stokes acopladas com a equação constitutiva de Carreau-Yasuda para a viscosidade dinâmica, para que sejam considerados os efeitos das propriedades não-Newtonianas do sangue. O Método de Otimização Topológica distribui regiões de sólido e fluido, dada uma restrição de volume, dentro de um domínio especificado de modo a obter uma geometria e configuração que minimize a dissipação de energia, tensão de cisalhamento e vorticidade, utilizando a pseudo-densidade do material como variável de projeto. Para aplicar este método a sistemas fluidos, um meio poroso fictício, baseado na equação de Darcy, é introduzido. O modelo de escoamento é implementado em sua forma discreta utilizando o Método de Elementos Finitos através da plataforma OpenSource FEniCS, aplicada para automatizar a solução dos modelos matemáticos baseados em equações diferenciais, e o problema de otimização é resolvido utilizando a biblioteca DOLFIN-adjoint e otimizador IPOpt. Topologias otimizadas de canais para fluxo de sangue, com foco em bypass arterial, são apresentadas para ilustrar o método proposto.
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Iwamura, Rafael Santos. "Minimax approach applied to topology optimization of structures subjected to multiple load cases." Instituto Tecnológico de Aeronáutica, 2013. http://www.bd.bibl.ita.br/tde_busca/arquivo.php?codArquivo=2834.
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This work investigates a topology optimization strategy for structures under multiple load cases. Typically compliance is calculated for each of the load cases in analysis and minimization is computed for a weighted average of the compliances, resulting in time consuming algorithms. A way to increase convergence speed is updating density on the element level. Instead of having an averaged compliance for the whole structure, it is proposed to compute it individually for every element. All load cases are analyzed, however only the ones of the maximum compliances are considered for sensitivity analysis. Thus compliance gradient is function of a few load cases at each element, reducing the processing time without significant weight penalty. The efficiency of the proposed technique is exemplified and compared to the one of a classical approach of multiple load case problem, solved using optimality criteria.
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Kim, Soojeong. "A 4-string tangle analysis of DNA-protein complexes based on difference topology." Diss., University of Iowa, 2010. https://ir.uiowa.edu/etd/528.
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An n-string tangle is a three dimensional ball with n-strings properly embedded in it. In late the 80's, C. Ernst and D. Sumners introduced a tangle model of protein-DNA complexes. This model assumes that the protein is a 3-dimensional ball and the protein-bound DNA are strings embedded inside the ball.
Originally the tangle model was applied to proteins such as Cre recombinate which binds two DNA segments. The protein breaks and rejoins the DNA segments and then creatss knotted DNA. When this kind of protein complex bounds circular DNA, there will be two DNA loops outside of the DNA-protein complex. Hence we can use a 2-string tangle model for this complex. More recently, Pathania, Jayaram and Harshey predicted that the topological structure within the Mu protein complex consists of three DNA segments containing five crossigs. Since Mu binds DNA sequences at 3 sites, the Mu protein-DNA complex can be modeled by a 3-string tangle. Darcy, Leucke and Vazquez analyzed Pathania et al's experimental results by using 3-tangle analysis.
Based on the 3-string tangle analysis of Mu protein-DNA complex, we addressed the possibility that a protein binds DNA sequences at four sites. Such a protein complex bound to a circular DNA molecule is modeled by a 4-string tangle with four loops outside of the tangle. In this thesis, we decided a biologically relevant 4-string tangle model. We also developed mathematics for solving tangle equations to predict the topology of DNA within the protein complex.
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Alm, Grundström Henrik. "Topology Optimization for Additive Manufacturing Considering Stress and Anisotropy." Thesis, Linköpings universitet, Mekanik och hållfasthetslära, 2017. http://urn.kb.se/resolve?urn=urn:nbn:se:liu:diva-141609.
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Additive manufacturing (AM) is a particularly useful manufacturing method for components designed using topology optimization (TO) since it allows for a greater part complexity than any traditional manufacturing method. However, the AM process potentially leads to anisotropic material properties due to the layer-by-layer buildup of parts and the fast and directional cooling. For Ti6Al4V tensile specimens built using electron beam melting (EBM), it has been observed that flat built specimens show superior strength and elastic moduli compared to top built specimens. Designs with the loading direction parallel to the build layers are therefore expected to show greater reliability. In this thesis a procedure is developed to optimize the AM build orientation considering anisotropic elastic material properties. A transversely isotropic material model is used to represent the in-plane and out-of-plane characteristics of AM produced parts. Two additional design variables are added to the TO formulation in order to control the orientation of the material using a coordinate transformation. Sensitivity analysis for the material direction variables is conducted for compliance as well as maximum von-Mises stress using a -norm stress aggregation function. The procedures for the AM build orientation optimization and stress constraints are implemented in the finite element software TRINITAS and evaluated using a number of examples in 2D and 3D. It is found that the procedure works well for compliance as well as stress but that a combination of these may lead to convergence issues due to contradicting optimal material orientations. An evaluation of the -norm stress aggregation function showed that a single global stress measure in combination with a stress correction procedure works well for most problems given that the mesh is refined enough to resolve the stresses accurately.
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Hartsell, Jack. "A Normal Form for Words in the Temperley-Lieb Algebra and the Artin Braid Group on Three Strands." Digital Commons @ East Tennessee State University, 2018. https://dc.etsu.edu/etd/3504.
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The motivation for this thesis is the computer-assisted calculation of the Jones poly- nomial from braid words in the Artin braid group on three strands, denoted B3. The method used for calculation of the Jones polynomial is the original method that was created when the Jones polynomial was first discovered by Vaughan Jones in 1984. This method utilizes the Temperley-Lieb algebra, and in our case the Temperley-Lieb Algebra on three strands, denoted A3, thus generalizations about A3 that assist with the process of calculation are pursued.
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Bolle, Jenny Helene. "Evaluating Topology Optimization as an alternative methodology for developing Vibration Test Fixtures." Thesis, Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, 2020. http://urn.kb.se/resolve?urn=urn:nbn:se:ltu:diva-79388.
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This thesis evaluates an alternative method for creating vibration test fixtures. The new method is based on producing fixtures by utilizing the external forces, that a fixture is subjected to during vibration tests, instead of creating it with estimations and guess-work, as it is done today. The purpose is to be able to create fixtures that have high natural frequencies and are reliable during tests and the goal is to create a computational model that corresponds with the real test conditions. The computational model was defined by applying gravitational loads in all six directions on a static solid model and the computation was solved with topology optimization, to create a structure with the most optimal material distribution. Data was collected in quantities and a model was chosen to work further with to create the version that fulfills the requirements. The final version of the fixture was optimized to an optimal weight of $2.5\;kg$ and produced with additive manufacturing in order to test it on an electrodynamic shaker. The result was a fixture with improved characteristics and a computational model proven valid. Kongsberg Automotive can now create vibration fixtures with higher eigenfrequencies, lower mass and lower manufacturing costs, that are more reliable in vibration tests.
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Padberg, Mary Therese. "Software for modeling protein-bound DNA: determining a geometric structure consistent with known topological data." Diss., University of Iowa, 2013. https://ir.uiowa.edu/etd/4890.
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For many years scientists have been working on more advanced methods to determine the structure of DNA under various conditions. However, research on the study of the shape of DNA segments bound by protein (protein-bound DNA) has been limited by the accuracy and dependability of laboratory techniques. These techniques vary from gel electrophoresis experiments, which can determine the topological shape of unbound DNA, to experiments that crystallize protein-bound DNA in a fixed state in order to determine the spatial location of non-hydrogen atoms. Each method comes with its own benefits and drawbacks. One drawback is experiments used to determine the exact geometry for protein-bound DNA often fail for large complexes. So when laboratory techniques fail to yield a geometric description of the DNA bound by protein, we turn to modeling software.
We introduce software that takes known protein-bound DNA topology and determines a potential geometry. An n-string tangle consists of n strings embedded in a three-dimensional ball with endpoints fixed on the boundary. The strings represent the DNA segments bound by protein. Starting with a topological tangle file from KnotPlot (a knot and tangle visualization program), our software minimizes over geometric parameters while keeping the topology fixed.
Our modeling software assumes the base pairs to be rigid bodies (or rectangles). Our routine minimizes over an energy function established by Dr. Wilma Olson et al. for the software package, 3DNA. Our program differs from 3DNA in that it can determine potential geometric structures while remaining consistent with the known topology. Thus, for protein-bound DNA whose topology has been identified, we can associate a likely geometry.
The energy function over which we minimize is given in terms of dimer geometric parameters derived from crystal structures of protein-bound DNA. A dimer refers to two consecutive DNA base pairs. Thus, not only is our solution topologically relevant, but the geometric solution is DNA sequence specific. Currently only two-dimensional models for protein-bound DNA tangles are easily available. Thus, one of the main benefits of our software is that it offers three-dimensional visualization of the protein-bound DNA segments. This modeling software is a great starting point for determining potential geometries for protein-bound DNA, analyzing the geometrical shape of the bound DNA, and learning more about how the topology and geometry of protein-bound DNA structures are associated.
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Garla, Venkatakrishnaiah Sharath Chandra, and Harivinay Varadaraju. "Validation of Black-and-White Topology Optimization Designs." Thesis, Linköpings universitet, Mekanik och hållfasthetslära, 2021. http://urn.kb.se/resolve?urn=urn:nbn:se:liu:diva-174807.
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Topology optimization has seen rapid developments in its field with algorithms getting better and faster all the time. These new algorithms help reduce the lead time from concept development to a finished product. Simulation and post-processing of geometry are one of the major developmental costs. Post-processing of this geometry also takes up a lot of time and is dependent on the quality of the geometry output from the solver to make the product ready for rapid prototyping or final production. The work done in this thesis deals with the post-processing of the results obtained from topology optimization algorithms which output the result as a 2D image. A suitable methodology is discussed where this image is processed and converted into a CAD geometry all while minimizing deviation in geometry, compliance and volume fraction. Further on, a validation of the designs is performed to measure the extracted geometry's deviation from the post-processed result. The workflow is coded using MATLAB and uses an image-based post-processing approach. The proposed workflow is tested on several numerical examples to assess the performance, limitations and numerical instabilities. The code written for the entire workflow is included as an appendix and can be downloaded from the website:https://github.com/M87K452b/postprocessing-topopt.
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Curwen, Vincent, and Alexander Saxin. "Analysis and optimal design of a titanium aircraft bracket using topology optimization." Thesis, Högskolan i Skövde, Institutionen för ingenjörsvetenskap, 2021. http://urn.kb.se/resolve?urn=urn:nbn:se:his:diva-20004.
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Sustainable engineering within product development is becoming increasingly important with the ever-growing amounts of resources used to sustain the human way of life in modern times. An effective way of helping to deal with this problem is to reduce the resources used in products and components across the world. This thesis explores the effectiveness of the topology optimization method in achieving significant material reductions whilst maintaining structural strength and integrity when designing an aircraft component. The part is an engine handling mounting bracket which will be optimized to be produced by additive manufacturing, and so restrictions imposed by traditional manufacturing methods are not considered, allowing for larger material reductions to be achieved. The original bracket part was provided by GE Electric, and the computer software Abaqus computer aided engineering with integrated TOSCA was used to solve the problem. Two trials were conducted, with the first being used to gain knowledge and understanding of the optimization features of the software. The basic requirements for the optimized design were that it should be able to withstand four given static load cases without undergoing plastic deformation, and these load cases were applied separately in trial 1 for simplicity. The second trial was conducted with a higher complexity, utilising multi-objective topology optimization which allowed the load cases to be weighted individually whilst being applied simultaneously during optimization. The resulting bracket part that was created with the help of the optimized topology from trial 2 reduced the volume of the original part by over 75%. This also left potential for further material reductions as the optimized part did not undergo plastic deformation when subject to any of the four load cases of the study. In conclusion, topology optimization seems to be extremely helpful when designing components that have clearly defined load cases, producing results that designers and engineers can have confidence in. The method does however have its flaws, such as difficulties in utilising the optimized topology directly to create a computer aided design part file. The post-processing process needed to achieve such a part is also time-consuming although it must be implemented to create a digital part that can be analysed and verified by FEA.
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Bouchon, Marika. "'Nexial-topology' situation modelling : health ecology and other general perspectives." Thesis, View thesis, 2008. http://hdl.handle.net/1959.7/uws:3698.
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ABSTRACT: This research generated a formal method for global ‘situation modelling’ of near-critical and critical phenomena. The new paradigms and the construction of mental reality or social spaces do not explain the damaged world we leave to our children and the degeneration of health. The ‘physical’ was explored experimentally through the reputed imperfection of the body in daily living and the ecology of its health. An ‘integral’ methodology allowed combining this with a study of general perspectives in many fields. This theoretical and empirical study was framed according to a third-order logic: (1) The variety and inconsistency of perspectives on the unclear notion of ‘health’ required a generalist (meta-)classification or organising principle applicable in particular to health. The method of ‘perspectival analysis’ is based on the field- and domain-specific vocabularies, number of categories, and image types used in formulating explanation/ experience in each framework, in both scientific and human domains. This theoretical study was (2) grounded in a ‘radical empirical’ study of the effects of nutrition and healing techniques on a low-grade chronic syndrome (not life threatening but connected to stress, inflammation, swelling, tissues wasting). A ‘local-case’ experimental research design (representative of an aspect of health), and new topographic ‘gauging’ techniques were devised to observe small spatial changes (positioning, distortion, distribution). The results and concrete/ practice models led to the same conclusion as the abstract study: all our perspectives on health, body and space, have some underlying systemic form, and have in common two unifying frames – duality and polarisation –, characteristic also of point-set theory derived frameworks. Using them allows ‘circumnavigating’ the essential of all possible perspectives, without becoming lost in their details. However, they leave non-local effects, anomalies (or ’bad behaviour’) and periodical instability unexplained. (3) These were investigated by studying behaviour (irrespective of whether internal or external), and ‘not well understood’ induced health manifestations, and by mapping their topologic properties of small deformation through (a) a ‘local’ cognitive consideration of experience construction, the research process itself, and the intellectual skill of model-making, (b) etymologic studies to track forward semantic developments and perspectival shifts and inversions, (c) a graphic study of the universal symbolic forms in models, traditions, and dreams, tracing them back to ‘world-origin’ models (appearance/occurrence), and shape-icons (mental, cultural), such as tree, ladder, mountain or vortex-vertex spiral.
This thesis examines health disturbance, physical distortions and cultural deformations, their usual descriptions as timed changes, and shows how two fundamental parameters of direction and motion (or movement, energy, 'Wind') define geometries of binding, or directional activation (or active projection). These culturo-mental geometries produce generic images of locally induced phenomena, and represent boundary phenomena globally as 'natural' in the spatial-physical world, and as 'hidden' or latent in the human world. Their downside is to introduce systematic instability in our expressions, models of culture/civilisation, as well as in health manifestations. All these are found to be rooted in modelling styles derived from the 'local' geometry of observing – framing – a field in 'perspective', mostly based on vision, audition, and skin surface (touch). These geo-Metries are used to explain and justify in particular the instability and recurrent crises of health in chronic syndromes and ageing, and the ‘badly behaved’ health of childhood and adult females (eg consequences of pregnancy). The conclusion imposed itself that the ‘physical world of humans’ is shaped through critical response and boundaries, and it appears that physical integrity, including sound health, sanity and even safety, cannot be preserved but by conscious alert attention or voluntary practice or effort (eg ‘workout’). Some experiences recounted in this work (some from the literature) led to an opposite presupposition. Three possible logics rule deployments of perspective into flat, spherical, and hyperbolic geometries (a known basis of mathematics). Which is used depends on the ‘local’ state of criticality (sense of urgency, emergency, pressure) of the observing body-brain-‘system’. It correlates with this universally assumed vertical axis, with the exclusive use [instruments too] of the senses of the head and of ‘skin-encapsulated’ derived systemic definitions of ‘the world’ and ‘the observer’ (self or body). These allow localising and attributing properties to one or the other or their combination. However, they can also be considered as undifferentiated properties, ‘non-local’ but governing, of the ‘physical world of humans’ as it is apprehended in daily living, manifesting in a surface-related sense of swelling and gravity. A simple form of geometric topology ‘without hole’ (without discontinuity), here introduced through two cognitive experiments, animations, and images, can describe this. The method of ‘nexial-topology’ produces an ‘animated imaging’ that can be used to model (but not ‘represent’ in word, number, or realistic/ naturalistic images) the situation reaching ‘critical boundary’. It then shows auto-reinforcing self-organisation and auto-destruction in ‘passing’ it. Yet, it can also be used as a ‘native gauging’ expressed in gesture or body posture, related to intuition, instinct, and the rare ‘thinking in image’. As such, it describes approaching ‘critical boundary’ (versus ‘reaching’) as auto-limiting. A crucial finding is that ‘spontaneous’ behaviours (non-induced, non-intended) can ensure the integrity of health under operation in most conditions, and stop extremes. Yet, they are usually deemed meaningless, random or useless, and are systematically suppressed by enculturation and prevented by civilised lifestyles. ‘Nexial-topology’ gives a clear meaning to them, and can model the ‘ease’ of health and of daily living. It gives access to more basic options, with wider effects, more immediate than all our solutions, often ignored because too obvious. For example, ‘global warming’ could be addressed as a non-local property and a deployment into crises to ‘stop’, rather than separate problems of water, resources, heated behaviour, inflammatory and ‘water diseases’.
KEYWORDS: Interdisciplinary research, cross-disciplinary methodologies, modal logic, fundamental problem, general relativity, localisation, physicalism, geometric quantization, occurrence, appearance, extension, projection, attribution, distributed, anthropic principle, anthropomorphism, unified, unbounded, left, right, spiral, viral, genetic drift, natural, life, human nature, human pressure, limit, extreme, threshold, validity, value, critical decision making, apperception, child cognition, sense, semantic drift, Four Elements, symbolic inversion.
THIS IS A MULTI-MEDIA THESIS. FOR A SITE MAP OF THE NAMES AND DISPLAY ONLINE OF THE 52 FILES OF THIS THESIS, PLEASE CONSULT THE SECTION: ORGANISATION OF THE MULTI-MEDIA MATERIALS IN THIS THESIS, IN THE FRONT PAGES FILE (SOURCE 2), BEFORE THE TABLE OF CONTENTS.
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Pearsall, Sam Alfred. "The Cantor set." CSUSB ScholarWorks, 1999. https://scholarworks.lib.csusb.edu/etd-project/1528.
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Svensson, Marcus. "Selection of a product component for topology optimization and additive manufacturing." Thesis, Jönköping University, JTH, Industriell produktutveckling, produktion och design, 2021. http://urn.kb.se/resolve?urn=urn:nbn:se:hj:diva-52791.
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This is a master thesis research on how to select the right components in a product, considering reducing the weight with topology optimization (TO) and adaption for additive manufacturing (AM). It is well established that manufacturing of complex structures can be achieved with AM, the possibility of integrating assembled components and improve features will therefore be investigated. The new component structure must still withstand the loads that it is subjected to during usage, to not permanently deform or break. In this research the studied product was a handheld Husqvarna chainsaw. Initially a feasibility study was conducted, where the product was disassembled and physically investigated for potential component cases. Additional knowledge was gathered with one semi structured interview per case, with experienced design engineers. Followed by one semi structured interview with AM experts, regarding available AM technique and similar material. Selection of case to continue with was based on the interviews information and Pughs decision matrix, with weighted criterions. TO were used for finding the optimal material distribution. The new component design was analyzed with linear finite element analysis to fulfill both the component and material stress requirements. Component orientation and support structure for AM was analyzed with computer aided engineering software. This resulted with integrating thirteen components for the engines cylinder into one component. The new design resulted in a weight reduction of 31%, while utilizing only 57% of the allowed stress limit. Also, the first 23 natural frequencies were improved with a new type of cooling fin structure, with an increased area of 15%. These results encourage the thesis workflow methodology usage for other products. In conclusion the established workflow of methods resulted in selecting a suitable case for integrating components with feature improvement and adaption of the new design with TO for AM, to reduce the weight.
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Van, Coller Henry. "A categorical study of compactness via closure." Thesis, Stellenbosch : Stellenbosch University, 2009. http://hdl.handle.net/10019.1/2351.
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Thesis (MSc (Mathemathical Sciences))--Stellenbosch University, 2009.We have the familiar Kuratowski-Mr owka theorem in topology, where compactness is characterised by a closure and a projection-map (X is compact i p : X Y ! Y is a closed mapping, for any space Y , i.e. p(A) = p(A) A X Y ). Using this as our starting point, we generalise compactness to a categorical setting. We then generalise even further to "asymmetric" compactness. Then we discuss a functional approach to compactness, where we do not explicitly mention closure operators. All this provides economical proofs as well as applications in di erent areas of mathematics.
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Dover, Kathryn. "Pattern Recognition in Stock Data." Scholarship @ Claremont, 2017. http://scholarship.claremont.edu/hmc_theses/105.
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Finding patterns in high dimensional data can be difficult because it cannot be easily visualized. There are many different machine learning methods to fit data in order to predict and classify future data but there is typically a large expense on having the machine learn the fit for a certain part of a dataset. We propose a geometric way of defining different patterns in data that is invariant under size and rotation. Using a Gaussian Process, we find that pattern within stock datasets and make predictions from it.
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Heller, Gabriella. "Topological Complexity in Protein Structures." Scholarship @ Claremont, 2014. http://scholarship.claremont.edu/pomona_theses/118.
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For DNA molecules, topological complexity occurs exclusively as the result of knotting or linking of the polynucleotide backbone. By contrast, while a few knots and links have been found within the polypeptide backbones of some protein structures, non-planarity can also result from the connectivity between a polypeptide chain and attached metal structures. In this thesis, we survey the known types of knots, links, and non-planar graphs in protein structures with and without including such bonds between proteins and metals. Then we present new examples of protein structures containing M\"obius ladders and other non-planar graphs as a result of these bound metal atoms. Finally, we propose hypothetical structures illustrating specific disulfide connectivities that would result in the key ring link, the Whitehead link and the 5_1 knot, the latter two of which have thus far not been identified within protein structures.
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Sanders, Scott. "Manifold Learning with Tensorial Network Laplacians." Digital Commons @ East Tennessee State University, 2021. https://dc.etsu.edu/etd/3965.
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The interdisciplinary field of machine learning studies algorithms in which functionality is dependent on data sets. This data is often treated as a matrix, and a variety of mathematical methods have been developed to glean information from this data structure such as matrix decomposition. The Laplacian matrix, for example, is commonly used to reconstruct networks, and the eigenpairs of this matrix are used in matrix decomposition. Moreover, concepts such as SVD matrix factorization are closely connected to manifold learning, a subfield of machine learning that assumes the observed data lie on a low-dimensional manifold embedded in a higher-dimensional space. Since many data sets have natural higher dimensions, tensor methods are being developed to deal with big data more efficiently. This thesis builds on these ideas by exploring how matrix methods can be extended to data presented as tensors rather than simply as ordinary vectors.
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Byttner, Wolf. "Classifying RGB Images with multi-colour Persistent Homology." Thesis, Linköpings universitet, Matematiska institutionen, 2019. http://urn.kb.se/resolve?urn=urn:nbn:se:liu:diva-157641.
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In Image Classification, pictures of the same type of object can have very different pixel values. Traditional norm-based metrics therefore fail to identify objectsin the same category. Topology is a branch of mathematics that deals with homeomorphic spaces, by discarding length. With topology, we can discover patterns in the image that are invariant to rotation, translation and warping. Persistent Homology is a new approach in Applied Topology that studies the presence of continuous regions and holes in an image. It has been used successfully for image segmentation and classification [12]. However, current approaches in image classification require a grayscale image to generate the persistence modules. This means information encoded in colour channels is lost. This thesis investigates whether the information in the red, green and blue colour channels of an RGB image hold additional information that could help algorithms classify pictures. We apply two recent methods, one by Adams [2] and the other by Hofer [25], on the CUB-200-2011 birds dataset [40] andfind that Hofer’s method produces significant results. Additionally, a modified method based on Hofer that uses the RGB colour channels produces significantly better results than the baseline, with over 48 % of images correctly classified, compared to 44 % and with a more significant improvement at lower resolutions.This indicates that colour channels do provide significant new information and generating one persistence module per colour channel is a viable approach to RGB image classification.
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Melin, Erik. "Digital Geometry and Khalimsky Spaces." Doctoral thesis, Uppsala University, Department of Mathematics, 2008. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-8419.
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Digital geometry is the geometry of digital images. Compared to Euclid’s geometry, which has been studied for more than two thousand years, this field is very young.
Efim Khalimsky’s topology on the integers, invented in the 1970s, is a digital counterpart of the Euclidean topology on the real line. The Khalimsky topology became widely known to researchers in digital geometry and computer imagery during the early 1990s.
Suppose that a continuous function is defined on a subspace of an n-dimensional Khalimsky space. One question to ask is whether this function can be extended to a continuous function defined on the whole space. We solve this problem. A related problem is to characterize the subspaces on which every continuous function can be extended. Also this problem is solved.
We generalize and solve the extension problem for integer-valued, Khalimsky-continuous functions defined on arbitrary smallest-neighborhood spaces, also called Alexandrov spaces.
The notion of a digital straight line was clarified in 1974 by Azriel Rosenfeld. We introduce another type of digital straight line, a line that respects the Khalimsky topology in the sense that a line is a topological embedding of the Khalimsky line into the Khalimsky plane.
In higher dimensions, we generalize this construction to digital Khalimsky hyperplanes, surfaces and curves by digitization of real objects. In particular we study approximation properties and topological separation properties.
The last paper is about Khalimsky manifolds, spaces that are locally homeomorphic to n-dimensional Khalimsky space. We study different definitions and address basic questions such as uniqueness of dimension and existence of certain manifolds.
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Dugast, Maël. "Géométrie et topologie des processus périodiquement corrélés induit par la dilation : Application à l'étude de la variabilité des épidémies pédiatriques saisonnières." Thesis, Lyon, 2018. http://www.theses.fr/2018LYSEI127/document.
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Chaque année lors de la période hivernale, des phénomènes épidémiques affectent l’organisation des services d’urgences pédiatriques et dégradent la qualité de la réponse fournie. Ces phénomènes présentent une forte variabilité qui rend leur analyse difficile. Nous nous proposons d’étudier cette volatilité pour apporter une vision nouvelle et éclairante sur le comportement de ces épidémies. Pour ce faire, nous avons adopté une vision géométrique et topologique originale directement issue d’une application de la théorie de la dilation: le processus de variabilité étant périodiquement corrélé, cette théorie fournit un ensemble de matrices dites de dilations qui portent toute l’information utile sur ce processus. Cet ensemble de matrices nous permet de représenter les processus stochastiques comme des éléments d’un groupe de Lie particulier, à savoir le groupe de Lie constitué de l’ensemble des courbes sur une variété. Il est alors possible de comparer des processus par ce biais. Pour avoir une perception plus intuitive du processus de variabilité, nous nous sommes ensuite concentrés sur le nuage de points formé par l’ensemble des matrices de dilations. En effet, nous souhaitons mettre en évidence une relation entre la forme temporelle d’un processus et l’organisation de ces matrices de dilations. Nous avons utilisé et développé des outils d’homologie persistante et avons établi un lien entre la désorganisation de ce nuage de points et le type de processus sous-jacents. Enfin nous avons appliqué ces méthodes directement sur le processus de variabilité pour pouvoir détecter le déclenchement de l’épidémie. Ainsi nous avons établi un cadre complet et cohérent, à la fois théorique et appliqué pour répondre à notre problématiqueEach year emergency department are faced with epidemics that affect their organisation and deteriorate the quality of the cares. The analyse of these outbreak is tough due to their huge variability. We aim to study these phenomenon and to bring out a new paradigm in the analysis of their behavior. With this aim in mind, we propose to tackle this problem through geometry and topology: the variability process being periodically correlated, the theory of dilation exhibit a set of matrices that carry all the information about this process. This set of matrices allow to map the process into a Lie group, defined as the set of all curves on a manifold. Thus, it is possible to compare stochastic processes using properties of Lie groups. Then, we consider the point cloud formed by the set of dilation matrices, to gain more intuitions about the underlying process. We proved a relation between the temporal aspect of the signal and the structure of the set of its dilation matrices. We used and developped persistent homology tools, and were able to classify non-stationary processes. Eventually, we implement these techniques directly on the process of arrivals to detect the trigger of the epidemics. Overall we established a complete and a coherent framework, both theoretical and practical
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Xin, Ying. "Complex Dynamical Systems: Definitions of Entropy, Proliferation of Epithelia and Spread of Infections and Information." Ohio University / OhioLINK, 2018. http://rave.ohiolink.edu/etdc/view?acc_num=ohiou1522955730251256.
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Miick, Tonja. "Minimizing Travel Time Through Multiple Media With Various Borders." TopSCHOLAR®, 2013. http://digitalcommons.wku.edu/theses/1246.
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This thesis consists of two main chapters along with an introduction andconclusion. In the introduction, we address the inspiration for the thesis, whichoriginates in a common calculus problem wherein travel time is minimized across two media separated by a single, straight boundary line. We then discuss the correlation of this problem with physics via Snells Law. The first core chapter takes this idea and develops it to include the concept of two media with a circular border. To make the problem easier to discuss, we talk about it in terms of running and swimming speeds. We first address the case where the starting and ending points for the passage are both on the boundary. We find the possible optimal paths, and also determine the conditions under which we travel along each path. Next we move the starting point to a location outside the boundary. While we are not able to determine the exact optimal path, we do arrive at some conclusions about what does not constitute the optimal path. In the second chapter, we alter this problem to address a rectangular enclosed boundary, which we refer to as a swimming pool. The variations in this scenario prove complex enough that we focus on the case where both starting and ending points are on the boundary. We start by considering starting and ending points on adjacent sides of the rectangle. We identify three possibilities for the fastest path, and are able to identify the conditions that will make each path optimal. We then address the case where the points are on opposite sides of the pool. We identify the possible paths for a minimum time and once again ascertain the conditions that make each path optimal. We conclude by briefly designating some other scenarios that we began to investigate, but were not able to explore in depth. They promise insightful results, and we hope to be able to address them in the future.
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Agerberg, Jens. "Statistical Learning and Analysis on Homology-Based Features." Thesis, KTH, Matematisk statistik, 2020. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-273581.
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Stable rank has recently been proposed as an invariant to encode the result of persistent homology, a method used in topological data analysis. In this thesis we develop methods for statistical analysis as well as machine learning methods based on stable rank. As stable rank may be viewed as a mapping to a Hilbert space, a kernel can be constructed from the inner product in this space. First, we investigate this kernel in the context of kernel learning methods such as support-vector machines. Next, using the theory of kernel embedding of probability distributions, we give a statistical treatment of the kernel by showing some of its properties and develop a two-sample hypothesis test based on the kernel. As an alternative approach, a mapping to a Euclidean space with learnable parameters can be conceived, serving as an input layer to a neural network. The developed methods are first evaluated on synthetic data. Then the two-sample hypothesis test is applied on the OASIS open access brain imaging dataset. Finally a graph classification task is performed on a dataset collected from Reddit.Stable rank har föreslagits som en sammanfattning på datanivå av resultatet av persistent homology, en metod inom topologisk dataanalys. I detta examensarbete utvecklar vi metoder inom statistisk analys och maskininlärning baserade på stable rank. Eftersom stable rank kan ses som en avbildning i ett Hilbertrum kan en kärna konstrueras från inre produkten i detta rum. Först undersöker vi denna kärnas egenskaper när den används inom ramen för maskininlärningsmetoder som stödvektormaskin (SVM). Därefter, med grund i teorin för inbäddning av sannolikhetsfördelningar i reproducing kernel Hilbertrum, undersöker vi hur kärnan kan användas för att utveckla ett test för statistisk hypotesprövning. Slutligen, som ett alternativ till metoder baserade på kärnor, utvecklas en avbildning i ett euklidiskt rum med optimerbara parametrar, som kan användas som ett ingångslager i ett neuralt nätverk. Metoderna utvärderas först på syntetisk data. Vidare utförs ett statistiskt test på OASIS, ett öppet dataset inom neuroradiologi. Slutligen utvärderas metoderna på klassificering av grafer, baserat på ett dataset insamlat från Reddit.
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Loreto, Renan Pires. "Topological states applied to spintronics devices." Universidade Federal de Viçosa, 2018. http://www.locus.ufv.br/handle/123456789/20365.
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Coordenação de Aperfeiçoamento de Pessoal de Nível Superior
Neste trabalho estudamos tres importantes sistemas magnéticos extensamente pesquisados nas últimas décadas. Na primeira parte, a proposta recente da utilização de skyrmions magnéticos, que são excitações topológicas tipo quasi-partícula em ferromagnetos, em memórias tipo racetrack, tem atraído a atenção de pesquisadores nos últimos anos abrindo um novo campo de estudo chamado skyrmionics, que é uma tentativa de utilizar estas estruuras magnéticas como transportadores de informação na próxima geração de de dispositivos spintrônicos. Para a utilização de skyrmions magnéticos, em alguns sistemas é necessário a inclusão de interação Dzyaloshinskii-Moriya e campos magnéticos externos no sistema. Neste trabalho, nós exploramos um sistema sem estes requisitos. Primeiro, propusemos um modo controlado de criação de skyrmions e skyrmioniums impressos em em uma nanofita de material ferromagnético com magnetização fora do plano. Após isso, investigamos o destacamento da estrutura da região abaixo de um nanodisco, responsável por imprimir esta estrutura. O transporte é feito por spin transfer torque devido a pulsos de corrente elétrica spin polarizada aplicadas na nanofita. A detecção da estrutura é feita por magnetoresistência túnel. Esta estrutura que se move, após deixar a região abaixo do disco, não é mais considerada um skyrmion e, calculando como a carga topológica evolui, a estrutura foi chamada de sóliton magnético ressonante. A segunda parte cobre os efeitos de geração de correntes puras de spin por Spin Pumping e efeito Seebeck de Spin e a conversão dessas correntes de spin em correntes de carga em isolantes topológicos a temperatura ambiente. A conversão de corrente de spin em corrente de carga é devido ao efeito Edelstein Inverso (IEE) que é possivel devido ao ’spin-momentum locking’ do elétron no nível de Fermi devido ao campo de Rashba. As medidas nas duas técnicas levaram ao mesmo valor do parâmetro IEE, mostrando que ambos os resultados são maneiras eficientes de converão de corrente de spin em corrente de carga. Na terceira parte, redes de nanomagnetos projetados para assemelhar-se a gelos de spin (estados magnéticos desordenados) e são conhecidos como gelos de spin artificiais e, estudos teóricos e experimentais da termodinâmica nestas redes. Nas redes retangulares de gelos de spin artificiais espera-se que mostrem diferentes transições de fase mudando a geometria do sistema. Esta dinâmica gerada por efeitos geométricos abrem uma possibilidade de explorar diferentes estados fundamentais e geração de monopolos magnéti- cos por efeitos térmicos. Aqui, mostramos que uma rede particular de gelos de spin artificiais se mostram com menos restrições para que as nanoilhas mudem magnetização em uma rede em particular e, comparndo o impacto de efeitos térmicos em mudanças de magnetização em diferentes sistemas, é possível encontrar o fenÃt’meno chamado geometrotermodinâmica.
In this work we study three important magnetic systems extensively researched in the past decades. In the first part, the recent proposition of the use of magnetic skyrmions, which are topological particle-like excitations in ferromagnets, in racetrack memories, have attracted a lot of attention recently opening up a new field of study called skyrmionics which is an attempt to use those magnetic structures as information carriers in next generation of spintronic devices. For usage of magnetic skyrmions, in some systems is necessary to include the Dzyaloshinskii- Moriya interaction (DMI) and the out-of-plane magnetic field into the system. In this work, we explore a system without these requirements. First, we propose a controlled way for the creation of magnetic skyrmions and skyrmioniums imprinted in a perpendicular magnetized ferromagnetic nanotrack. Then we investigate the detachment of the imprinted spin textures from the underneath of the nanodisk, the transport by the spin-transfer torque imposed by spin-polarized current pulses applied in the nanotrack and the detection by Tunnel Magnetoresistance (TMR). We notice that the moving structure is not a skyrmion after is detached, and by calculating how the topological charge behaves, we have called it the resonant magnetic soliton (RMS). The second part covers the generation of spin currents by Spin Pumping and Spin Seebeck effects and the conversion of this spin current to charge current in (Bi 0.22 Sb 0.78 ) 2 T e 3 topological insulators at room temperature. The spin-to-charge current conversion is attributed to the inverse Edelstein effect (IEE) made possible by the spin-momentum locking in the electron Fermi contours due to the Rashba field. The measurements by the two techniques yield the same value for the IEE parameter, showing that those methods can be an efficient way to the spin to charge current in topological insulators. In the third part, arrays of nanomagnets designed to resemble spin ice materials (disordered magnetic states) are known as artificial spin ices (ASI). Here we study, both theoretically and experimentally the thermodynamic effects on streched arrays of spin ices. The rectangular artificial spin ices (RASI) is expected do show different phase transitions by changing the geometry of the system. This geometrically driven dynamics in ASI can open up the panorama of exploring distinct ground states and thermally generated magnetic monopole excitations. Here, it is shown that a particular RASI lattice experience less restriction to flip precisely in a kind of rhombic lattice and by comparing the impact of thermal effects on the spin flips in these three appropriate different RASI arrays, it is possible to find the phenomenon that we call ASI geometrothermodynamics.
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(11008509), Nathanael D. Cox. "Two Problems in Applied Topology." Thesis, 2021.
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In this thesis, we present two main results in applied topology.
In our first result, we describe an algorithm for computing a semi-algebraic description of the quotient map of a proper semi-algebraic equivalence relation given as input. The complexity of the algorithm is doubly exponential in terms of the size of the polynomials describing the semi-algebraic set and equivalence relation.
In our second result, we use the fact that homology groups of a simplicial complex are isomorphic to the space of harmonic chains of that complex to obtain a representative cycle for each homology class. We then establish stability results on the harmonic chain groups.
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Chou, Shih-Min, and 周仕敏. "「Infinity‧∞」－Concept of Topology applied in Jewelry design." Thesis, 2009. http://ndltd.ncl.edu.tw/handle/01297406355707121119.
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碩士輔仁大學
應用美術學系碩士班
97
Math is a fabrication of imagination. It originated from logic and creativity. By means of abstract thinking way, math develops a concept world with reasons. This research combines technology and an artistic creation. “Topology” is the basis sprits of this concept, especially the idea “continuity”, which comes up with another idea – infinity. We transfer all the concepts with shape producing. Digital technology, lacquer, and polyester resins are used with innovation and traditional at the same time. In order to extend the structure of the math construction, and then could be materialized into my work, software is used a lot in this research. Finally, lacquer is the tool to make better performance of color. I wish people who come to visit my work could enjoy the aesthetic feeling from math, find out the special shape and then realize the concept of Topology. That is either a part of inside or maybe outside or it perhaps an infinite circulation. This brings more meaning from this work.
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Yeung, Melissa L. "Applied Computational Topology for Point Clouds and Sparse Timeseries Data." Thesis, 2017. https://thesis.library.caltech.edu/9960/1/melissayeung_thesis.pdf.
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The proliferation of sensors and advancement of technology has led to the production and collection of unprecedented amounts of data in recent years. The data are often noisy, non-linear, and high-dimensional, and the effectiveness of traditional tools may be limited. Thus, the technological advances that enable the ubiquitous collection of data from the cosmological scale to the subatomic scale also necessitate the development of complementary tools that address the new nature of the data.
Recently, there has been much interest in and success with developing topologically-motivated techniques for data analysis. These approaches are especially useful when a topological method is sensitive to large- and small-scale features that might not be detected by methods that require a level of geometric detail that is not provided by the data or by methods that may obscure geometric features, such as principal component analysis (PCA), multi–dimensional scaling (MDS), and cluster analysis.
Our work explores topological data analysis through two frameworks.
In the first part, we provide a tool for detecting material coherence from a set of spatially sparse particle trajectories via the study of a map induced on homology by the braid corresponding to the motion of particles. While the theory of coherent structures has received a great deal of attention and benefited from many advances in recent years, many of these techniques are limited when the data are sparse. We demonstrate through various examples that our work provides a practical and scalable tool for identifying coherent sets from a sparse set of particle trajectories using eigenanalysis.
In the second part, we formalize the local-to-global structure captured by topology in the setting of point clouds. We extend existing tools in topological data analysis and provide a theoretical framework for studying topological features of a point cloud over a range of resolutions, enabling the analysis of topological features using statistical methods. We apply our tools to the analysis of high-dimensional geospatial sensor data and provide a statistic for quantifying climate anomalies.
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CHEN, PIN-JUNG, and 陳品融. "Multi-Phase High-Step-Up Topology Applied to Thermoelectric Converter." Thesis, 2019. http://ndltd.ncl.edu.tw/handle/q2hjwt.
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碩士國立臺北科技大學
電機工程系
107
A high step-up converter with a non-isolated multi-input-single-output (MISO) structure is presented herein, and applied to the thermoelectric conversion system. The converter adopts coupled inductors and switched capacitors to increase the voltage gain. In order to reduce the voltage spikes created from leakage inductors, two active clamp circuits, with zero voltage switching (ZVS) are employed. Furthermore, number of inputs the converter can be increased. In this thesis, the basic principles of the converter is firstly described and analyzed, and then the design of the hardware circuit is followed. According the feasibility of the proposed converter is verified by simulation based on Powersim (PSIM) and the effectiveness of such a converter is demonstrated by voltage mode control. Afterwards, this converter is applied to the thermoelectric conversion system with the three-point-weighting method, to realize the maximum power point tracking. A field programmable logic gate array (FPGA), named EP3C5E1446CBN, is used as a circuit control kernel, and together with thermoelectric modules, named TG12-8L manufactured by Marlow Industries Inc., is utilized to demonstrate the feasibility of the proposed thermoelectric conversion system.
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Li, Yen-Jui, and 李彥叡. "Exploration of penalty functions applied to design variables in topology optimization." Thesis, 2010. http://ndltd.ncl.edu.tw/handle/06433491538445980092.
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碩士國立中興大學
機械工程學系所
98
After Bendsoe and Kikuchi introduced the homogenization method to solve the structural topology optimization problems, many research results have been reported. In this thesis, the objective is to generate a minimum compliance topology of a structure subject to a material constraint in a given design space. The design variable is the normalized density of each finite element in the design space, and the Young’s modulus is assumed to be a function of the normalized density. Five formulas with the features of penalization and encouragement are developed to compete with the commonly used method SIMP (Solid Isotropic Material with Penalization). The basic idea of these formulas is to penalize the design variables with value between 0 and 0.5 and encourage the design variables with value between 0.5 and 1. Through these efforts, the chance of most design variables approaching 0 or 1 will be increased. Based on the results of the numerical examples, some of the formulas proposed in this thesis indeed show some positive outcomes.
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Lin, Jia-Jie, and 林嘉頡. "Base on Average Circuit Method Applied to the DC-DC Converter Topology Analysis." Thesis, 2014. http://ndltd.ncl.edu.tw/handle/tmhfc9.
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碩士國立臺北科技大學
電機工程系研究所
102
This thesis presents the modeling which is based on averaging circuit to solve the problem of traditional derivation method will lose the original circuit structure, whose approach to guide the analysis of the switching network on / off, and replace the time-variable switch become to dependent voltage source or current source. It’s not only retain the original architecture, but also eliminate time-varying issues with ON/OFF. The focus of this research include: (1) Retain the original structure, find the switch position from a dependent source location, and can be derivation small signal model or circuit transfer function by dependent source; (2) Can be used in multi-switch network with a variety of operating modes in the switch network, improving traditional methods and previous literature only in the dual switching issues; (3) By analysis dependent source circuit direction and polarity can be know whether it will affect the zero point of the circuit, without going through the difficult mathematical calculations derived. To prove the proposed methods, this study will have a step-down circuit topology for a three-switch networks. Calculate the small-signal averaging equation and derive the circuit of the controller to obtain buck circuit which is 5V to 3.3V. The control of this circuit is used digital control. The Digital Signal Processor is using TMS320F28027 produced by Texas Instruments. Use programming language to implementation digital control. Through a digital proportional-integral controller with PWM generator to control power switch and allowing the system output 3.3V on different load.
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Andersen, Robert N. "Homotopy construction techniques applied to the cell like dimension raising problem and to higher dimensional dunce hats /." 1990. http://hdl.handle.net/1957/16964.
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Bouchon, Marika, University of Western Sydney, College of Arts, and Centre for Social Ecology Research. "'Nexial-topology' situation modelling : health ecology and other general perspectives." 2008. http://handle.uws.edu.au:8081/1959.7/28676.
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ABSTRACT: This research generated a formal method for global ‘situation modelling’ of near-critical and critical phenomena. The new paradigms and the construction of mental reality or social spaces do not explain the damaged world we leave to our children and the degeneration of health. The ‘physical’ was explored experimentally through the reputed imperfection of the body in daily living and the ecology of its health. An ‘integral’ methodology allowed combining this with a study of general perspectives in many fields. This theoretical and empirical study was framed according to a third-order logic: (1) The variety and inconsistency of perspectives on the unclear notion of ‘health’ required a generalist (meta-)classification or organising principle applicable in particular to health. The method of ‘perspectival analysis’ is based on the field- and domain-specific vocabularies, number of categories, and image types used in formulating explanation/ experience in each framework, in both scientific and human domains. This theoretical study was (2) grounded in a ‘radical empirical’ study of the effects of nutrition and healing techniques on a low-grade chronic syndrome (not life threatening but connected to stress, inflammation, swelling, tissues wasting). A ‘local-case’ experimental research design (representative of an aspect of health), and new topographic ‘gauging’ techniques were devised to observe small spatial changes (positioning, distortion, distribution). The results and concrete/ practice models led to the same conclusion as the abstract study: all our perspectives on health, body and space, have some underlying systemic form, and have in common two unifying frames – duality and polarisation –, characteristic also of point-set theory derived frameworks. Using them allows ‘circumnavigating’ the essential of all possible perspectives, without becoming lost in their details. However, they leave non-local effects, anomalies (or ’bad behaviour’) and periodical instability unexplained. (3) These were investigated by studying behaviour (irrespective of whether internal or external), and ‘not well understood’ induced health manifestations, and by mapping their topologic properties of small deformation through (a) a ‘local’ cognitive consideration of experience construction, the research process itself, and the intellectual skill of model-making, (b) etymologic studies to track forward semantic developments and perspectival shifts and inversions, (c) a graphic study of the universal symbolic forms in models, traditions, and dreams, tracing them back to ‘world-origin’ models (appearance/occurrence), and shape-icons (mental, cultural), such as tree, ladder, mountain or vortex-vertex spiral. This thesis examines health disturbance, physical distortions and cultural deformations, their usual descriptions as timed changes, and shows how two fundamental parameters of direction and motion (or movement, energy, 'Wind') define geometries of binding, or directional activation (or active projection). These culturo-mental geometries produce generic images of locally induced phenomena, and represent boundary phenomena globally as 'natural' in the spatial-physical world, and as 'hidden' or latent in the human world. Their downside is to introduce systematic instability in our expressions, models of culture/civilisation, as well as in health manifestations. All these are found to be rooted in modelling styles derived from the 'local' geometry of observing – framing – a field in 'perspective', mostly based on vision, audition, and skin surface (touch). These geo-Metries are used to explain and justify in particular the instability and recurrent crises of health in chronic syndromes and ageing, and the ‘badly behaved’ health of childhood and adult females (eg consequences of pregnancy). The conclusion imposed itself that the ‘physical world of humans’ is shaped through critical response and boundaries, and it appears that physical integrity, including sound health, sanity and even safety, cannot be preserved but by conscious alert attention or voluntary practice or effort (eg ‘workout’). Some experiences recounted in this work (some from the literature) led to an opposite presupposition. Three possible logics rule deployments of perspective into flat, spherical, and hyperbolic geometries (a known basis of mathematics). Which is used depends on the ‘local’ state of criticality (sense of urgency, emergency, pressure) of the observing body-brain-‘system’. It correlates with this universally assumed vertical axis, with the exclusive use [instruments too] of the senses of the head and of ‘skin-encapsulated’ derived systemic definitions of ‘the world’ and ‘the observer’ (self or body). These allow localising and attributing properties to one or the other or their combination. However, they can also be considered as undifferentiated properties, ‘non-local’ but governing, of the ‘physical world of humans’ as it is apprehended in daily living, manifesting in a surface-related sense of swelling and gravity. A simple form of geometric topology ‘without hole’ (without discontinuity), here introduced through two cognitive experiments, animations, and images, can describe this. The method of ‘nexial-topology’ produces an ‘animated imaging’ that can be used to model (but not ‘represent’ in word, number, or realistic/ naturalistic images) the situation reaching ‘critical boundary’. It then shows auto-reinforcing self-organisation and auto-destruction in ‘passing’ it. Yet, it can also be used as a ‘native gauging’ expressed in gesture or body posture, related to intuition, instinct, and the rare ‘thinking in image’. As such, it describes approaching ‘critical boundary’ (versus ‘reaching’) as auto-limiting. A crucial finding is that ‘spontaneous’ behaviours (non-induced, non-intended) can ensure the integrity of health under operation in most conditions, and stop extremes. Yet, they are usually deemed meaningless, random or useless, and are systematically suppressed by enculturation and prevented by civilised lifestyles. ‘Nexial-topology’ gives a clear meaning to them, and can model the ‘ease’ of health and of daily living. It gives access to more basic options, with wider effects, more immediate than all our solutions, often ignored because too obvious. For example, ‘global warming’ could be addressed as a non-local property and a deployment into crises to ‘stop’, rather than separate problems of water, resources, heated behaviour, inflammatory and ‘water diseases’. KEYWORDS: Interdisciplinary research, cross-disciplinary methodologies, modal logic, fundamental problem, general relativity, localisation, physicalism, geometric quantization, occurrence, appearance, extension, projection, attribution, distributed, anthropic principle, anthropomorphism, unified, unbounded, left, right, spiral, viral, genetic drift, natural, life, human nature, human pressure, limit, extreme, threshold, validity, value, critical decision making, apperception, child cognition, sense, semantic drift, Four Elements, symbolic inversion. THIS IS A MULTI-MEDIA THESIS. FOR A SITE MAP OF THE NAMES AND DISPLAY ONLINE OF THE 52 FILES OF THIS THESIS, PLEASE CONSULT THE SECTION: ORGANISATION OF THE MULTI-MEDIA MATERIALS IN THIS THESIS, IN THE FRONT PAGES FILE (SOURCE 2), BEFORE THE TABLE OF CONTENTS.Doctor of Philosophy (PhD)
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"The Domain Dependence of Chemotaxis in a Two-Dimensional Turbulent Flow." Master's thesis, 2015. http://hdl.handle.net/2286/R.I.34877.
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abstract: Presented is a study on the chemotaxis reaction process and its relation with flow topology. The effect of coherent structures in turbulent flows is characterized by studying nutrient uptake and the advantage that is received from motile bacteria over other non-motile bacteria. Variability is found to be dependent on the initial location of scalar impurity and can be tied to Lagrangian coherent structures through recent advances in the identification of finite-time transport barriers. Advantage is relatively small for initial nutrient found within high stretching regions of the flow, and nutrient within elliptic structures provide the greatest advantage for motile species. How the flow field and the relevant flow topology lead to such a relation is analyzed.Dissertation/Thesis
Masters Thesis Mathematics 2015
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Herr, Daniel. "Open books on contact three orbifolds." 2013. https://scholarworks.umass.edu/dissertations/AAI3603097.
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In 2002, Giroux showed that every contact structure had a corresponding open book decomposition. This was the converse to a previous construction of Thurston and Winkelnkemper, and made open books a vital tool in the study of contact three-manifolds. We extend these results to contact orbifolds, i.e. spaces that are locally diffeomorphic to the quotient of a contact manifold and a compatible finite group action. This involves adapting some of the main concepts and constructions of three dimensional contact geometry to the orbifold setting.
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(11205636), Sarah B. Percival. "Efficient Computation of Reeb Spaces and First Homology Groups." Thesis, 2021.
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This thesis studies problems in computational topology through the lens of semi-algebraic geometry. We first give an algorithm for computing a semi-algebraic basis for the first homology group, H1(S,F), with coefficients in a field F, of any given semi-algebraic set S⊂Rk defined by a closed formula. The complexity of the algorithm is bounded singly exponentially. More precisely, if the given quantifier-free formula involves s polynomials whose degrees are bounded by d, the complexity of the algorithm is bounded by (sd)kO(1).This algorithm generalizes well known algorithms having singly exponential complexity for computing a semi-algebraic basis of the zero-th homology group of semi-algebraic sets, which is equivalent to the problem of computing a set of points meeting every semi-algebraically connected component of the given semi-algebraic set at a unique point. We then turn our attention to the Reeb graph, a tool from Morse theory which has recently found use in applied topology due to its ability to track the changes in connectivity of level sets of a function. The roadmap of a set, a construction that arises in semi-algebraic geometry, is a one-dimensional set that encodes information about the connected components of a set. In this thesis, we show that the Reeb graph and, more generally, the Reeb space, of a semi-algebraic set is homeomorphic to a semi-algebraic set, which opens up the algorithmic problem of computing a semi-algebraic description of the Reeb graph. We present an algorithm with singly-exponential complexity that realizes the Reeb graph of a function f:X→Y as a semi-algebraic quotient using the roadmap of X with respect to f.