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1
Santos, Josà Adriano Fernandes dos. "Applied mathematics to geography." Universidade Federal do CearÃ, 2016. http://www.teses.ufc.br/tde_busca/arquivo.php?codArquivo=17058.
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Partindo do cenÃrio interdisciplinar em que a MatemÃtica se encontra, este trabalho se resume a apresentar aplicaÃÃes oriundos da Geografia dentro da contextualizaÃÃo matemÃtica. Os PCNâs (1998), documentos que regem a educaÃÃo atual brasileira, deixa clara importÃncia do trabalho interdisciplinar no ensino, bem como a relevÃncia de um ensinamento contextualizado baseado na pratica e vivÃncia histÃrica do homem. Por sua vez, na Geografia foi visto que a cartografia traz contribuiÃÃes relevantes à matemÃtica, e que a trigonometria à uma das ferramentas principais utilizadas nesta conjuntura, tanto por parte da geometria euclidiana
quanto da geometria nÃo-euclidiana. Assim neste trabalho foram apresentadas algumas aplicaÃÃes retiradas do estudo da cartografia que, com a ajuda da matemÃtica e principalmente
da trigonometria (plana e esfÃrica) foram resolvidas. Dando sequÃncia, ainda com foco na cartografia, especificamente no estudo de mapas e projeÃÃes, foi dada Ãnfase à ProjeÃÃo
CilÃndrica de Mercator e respectivas explicaÃÃes matemÃticas para a chamada arte de projetar num plano, no caso, Ã projeÃÃo da esfera num plano, com suas devidas explicaÃÃes matemÃticas
para tal feito. Com o tempo e o surgimento do cÃlculo infinitesimal, foi mostrado aqui a determinaÃÃo da chamada variÃvel de Mercator, e sua origem. Em seguida com a ajuda da
Geometria Diferencial dando Ãnfase aos estudos de Gauss, foi apresentada a nÃo isometria entre o plano e a esfera, e que a curvatura gaussiana à a funÃÃo definidora para tal fato. AtravÃs das formas fundamentais e do Teorema egrÃgio aqui tambÃm apresentadas, os estudos de Gauss dentro da geometria diferencial foram definidores para a explicaÃÃo mais atual da variÃvel de Mercator, contribuindo assim para o esclarecimento da famosa projeÃÃo feita por Mercator que ficou na histÃria por sua perfeiÃÃo.<br>From the interdisciplinary scenario in which mathematics is, this work comes down to present applications coming from Geography within the mathematical context. The NCP's (1998), documents governing the current Brazilian education, makes clear the importance of interdisciplinary work in education, and the importance of a contextualized teaching based on practical and historical experience of man. In turn, the geography was seen that mapping brings
outstanding contributions to mathematics, and trigonometry is one of the main tools used in this context, both by the Euclidean geometry as the non-Euclidean geometry. So in this paper were presented some applications withdrawn from the study of cartography, with the help of mathematics and especially Trigonometry (flat and spherical) were resolved. Continuing, still focusing on cartography, specifically in the study of maps and projections, emphasis was given
to Cylindrical Mercator projection and their mathematical explanations for the so-called art of designing a plan in case the projection of the sphere in a plane, with its appropriate mathematical explanations for such a feat. With time and the emergence of infinitesimal calculus, it was
shown here to determine the variable called Mercator and its origin. Then with the help of differential geometry emphasizing Gauss studies, it was presented not isometry between the plane and the sphere, and the Gaussian curvature is the defining function for this fact. Through
the fundamental forms and egregious Theorem here also presented the Gauss studies in differential geometry were defining for the most current explanation of Mercator variable, thus contributing to the clarification of the famous projection made by Mercator that went down in
history for its perfection.
2
May, Andrew. "Nonlinear systems in applied mathematics." Thesis, University of Exeter, 2000. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.312068.
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Hershberger, Geoffrey D. "APPLIED TEMPERAMENT." UKnowledge, 2018. https://uknowledge.uky.edu/music_etds/126.
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The following document was created in order to promote intonation consensus in ensembles and to better facilitate learning in educational settings. Non-keyboard instruments provide musicians an opportunity to make nearly infinitesimal adjustments to pitch while performing; this creates difficulties for students and challenges even the most seasoned professionals. Non-keyboard musicians struggle their whole lives to play in tune, and even when one knows exactly where they want to place a pitch, technical difficulties can foul any musician's performance. When performing solo, the musician must choose a tuning system that is suitable for the music being performed, and attempt to realize it. When performing in ensembles, the need for consensus and a systematic approach become more apparent. When performing with keyboards, the difficulties are increased as further compromises are required. This research was conducted with the intention to assist non-keyboard instrumentalists in selecting and recreating an appropriate temperament. Additionally, the author hopes that keyboard instrumentalists will be inclined to make a consideration for the non-keyboard instruments when selecting their temperament. The following document contains information useful to those wishing to employ a consistent approach to tuning. Presented here are the acoustic phenomena that have perplexed scholars around the world for the last 2600 years. The history and science of these acoustic questions will be demonstrated and discussed.
4
Veprauskas, Amy. "On the dynamic dichotomy between positive equilibria and synchronous 2-cycles in matrix population models." Thesis, The University of Arizona, 2016. http://pqdtopen.proquest.com/#viewpdf?dispub=10124871.
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<p> For matrix population models with nonnegative, irreducible and primitive inherent projection matrices, the stability of the branch of positive equilibria that bifurcates from the extinction equilibrium as the dominant eigenvalue of the inherent projection matrix increases through one is determined by the direction of bifurcation. However, if the inherent projection matrix is imprimitive this bifurcation becomes more complicated. This is the result of the simultaneous departure of multiple eigenvalues from the unit complex circle. Matrix models with imprimitive projection matrices commonly appear in models of semelparous species, which are characterized by one reproductive event that is often followed by death. </p><p> Due to the imprimitivity of the projection matrix, semelparous Leslie models exhibit two contrasting dynamics, either equilibria in which all age classes are present or synchronized cycles in which age classes are separated temporally. The two-stage semelparous Leslie model has index of imprimitivity two, meaning that two eigenvalues simultaneously leave the unit circle when the dominant eigenvalue increases past one. This model exhibits a dynamic dichotomy in which the two steady states have opposite stability properties. </p><p> We show that this dynamic dichotomy is a general feature of <i> synchrony models</i> which are characterized by the simultaneous creation of a branch of positive equilibria and a branch of synchronous 2-cycles when the extinction equilibrium destabilizes (Chapter 3). A synchrony model must, necessarily, have index of imprimitivity two but is not limited to models of semelparous species. We provide a specific example of a synchrony model for an iteroparous species which is motivated by observations of a cannibalistic gull population (Chapter 2). We also extend the study of the synchrony model to a Darwinian model which couples population dynamics with the dynamics of a suite of evolving phenotypic traits (Chapter 4). For the evolutionary synchrony model, we show that the dynamic dichotomy occurs provided that fitness, as measured by the spectral radius, is maximized. In addition, we examine the dynamic dichotomy for semelparous species in a continuous-time setting (Chapter 5).</p>
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Kliegl, Markus Vinzenz. "Explorations in the mathematics of inviscid incompressible fluids." Thesis, Princeton University, 2016. http://pqdtopen.proquest.com/#viewpdf?dispub=10010743.
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<p> The main subject of this dissertation is smooth incompressible fluids. The emphasis is on the incompressible Euler equations in all of <b>R</b><sup> 2</sup> or <b>R</b><sup>3</sup>, but many of the ideas and results can also be adapted to other hydrodynamic systems, such as the Navier-Stokes or surface quasi-geostrophic (SQG) equations. A second subject is the modeling of moving contact lines and dynamic contact angles in inviscid liquid-vapor-solid systems under surface tension. </p><p> The dissertation is divided into three independent parts: First, we introduce notation and prove useful identities for studying incompressible fluids in a pointwise Lagrangian sense. The main purpose is to provide a unified treatment of results scattered across the literature. Furthermore, we prove several analogs of Constantin’s local pressure formula for other nonlocal operators, such as the Biot-Savart law and Leray projection. Also, we define and study properties of a Lagrangian locally compact Abelian group in terms of which some nonlocal formulas encountered in fluid dynamics may be interpreted as convolutions. </p><p> Second, we apply the algebraic theory of scalar polynomial orthogonal invariants to the incompressible Euler equations in two and three dimensions. Using this framework, we give simplified proofs of results of Chae and Vieillefosse. We also investigate other uses of orthogonal transformations, such as diagonalizing the deformation tensor along a particle trajectory, and comment on relative advantages and disadvantages. These techniques are likely to be useful in other orthogonally invariant PDE systems as well. </p><p> Third, we propose an idealized inviscid liquid-vapor-solid model for the macroscopic study of moving contact lines and dynamic contact angles. Previous work mostly addresses viscous systems and frequently ignores a singular stress present when the contact angle is not at its equilibrium value. We also examine and clarify the role that disjoining pressure plays and outline a program for further research.</p>
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Steingart, Alma. "Conditional inequalities : American pure and applied mathematics, 1940-1975." Thesis, Massachusetts Institute of Technology, 2011. http://hdl.handle.net/1721.1/84367.
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Thesis (Ph. D. in History, Anthropology, and Science, Technology and Society (HASTS))--Massachusetts Institute of Technology, Program in Science, Technology and Society, 2011.<br>Cataloged from PDF version of thesis.<br>Includes bibliographical references (pages 317-336).<br>This study investigates the status of mathematical knowledge in mid-century America. It is motivated by questions such as: when did mathematical theories become applicable to a wide range of fields from medicine to the social science? How did this change occur? I ask after the implications of this transformation for the development of mathematics as an academic discipline and how it affected what it meant to be a mathematician. How did mathematicians understand the relation between abstractions and generalizations on the one hand and their manifestation in concrete problems on the other? Mathematics in Cold War America was caught between the sciences and the humanities. This dissertation tracks the ways this tension between the two shaped the development of professional identities, pedagogical regimes, and the epistemological commitments of the American mathematical community in the postwar period. Focusing on the constructed division between pure and applied mathematics, it therefore investigates the relationship of scientific ideas to academic and governmental institutions, showing how the two are mutually inclusive. Examining the disciplinary formation of postwar mathematics, I show how ideas about what mathematics is and what it should be crystallized in institutional contexts, and how in turn these institutions reshaped those ideas. Tuning in to the ways different groups of mathematicians strove to make sense of the transformations in their fields and the way they struggled to implement their ideological convictions into specific research agendas and training programs sheds light on the co-construction of mathematics, the discipline, and mathematics as a body of knowledge. The relation between pure and applied mathematics and between mathematics and the rest of the sciences were disciplinary concerns as much as they were philosophical musings. As the reconfiguration of the mathematical field during the second half of the twentieth century shows, the dynamic relation between the natural and the human sciences reveals as much about institutions, practices, and nations as it does about epistemological commitments.<br>by Alma Steingart.<br>Ph.D.in History, Anthropology, and Science, Technology and Society (HASTS
7
Jones, Piet. "Structure learning of gene interaction networks." Thesis, Stellenbosch : Stellenbosch University, 2014. http://hdl.handle.net/10019.1/86650.
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Thesis (MSc)--Stellenbosch University, 2014.<br>ENGLISH ABSTRACT: There is an ever increasing wealth of information that is being generated regarding
biological systems, in particular information on the interactions and
dependencies of genes and their regulatory process. It is thus important to be
able to attach functional understanding to this wealth of information. Mathematics
can potentially provide the tools needed to generate the necessary
abstractions to model the complex system of gene interaction.
Here the problem of uncovering gene interactions is cast in several contexts,
namely uncovering gene interaction patterns using statistical dependence, cooccurrence
as well as feature enrichment. Several techniques have been proposed
in the past to solve these, with various levels of success. Techniques
have ranged from supervised learning, clustering analysis, boolean networks
to dynamical Bayesian models and complex system of di erential equations.
These models attempt to navigate a high dimensional space with challenging
degrees of freedom.
In this work a number of approaches are applied to hypothesize a gene
interaction network structure. Three di erent models are applied to real biological
data to generate hypotheses on putative biological interactions. A
cluster-based analysis combined with a feature enrichment detection is initially
applied to a Vitis vinifera dataset, in a targetted analysis. This model
bridges a disjointed set of putatively co-expressed genes based on signi cantly
associated features, or experimental conditions. We then apply a cross-cluster
Markov Blanket based model, on a Saccharomyces cerevisiae dataset. Here
the disjointed clusters are bridged by estimating statistical dependence relationship
across clusters, in an un-targetted approach. The nal model applied
to the same Saccharomyces cerevisiae dataset is a non-parametric Bayesian method that detects probeset co-occurrence given a local background and inferring
gene interaction based on the topological network structure resulting
from gene co-occurance. In each case we gather evidence to support the biological
relevance of these hypothesized interactions by investigating their relation
to currently established biological knowledge.
The various methods applied here appear to capture di erent aspects of
gene interaction, in the datasets we applied them to. The targetted approach
appears to putatively infer gene interactions based on functional similarities.
The cross-cluster-analysis-based methods, appear to capture interactions
within pathways. The probabilistic-co-occurrence-based method appears to
generate modules of functionally related genes that are connected to potentially
explain the underlying experimental dynamics.<br>AFRIKAANSE OPSOMMING: Daar is 'n toenemende rykdom van inligting wat gegenereer word met betrekking
tot biologiese stelsels, veral inligting oor die interaksies en afhanklikheidsverhoudinge
van gene asook hul regulatoriese prosesse. Dit is dus belangrik om
in staat te wees om funksionele begrip te kan heg aan hierdie rykdom van inligting.
Wiskunde kan moontlik die gereedskap verskaf en die nodige abstraksies
bied om die komplekse sisteem van gene interaksies te modelleer.
Hier is die probleem met die beraming van die interaksies tussen gene
benader uit verskeie kontekste uit, soos die ontdekking van patrone in gene
interaksie met behulp van statistiese afhanklikheid , mede-voorkoms asook
funksie verryking. Verskeie tegnieke is in die verlede voorgestel om hierdie
probleem te benader, met verskillende vlakke van sukses. Tegnieke het gewissel
van toesig leer , die groepering analise, boolean netwerke, dinamiese Bayesian
modelle en 'n komplekse stelsel van di erensiaalvergelykings. Hierdie modelle
poog om 'n hoë dimensionele ruimte te navigeer met uitdagende grade van
vryheid.
In hierdie werk word 'n aantal benaderings toegepas om 'n genetiese interaksie
netwerk struktuur voor te stel. Drie verskillende modelle word toegepas
op werklike biologiese data met die doel om hipoteses oor vermeende biologiese
interaksies te genereer. 'n Geteikende groeperings gebaseerde analise gekombineer
met die opsporing van verrykte kenmerke is aanvanklik toegepas op 'n
Vitis vinifera datastel. Hierdie model verbind disjunkte groepe van vermeende
mede-uitgedrukte gene wat gebaseer is op beduidende verrykte kenmerke, hier
eksperimentele toestande . Ons pas dan 'n tussen groepering Markov Kombers
model toe, op 'n Saccharomyces cerevisiae datastel. Hier is die disjunkte groeperings
ge-oorbrug deur die beraming van statistiese afhanklikheid verhoudings tussen die elemente in die afsondelike groeperings. Die nale model was ons
toepas op dieselfde Saccharomyces cerevisiae datastel is 'n nie- parametriese
Bayes metode wat probe stelle van mede-voorkommende gene ontdek, gegee 'n
plaaslike agtergrond. Die gene interaksie is beraam op grond van die topologie
van die netwerk struktuur veroorsaak deur die gesamentlike voorkoms gene.
In elk van die voorgenome gevalle word ons hipotese vermoedelik ondersteun
deur die beraamde gene interaksies in terme van huidige biologiese kennis na
te vors.
Die verskillende metodes wat hier toegepas is, modelleer verskillende aspekte
van die interaksies tussen gene met betrekking tot die datastelle wat
ons ondersoek het. In die geteikende benadering blyk dit asof ons vermeemde
interaksies beraam gebaseer op die ooreenkoms van biologiese funksies. Waar
die a eide gene interaksies moontlik gebaseer kan wees op funksionele ooreenkomste
tussen die verskeie gene. In die analise gebaseer op die tussen
modelering van gene groepe, blyk dit asof die verhouding van gene in bekende
biologiese substelsels gemodelleer word. Dit blyk of die model gebaseer op die
gesamentlike voorkoms van gene die verband tussen groepe van funksionele
verbonde gene modelleer om die onderliggende dinamiese eienskappe van die
experiment te verduidelik.
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Brubaker, Nicholas Denlinger. "Mathematical theory of electro-capillary surfaces." Thesis, University of Delaware, 2013. http://pqdtopen.proquest.com/#viewpdf?dispub=3594897.
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<p> Historically, electrostatic forces and capillary surfaces have been a main focus of scientific inquiry. Recently, with the move towards miniaturization in technology, systems that include the interplay of these two phenomena have become more relevant than ever. This is because at small scales, capillary and electrostatic forces come to dominate familiar macro scale forces and consequently, govern the behavior of many components used in modern technology. In particular, these <i>electro-capillary</i> systems have been applied to areas such self-assembly, “lab-on-a-chip” devices, microelectromechanical systems and mass spectrometry. </p><p> In this dissertation, we study two such systems. The first system involves subjecting a planar soap film to a vertically directed electric field. The second is an extension of the first that includes the small effect of gravity (or, similarly, a constant external pressure). Mathematical models for these systems are developed via variational techniques to describe the equilibrium deflection of the soap-film. In contrast to the standard theory, these models include the full effect of capillarity, yielding two prescribed mean curvature problems. These problems are then studied for general and specific domains, using a combination of analytic, asymptotic and numerical techniques. A detailed analysis of the solution set reveals several interesting bifurcation structures. Highlighted areas include a blow-up in the gradient, which occurs at the onset of strictly parametric solutions, and a prediction of the so-called pull-in instability with respect to the aspect ratio of the system, which provides an update to the standard theory. The work here illustrates the effect of including the mean curvature operator in such models and starts to build a general theory of electro-capillary surfaces.</p>
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Li, Song. "Numerical methods for stable inversion of nonlinear systems." Diss., Georgia Institute of Technology, 2002. http://hdl.handle.net/1853/15028.
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Labra, Bahena Luis R. "Multilevel Solution of the Discrete Screened Poisson Equation for Graph Partitioning." Thesis, California State University, Long Beach, 2017. http://pqdtopen.proquest.com/#viewpdf?dispub=10638940.
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<p> A new graph partitioning algorithm which makes use of a novel objective function and seeding strategy, Product Cut, frequently outperforms standard clustering methods. The solution strategy on solving this objective depends on developing a fast solution method for the systems of graph--based analogues of the screened Poisson equation, which is a well-studied problem in the special case of structured graphs arising from PDE discretization. </p><p> In this work, we attempt to improve the powerful Algebraic Multigrid (AMG) method and build upon the recently introduced Product Cut algorithm. Specifically, we study the consequences of incorporating a dynamic determination of the diffusion parameter by introducing a prior to the objective function. This culminates in an algorithm which seems to partially eliminate an advantage present in the original Product Cut algorithm's slower implementation. </p><p>
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Gould, Andrew James. "God's Number in the Simultaneously-Possible Turn Metric." Thesis, The University of Wisconsin - Milwaukee, 2018. http://pqdtopen.proquest.com/#viewpdf?dispub=10686488.
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<p> In 2010 it was found that God’s number is 20 in the face turn metric. That is, if the Rubik’s cube hasn’t been disassembled, it can always be solved in 20 twists or fewer, but sometimes requires 20 twists. However, the face turn metric only allows one face to be turned at a time for a total of 18 generators, or 18 possible twists at any time. This dissertation allows opposing, parallel faces to be twisted independent amounts at the same time and still get counted as 1 twist for a total of 45 generators. A new optimal-solving program was constructed, and the results so far show that God’s number is at least 16 for the simultaneously-possible turn metric. </p><p> I note that in 3 dimensions the simultaneously-possible turn metric is the same as the axial turn metric (or robot turn metric), but not in 4 dimensions nor higher (e.g. 2×2×2×2, 3×3×3×3, 4×4×4×4, etc.—not to be confused with the 3-dimensional 4×4×4 cube). This difference is also described.</p><p>
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Farnham, Rodrigo Bouchardet. "Processing and inpainting of sparse data as applied to atomic force microscopy imaging." California State University, Long Beach, 2013.
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Lim, Kyung-Taek. "The Spherical Mean Value Operators on Euclidean and Hyperbolic Spaces." Tufts University, 2013.
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McGregor-Dorsey, Zachary Strider. "Some properties of full heaps." Thesis, University of Colorado at Boulder, 2013. http://pqdtopen.proquest.com/#viewpdf?dispub=3562010.
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<p> A full heap is a labeled infinite partially ordered set with labeling taken from the vertices of an underlying Dynkin diagram, satisfying certain conditions intended to capture the structure of that diagram. The notion of full heaps was introduced by R. Green as an affine extension of the minuscule heaps of J. Stembridge. Both authors applied these constructions to make observations of the Lie algebras associated to the underlying Dynkin diagrams. The main result of this thesis, Theorem 4.7.1, is a complete classification of all full heaps over Dynkin diagrams with a finite number of vertices, using only the general notion of Dynkin diagrams and entirely elementary methods that rely very little on the associated Lie theory. The second main result of the thesis, Theorem 5.1.7, is an extension of the Fundamental Theorem of Finite Distributive Lattices to locally finite posets, using a novel analogue of order ideal posets. We apply this construction in an analysis of full heaps to find our third main result, Theorem 5.5.1, an <i>ADE</i> classification of the full heaps over simply laced affine Dynkin diagrams.</p>
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Rael, Michael Brian. "Results on the Parabolic Anderson Model." Thesis, University of California, Irvine, 2013. http://pqdtopen.proquest.com/#viewpdf?dispub=3562176.
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<p> In this dissertation we present various results pertaining to the Parabolic Anderson Model. First we show that the Lyapunov exponent, λ(κ), of the Parabolic Anderson Model in continuous space with Stratonovich differential is <i>O</i>(κ<sup>1/3</sup>) near 0. We prove the required upper bound, the lower bound having been proven in (Cranston & Mountford 2006). </p><p> Second, we prove the existence of stationary measures for the Parabolic Anderson Model in continuous space with Ito differential. Furthermore, we prove that these measures are associated and determined by the average mass of the initial configuration. </p><p> Finally we present progress towards computing the Lyapunov exponent of the Quasi-Stationary Parabolic Anderson Model. We prove a smaller upper bound on λ(κ), improving on the work in (Boldrighini, Molchanov, & Pellegrinotti 2007), but our bound is not sharp. Computing λ(κ) in this model remains an open problem.</p>
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Enos, Graham. "Binary Edwards curves in elliptic curve cryptography." Thesis, The University of North Carolina at Charlotte, 2013. http://pqdtopen.proquest.com/#viewpdf?dispub=3563153.
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<p> Edwards curves are a new normal form for elliptic curves that exhibit some cryptographically desirable properties and advantages over the typical Weierstrass form. Because the group law on an Edwards curve (normal, twisted, or binary) is <i>complete</i> and <i>unified,</i> implementations can be safer from side channel or exceptional procedure attacks. The different types of Edwards provide a better platform for cryptographic primitives, since they have more security built into them from the mathematic foundation up. </p><p> Of the three types of Edwards curves—original, twisted, and binary—there hasn't been as much work done on binary curves. We provide the necessary motivation and background, and then delve into the theory of binary Edwards curves. Next, we examine practical considerations that separate binary Edwards curves from other recently proposed normal forms. After that, we provide some of the theory for binary curves that has been worked on for other types already: pairing computations. We next explore some applications of elliptic curve and pairing-based cryptography wherein the added security of binary Edwards curves may come in handy. Finally, we finish with a discussion of <i>e2c2, </i> a modern C++11 library we've developed for Edwards Elliptic Curve Cryptography.</p>
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Crowder, Tanner. "Representations of Quantum Channels." Thesis, Howard University, 2013. http://pqdtopen.proquest.com/#viewpdf?dispub=3591941.
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<p>The Bloch representation of an <i>n</i>-qubit channel provides a way to represent quantum channels as certain affine transformations on [special characters omitted]. In higher dimensions (<i>n</i> > 1), the correspondence between quantum channels and their Bloch representations is not well-understood. Partly motivated by the ability to simplify the calculation of information theoretic quantities of a qubit channel using the Bloch representation, in this thesis we investigate the correspondence between a channel and its Bloch representation with an emphasis on <i>unital n</i>-qubit channels, in which case the Bloch representation is linear.</p><p> The thesis is divided into three main sections. First we focus our attention on qubit channels. For certain sets of quantum channels, we establish the surprising existence of a special isomorphism into the set of <i> classical channels.</i> We classify the sets of qubit channels with this property and show that information theoretic quantities are preserved by such classical representations. In a natural progression, we prove some well-known facts about SO(3), the proofs of which are either nonexistent or difficult to find in the literature. Some of this work is based on [12, 13].</p><p> In the next section, we consider the multi-qubit channels and show that every finite group can be realized as a subgroup of the quantum channels; this approach allows for the construction of a quantum representation for the free affine monoid over any finite group and gives a classical representation for it. We extend some fundamental results from [26, 28] to the multi-qubit case, including that the set of diagonal Bloch matrices is equal to the free affine monoid over the involution group [special characters omitted]. Some of this work appeared in [10]. </p><p> Lastly, we study the extreme points for the set of <i>n</i>-qubit channels. There are two types of extreme points: invertible and non-invertible; invertible channels are non-singular maps for which the inverse is also a channel. We briefly study the non-invertible extreme points and then parameterize and analyze the invertible<i>n</i>-qubit Bloch matrices, which form a compact connected Lie group. We calculate the Lie algebra and give an explicit generating set for the invertible Bloch matrices and a maximal torus.</p>
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Fouts, Kelly Jean. "On a Ring Associated to F[x]." Thesis, Baylor University, 2013. http://pqdtopen.proquest.com/#viewpdf?dispub=3593302.
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<p>For a field <i>F</i> and the polynomial ring <i>F</i> [<i>x</i>] in a single indeterminate, we define [special characters omitted] = {α ∈ End<i><sub>F</sub></i>(<i>F</i> [x]) : α(<i>f</i>) ∈ <i>f F</i> [<i>x </i>] for all <i>f</i> ∈ <i>F</i> [<i> x</i>]}. Then [special characters omitted] is naturally isomorphic to <i>F</i> [<i>x</i>] if and only if <i>F</i> is infinite. If <i>F</i> is finite, then [special characters omitted] has cardinality continuum. We study the ring [special characters omitted] for finite fields <i>F.</i> For the case that <i>F </i> is finite, we discuss many properties and the structure of [special characters omitted].</p>
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Lubovsky, Arthur. "Alcove models for Hall-Littlewood polynomials and affine crystals." Thesis, State University of New York at Albany, 2013. http://pqdtopen.proquest.com/#viewpdf?dispub=3594475.
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<p> The alcove model of Cristian Lenart and Alexander Postnikov describes highest weight crystals of semisimple Lie algebras in terms of so-called alcove walks. We present a generalization, called the quantum alcove model, which has been related to tensor products of column shape Kirillov-Reshetikhin crystals, for all untwisted affine types. </p><p> We also investigate Ram's version of Schwer's formula for Hall-Littlewood <i> P</i>-polynomials in type <i>A,</i> which is expressed in terms of the alcove model. We connect it to a formula similar in flavor to the Haglund-Haiman-Loehr formula, which is expressed in terms of fillings of Young diagrams.</p>
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Lee, Jaepil. "Computation of Floer Invariant of (2; 2n)-Torus link Complement." Thesis, State University of New York at Stony Brook, 2013. http://pqdtopen.proquest.com/#viewpdf?dispub=3596400.
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<p> A closed three manifold invariant Heegaard Floer homology was generalized to bordered Heegaard Floer homology, defined by Robert Lipshitz, Peter Ozsváth and Dylan Thurston. Bordered Heegaard Floer homology is an invariant of three manifold with connected boundary, and its variant doubly bordered Floer homology is a bimodule defined on three manifold with two disconnected boundary components. In this thesis, we compute bordered Floer homology of (2,2<i>n</i>)-torus link complement.</p>
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Varner, Gregory Alan. "Stochastically Perturbed Navier-Stokes System on the Rotating Sphere." Thesis, University of Missouri - Columbia, 2013. http://pqdtopen.proquest.com/#viewpdf?dispub=3576093.
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<p> We show the existence and uniqueness of an invariant measure for the kick-forced Navier-Stokes system on the 2-dimensional sphere, first without deterministic force and then with a time-independent deterministic force. The existence and uniqueness of an invariant measure for the white noise forced Navier-Stokes system on the 2- dimensional sphere without a deterministic forcing is also shown.</p><p> We examine the support of the invariant measure and give a description of the support of the measure in general, and in several special cases, for the kick-forced flow. The support of the invariant measure for the white noise forced equations is shown to be the entire space of admissible vector fields of the sphere.</p>
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Zerihun, Tadesse G. "Nonlinear Techniques for Stochastic Systems of Differential Equations." Scholar Commons, 2013. http://scholarcommons.usf.edu/etd/4970.
Full textAbstract:
Two of the most well-known nonlinear methods for investigating nonlinear dynamic processes in sciences and engineering are nonlinear variation of constants parameters and comparison method. Knowing the existence of solution process, these methods provide a very powerful tools for investigating variety of problems, for example, qualitative and quantitative properties of solutions, finding error estimates between solution processes of stochastic system and the corresponding nominal system, and inputs for the designing engineering and industrial problems. The aim of this work is to systematically develop mathematical tools to undertake the mathematical frame-work to investigate a complex nonlinear nonstationary stochastic systems of differential equations.
A complex nonlinear nonstationary stochastic system of differential equations are decomposed into nonlinear systems of stochastic perturbed and
unperturbed differential equations. Using this type of decomposition, the fundamental properties of solutions of nonlinear stochastic unperturbed
systems of differential equations are investigated(1). The fundamental properties are used to find the representation of solution process of nonlinear stochastic complex perturbed system in terms of solution process of nonlinear stochastic unperturbed system(2).
Employing energy function method and the fundamental properties of It\^{o}-Doob type stochastic auxiliary system of differential equations, we
establish generalized variation of constants formula for solution process of perturbed stochastic system of differential equations(3). Results
regarding deviation of solution of perturbed system with respect to solution of nominal system of stochastic differential equations are developed(4). The obtained results are used to study the qualitative properties of perturbed stochastic system of differential equations(5). Examples are given to illustrate the usefulness of the results.
Employing energy function method and the fundamental properties of It\^{o}-Doob type stochastic auxiliary system of differential equations, we establish
generalized variational comparison theorems in the context of stochastic and deterministic differential for solution processes of perturbed stochastic system of differential equations(6). Results regarding deviation of solutions with respect to nominal stochastic system are also developed(7). The obtained results are used to study the qualitative properties of perturbed stochastic system(8). Examples are given to illustrate the usefulness of the results.
A simple dynamical model of the effect of radiant flux density and CO_2
concentration on the rate of photosynthesis in light, dark
and enzyme reactions are analyzed(9). The coupled system of dynamic equations are solved numerically for some values
of rate constant and radiant flux density. We used Matlab to solve the
system numerically. Moreover, with the assumption that dynamic model of CO_2 concentration
is studied.
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Megson, Peter. "Experiments on Surfactants and Thin Fluid Films." Scholarship @ Claremont, 2014. http://scholarship.claremont.edu/hmc_theses/64.
Full textAbstract:
We investigate the spatiotemporal dynamics of a surfactant monolayer on a thin fluid film spreading inward into a region devoid of surfactant, a system motivated by the alveolus of the human lung. We perform experiments that simultaneously measure the fluid height profile and the fluorescence intensity due to our fluorescent surfactant, NBD-PC. We perform experiments on both a Newtonian layer of glycerol and a shear-thinning fluid layer consisting of xanthan gum mixed with glycerol. We can very successfully extract height profiles on the xanthan gum fluid, although the simultaneous measurement of fluorescent intensity profiles proved problematic, as the laser tended to stymie the fluorescent intensity measurement. We attempt and find some success with simply measuring surfactant fluorescent intensity by itself and reconstructing behavior between the two separate measurements. We were ultimately able to make a comparative measurement of the velocity of the leading edge of surfactant on xanthan gum and glycerol.
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Polk, Jada Philous. "On the estimation of the black-capped vireo (Vireo atricapillus) territory density using geographic information systems technology." DigitalCommons@Robert W. Woodruff Library, Atlanta University Center, 1996. http://digitalcommons.auctr.edu/dissertations/2581.
Full textAbstract:
This study is based on a 1994 survey of the nesting and territory preferences of the black-capped vireo, a small migratory songbird, within Fort Hood, Texas. By Federal Government Order 51 FR 44808-44812 of 1987 (Tazik et al., 1992), these birds were declared an endangered species based on a series of studies by J. D. Cornelius in 1985 and 1986 (Tazik et al., 1993).
In this study, it has been shown that the vireo nesting and territory preferences are not uniform across Fort Hood installation grounds, rather the preference is towards the north to northwest. The vegetation in this region consists of oak woodlands, with grassy undergrowth; the elevation is at most 260 meters above sea level; and the geology yields loose and chalky limestone. In addition, the territory intensity, λij(s), for each point s(x,y) in the ijth grid cell on the military installation, has been estimated. For each such grid cell, the probability of a successful territory is given by
Geographic Information Systems (GIS) raster color maps of territory distribution of the vireo have been produced. These maps were overlaid on the slope, aspect, soils, elevation, vegetation, and military activities coverages. With the density estimate of nesting success and the GIS maps, territory position preferences were identified, thus, helping in the Land Management Plan for the preservation of the black-capped vireo on the Fort Hood Military Installation.
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Zhong, Ming. "Hierarchical Reconstruction Method for Solving Ill-posed Linear Inverse Problems." Thesis, University of Maryland, College Park, 2016. http://pqdtopen.proquest.com/#viewpdf?dispub=10128674.
Full textAbstract:
<p> We present a detailed analysis of the application of a multi-scale Hierarchical Reconstruction method for solving a family of ill-posed linear inverse problems. When the observations on the unknown quantity of interest and the observation operators are known, these inverse problems are concerned with the recovery of the unknown from its observations. Although the observation operators we consider are linear, they are inevitably ill-posed in various ways. We recall in this context the classical Tikhonov regularization method with a stabilizing function which targets the specific ill-posedness from the observation operators and preserves desired features of the unknown. Having studied the mechanism of the Tikhonov regularization, we propose a multi-scale generalization to the Tikhonov regularization method, so-called the Hierarchical Reconstruction (HR) method. First introduction of the HR method can be traced back to the Hierarchical Decomposition method in Image Processing. The HR method <i> successively</i> extracts information from the previous hierarchical residual to the current hierarchical term at a <i>finer</i> hierarchical <i> scale.</i> As the sum of all the hierarchical terms, the hierarchical sum from the HR method provides an reasonable approximate solution to the unknown, when the observation matrix satisfies certain conditions with specific stabilizing functions. When compared to the Tikhonov regularization method on solving the same inverse problems, the HR method is shown to be able to decrease the total number of iterations, reduce the approximation error, and offer self control of the approximation distance between the hierarchical sum and the unknown, thanks to using a ladder of <i>finitely many</i> hierarchical scales. We report numerical experiments supporting our claims on these advantages the HR method has over the Tikhonov regularization method.</p>
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Sambandham, Bhuvaneswari. "Analysis of Sequential Caputo Fractional Differential Equations with Applications." Thesis, University of Louisiana at Lafayette, 2016. http://pqdtopen.proquest.com/#viewpdf?dispub=10163318.
Full textAbstract:
<p> The solution for sequential Caputo linear fractional differential equations with variable coefficients of order q, 0 < q < 1 can be obtained from symbolic representation form. Since the iterative method developed in Chapter 2 is time-consuming even for the simple linear fractional differential equations with variable coefficients, the direct numerical approximation developed in Chapter 3 is very useful tool when computing the linear and non-linear fractional differential equations of a specific type. This direct numerical method is useful in developing the monotone method and the quasilinearization method for non-linear problems. As an application of this result, we have obtained the numerical solution for a special Ricatti, type of differential equation which blows up in finite time. The generalized monotone iterative method with coupled lower and upper solutions yields monotone natural sequence which converges uniformly and monotonically to coupled minimal and maximal solutions of Caputo fractional boundary value problem. We obtain the existence and uniqueness of sequential Caputo fractional boundary value problems with mixed boundary conditions with the Green's function representation.</p>
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Yek, Vorleak. "Numerical Investigation on the Projection Method for the Incompressible Navier-Stokes Equations on MAC Grid." Thesis, California State University, Long Beach, 2018. http://pqdtopen.proquest.com/#viewpdf?dispub=10825591.
Full textAbstract:
<p> The motion of a viscous fluid flow is described by the well-known Navier-Stokes equations. The Navier-Stokes equations contain the conservation laws of mass and momentum, and describe the spatial-temporal change of the fluid velocity field. This thesis aims to investigate numerical solvers for the incompressible Navier-Stokes equations in two and three space dimensions. In particular, we focus on the second-order projection method introduced by Kim and Moin, which was extended from Chorin’s first-order projection method. We apply Fourier-Spectral methods for the periodic boundary condition. Numerically, we discretize the system using central differences scheme on Marker and Cell (MAC) grid spatially and the Crank-Nicolson scheme temporally. We then apply the fast Fourier transform to solve the resulting Poisson equations as sub-steps in the projection method. We will verify numerical accuracy and provide the stability analysis using von Neumann. In addition, we will simulate the particles' motion in the 2D and 3D fluid flow.</p><p>
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Oliver, Graeme John. "Modelling of welding with various constitutive models for steel." Master's thesis, University of Cape Town, 1994. http://hdl.handle.net/11427/17443.
Full textAbstract:
Bibliography: pages 102-106.<br>This dissertation is an attempt at the quality analysis of constitutive modelling of welding as a coupled thermo-mechanical or thermo-mechanical-metallurgical problem. Three types of inelastic theories of continua: unified viscoplasticity based on dislocation density theory, unified viscoplasticity based on potential theory, and transformation induced plasticity have been chosen for quantitative investigation. Material models proposed by Anand, Estrin and Mecking, Estrin, Robinson, and Leblond et.al. have been implemented into the finite element program ABAQUS. Specific subroutines have been written specifically for each constitutive equation. The material model implementation is based on the implicit solution of stress-strain relations and the derivation of associated constitutive tangent moduli necessary for the Nonlinear Finite Element solution procedures. Material model comparisons are based on numerical results obtained for the welding of thick plates; that is the bench mark problem considered in this thesis.
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Breitsch, Nathan W. "Techniques for the Study of Biological Coupled Oscillator Systems." Ohio University Honors Tutorial College / OhioLINK, 2014. http://rave.ohiolink.edu/etdc/view?acc_num=ouhonors1399892563.
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Alsenafi, Abdulaziz. "Segregation Dynamics Motivated by Territorial Markings:The Transition from a Particle to a Continuum Model." Case Western Reserve University School of Graduate Studies / OhioLINK, 2016. http://rave.ohiolink.edu/etdc/view?acc_num=case1467727114.
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Woodward, III Robert Bruce. "Quantifying Cultural Changes Through A Half-Century Of Song Lyrics And Books." ScholarWorks @ UVM, 2016. http://scholarworks.uvm.edu/graddis/631.
Full textAbstract:
Music is an ever-changing cultural reflection. It is deeply integrated into our society, ubiquitous
in movies, television shows, restaurants, sport venues, churches and a plethora of
other places. This thesis proposes that we consider the lyrics in popular music, as determined
by Billboards Hot 100 chart, as a natural medium to analyze the changes in culture
over the past half-century. Using this collection of lyrics, we analyze the change in relative
frequency of individual words over time, and compare to works of literature. Furthermore,
we use the ranking in the Top 100 as a metric with which to explore the relationship between
usage of particular words and the popularity of the respective songs. We find that our
data coincides with a previous hypothesis that the relative happiness of lyrics has decreased
over time, and find that this also applies to the relative happiness of popular music.
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Penev, Kalin. "Adaptive search heuristics applied to numerical optimisation." Thesis, Southampton Solent University, 2004. http://ssudl.solent.ac.uk/598/.
Full textAbstract:
The objective of the research project involves investigation of evolutionary computational methods, in particular analysis of population-based search heuristics, and abstraction of core cognition, which may lead to the design of a novel adaptive search algorithm capable of high performance and reliability. The thesis proposes a novel adaptive heuristic method called Free Search (FS). Free Search can be classified as a population-based evolutionary computational method. It gradually changes a set of solutions until satisfaction of certain criteria. The algorithm operates with real-value numbers. It is designed for continuous or partially discontinuous search space. Free Search harmonizes several advanced ideas, which lead to high overall performance. The study includes exploration of selected population-based evolutionary methods, namely : real-value coded Generic Algorithm BLX-a; Particle Swarm Optimisation (PSO); Ant Colony Optimisation (ACO); and Differential Evolution (DE). Common, substantial for the search purposes features, relationships and events are abstracted from the algorithms analysed. The events abstracted are generalised in a theoretical model of population-based heuristic search. The model supports significantly identification of essential advantages and disadvantages of population-based search algorithms and leads to establishment of a novel concept different from other evolutionary algorithms. Free Search together with GA BLX-a, PSO and DE are applied to heterogenous, numerical, non-linear, non-discrete, optimisation problems. The results are presented and discussed. A comparative analysis demonstrates better overall performance of FS than other explored methods. The capability of FS to cope with all tests illustrates a new quality - adaptation to the problem without concrete or specialised configuration of the search parameters. Free Search is tested aditionally with a hard, non-linear, constrained optimisation problem - the so-called bump problem. FS outperforms other methods applied to that problem. Results achieved from Free Search, currently unapproachable for other search algorithms are presented. Free Search opens a new area for research in the domain of adaptive intelligent systems. It can contribute also in general to Computer Science in the modelling of uncertain individual behaviour.
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Piper, Steven Edward. "Mathematical demography of the Cape vulture." Doctoral thesis, University of Cape Town, 1994. http://hdl.handle.net/11427/19843.
Full textAbstract:
The Cape Vulture Gyps coprotheres is one of the world's largest avian scavengers and was once widely distributed in southern Africa, to which it is endemic. It has suffered major changes of fortune in recorded history and has, at least twice, undergone large range contractions and expansions in the Cape Province. It has variously been classified as 'rare', 'vulnerable' or 'threatened'. It is currently thought, by some, to be in decline. The central aim of these researches is to answer the 'Grand Question': What is the probability that the Cape Vulture will survive well into the twenty-first century as a free-flying bird? This is followed by a secondary question: What is the stability of the population in space, time and age-structure?
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Muchatibaya, Gift. "Mathematical modelling of unsteady contact melting." Doctoral thesis, University of Cape Town, 2008. http://hdl.handle.net/11427/4912.
Full textAbstract:
Includes abstract.<br>Includes bibliographical references (leaves 115-122).<br>The work in this thesis deals with the heat transfer and fluid flow problem encountered in the analysis of an unsteady contact melting process. Chapters 2 and 3 deal with only the heat transfer problem without fluid flow. In Chapter 2 the pre-melting problem is treated. The focus is to obtain the best approximate analytical solution to be used in the melting phase where there are no known exact solutions. The approximate solutions are constructed using the heat balance integral method.
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Parsons, R. W. "Mathematical models of chemical reactions." Thesis, Bucks New University, 1985. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.371228.
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Corker, Thomas A. "Mathematical morphology applied to the reduction of interferograms." Thesis, Georgia Institute of Technology, 1990. http://hdl.handle.net/1853/15506.
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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.
Full textAbstract:
Thesis (MSc (Mathemathical Sciences))--Stellenbosch University, 2009.<br>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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Rasolofoson, Faraniaina. "A comparative study on the impact of different fluxes in a discontinuous Galerkin scheme for the 2D shallow water equations." Thesis, Stellenbosch : Stellenbosch University, 2014. http://hdl.handle.net/10019.1/86610.
Full textAbstract:
Thesis (MSc)--Stellenbosch University, 2014.<br>ENGLISH ABSTRACT: Shallow water equations (SWEs) are a set of hyperbolic partial differential
equations that describe the flow below a pressure surface in a fluid. They are
widely applicable in the domain of fluid dynamics. To meet the needs of engineers
working on the area of fluid dynamics, a method known as spectral/hp
element method has been developed which is a scheme that can be used with
complicated geometry. The use of discontinuous Galerkin (DG) discretisation
permits discontinuity of the numerical solution to exist at inter-element surfaces.
In the DG method, the solution within each element is not reconstructed
by looking to neighbouring elements, thus the transfer information between elements
will be ensured through the numerical fluxes. As a consequence, the
accuracy of the method depends largely on the definition of the numerical
fluxes. There are many different type of numerical fluxes computed from Riemann
solvers. Four of them will be applied here respectively for comparison
through a 2D Rossby wave test case.<br>AFRIKAANSE OPSOMMING: Vlakwatervergelykings (SWEs) is ’n stel hiperboliese parsiële differensiaalvergelykings
wat die vloei onder ’n oppervlak wat druk op ’n vloeistof uitoefen
beskryf. Hulle het wye toepassing op die gebied van vloeidinamika. Om aan die
behoeftes van ingenieurs wat werk op die gebied van vloeidinamika te voldoen
is ’n metode bekend as die spektraal /hp element metode ontwikkel. Hierdie
metode kan gebruik word selfs wanneer die probleem ingewikkelde grenskondisies
het. Die Diskontinue Galerkin (DG) diskretisering wat gebruik word
laat diskontinuïteit van die numeriese oplossing toe om te bestaan by tussenelement
oppervlakke. In die DG metode word die oplossing binne elke element
nie gerekonstrueer deur te kyk na die naburige elemente nie. Dus word die oordrag
van informasie tussen elemente verseker deur die numeriese stroomterme.
Die akkuraatheid van hierdie metode hang dus grootliks af van die definisie
van die numeriese stroomterme. Daar is baie verskillende tipe numeriese strometerme
wat bereken kan word uit Riemann oplossers. Vier van hulle sal hier
gebruik en vergelyk word op ’n 2D Rossby golf toets geval.
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Wilde, S. J. "Complex approximation algorithms applied to antenna arrays." Thesis, Cranfield University, 1994. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.240815.
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Gomez, Austin G. "Invisibility: A Mathematical Perspective." Scholarship @ Claremont, 2013. http://scholarship.claremont.edu/cmc_theses/698.
Full textAbstract:
The concept of rendering an object invisible, once considered unfathomable, can now be deemed achievable using artificial metamaterials. The ability for these advanced structures to refract waves in the negative direction has sparked creativity for future applications. Manipulating electromagnetic waves of all frequencies around an object requires precise and unique parameters, which are calculated from various mathemat- ical laws and equations. We explore the possible interpretations of these parameters and how they are implemented towards the construction of a suitable metamaterial. If carried out correctly, the wave will exit the metamaterial exhibiting the same behavior as when it had entered. Thus, an outside observer will not be able to recognize any abnormal changes in wave frequency or direction. This paper will survey studies and technologies from the past 20 years to arrive at a concise mathematical examination of the possibilities and inherent issues under the umbrella of modern ”cloaking.”
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Ambrose, Joseph Paul. "Dynamic field theory applied to fMRI signal analysis." Diss., University of Iowa, 2016. https://ir.uiowa.edu/etd/2035.
Full textAbstract:
In the field of cognitive neuroscience, there is a need for theory-based approaches to fMRI data analysis. The dynamic neural field model-based approach has been developing to meet this demand. This dissertation describes my contributions to this approach. The methods and tools were demonstrated through a case study experiment on response selection and inhibition. The experiment was analyzed via both the standard behavioral approach and the new model-based method, and the two methods were compared head to head. The methods were quantitatively comparable at the individual-level of the analysis. At the group level, the model-based method reveals distinct functional networks localized in the brain. This validates the dynamic neural field model-based approach in general as well as my recent contributions.
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Müller, Andrea. "Humpback whales, rock lobsters and mathematics : exploration of assessment models incorporating stock-structure." Master's thesis, University of Cape Town, 2011. http://hdl.handle.net/11427/11342.
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This thesis presents four marine resource assessments; three concern the Southern Hemisphere (SH) humpback whale (Megaptera novaeangliae) and one the South African east coast rock lobster Palinurus delagoae. It also sets out the statistical background to the methodology employed in the assessments, including an outline of the Bayesian approach, Bayes' theorem, and the sampling-importance re-sampling (SIR) as well as the Markov Chain Monte Carlo (MCMC) methods.
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Xiros, Nikolaos I. "Mathematical Formulation of Fusion Energy Magnetohydrodynamics." ScholarWorks@UNO, 2017. https://scholarworks.uno.edu/td/2438.
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Chapter 1 presents the basic principles of Controlled Thermonuclear Fusion, and the approaches to achieve nuclear fusion on Earth. Furthermore, the basic components of the Tokamak, the reactor which will house the fusion reaction, are analyzed. Finally, the chapter ends with a discussion on how the present thesis is related to the Controlled Thermonuclear Fusion. Chapter 2 introduces briefly the basic concepts of the Electromagnetic and Magnetohydrodynamic theories as well as MHD turbulence. Chapter 3 presents a first glance in OpenFOAM CFD library. Chapter 4 introduces the Orszag-Tang vortex flow, which is a benchmark test case for MHD numerical models. Also, the results obtained by the model developed in this thesis are presented and discussed. Chapter 5 describes an analytical solution method for the MHD natural convection in an internally heated horizontal shallow cavity. Also, a finite volume numerical model is presented for solving the aforementioned problem and properly validated. The results of the numerical model are compared with the analytical solutions for a range of Rayleigh and Hartmann numbers. Finally, conclusions based on this work are drawn and recommendations for future work are made.
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Wolf, Roseanne Marie. "Defining new insight into fatal human arrhythmia: a mathematical analysis." Diss., University of Iowa, 2012. https://ir.uiowa.edu/etd/3013.
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Background: Normal cardiac excitability depends upon the coordinated activity of ion channels and transporters. Mutations in genes encoding ion channels affecting their biophysical properties have been known for over twenty years as a root cause of potentially fatal human electrical rhythm disturbance (arrhythmias). More recently, defects in ion channel associated protein (e.g. adapter, regulatory, cytoskeletal proteins) have been shown to cause arrhythmia. Mathematical modeling is ideally suited to integrate large volumes of cellular and in vivo data from human patients and animal disease models with the over goal of determining cellular mechanisms for these atypical human cardiac diseases that involve complex defects in ion channel membrane targeting and/or regulation. Methods and Results: Computational models of ventricular, atrial, and sinoatrial cells were used to determine the mechanism for increased susceptibility to arrhythmias and sudden death in human patients with inherited defects in ankyrin-based targeting pathways. The loss of ankyrin-B was first incorporated into detailed models of the ventricular myocyte to identify the cellular mechanism for arrhythmias in human patients with loos-of-function mutations in ANK2 (encodes ankyrin-B). Mathematical modeling was used to identify the cellular pathway responsible for abnormal Ca2+ handling and cardiac arrhythmias in ventricular cells. A multi-scalar computational model of ankyrin-B deficiency in atrial and sinoatrial cells and tissue was then developed to determine the mechanism for the increased susceptibility to atrial fibrillation in these human patients. Finally, a state-based Markov model of the voltage-gated Na+ channel was incorporated into a ventricular cell model and parameter estimation was performed to determine the mechanism for a new class of human arrhythmia variants that confer susceptibility to arrhythmia by interfering with a regulatory complex comprised of a second member of the ankyrin family, ankyrin-G. Conclusions: Ca2+ accumulation was observed at baseline in the ankyrin-B deficient ventricular model, with pro-arrhythmic spontaneous release and afterdepolarizations in the presence of simulated â-adrenergic stimulation, consistent with the finding of catecholaminergic-induced arrhythmias in human patients. The simulations demonstrated that loss of membrane Na+/Ca2+ exchanger and Na+-K+-ATPase contributed to Ca2+ overload and afterdepolarizations, with loss of Na+/Ca2+ exchanger as the dominant mechanism. In the atrial model of ankyrin-B deficiency, the loss of the L-type Ca2+ channel targeting was identified as the dominant mechanism for the initiation of atrial fibrillation. Finally, the simulations showed that human variants affecting ankyrin-G dependent regulation of NaV1.5 results in arrhythmia by mimicking the phosphorylation of the channel. Most importantly, mathematical modeling has been used to the molecular mechanism underlying human arrhythmia syndromes.
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Lookabill, Kerri Colleen. "A descriptive study of the impact of planning time on the utilization o fthe national council of teachers of mathematics process standards within the algebra 1 and applied mathematics subhect fields." [Huntington, WV : Marshall University Libraries], 2008. http://www.marshall.edu/etd/descript.asp?ref=.
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Malosha, Peter. "PRICING AN AMERICAN CALL ON DEVIDEND PAYING STOCK." Thesis, Mälardalen University, Department of Mathematics and Physics, 2007. http://urn.kb.se/resolve?urn=urn:nbn:se:mdh:diva-475.
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<p>Abstract</p><p>The aim of this paper is to implement and create a Java applet that performs the simulation of Fu and Hu model .The graphical result is presented on how investor can handle an American call option with discrete dividends paying stock. The technical of stochastic approximation algorithm is used to obtain the gradient, step size and observation length. The thesis is based on Fu and Hu model (2005).</p>
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Hunt, Colleen Helen. "Inference for general random effects models." Title page, table of contents and abstract only, 2003. http://web4.library.adelaide.edu.au/theses/09SM/09smh9394.pdf.
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"October 13, 2003" Bibliography: leaves 102-105. This work describes methods associated with general random effects models. Part one describes a technique for investigating mean-variance relationships in random effects models. Part two derives and approximation to the likelihood function using a Laplace expansion to the fourth order.
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Rahantamialisoa, Faniry Nadia Zazaravaka. "Complex fluid dynamical computations via the Finite Volume Method." Master's thesis, University of Cape Town, 2018. http://hdl.handle.net/11427/29860.
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Numerical simulations of the complex flows of viscoelastic fluids are investigated. The viscoelastic fluids are modelled, primarily, via the Johnson-Segalman constitutive model. Our Numerical approach is based on finite volume method, based on the Johnson-Segalman constitutive model and implemented on the OpenFOAM® platform. The Johnson-Segalman model also easily reduces to the Oldroyd-B model under certain conditions of the material parameters. Since computations using the Oldroyd-B model have been extensively documented in the literature, we take advantage of the mathematical modelling connection between the Johnson-Segalman and Oldroyd-B models to validate the accuracy of our Johnson-Segalman solver via reduction to the Oldroyd-B model. Numerical validation of our results is conducted via the most commonly used benchmark problems. The final aim of our work is to assess the viability and efficiency of our numerical solver via an investigation into the complex fluid dynamical processes associated with shear banding.
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Brakel, Thomas W. "Mathematical modelling of the Czochralski crystal growth process." Doctoral thesis, University of Cape Town, 2006. http://hdl.handle.net/11427/4868.
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Includes bibliographical references (leaves 142-149).<br>In this document a mathematical model for the Czochralski crystal growth process is developed. The trend in current research involves developing cumbersome numerical simulations that provide little or no understanding of the underlying physics. We attempt to review previous research methods, mainly devoted to silicon, and develop a novel analytical tool for indium antimonide (lnSb) crystal growth. This process can be subdivided into two categories: solidification and fluid mechanics. Thus far, crystal solidification of the Czochralski process has been described in the literature mainly qualitatively. There has been little work in calculating actual solidification dynamics. Czochralski crystal growth is a very sensitive process, particularly for lnSb, so it is crucial to describe the system as accurately as possible. A novel ID quasi-steady method is proposed for the shape and temperature field of an lnSb crystal, incorporating the effects of the melt. The fluid mechanics of the Czochralski melt have been modelled by numerous researchers,with calculations performed using commercial software. However, a descriptionof the buoyancy and rotation interaction in the melt has not been adequatelyperformed. Many authors have presented flow patterns but none have indicated either: melt conditions preferential for crystal growth or at least a description of a typical melt structure. In this work, a scale analysis is performed that implies an idealized flow structure. An asymptotic model is then derived based on this order of magnitude analysis, resulting in a fast and efficient fluid flow calculation. The asymptotic model is validated against a numerical solution to ensure that the macroscopic features of the flow structure are present. The asymptotic model does not show exact agreement, but does provide an estimate of the melt heat flux that is necessary for the solidification calculation. The asymptotic model is also used to predict macroscopic changes in the melt due to rotation.