Dissertations / Theses on the topic 'Torus'
To see the other types of publications on this topic, follow the link: Torus.
Create a spot-on reference in APA, MLA, Chicago, Harvard, and other styles
Consult the top 50 dissertations / theses for your research on the topic 'Torus.'
Next to every source in the list of references, there is an 'Add to bibliography' button. Press on it, and we will generate automatically the bibliographic reference to the chosen work in the citation style you need: APA, MLA, Harvard, Chicago, Vancouver, etc.
You can also download the full text of the academic publication as pdf and read online its abstract whenever available in the metadata.
Browse dissertations / theses on a wide variety of disciplines and organise your bibliography correctly.
1
Hill, Peter Clifford. "On double-torus knots." Thesis, National Library of Canada = Bibliothèque nationale du Canada, 1998. http://www.collectionscanada.ca/obj/s4/f2/dsk2/tape15/PQDD_0011/NQ35186.pdf.
Full text
2
Davis, Eric Wesley. "Diffusion in the Io plasma torus and its relation to the torus spatial structure." Diss., The University of Arizona, 1991. http://hdl.handle.net/10150/185421.
Full textAbstract:
This is a study of the plasma diffusion processes relevant to the physical nature of the Io plasma torus at Jupiter. A knowledge of the diffusion processes involved in the Io plasma torus is essential to an understanding of the spatial structure and energetics of the torus. The only published theory of Io torus plasma diffusion, centrifugally driven flux tube interchange instability, is based on turbulent plasma interchange instability. We have examined physical properties that lead us to conclude that flux tube interchange diffusion is not a valid mechanism in the plasma torus. The collisional nature of the hot torus plasma is seen through its observed EUV emissions which dominate the energy loss from the system. Further, the torus plasma parameters fall in the range of values satisfying the criteria for the use of collisional transport theory to derive a collisional diffusion coefficient. The collisional nature of the torus plasma is characterized in the long mean free path regime where classical transport theory breaks down. We study the Chapman-Enskog method of calculating the plasma diffusion coefficient from a solution of the Boltzmann equation. Simplifying approximations of a fully ionized plasma dominated by Coulomb elastic charged particle collisions are made to derive an ad hoc non-classical diffusion coefficient which results in slow differential diffusion rates for the various sulfur and oxygen ions in the plasma torus. The radial spatial structure and energetics of the plasma torus is modeled by employing the collisional diffusion coefficient in a computer model calculation of collisional ionization-diffusive equilibrium and energy branching. The computer model employs the known significant plasma reactions involving the torus sulfur and oxygen species, utilizing the most recently available atomic parameters. In view of the failure of Neutral Cloud Theory to adequately power the copious amounts of UV radiation emitted by the Io plasma torus, we employed the radial plasma model to investigate this "energy crisis." Toward this end, we investigate the application to our plasma model of a proposed heterogeneous source of energetic electrons and a proposal of inward diffusing energetic outer-magnetospheric OII and SII ions as ad hoc heat inputs to the plasma torus electrons, in order to maintain a steady state energy balance.
3
Koch, Tino. "Hyperbolische einfach-punktierte Torus-Bündel." [S.l. : s.n.], 1999. http://deposit.ddb.de/cgi-bin/dokserv?idn=957665474.
Full text
4
Ho, Ieng Chon. "The Hardy spaces on torus." Thesis, University of Macau, 2017. http://umaclib3.umac.mo/record=b3691576.
Full text
5
IMPELLIZIERI, FILLIPO DE SOUZA LIMA. "DOMINO TILINGS OF THE TORUS." PONTIFÍCIA UNIVERSIDADE CATÓLICA DO RIO DE JANEIRO, 2015. http://www.maxwell.vrac.puc-rio.br/Busca_etds.php?strSecao=resultado&nrSeq=26336@1.
Full textAbstract:
PONTIFÍCIA UNIVERSIDADE CATÓLICA DO RIO DE JANEIROCOORDENAÇÃO DE APERFEIÇOAMENTO DO PESSOAL DE ENSINO SUPERIOR
FUNDAÇÃO DE APOIO À PESQUISA DO ESTADO DO RIO DE JANEIRO
PROGRAMA DE SUPORTE À PÓS-GRADUAÇÃO DE INSTS. DE ENSINO
Consideramos o problema de contar e classificar coberturas por dominós de toros quadriculados. O problema de contagem para retângulos foi estudado por Kasteleyn e usamos muitas de suas ideias. Coberturas por dominós de regiões planares podem ser representadas por funções altura; para um toro dado por um reticulado L, estas funções exibem L-quasiperiodicidade aritmética. As constantes aditivas determinam o fluxo da cobertura, que pode ser interpretado como um vetor no reticulado dual (2L) asterisco. Damos uma caracterização dos valores de fluxo efetivamente realizados e de como coberturas correspondentes se comportam. Também consideramos coberturas por dominós do reticulado quadrado infinito; coberturas de toros podem ser vistas como um caso particular destas. Descrevemos a construção e uso de matrizes de Kasteleyn no problema de contagem, e como elas podem ser aplicadas para contar coberturas com valores de fluxo prescritos. Finalmente, estudamos a distribuição limite do número de coberturas com um dado valor de fluxo quando o reticulado L sofre uma dilatação uniforme.
We consider the problem of counting and classifying domino tilings of a quadriculated torus. The counting problem for rectangles was studied by Kasteleyn and we use many of his ideas. Domino tilings of planar regions can be represented by height functions; for a torus given by a lattice L, these functions exhibit arithmetic L-quasiperiodicity. The additive constants determine the flux of the tiling, which can be interpreted as a vector in the dual lattice (2L) asterisk. We give a characterization of the actual flux values, and of how corresponding tilings behave. We also consider domino tilings of the infinite square lattice; tilings of tori can be seen as a particular case of those. We describe the construction and usage of Kasteleyn matrices in the counting problem, and how they can be applied to count tilings with prescribed flux values. Finally, we study the limit distribution of the number of tilings with a given flux value as a uniform scaling dilates the lattice L.
6
Wyld, Kira A. "Sudoku Variants on the Torus." Scholarship @ Claremont, 2017. http://scholarship.claremont.edu/hmc_theses/103.
Full textAbstract:
This paper examines the mathematical properties of Sudoku puzzles defined on a Torus. We seek to answer the questions for these variants that have been explored for the traditional Sudoku. We do this process with two such embeddings. The end result of this paper is a deeper mathematical understanding of logic puzzles of this type, as well as a fun new puzzle which could be played.
7
Nguyenhuu, Rick Hung. "Torus embedding and its applications." CSUSB ScholarWorks, 1998. https://scholarworks.lib.csusb.edu/etd-project/1572.
Full text
8
Armitage, Ted. "Broadcasting on torus-like chordal rings." Thesis, National Library of Canada = Bibliothèque nationale du Canada, 1996. http://www.collectionscanada.ca/obj/s4/f2/dsk3/ftp05/mq24084.pdf.
Full text
9
Bettersworth, Zachary S. "Nullification of Torus Knots and Links." TopSCHOLAR®, 2016. http://digitalcommons.wku.edu/theses/1626.
Full textAbstract:
Knot nullification is an unknotting operation performed on knots and links that can be used to model DNA recombination moves of circular DNA molecules in the laboratory. Thus nullification is a biologically relevant operation that should be studied.
Nullification moves can be naturally grouped into two classes: coherent nullification, which preserves the orientation of the knot, and incoherent nullification, which changes the orientation of the knot. We define the coherent (incoherent) nullification number of a knot or link as the minimal number of coherent (incoherent) nullification moves needed to unknot any knot or link. This thesis concentrates on the study of such nullification numbers. In more detail, coherent nullification moves have already been studied at quite some length. This is because the preservation of the previous orientation of the knot, or link, makes the coherent operation easier to study. In particular, a complete solution of coherent nullification numbers has been obtained for the torus knot family, (the solution of the torus link family is still an open question). In this thesis, we concentrate on incoherent nullification numbers, and place an emphasis on calculating the incoherent nullification number for the torus knot and link family. Unfortunately, we were unable to compute the exact incoherent nullification numbers for most torus knots. Instead, our main results are upper and lower bounds on the incoherent nullification number of torus knots and links. In addition we conjecture what the actual incoherent nullification number of a torus knot will be.
10
Valente, Marcelo. "Torus Palatinus: estudo por Tomografia Computadorizada\"." Universidade de São Paulo, 1999. http://www.teses.usp.br/teses/disponiveis/5/5151/tde-18092014-113201/.
Full textAbstract:
Estudou-se prospectivamente o comportamento das calcificações, da atrofia, das alterações da substância branca e alterações vasculares nas imagens de tomografia computadorizada de crânio de 162 crianças e adolescentes infectados pelo vírus da imunodeficiência humana (HIV) por transmissão vertical e que estavam ou estiveram em acompanhamento clínico no Ambulatório de Infectologia Pediátrica do Instituto da Criança do Hospital das Clínicas da Faculdade de Medicina da Universidade de São Paulo, entre 1992 e 2002. Analisaram-se as possíveis correlações entre estas alterações e seu aspecto evolutivo. Para tal finalidade, foram avaliadas 606 tomografias computadorizadas de crânio (média de 3,74 exames por paciente), as quais constituíram o grupo de estudo. Após a caracterização quanto à presença ou não das alterações supracitadas, e suas possíveis inter-relações, realizou-se a análise estatística dos resultados obtidos através do teste exato de Fisher com nível de significância de 5%. Posteriormente, os mesmo aspectos foram avaliados em função do seu comportamento evolutivo em um subgrupo de 61 pacientes (média, 4,18 exames por paciente, totalizando 321 exames tomográficos). Estes pacientes tinham, pelo menos, quatro estudos tomográficos seriados (com intervalo mínimo de noventa dias entre os exames subseqüentes e pelo menos dois anos de intervalo total entre o primeiro e o último exame). As alterações tomográficas foram abordadas individual e qualitativamente segundo o critério de presença e intensidade. Inicialmente, o conjunto dos resultados foi tratado de forma individual (para cada paciente) e, depois, em relação à totalidade do grupo em questão. As calcificações foram encontradas em 46,30% dos pacientes; a atrofia, em 37,65%; as alterações da substância branca, em 25,93%; as anomalias vasculares, em 25,19%. Constatou-se uma correlação significativa entre as alterações de substância branca e a atrofia, bem como entre as calcificações e as alterações vasculares. A análise evolutiva destas características demonstrou haver um acréscimo significativo das alterações entre o momento inicial e o quarto momento no conjunto das alterações, sobretudo para as calcificações e para as alterações vasculares. Concluiu-se que as calcificações e a atrofia foram as alterações mais freqüentes nesta série de crianças e adolescentes com HIV adquirido por transmissão vertical. A atrofia e as alterações da substância branca apresentaram uma inter-relação importante na amostra descritiva, assim como as alterações vasculares e as calcificações mostraram uma associação evolutiva significativa em relação à sua progressãoWe prospectively studied the behavior of calcifications, atrophy, white matter and vascular abnormalities on the images of computed tomography (CT) of 162 children and adolescents infected with the human immunodeficiency virus (HIV) acquired by vertical transmission, who are or were clinically followed in the Ambulatory of Pediatric Infectology of the Children Institute at the Clinics Hospital of University of São Paulo Medical School, from 1992 to 2002. We analyzed the possible correlation between these abnormalities, as well as, their evolutive aspects. For this purpose, we evaluated 606 CT scans (mean 3.74 exams per patient), which composed the group of study. After the characterization according to the presence or not of the anomalies mentioned above, and their possible inter-relations, we performed a statistical analysis of the obtained results with the Fisher test with a level of significance below 5%. Later, these aspects were evaluated regarding its evolutive behavior in a subgroup of 61 patients (mean, 4.18 exams per patient, summing 321 exams). These patients had, at least, four serial cranial CT (with minimum interval of ninety days between the subsequent exams and, at least, two years of total interval between the first and the fourth exam). The cranial CT abnormalities presented were assessed individually as absent or present. Initially, the set results were assessed individually (for each patient) and, later in relation to the totality of the group. Calcifications were found in 46.30% of all patients, atrophy in 37.65%, white matter abnormalities in 25.93% and vascular anomalies in 25.19%. We found a significant correlation between white matter abnormalities and atrophy, as well as, between calcifications and vascular anomalies. Evolutive analysis of these characteristics demonstrated a significant increase of the abnormalities between the first and the fourth moment, with emphasis to the calcifications and vascular anomalies. We concluded that, calcifications and atrophy were the most frequent abnormalities in this series of children and adolescents with HIV acquired by vertical transmission. Atrophy and white matter abnormalities presented a significant correlation in the descriptive sample, as well as, vascular anomalies and calcifications that also demonstrated a significant evolutive association regarding its progression
11
Loureiro, Luiz Tiaraju dos Reis. "Um estudo sobre a máquina Torus." reponame:Biblioteca Digital de Teses e Dissertações da UFRGS, 2008. http://hdl.handle.net/10183/21841.
Full textAbstract:
Este trabalho apresenta as características básicas de uma máquina elétrica com fluxo axial, ímãs permanentes, rotor duplo e estator com enrolamentos toroidais montado entre os rotores. A máquina foi construída no Laboratório de Máquinas Elétricas, Acionamentos e Energia da Escola de Engenharia da UFRGS. O trabalho contém modelos analíticos para as induções magnéticas dos ímãs permanentes e dos enrolamentos de armadura. A partir dos modelos foram desenvolvidas expressões para o cálculo de forças eletromotrizes e de conjugados, sendo utilizado um software de matemática simbólica para realização dos cálculos. É apresentada uma comparação entre os resultados obtidos através do modelo analítico e os resultados obtidos por simulação numérica. Alguns resultados são comparados também com valores experimentais. As expressões para o cálculo de conjugado desenvolvido pela máquina serão detalhadas em uma etapa posterior. Foi obtida uma razoável coerência entre os dados comparados.This work presents the basic features of an axial flux, permanent magnet, double rotor and toroidal windings mounted between the rotors. The machine was built in the Laboratory of Electrical Machines, Drives and energy of the School of Engineering of the Federal University of Rio Grande do Sul. The work contains analytical models of permanent magnets and armature windings magnetic inductions. Based in models, expressions of electromotive forces and torques were derived. The calculations were performed with a symbolical mathematical software. It is presented a comparison between results obtained with analytical model and results of the numerical simulation. Some comparisons include experimental results. The expressions of machine torque will be detailed in a next phase. The compared results present an acceptable conformity.
12
Jackson, Delbert James. "Electromagnetic levitation of a solid metallic torus." Thesis, National Library of Canada = Bibliothèque nationale du Canada, 2000. http://www.collectionscanada.ca/obj/s4/f2/dsk1/tape4/PQDD_0015/MQ54127.pdf.
Full text
13
Skala, Matthew Adam. "Generation of graphs embedded on the torus." Thesis, National Library of Canada = Bibliothèque nationale du Canada, 2001. http://www.collectionscanada.ca/obj/s4/f2/dsk3/ftp05/MQ62561.pdf.
Full text
14
Fremling, Mikael. "Quantum Hall Wave Functions on the Torus." Doctoral thesis, Stockholms universitet, Fysikum, 2015. http://urn.kb.se/resolve?urn=urn:nbn:se:su:diva-115616.
Full textAbstract:
The fractional quantum Hall effect (FQHE), now entering it's fourth decade, continues to draw attention from the condensed matter community. New experiments in recent years are raising hopes that it will be possible to observe quasi-particles with non-abelian anyonic statistics. These particles could form the building blocks of a quantum computer. The quantum Hall states have topologically protected energy gaps to the low-lying set of excitations. This topological order is not a locally measurable quantity but rather a non-local object, and it is one of the keys to it's stability. From an early stage understanding of the FQHE has been facilitate by constructing trial wave functions. The topological classification of these wave functions have given further insight to the nature of the FQHE. An early, and successful, wave function construction for filling fractions ν=p/(2p+1) was that of composite fermions on planar and spherical geometries. Recently, new developments using conformal field theory have made it possible to also construct the full Haldane-Halperin hierarchy wave functions on planar and spherical geometries. In this thesis we extend this construction to a toroidal geometry, i.e. a flat surface with periodic boundary conditions. One of the defining features of topological states of matter in two dimensions is that the ground state is not unique on surfaces with non trivial topology, such as a torus. The archetypical example is the fractional quantum Hall effect, where a state at filling fraction ν=p/q, has at least a q-fold degeneracy on a torus. This has been shown explicitly for a few cases, such as the Laughlin states and the the Moore-Read states, by explicit construction of candidate electron wave functions with good overlap with numerically found states. In this thesis, we construct explicit torus wave functions for a large class of experimentally important quantum liquids, namely the chiral hierarchy states in the lowest Landau level. These states, which includes the prominently observed positive Jain sequence at filling fractions ν=p/(2p+1), are characterized by having boundary modes with only one chirality. Our construction relies heavily on previous work that expressed the hierarchy wave functions on a plane or a sphere in terms of correlation functions in a conformal field theory. This construction can be taken over to the torus when care is taken to ensure correct behaviour under the modular transformations that leave the geometry of the torus unchanged. Our construction solves the long standing problem of engineering torus wave functions for multi-component many-body states. Since the resulting expressions are rather complicated, we have carefully compared the simplest example, that of ν=2/5, with numerically found wave functions. We have found an extremely good overlap for arbitrary values of the modular parameter τ, that describes the geometry of the torus. Having explicit torus wave functions allows us to use the methods developed by Read and Read \& Rezayi to numerically compute the quantum Hall viscosity. Hall viscosity is conjectured to be a topologically protected macroscopic transport coefficient characterizing the quantum Hall state. It is related to the shift of the same QH-fluid when it is put on a sphere. The good agreement with the theoretical prediction for the 2/5 state strongly suggests that our wave functions encodes all relevant topologically information. We also consider the Hall viscosity in the limit of a very thin torus. There we find that the viscosity changes as we approach the thin torus limit. Because of this we study the Laughlin state in that limit and see how the change in viscosity arises from a change in the Hamiltonian hopping elements. Finally we conclude that there are both qualitative and quantitative difference between the thin and the square torus. Thus, one has to be careful when interpreting results in the thin torus limit.At the time of the doctoral defense, the following paper was unpublished and had a status as follows: Paper 4: Manuscript.
15
van, Caspel Moos. "The topological Casimir effect on a torus." Thesis, University of British Columbia, 2013. http://hdl.handle.net/2429/44948.
Full textAbstract:
The conventional Casimir effect manifests itself as a quantum mechanical force between two plates, that arises from the quantization of the electromagnetic field in the enclosed vacuum. In this thesis the existence is discussed of an extra, topological term in the Casimir energy at finite temperatures. This topological Casimir effect emerges due to the nontrivial topological features of the gauge theory: the extra energy is the result of tunneling transitions between states that are physically the same but topologically distinct. It becomes apparent when examining, for instance, periodic boundary conditions. I explicitly calculate the new term for the simplest example of such a system, a Euclidean 4-torus. By dimensional reduction, this system is closely related to two dimensional electromagnetism on a torus, which is well understood. It turns out that the topological term is extremely small compared to the conventional Casimir energy, but that the effect is very sensitive to an external magnetic field. The external field plays the role of a topological theta parameter, analogous to the theta vacuum in Yang-Mills theory. The topological Casimir pressure and the induced magnetic field show a distinctive oscillation as a function of the external field strength, something that can hopefully be observed experimentally.
16
Osório, Jonas Obert Martins. "Análise da máquina Torus sob frenagem eletrodinâmica." reponame:Biblioteca Digital de Teses e Dissertações da UFRGS, 2011. http://hdl.handle.net/10183/38777.
Full textAbstract:
Este trabalho foi desenvolvido com o objetivo de estudar a aplicação, para sistema de frenagem veicular, de uma máquina elétrica sem escovas, de armadura toroidal, e fluxo magnético axial produzido por ímãs permanentes de terras raras, a chamada máquina Torus. A máquina foi construída no LMEAE e estudada inicialmente como motor em outro trabalho. Mas, para que se possa avaliar seu funcionamento em sistema de frenagem, o foco é do ponto de vista da máquina como gerador. São realizados testes dinâmicos e estáticos experimentalmente e modelo numérico pelo método dos elementos finitos com um formato de ímãs permanentes de seção setorial, possibilitando o comparativo com a versão anterior da máquina que empregou ímãs de seção quadrada. Mudanças físicas e no sistema de acionamento da máquina, e ensaios de frenagem dinâmica foram realizados. Modelagem analítica para indução magnética foi desenvolvida utilizando-se da técnica de Transformação Conforme. O trabalho busca apresentar as características da máquina e justificativas que demonstram o seu potencial de aplicabilidade em um subsistema veicular sob frenagem regenerativa e a capacidade de fornecimento de energia a um sistema de armazenamento com uma parte de energia cinética, ou seja, baterias e supercapacitores.This work is carried out with the aim to study the application, by a vehicular braking system, of a brushless electrical machine with a toroidal armature core, and axial magnetic flux delivered by rare earth permanent magnets, the so-called Torus machine. The machine was built in the LMEAE, and previously studied as a motor by other work. However, in order to assess its performance in a braking system, the focus is the point of view of the machine as a generator. Static and dynamic tests are implemented as well as a numerical model by means of the finite element method, in order to compare the machine with sector poles permanent magnets and with square magnet poles. Physical changes and on the driving system of the machine, and dynamic braking tests are performed. The analytical modelling for the magnetic induction was developed using the technique of conformal transformation. The study aims to present the features of the machine and demonstrates its potential applicability to a vehicular subsystem under regenerative braking and the ability to supply an energy storage system with part of the kinetic energy, i.e. batteries and super capacitors.
17
Hlavacek, Amy Lee. "9-vertex irreducible graphs on the torus /." The Ohio State University, 1997. http://rave.ohiolink.edu/etdc/view?acc_num=osu1487944660932981.
Full text
18
Jäger, T., and A. Passeggi. "On torus homeomorphisms semiconjugate to irrational rotations." Cambridge University Press, 2015. https://tud.qucosa.de/id/qucosa%3A39051.
Full textAbstract:
In the context of the Franks–Misiurewicz conjecture, we study homeomorphisms of the two-torus semiconjugate to an irrational rotation of the circle. As a special case, this conjecture asserts uniqueness of the rotation vector in this class of systems. We first characterize these maps by the existence of an invariant ‘foliation’ by essential annular continua (essential subcontinua of the torus whose complement is an open annulus) which are permuted with irrational combinatorics. This result places the considered class close to skew products over irrational rotations. Generalizing a well-known result of Herman on forced circle homeomorphisms, we provide a criterion, in terms of topological properties of the annular continua, for the uniqueness of the rotation vector. As a byproduct, we obtain a simple proof for the uniqueness of the rotation vector on decomposable invariant annular continua with empty interior. In addition, we collect a number of observations on the topology and rotation intervals of invariant annular continua with empty interior.
19
Milani, Federico. "Disruption prediction at JET (Joint European Torus)." Thesis, Aston University, 1998. http://publications.aston.ac.uk/10606/.
Full textAbstract:
The sudden loss of the plasma magnetic confinement, known as disruption, is one of the major issue in a nuclear fusion machine as JET (Joint European Torus), Disruptions pose very serious problems to the safety of the machine. The energy stored in the plasma is released to the machine structure in few milliseconds resulting in forces that at JET reach several Mega Newtons. The problem is even more severe in the nuclear fusion power station where the forces are in the order of one hundred Mega Newtons. The events that occur during a disruption are still not well understood even if some mechanisms that can lead to a disruption have been identified and can be used to predict them. Unfortunately it is always a combination of these events that generates a disruption and therefore it is not possible to use simple algorithms to predict it. This thesis analyses the possibility of using neural network algorithms to predict plasma disruptions in real time. This involves the determination of plasma parameters every few milliseconds. A plasma boundary reconstruction algorithm, XLOC, has been developed in collaboration with Dr. D. Ollrien and Dr. J. Ellis capable of determining the plasma wall/distance every 2 milliseconds. The XLOC output has been used to develop a multilayer perceptron network to determine plasma parameters as ?i and q? with which a machine operational space has been experimentally defined. If the limits of this operational space are breached the disruption probability increases considerably. Another approach for prediction disruptions is to use neural network classification methods to define the JET operational space. Two methods have been studied. The first method uses a multilayer perceptron network with softmax activation function for the output layer. This method can be used for classifying the input patterns in various classes. In this case the plasma input patterns have been divided between disrupting and safe patterns, giving the possibility of assigning a disruption probability to every plasma input pattern. The second method determines the novelty of an input pattern by calculating the probability density distribution of successful plasma patterns that have been run at JET. The density distribution is represented as a mixture distribution, and its parameters arc determined using the Expectation-Maximisation method. If the dataset, used to determine the distribution parameters, covers sufficiently well the machine operational space. Then, the patterns flagged as novel can be regarded as patterns belonging to a disrupting plasma. Together with these methods, a network has been designed to predict the vertical forces, that a disruption can cause, in order to avoid that too dangerous plasma configurations are run. This network can be run before the pulse using the pre-programmed plasma configuration or on line becoming a tool that allows to stop dangerous plasma configuration. All these methods have been implemented in real time on a dual Pentium Pro based machine. The Disruption Prediction and Prevention System has shown that internal plasma parameters can be determined on-line with a good accuracy. Also the disruption detection algorithms showed promising results considering the fact that JET is an experimental machine where always new plasma configurations are tested trying to improve its performances.
20
Barker, Stephen J. "Interchanging Two Notations for Double-torus Links." Digital Commons @ East Tennessee State University, 2016. https://dc.etsu.edu/etd/2616.
Full textAbstract:
Knot theory is a relatively young branch of mathematics, still less than a century old. The development of the Jones polynomial in 1984 led to increased activity in knot theory. Though work is constantly being done in this field, notably the classification of torus knots, double-torus knots are still lacking such a complete understanding. There exists two notations, those of Rick Norwood and of Peter Hill, that describe knots on the double-torus. The ambition of this thesis is to begin to make the case that it is possible to render these two notations interchangeable. Illustrating this will require examining the two notations and finding a way to change one into the other, then check if this process is reversible. If not, then proceed to develop a method that works to convert the second notation back to the first.
21
Ishibashi, Hiroki. "Torus routing in the presence of multicasts." CSUSB ScholarWorks, 1996. https://scholarworks.lib.csusb.edu/etd-project/1251.
Full text
22
OBERTI, CHIARA. "Induction effects of torus knots and unknots." Doctoral thesis, Università degli Studi di Milano-Bicocca, 2015. http://hdl.handle.net/10281/87792.
Full textAbstract:
In questa tesi si analizzano gli effetti di induzione di un campo sorgente stazionario nella forma di un filamento a nodo o non-nodo torico. Studi simili sono stati compiuti per geometrie rettilinee, circolari o elicoidali, ma poco o nulla è noto per geometrie e topologie più complesse. I nodi torici sono un raro esempio di curve spaziali chiuse con topologia non banale che ammettono una descrizione matematicamente semplice; per questo rappresentano un interessante caso da studiare. Inoltre, poiché i nodi torici sono anche un buon modello matematico per studiare strutture di campo intrecciate, questo lavoro offre utili informazioni per svariate applicazioni possibili, dalle scienze fisiche (fisica del sole e astrofisica, dinamica vorticosa, fisica della fusione) alla tecnologia (telecomunicazioni, progettazione di nuovi materiali, analisi di dati). Il lavoro è organizzato in 4 capitoli.
Nel capitolo 1 presentiamo uno studio esaustivo di proprietà geometriche e topologiche dei nodi/non-nodi torici. Usando una parametrizzazione standard, dimostriamo l'esistenza e determiniamo la posizione di punti di flesso per una data configurazione critica, e prescriviamo la condizione per rimuovere la singolarità associata alla torsione nel punto di flesso. Mostriamo che in prima approssimazione la lunghezza cresce linearmente con il numero di avvolgimenti ed è proporzionale al numero minimo di incroci. Prendendo il numero di avvolgimento, definito come rapporto tra gli avvolgimenti meridiani e quelli longitudinali, come misura di complessità topologica, ne analizziamo l'influenza su varie proprietà globali, quali lunghezza, curvatura, torsione totale e distorsione.
Nel capitolo 2 analizziamo l'influenza del numero di avvolgimento e di altre proprietà geometriche su induzione, energia ed elicità. Per far questo si assume che il filamento fisico abbia sezione trasversale infinitesima e si usa la legge di Biot-Savart adattata alla particolare parametrizzazione scelta. Si studiano le linee di campo indotto per numerosi nodi/non-nodi torici su vari piani trasversali. Si mostra che l'intensità del campo indotto dipende linearmente dal numero di avvolgimenti longitudinali. Si forniscono maggiorazioni e minorazioni per l'energia e una stima dell'elicità in termini del numero di distorsione.
Nel capitolo 3 compariamo i contributi d'induzione locali e globali in relazione al numero di avvolgimento, derivando espansioni asintotiche della funzione integranda. Mostriamo che i termini locali di ordine principale in generale non sono sufficienti a fornire accurate informazioni globali; tuttavia, mostriamo che per alcuni valori del numero di avvolgimento i comportamenti locali e globali sono in buon accordo.
Nel capitolo 4 analizziamo gli effetti del numero di avvolgimento sull'auto-induzione per punti asintoticamente vicini al campo sorgente. Poiché al limite l'integrale di Biot-Savart diventa singolare, lo regolarizziamo applicando la prescrizione analitica di Moore e Saffman (1972). Mentre al primo ordine l'auto-induzione è proporzionale alla curvatura locale, determiniamo l'influenza del numero di avvolgimento sui termini successivi, mostrando che i suoi effetti sono comparabili con quelli dati da una distribuzione di campo sorgente sulla sezione trasversale finita del filamento.The induction effects due to a steady source field in the shape of a torus knot or unknot filament are analysed in detail. Similar studies for rectilinear, circular or helical geometries have been done in the past, but very little is known for more complex geometries and topologies. Torus knots provide a rare example of closed, space curves of non-trivial topology, that admit a mathematically simple description; for this reason they represent an interesting case study to consider. Moreover, since torus knots are also a good mathematical model for studying braided field line structures, the present work provides useful information for a wide range of possible applications, from physical sciences (solar physics and astrophysics, vortex dynamics, fusion physics) to technology (telecommunication, new materials design, data analysis). The work is organized in 4 chapters. In chapter 1 we present a comprehensive study of geometric and topological properties of torus knots and unknots. By using a standard parametrization, we demonstrate the existence, and determine the location, of inection points for a given critical configuration, and prescribe the condition for removing the singularity associated with torsion at the inflection point. We show that, to first approximation, total length grows linearly with the number of coils, and it is proportional to the minimum crossing number of the knot type. By taking the winding number, given by the ratio between meridian and longitudinal wraps, as measure of topological complexity of the knot, we analyse its influence on several global quantities, such as total length, curvature, torsion and writhe. In chapter 2 we analyse the influence of the winding number and other geometric properties on induction, energy and helicity. This is done by assuming the physical filament of infinitesimally small cross-section and by using the Biot-Savart law adapted for the particular parametrization chosen. Field line patterns of the induced field are obtained for a large family of knots/unknots on several cross-sectional planes. The intensity of the induced field is shown to depend linearly on the number of toroidal coils. We provide bounds on energy, and an estimate of helicity in terms of writhe. In chapter 3 we compare local and global induction contributions in relation to the winding number, by providing asymptotic expansions of the integrand function. We show that in general local leading order terms are not sufficient to provide accurate global information; nevertheless, for some values of the winding number local and global behaviours are found to be in good agreement. In chapter 4 we investigate the influence of the winding number on the binormal component of the self-induction a point asymptotically near to the source field. Since in the limit the Biot-Savart integral becomes singular, we apply the analytical prescription of Moore and Saffman (1972) to regularize it. While to leading order the self-induction is proportional to local curvature, we derive an integral formula for next terms, including higher order local terms together with non-local terms, and we study its dependence on the winding number by showing that the dominant contribution is generally given by non-local terms.
23
Hötte, Heike. "Eine Verallgemeinerung komplexer Tori." [S.l. : s.n.], 2004. http://deposit.ddb.de/cgi-bin/dokserv?idn=972090606.
Full text
24
Schilder, Frank. "Numerische Approximation quasiperiodischer invarianter Tori unter Anwendung erweiterter Systeme." [S.l. : s.n.], 2004. http://deposit.ddb.de/cgi-bin/dokserv?idn=974849979.
Full text
25
Kopp, Thomas Jakob. "Zusammenhang zwischen Hydrodynamik und Stofftransport im Torus-Bioreaktor /." [S.l.] : [s.n.], 1985. http://e-collection.ethbib.ethz.ch/show?type=diss&nr=7913.
Full text
26
Button, Jack Oliver. "Quasi-Fuchsian space of the once-punctured torus." Thesis, University of Warwick, 1994. http://wrap.warwick.ac.uk/107552/.
Full textAbstract:
In this thesis we look at two generator groups of Möbius transformations where the commutator of the generators is parabolic. In particular we are interested in quasi- Fuchsian groups T whose quotient surface fl/T consists of two once-punctured tori. The set of all such quasi-Fuchsian groups, which is called the quasi-Fuchsian space of the once-punctured torus, is defined in chapter 1. In chapter 2 we introduce two sets of suitable coordinates for quasi-Fuchsian space. The first is the well-known trace parameters and the other set of coordinates involves an appropriate normalisation of conjugacy classes of quasi-Fuchsian groups. We study a special class of quasi-Fuchsian groups in chapter 3 which are those groups obtained by pairing four classical circles, each of which is tangent to its neighbours. We find the exact subset of quasi-Fuchsian space where these groups lie and investigate their limiting behaviour. In chapter 4 we return to the whole of quasi-Fuchsian space of the once-punctured torus and investigate what happens when we change the generators of such a group T. In particular we reduce the modulus of the traces of generators of T, and use this information to build up a substantial picture of quasi-Fuchsian space. In the last chapter we look at the traces of elements of one particular group, which gives rise to the Diophantine equation a2 + b2+c2 = 3a6c studied by Markoff. If we arrange a solution triple of natural numbers (a, 6, c) in ascending order, so that a < b < c, it has long been conjectured that the largest number uniquely determines the triple. We finish by proving that if c, is prime then this statement is true. We show this using only algebraic number theory, but we mention the geometric motivation which originally gave the ideas for the proof, and where it appears in the earlier chapters.
27
Mezzadri, Francesco. "Boundary conditions for torus maps and spectral statistics." Thesis, University of Bristol, 1999. http://hdl.handle.net/1983/dcba3276-00be-4bae-a89f-f864750e77ff.
Full text
28
Butler, Joe R. "The Torus Does Not Have a Hyperbolic Structure." Thesis, University of North Texas, 1992. https://digital.library.unt.edu/ark:/67531/metadc500333/.
Full textAbstract:
Several basic topics from Algebraic Topology, including fundamental group and universal covering space are shown. The hyperbolic plane is defined, including its metric and show what the "straight" lines are in the plane and what the isometries are on the plane. A hyperbolic surface is defined, and shows that the two hole torus is a hyperbolic surface, the hyperbolic plane is a universal cover for any hyperbolic surface, and the quotient space of the universal cover of a surface to the group of automorphisms on the covering space is equivalent to the original surface.
29
Prashant. "Global Attractor for mKdV Equation on 1D Torus." Kyoto University, 2018. http://hdl.handle.net/2433/235978.
Full text
30
Krebser, Urs André. "Biologische Leistungsfähigkeit des Torus-Bioreaktors unter Variation der Mediumseigenschaften /." [S.l.] : [s.n.], 1987. http://e-collection.ethbib.ethz.ch/show?type=diss&nr=8213.
Full text
31
Ichikawa, Kohei. "Study of Dust-Torus Properties around Supermassive Black Holes." 京都大学 (Kyoto University), 2015. http://hdl.handle.net/2433/199105.
Full text
32
Zhang, Lei. "Rotation sets and pseudo-rotation sets for torus maps." Thesis, National Library of Canada = Bibliothèque nationale du Canada, 1997. http://www.collectionscanada.ca/obj/s4/f2/dsk3/ftp04/nq22505.pdf.
Full text
33
Kotapati, Kamala. "The buffer management in wormhole-routed torus multicomputer networks." Thesis, National Library of Canada = Bibliothèque nationale du Canada, 1998. http://www.collectionscanada.ca/obj/s4/f2/dsk2/ftp03/MQ26980.pdf.
Full text
34
Crisp, David J. "The Markoff spectrum and geodesics on the punctured torus /." Title page, contents and abstract only, 1993. http://web4.library.adelaide.edu.au/theses/09PH/09phc9321.pdf.
Full text
35
Jabuni, Muna. "Analytic Representations of Finite Quantum Systems on a Torus." Thesis, University of Bradford, 2010. http://hdl.handle.net/10454/4856.
Full textAbstract:
Quantum systems with a finite Hilbert space, where position x and momen- tum p take values in Z(d) (integers modulo d), are studied. An analytic representation of finite quantum systems is considered. Quantum states are represented by analytic functions on a torus. This function has exactly d zeros, which define uniquely the quantum state. The analytic function of a state can be constructed using its zeros. As the system evolves in time, the d zeros follow d paths on the torus. Examples of the paths ³n(t) of the zeros, for various Hamiltonians, are given. In addition, for given paths ³n(t) of the d zeros, the Hamiltonian is calculated. Furthermore, periodic finite quantum systems are considered. Special cases where M of the zeros follow the same path are also studied, and general ideas are demonstrated with several ex- amples. Examples of the path with multiplicity M = 1; 2; 3; 4; 5 are given. It is evidenced within the study that a small perturbation of the initial values of the zeros splits a path with multiplicity M into M different paths.
36
Cova, Ramón José Cova. "CP¹ model on a sphere and on a torus." Thesis, Durham University, 1997. http://etheses.dur.ac.uk/4851/.
Full textAbstract:
The work in this thesis is concerned with the numerical study of some stability and scattering properties of two CP¹ models in three dimensional space-time: The non-linear 0(3) model and its modified Skyrme version. Chapter 3 focuses principally on the Skyrme model on compactified plane, the topological sphere. Such model is obtained by supplementing the ordinary 0(3) lagrangian with both a Skyrme term and a potential term which, in the present work, has a rather general form. Under the numerical simulation the skyrmions behave stably and scatter either back-to-back or at 90 to the initial direction of motion, depending on the initial velocity. In the 0(3) limit the solitons are no longer stable and scatter at 90 irrespective of the speed. In the fourth chapter the 0(3) model is studied on a flat torus. Its solitons exhibit the usual instability but can be stabilised by the sole addition of a Skyrme term to the lagrangian. Scattering at right angles is observed in all cases considered, including skyrmions colliding at speeds that would bounce them back were they evolving in compactified plane. The periodic 0(3) model has no analytic solutions of degree one, so when a field configuration that resembles a single soliton is numerically evolved, it shrinks to become infinitely thin. Interestingly, such ansatz may be regarded as a soliton of unit topological charge in the context of the periodic skyrmion model. Chapter 5 closes with a summary and suggestions for future research.
37
Lloyd, Simon Trevor. "Cr closing lemma results for flows on the torus." Thesis, University of Warwick, 2006. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.443968.
Full text
38
Suzuki, Yasuhiro. "Free-Ｂoundary MHD Equilibria of Non-Ａxisymmetric Torus Plasmas." Kyoto University, 2003. http://hdl.handle.net/2433/148450.
Full textAbstract:
Kyoto University (京都大学)0048
新制・課程博士
博士(エネルギー科学)
甲第10435号
エネ博第75号
新制||エネ||22(附属図書館)
UT51-2003-N926
京都大学大学院エネルギー科学研究科エネルギー基礎科学専攻
(主査)教授 近藤 克己, 教授 佐野 史道, 教授 前川 孝
学位規則第4条第1項該当
39
La, Fleur Stephen J. "Some fundamentals for Nielsen theory on torus configuration spaces." abstract and full text PDF (free order & download UNR users only), 2008. http://0-gateway.proquest.com.innopac.library.unr.edu/openurl?url_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:dissertation&res_dat=xri:pqdiss&rft_dat=xri:pqdiss:1453597.
Full text
40
Wheeler, Jean-David. "Non-elliptical point contacts : The Torus-on-Plane conjunction." Thesis, Lyon, 2016. http://www.theses.fr/2016LYSEI131/document.
Full textAbstract:
Cette thèse est dédiée à l’étude des contacts lubrifiés tore-plan sous diverses conditions. Ces contacts se situent à l’interface entre l’extrémité torique des rouleaux et le collet de la bague dans les roulements à rouleaux. La première complexité de cette étude provient de la géométrie particulière des solides concernés. La deuxième est générée par la cinématique complexe qui règne dans ces contacts. Afin de comprendre les mécanismes physiques à l’œuvre, une approche duale (expérimentale et numérique) est adoptée. Le banc d’essai Jérotrib permet une première étude basée sur l’hypothèse que le contact élastohydrodynamique tore-plan est similaire à un contact elliptique équivalent. Grâce à une méthode d’interférométrie optique en lumière blanche qui a été adaptée aux spécificités du contact en question, des mesures précises de l’épaisseur de film ont été effectuées dans un nombre significatif de conditions. Sur cette base, un modèle numérique thermo-élastohydrodynamique a été validé avec précision. Ce dernier a permis d’étudier les écoulements de fluide à l’entrée du contact afin de mettre en évidence leur influence sur le champ d’épaisseur de film. Le modèle numérique a ensuite été amélioré afin de prendre en compte la vraie forme des solides. Il a été validé en épaisseur de film par le banc d’essai Tribogyr, dans des conditions similaires à celles rencontrées dans les vrais roulements. Il a été montré que le cisaillement du fluide est responsable de l’échauffement des solides, qui diminue par suite l’épaisseur de film : ceci souligne la nécessité de modéliser cet échauffement global pour prédire la séparation des surfaces. Par ailleurs, lors de l’étude, le champ de pression et d’épaisseur de film ont perdu leurs symétries à cause de la cinématique et de la forme des solides. Toutefois, le comportement du contact est resté similaire à celui d’un contact elliptique, en dehors de certains cas limitesThis thesis is dedicated to the study of torus on plane contacts under various operating conditions. They can be found at the interface between the torus roller-end and the flange in roller bearings. The first challenge of this thesis is to deal with unusual mating geometries. The other challenge is the presence of a complex kinematic which operates in these contacts. In order to further develop the understanding of such a contact, a dual approach (experimental and numerical) is adopted. The Jérotrib test-rig enables a first study, by considering that the élastohydrodynamic torus on plane contact can be modelled by an elliptical equivalent contact. Thanks to a differential colorimetric interferometry method which was improved and adapted during the thesis, precise film thickness measurements are carried out under a rather wide range of operating conditions. A thermo-elastohydrodynamic numerical model is developed and validated by comparing its results to the ones of the test-rig. A numerical study on film forming is then proposed and the role of the contact ellipticity is investigated. The numerical model is improved in order to take into account the actual shape of the solids. A film thickness validation of the model is proposed, thanks to measurements performed on the Tribogyr test-rig. The operating conditions are very similar to the one encountered in actual bearings, and the mating solids have representative geometries: it is an actual torus-on-plane contact. It is demonstrated that the lubricant shearing is responsible for the solids temperature rise, which in its turn, reduces the film thickness. It appears mandatory to be able to predict this global warming of the bodies. It is also demonstrated that the pressure and film thickness distributions lose their symmetry because of the spinning kinematic and the solids shape. However, the behaviour of the torus-on-plane contact appears very similar to the one of an elliptical equivalent contact, apart from some limit cases
41
Prabhudev, Pavan. "Investigation of Larminar Flow inside a Torus in OpenFOAM." Thesis, KTH, Mekanik, 2019. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-260334.
Full textAbstract:
The work deals with an investigation of steady, laminar and incompressible flow inside a toroidal pipe. In particular, our aim is to investigate the effects of curvature and the Reynolds-number on the flow features. Numerical simulation are performed with the open-source CFD code OpenFOAM and the results are compared with the available data in the literature [Canton et. Al 2017, Int. J. Heat Fluid Flow]. The analysis shows that by increasing the curvature, the flow features are altered. This change in flow features becomes more important as the curvature increases. A complete description of friction factor and secondary flow quantities is provided, and a comparison with reference data allows to assess the reliability of OpenFOAM for this study case by providing results in an easier way than with more advanced codes such as Nek5000.
42
Azeez, Babatunde. "Reliable low latency I/O in torus-based interconnection networks." Texas A&M University, 2005. http://hdl.handle.net/1969.1/4842.
Full textAbstract:
In today's high performance computing environment I/O remains the main bottleneck in
achieving the optimal performance expected of the ever improving processor and
memory technologies. Interconnection networks therefore combines processing units,
system I/O and high speed switch network fabric into a new paradigm of I/O based
network. It decouples the system into computational and I/O interconnections each
allowing "any-to-any" communications among processors and I/O devices unlike the
shared model in bus architecture. The computational interconnection, a network of
processing units (compute-nodes), is used for inter-processor communication in carrying
out computation tasks, while the I/O interconnection manages the transfer of I/O requests
between the compute-nodes and the I/O or storage media through some dedicated I/O
processing units (I /O-nodes). Considering the special functions performed by the I/O
nodes, their placement and reliability become important issues in improving the overall
performance of the interconnection system.
This thesis focuses on design and topological placement of I/O-nodes in torus based
interconnection networks, with the aim of reducing I/O communication latency between
compute-nodes and I/O-nodes even in the presence of faulty I/O-nodes. We propose an
efficient and scalable relaxed quasi-perfect placement scheme using Lee distance error
correction code such that compute-nodes are at distance-t or at most distance-t+1 from an
I/O-node for a given t. This scheme provides a better and optimal alternative placement
than quasi perfect placement when perfect placement cannot be found for a particular
torus. Furthermore, in the occurrence of faulty I/O-nodes, the placement scheme is also
used in determining other alternative I/O-nodes for rerouting I/O traffic from affected
compute-nodes with minimal slowdown. In order to guarantee the quality of service
required of inter-processor communication, a scheduling algorithm was developed at the router level to prioritize message forwarding according to inter-process and I/O messages
with the former given higher priority.
Our simulation results show that relaxed quasi-perfect outperforms quasi-perfect and the
conventional I/O placement (where I/O nodes are concentrated at the base of the torus
interconnection) with little degradation in inter-process communication performance.
Also the fault tolerant redirection scheme provides a minimal slowdown, especially when
the number of faulty I/O nodes is less than half of the initial available I/O nodes.
43
Yuyama, Tetsumori. "An Energy Limit of Hot Electrons in a Bumpy Torus." 京都大学 (Kyoto University), 2000. http://hdl.handle.net/2433/151679.
Full text
44
Figueroa, Salgado Pablo Salvador. "Construction of Solutions to Liouville Type Equations on The Torus." Tesis, Universidad de Chile, 2011. http://www.repositorio.uchile.cl/handle/2250/102683.
Full text
45
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.
Full textAbstract:
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 (2,2n)-torus link complement.
46
Bergmann, Ronny [Verfasser]. "Translationsinvariante Räume multivariater anisotroper Funktionen auf dem Torus / Ronny Bergmann." Aachen : Shaker, 2013. http://d-nb.info/105034264X/34.
Full text
47
Fiedler, Joseph Robert. "On cubic graphs that are edge critical for the torus /." The Ohio State University, 1988. http://rave.ohiolink.edu/etdc/view?acc_num=osu148759205022724.
Full text
48
Ritchey, Katherine. "Computational Topology for Configuration Spaces of Disks in a Torus." The Ohio State University, 2019. http://rave.ohiolink.edu/etdc/view?acc_num=osu1562945889197152.
Full text
49
Segerman, Henry. "Incompressible surfaces in hyperbolic punctured torus bundles are strongly detected /." May be available electronically:, 2007. http://proquest.umi.com/login?COPT=REJTPTU1MTUmSU5UPTAmVkVSPTI=&clientId=12498.
Full text
50
HILTON, DOUGLAS ALAN. "A PARTIALLY COLLISIONAL MODEL OF THE TITAN HYDROGEN TORUS (SATURN)." Diss., The University of Arizona, 1987. http://hdl.handle.net/10150/184064.
Full textAbstract:
A numerical model has been developed for atomic hydrogen densities in the Titan hydrogen torus. The effects of occasional collisions were included in order to accurately simulate physical conditions inferred from the Voyager 1 and 2 Ultraviolet Spectrometer (UVS) results of Broadfoot et al. (1981) and Sandel et al. (1982). The model employed Lagrangian perturbation of orbital elements of hydrogen atoms launched from Titan and Monte-Carlo simulation of collisions and loss mechanisms. The torus is found to be azimuthally symmetric with the density sharply peaked at Titan's orbit, and decreasing rapidly in the outward and perpendicular directions and more gradually inward from 17 to 5 R(s). The energetic hydrogen atoms from Saturn's upper atmosphere, first predicted by Shemansky and Smith (1982), were also investigated. Collisions of these Saturnian atoms with the torus population do not contribute to the torus density, and will lead to a net loss of torus atoms if their launch speeds from Saturn extend above 40 km/sec. The Saturnian atoms produce a corona which was modelled using the theory of Chamberlain (1963). Based on the energetic hydrogen production rate given by Shemansky and Smith (1986), the coronal density at Saturn's exobase is taken to be 200 to 300 cm⁻³, decreasing to 3 or 4 cm⁻³ at 20 R(s). Without the coronal population, the torus model does not reproduce the Voyager 2 UVS Lyman α intensities because the hydrogen atoms are too closely confined toward Titan's orbital plane. The observations can be reproduced by a model that includes the corona and has central plane maxima of 62 cm⁻³ at Titan's orbit and 318 cm⁻³ at Saturn's exobase. The effect of Titan's exospheric temperature (T(E)) on torus structure is seen in the column abundances perpendicular to the central plane at radii of 5 to 15 R(s). Spacecraft observations of these column abundances should allow verification of T(E) to within about 100°K. Similar observations of other species expected to be present in the torus, such as H₂, N, and N₂, would indicate their approximate launch speeds from Titan and thus the relative importance of thermal and non-thermal loss mechanisms.