Made available in DSpace on 2016-12-12T20:15:54Z (GMT). No. of bitstreams: 1 Ricardo.pdf: 234338 bytes, checksum: eaaa6850428d0b0cd2416457f7f85355 (MD5) Previous issue date: 2011-02-25 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior / The gravitational field and wave equations with arbitrary sources that take place in the two-component spinor forrnalisms of Infeld and van der Waerden for General Relativity are already exhibited in the literature. In the present work, we implernent geometric electro¬magnetic sources to derive the expressions for the corresponding right-hand sides of those equations. A notable result that emerges here is the occurrence of source contributions which absorb in one of the formalisms certain electromagnetic durrent densities. / Os formalismos espinoriais de Infeld e van der Waerden são utilizados para descrever a estrutura de curvaturas espaço-temporais da Relatividade Geral. São apresentados os con¬textos métricos dé cada formalismo assim como o comportamento de seus objetos básicos sob transformações de calibre de Weyl. O desdobramento de curvaturas em partes pura¬mente gravitacionais e puramente eletromagnéticas como dadas originalmente por Infeld e van der Waerden é exibido. Os espinores de curvatura e suas propriedades são então onsiderados. Com base na implementação de um conjunto de comutadores covariantes livres de torção obtemos inicialmerite o conjunto de equações de onda para grávitons com fontes generalizadas que é bem conhecido na literatura. Tais equações de onda gravita¬cionais são subsequentemente particularizadas para a situação que envolve a presença de fontes eletromagnéticas geométricas. Um resultado notável obtido aqui é que as fontes em um dos formalismos absorvem certas densidades de corrente eletromagnética.

Made available in DSpace on 2016-12-12T20:15:54Z (GMT). No. of bitstreams: 1 Andre M Kuerten.pdf: 196303 bytes, checksum: 95e9ad77910399de6a84c183679a6b21 (MD5) Previous issue date: 2011-03-01 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior / The electromagnetic wave equations that occur in the two-component spinor formalisms of Infeld and van der Waerden for General Relativity are considered. Use is made of certain geometric current densities that emerge naturally within the context of one of the formalisms to show that the respective wave functions are null entities. / Este trabalho tem como um dos objetivos centrais considerar as equações de onda eletromagnéticas que estão envolvidas nas estruturas de curvatura dos formalismos espinoriais de Infeld e van der Waerden para a Relatividade Geral. Equações de onda para fótons com fontes que portam um caráter geométrico emergem no contexto de um dos formalismos e desempenham o papel principal aqui. Tais fontes foram condicionadas à equação da continuidade e deste modo se examinou o efeito produzido por elas no formato das equações de onda. O principal resultado obtido aqui é que as funções de onda correspondentes são espinores nulos.

Nesse trabalho apresentamos o estudo do artigo [25] que analisa a existência de atratores globais para uma classe de equações da onda amortecida da forma \'épsilon u IND. tt\' + \'alpha\' (x) u IND. t\' + \'BETA\' (x)u - \'\\SIGMA SOBRE i, j\' \'\\PARTIAL ind. I\' (\'a IND. i j\' (x) \'PARTIAL IND. j u\') = f(x, u) , x PERTENCE A ÔMEGA\'\', t \'PERTENCE A\' [0,\'infinito\'), u (x, t) = 0, x \'PERTENCE A\' \'\\PARTIAL ÔMEGA\', t \'PERTENCE A\' [0, \'infinito\') definidas em um domínio arbitrário \'ÔMEGA\' / In this work we describe the results of the paper [25]. In [25] the authors prove existence of global attractors for the following semilinear damped wave equation \'\\épsilon u IND. t\'t + \'alpha\'(x)u IND. t\' + \'beta\' (x)u - \'\\SIGMA SOBRE i, j \'\\PARTIAL IND. i\' (\'a IND. i j\' (x) \'\\PARTIAL IND. j u\') = f (x, u), x \'IT BELONGS\' \'ÔMEGA\', t \'IT BELONGS\' [0, \'INFINITY\'), u(x,t), x \'IT BELONGS\' \'\\PARTIAL ÔMEGA\', t \'IT BELONGS\' [), \'INFINITY\'0 on an arbitrary domain \'OMEGA\'

Neste trabalho é estudada a equação de Dirac com uma superposição do campo de Aharonov-Bohm (AB) e de um campo magnético colinear uniforme, que nós chamamos de campo magneto-solenoidal (MS). Usando a teoria de von Neumann das extensões auto-adjuntas de operadores simétricos, nós construímos no caso de 2+ 1 dimensões uma família uni paramétrica de hamiltonianos de Dirac auto-adjuntos especificados pelas condições de contorno no solenóide AB, e encontramos o espectro e as auto-funções para cada valor do parâmetro de extensão. Em seguida, reduzimos o problema em 3+ 1 dimensões ao problema em 2+ 1 dimensões pela escolha apropriada do operador de spin, o que permite realizar todo o programa de construção de extensões auto-adjuntas, e assim, também permite obter os espectros e auto-funções em termos do problema em 2+1 dimensões. Ademais, nós apresentamos o método reduzido de extensões auto-adjuntas do hamiltoniano radial de Dirac com o campo MS. Depois nós consideramos o caso regularizado do solenóide de raio finito. Nós estudamos a estrutura das autofunções e a sua dependência com o comportamento do campo magnético dentro do solenóide. Considerando o limite de raio zero para o valor fixo do fl.mm magnético, nós obtemos um hamiltoniano auto-adjunto particular que corresponde à condição de contorno específica para o caso do campo magneto-solenoidal com o solenóide AB. Nós chamamos estes casos particulares das extensões auto-adjuntas extensões naturais. Para completeza da investigação nós estudamos também o comportamento de uma partícula sem spin no campo magneto-solenoidal regularizado. A etapa seguinte da investigação é a construção das funções de Green da equação de Dirac com o campo MS em 2 + 1 e 3 + 1 dimensões. As funções de Green são construídas por meio de um somatório sobre o conjunto completo das soluções da equação de Dirac. Ao construir as funções de Green, nós usamos as soluções exatas da equação de Dirac, que são relacionadas a valores específicos do parâmetro de extensão. Estes valores correspondem às extensões naturais. Depois nós estendemos os resultados ao caso em 3 + 1 dimensões. Nós apresentamos também as funções de Green não relativísticas e as funções de Green de uma partícula relativística escalar. / ln the present work the Dirac equation with the supereposition of the Aharonov-Bohm (AB) field and a collinear uniform magnetic field, which we call a magnetic-solenoid (MS) field, is studied. Using von Neumann\'s theory of the self-adjoint extensions of symmetric operators, in 2 + 1 dimensions we construct a one-parameter family of self-adjoint Dirac Hamiltonians specified by boundary conditions at the AB solenoid and find the spectrurn and eigenfunctions for each value of the extension parameter. We reduce the (3 + 1)-dimensional. problem to the (2 + 1)-dimensional one by a proper choice of the spin operator, which allows realizing all the programme of constructing self-adjoint extensions and finding spectra and eigenfunctions in the previous tenns. We also present the reduced self-adjoint extension method for the radial Dirac Hamiltonian with the MS field. We then turn to the regularized case of finite-radius solenoid. We study the structure of the corresponding eigenfunctions and their dependence on the behavior of the magnetic field inside the solenoid. Considering the zero-radius limit with the fixed value of the magnetic flux, we obtain a concrete self-adjoint Hamiltonian corresponding to a specific boundary condition for the case of the magnetic-solenoid field \'W-ith the AB solenoid. These particular cases of self-adjoint extensions we call natural extensions. For completeness we also study the behavior of the spinless particle in the regularized magnetic-solenoid field. Successive step of our investigation is a construction of the Green functions of the Dirac equation with the MS field in 2 + 1 and 3 + 1 dimensions. The Green functions are constructed by means of summation over the complete set of solutions of the Dirac equation. Constructing the Green functions, we use the exact solutions of the Dirac equation that are related to the specific values of the extension parameter. These values correspond to the natural extension. Then we extend the results to the (3 + 1)-dimensional case. For the sake of completeness, we present nonrelativistic Green functions and Green functions of the relativistic scalar particle.

No description available.

Thesis (MScEng)--Stellenbosch University, 2014. / ENGLISH ABSTRACT: This research project focuses on sanitary sewer systems. When performing an analysis of a sewer drainage system with known constraints, an appropriate model needs to be chosen depending on the objectives of the analysis. Uncertainties are also present in the analysis of sewer drainage systems. The uncertainties and the errors in hydraulic models need to be understood and considered. The required level of accuracy and the type of hydraulic problem that needs to be solved may alter the complexity of the hydraulic model used to solve a drainage system. The wide variety of available simulation models further complicates model selection. With various models available, selecting the most appropriate model for a particular drainage system simulation is important. The various models for sewer drainage system analysis can be categorised in different ways. For example, it is possible to categorise models according to their purpose, which could be evaluation, design or planning. Evaluation models are mainly used to test whether existing systems or planned systems are adequate and require the highest hydraulic detail. Design models are used to determine the size of conduits within a drainage system and require moderate levels of hydraulic detail. Planning models are primarily used for strategic planning and decision making for urban or regional drainage systems and require the least amount of hydraulic detail. An understanding of the available models is required in order to choose the most suitable simulation model for the desired purpose. Some models are derived from the Saint-Venant equations of flow. The most detailed models are typically referred to as fully dynamic wave models and utilise all the components of the Saint-Venant flow equations. By removing terms from the Saint-Venant equations a kinematic wave model can be created. Some less complex models ignore basic principles of hydraulics in order to make assumptions that simplify the process of simulating flows. In this thesis three different models were compared: a detailed model using fully dynamic flow equations, a simplified model using kinematic wave equations and a basic model using contributor hydrograph routing equations. For the drainage system analysis SWMM-EXTRAN was used as the fully dynamic wave model, SWMM-TRANSPORT was used as the kinematic wave model and SEWSAN was used as the contributor hydrograph model. Two drainage systems situated in South Africa were used as case studies and are referred to as Drainage System A and Drainage System B in this thesis. The actual flow rate was recorded at two points with flow loggers, one in each of the two systems. The flow rate was continually recorded at 1 hour intervals for the period 1 July 2010 to 9 July 2010 in Drainage System A as well as in Drainage System B. The same input parameters were used for each model allowing the modelled flow rates to be compared to the measured flow rates. The models provided peak flow results that were within 2% of the measured peak flow rates and the modelled mean flows were within 8.5% of the measured mean flows in most situations. However, when rapidly varied flows occurred the kinematic wave and contributor hydrograph models returned conservative results as they were unable to account for hydraulic effects such as acceleration. The effect of acceleration became most pronounced up and downstream of drop structures and sections where the slope changed considerably. The kinematic wave and contributor hydrograph models were therefore unable to accurately simulate surcharge conditions. The results suggest that the fully dynamic wave model can be used in all scenarios. The kinematic wave model can be used for a design analysis if no hydraulic structures occur in the system. The contributor hydrograph model should not be used for an evaluation analysis, but can be used for a design analysis if a relatively high level of confidence in the parameter set exists and no areas of rapidly varying flow or hydraulic structures exist within the system. / AFRIKAANSE OPSOMMING: Hierdie navorsing projek is gefokus op riool dreineringsisteme. Wanneer ʼn analise van ʼn riool dreineringsisteem met bekende beperkinge onderneem word, moet ʼn geskikte model gekies word afhangende van die doelwitte van die analise. Onbekendes is ook teenwoordig in die analise van riool dreineringsisteme. Dit word belangrik dat die onsekerhede en die foute in hidroliese modelle moet verstaan en oorweeg word. Die verwagte vlak van akkuraatheid en die tipe hidroliese probleem wat opgelos moet word mag die ingewikkeldheid van die hidroliese probleem, wat gebruik word om ʼn rioolsisteem op te los, verander. Die wye verskeidenheid van beskikbare simulasie modelle bemoeilik verder die keuse van ʼn model. Met etlike modelle beskikbaar vir seleksie, is die mees geskikte model vir ʼn spesifieke dreineringsisteem simulasie belangrik. Die verskeie modelle vir riool dreineringsisteem analise kan op verskillende wyses gekategoriseer word. Byvoorbeeld, dit is moontlik om modelle te kategoriseer volgens hulle doel, wat evaluasie, ontwerp en beplanning kan wees. Evaluasiemodelle word hoofsaaklik gebruik om te toets of huidige of beplande sisteme voldoende is en of hulle die hoogs moontlike hidroliese besonderhede benodig. Ontwerpmodelle word gebruik om die grootte van ʼn leipyp binne ʼn rioolsisteem te bepaal en benodig matige vlakke van hidroliese besonderhede. Beplanningsmodelle word hoofsaaklik gebruik vir strategiese beplanning en besluitneming vir stedelike en landelike rioolsisteme en benodig die laagste vlak van hidroliese data. ʼn Begrip van die beskikbare modelle is nodig om ʼn keuse te maak rakende die mees geskikte simulasie model vir die verlangde doelwit. Sommige modelle is afkomstig van die Saint-Venant vergelykings van vloei. Die mees gedetailleerde modelle word tipies na verwys as die volledige dinamiese golf modelle en benut alle komponente van die Saint-Venant vloei vergelykings. Deur die verwydering van terme van die Saint-Venant vergelykings kan ʼn kinematiese golf model daargestel word. Sommige minder gekompliseerde modelle ignoreer die basiese beginsels van hidrologie om aannames te maak wat die proses van golf simulering vereenvoudig. In hierdie tesis is drie verskillende modelle vergelyk; ʼn gedetailleerde model wat volledige dinamiese vloeivergelykings gebruik; ʼn vereenvoudigde model wat kinematiese golfvergelykings gebruik en ʼn basiese model wat bydraende hidroliese versending vergelykings. Vir die dreineringsisteem analise was SWMM-EXTRAN gebruik as die volledige dinamiese golfmodel, SWMM-TRANSPORT was gebruik as die kinetiese golfmodel en SEWSAN was gebruik as die bydraende hidroliese model. Twee dreineringsisteme in Suid-Afrika was gebruik as gevallestudies en word na verwys as Dreineringsisteem A en Dreineringsisteem B. Die werklike vloeikoers was aangeteken by twee punte met vloeimeters, een in elk van die sisteme. Die vloeikoers was deurlopend opgeteken met 1 uur tussenposes vir die periode 1 Julie 2010 tot 9 Julie 2010 in Dreinering Sisteem A sowel as Dreinering Sisteem B. Dieselfde inset parameters was gebruik vir elke model wat dit moontlik gemaak het dat die gemoduleerde vloeikoerse met die gemete vloeikoerse vergelyk kon word. Die modelle het spits vloeiresultate voorsien wat binne 2% van die gemete spits vloeikoerse was en, in die meeste situasies, dat die gemoduleerde gemiddelde vloei binne 8.5% van die gemete gemiddelde vloei was. Wanneer vinnig varierende vloei voorgekom het, die kinetiese golf and bydraende hidrograaf modelle konserwatiewe resultate gelewer het, aangesien hulle nie in staat was om hidroliese effekte soos versnelling te verklaar nie. Die effek van versnelling was op sy duidelikste stroomopwaarts en stroomafwaarts onder valstrukture en by gedeeltes waar die helling aansienlik verander het. Die kinetiese golf en bydraer hidrograaf modelle was gevolglik nie in staat om oorladingsomstandighede akkuraat te simuleer nie. Die resultate wys dat die volledige dinamiese vloeimiddel gebruik kan word in alle omstandighede. Die kinematiese vloeimiddel kan gebruik word vir ʼn ontwerp analise indien geen hidroliese struktuur in die sisteem voorkom nie. Die bydraer hidrograaf model behoort nie gebruik te word vir ʼn evaluerings analise nie, maar kan gebruik word vir ʼn ontwerp analise indien ʼn relatiewe hoë vlak van vertroue in die parameter stel bestaan en geen area van vinnig veranderende vloei of hidroliese strukture binne die sisteem bestaan nie.

In this study, the mapped Galerkin method was applied to solve the vector wave equation based on H&amp / #8722 / field and to obtain the propagation constant in x &amp / #8722 / y space. The vector wave equation was solved by the transformation of the infinite x &amp / #8722 / y plane onto a unit square. Two-dimensional Fourier series expansions were used in the solutions. Modal fields and propagation constants of dielectric waveguides were calculated. In the first part of the study, all of the calculations were made in step index fibers. Transverse magnetic fields were obtained in the u &amp / #8722 / v and x &amp / #8722 / y space through the solution of the matrix eigenvalue equation. Some graphics were plotted in the light of the results obtained. The results are found to be in accord with the results of other numerical techniques and exact solutions. After that, the propagation constant in x&amp / #8722 / y space was calculated with ease using the solution of the modal field components. In the second part of the study, the similar calculations were made in graded index fibers.

Analytical solutions for the linear and nonlinear shallow-water wave equations are developed for evolution and runup of tsunamis &ndash / long waves&ndash / over one- and two-dimensional bathymetries. In one-dimensional case, the nonlinear equations are solved for a plane beach using the hodograph transformation with eigenfunction expansion or integral transform methods under different initial conditions, i.e., earthquake-generated waves, wind set-down relaxation, and landslide-generated waves. In two-dimensional case, the linear shallow-water wave equation is solved for a flat ocean bottom for initial waves having finite-crest length. Analytical verification of source focusing is presented. The role of focusing in unexpectedly high tsunami runup observations for the 17 July 1998 Papua New Guinea and 17 July 2006 Java Island, Indonesia tsunamis are investigated. Analytical models developed here can serve as benchmark solutions for numerical studies.

Thesis (Ph.D.)--Ohio State University, 2005. / Title from first page of PDF file. Document formatted into pages; contains ix, 176 p.; also includes graphics. Includes bibliographical references (p. 172-176). Available online via OhioLINK's ETD Center

Made available in DSpace on 2016-12-12T20:15:51Z (GMT). No. of bitstreams: 1 Samuel.pdf: 168206 bytes, checksum: 40d95c0a09ac92adcf9bcbad607d64e9 (MD5) Previous issue date: 2015-02-23 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior / The world formulation of the full theory of classical Proca .elds in generally relativistic spacetimes is reviewed. Subsequently the entire set of .eld equations is transcribed in a straightforward way into the framework of one of the Infeld-van der Waerden formalisms. Some well-known calculational techniques are then utilized for deriving the wave equations that control the propagation of the .elds allowed for. It appears that no interaction couplings between such .elds and electromagnetic curvatures are ultimately carried by the wave equations at issue. What results is, in e¤ect, that the only interactions which occur in the theoretical context under consideration involve strictly Proca .elds and wave functions for grávitons. / A teoria de campos clássicos de Proca em espaços-tempo curvos sem torção é apresentada. Em particular, deduzir-se-á a equação de onda covariante mundo para um potencial de Proca. Uma versão da teoria em termos de espinores de duas componentes é subsequentemente exibida levando-se a cabo uma transcrição direta para o contexto de um dos formalismos espinoriais de Infeld e van der Waerden. Algumas técnicas calculacionais bem conhecidas serão subsequentemente utilizadas para derivar as equações de onda que controlam a propagação dos campos. Estes procedimentos sugerem que nas equações de onda resultantes não ocorre interação entre os campos externos e curvaturas eletromagnéticas. O que resulta é, com efeito, que a única interação que ocorre nesse contexto teórico envolve estritamente os campos de Proca e funções de onda para grávitons.