<p>The subject of this work is the theoretical analysis of the mean-field and many-body properties of an impurity in a Bose-Einstein condensate in a double well potential. By investigating the stationary mean-field properties we show that a critical value of the boson-impurity interaction energy, W_c, corresponds to a pitchfork bifurcation in the number difference variable in the mean-field theory. Comparing W_c to the value of W where the many-body ground state wave function begins to split shows a direct correlation signaling a connection between the many-body and mean-field theories. Investigation of the mean-field dynamics shows that chaos emerges for W > W_c in the vicinity of an unstable equilibrium point generated by the pitchfork bifurcation. An entropy is defined to quantify the chaos and compared to the entanglement entropy between the BEC and the impurity. The mean-field entropy shows a large gradient at W_c whereas the entanglement entropy shows no apparent features around the same value of W. An increase in correlations between nearest neighbour many-body eigenvalues is seen as W is increased providing evidence for ``quantum chaos''.</p> / Master of Science (MSc)

Det här projektet har varit på uppdrag av Kalmar Energi AB och har utförts på kraftvärmeanläggningen Moskogen. Projektet syftade till att undersöka om återvinning av rökgaskondensat till spädvatten var möjlig och ekonomiskt försvarbart. Denna åtgärd skulle potentiellt kunna minska anläggningens råvattenkonsumtion och det skulle leda till en ekonomisk besparing. Åtgärden skulle även bidra till att anläggningen blev mer självförsörjande och mindre känslig vid störningar på det lokala råvattennätet. Mätningar av flöden på rökgaskondensatsproduktionen, halter av föroreningar och råvattenkonsumtionen gav viktiga parametrar för kontakt med leverantör av reningssystem. Samarbete upprättades med Eurowater AB där två olika reningsanläggningar togs fram och delgavs Kalmar Energi AB. Kostnaden för de två olika förslagen och respektive råvattenbesparing gav två avskrivningstider för investeringarna. Slutsatsen som drogs av projektet var att en installation av en reningsanläggning för återvinning av rökgaskondensatet var möjlig. / This project has been commissioned by Kalmar Energi AB and has been carried out at the CHP plant Moskogen. The project aimed to investigate whether recycling of flue gas condensate was possible and economically justifiable. This measure could potentially reduce the plant´s raw water consumption and would result in economic savings. The measure would also help the plant become more self-sufficient and less sensitive to disturbances on the local raw water distribution net.  Measurements of the flow of flue gas condensate, levels of pollution and raw water consumption gave important parameters for contact with the purification supplier. We entered a collaboration with Eurowater AB where two different purification plants were presented to Kalmar Energi AB. The cost of the two different proposals and their respective raw water savings gave two different payback periods in which the initial investment would be recouped by the client. The conclusion drawn from the project is that the installation of a purification plant for recycling of flue gas condensate was possible.

The master thesis deals with the design, tracing and dimensioning of condensate pipeline. In the beginning, a preliminary calculation of heat balance is done. It is followed by a description of the main condensate system supplemented by the computational design of pipeline and the calculation of pressure losses in this pipeline. The crucial part of the thesis is the calculation of pressure losses, which is done in two ways. The first approach to calculation of pressure losses in the pipeline is calculated using values of representative resistance coefficient for pipe ele-ments using Idelchik literature and for individual types of valves using values from datasheets of Siemens Energy suppliers. In the second approach to calculation representative resistance coefficients for pipe elements and individual types of valves CRANE literature are used. Then both approaches of choosing representative resistance coefficients are compared and evaluated. Based on the calculated values, a suitable pump is selected at the end of the master thesis.

[pt] Campos de petróleo com gás não associado do tipo gás condensado possuem destaque pelo maior valor econômico agregado associado a seu recurso energético: a expressiva quantidade de condensado produzida, além do próprio gás. Porém, tais reservatórios possuem um comportamento termodinâmico particular, induzindo mudanças de composição e, consequentemente, fase ao longo do processo de produção por depleção. Nas condições de reservatório, por exemplo, pode ocorrer o fenômeno chamado de condensate blockage, em que bancos de condensado se formam, geralmente em regiões próximas aos poços, dificultando assim o escoamento e afetando a produção de gás. A fim de definirmos a melhor estratégia de gerenciamento de um projeto a ser implementado ao longo da explotação desse tipo de reservatório, uma ferramenta importante utilizada pelos engenheiros é a simulação numérica. Especialmente relacionadas à representação do fenômeno físico-químico citado, nas simulações se utilizam as curvas de permeabilidade relativa. Na realidade, porém, existe uma certa limitação de representatividade do fenômeno nos ensaios laboratoriais praticados pela indústria e os melhores insumos poderiam ser fornecidos por simulações em rede de poros, com modelos que representem a sua alteração com função das mudanças na tensão interfacial e na velocidade de escoamento ao longo do reservatório. A reprodução de uma simulação de escoamento em rede de poros para a escala mais próxima possível em uma simulação de simulador comercial de diferenças finitas é validada. Da simulação em rede de poros até a escala de campo praticada nas simulações de reservatórios, uma metodologia de scale-up é proposta, utilizando um processo de otimização, procurando ser fiel à curva de permeabilidade relativa original, em escala de microporo, obtida simulando fenomenologicamente o processo de condensação no reservatório, através de um modelo que reproduza sua dependência com a velocidade desenvolvida pelas fases em meio poroso. A comparação de produtividades na escala de campo e na evolução da saturação de condensado em regiões próximas aos poços foi apresentada para as três curvas de permeabilidade relativa utilizadas. Os resultados mostram que a metodologia proposta consegue ser mais fiel à influência da condensação no reservatório sobre a produtividade dos poços quando comparada ao insumo de curva de permeabilidade relativa de ensaio laboratorial que apresenta o condensado mais móvel. / [en] Oil fields with non-associated gas like gas condensate type stand out due to the higher added economic value associated with their energy resource: the significant amount of condensate produced, in addition to the gas itself. However, such reservoirs have a particular thermodynamic behavior, inducing changes in composition and, consequently, phase throughout the depletion production process. Under reservoir conditions, for example, the phenomenon called condensate blockage may occur, in which bridges of condensate are formed, usually in regions close to the wells, thus hindering flow and affecting gas production. In order to define the best management strategy for a project to be implemented throughout the exploitation of this type of reservoir, an important tool used by engineers is numerical simulation. The relative permeability curves are used in the simulations, especially related to the representation of the mentioned physical phenomenon. In reality, however, there is a specific limitation of representativeness of the phenomenon in the laboratory tests carried out by the industry, and the best inputs could be provided by simulations in a pore network, with models that represent its alteration as a function of changes in interfacial tension and flow velocity along the reservoir. The reproduction of a pore network flow simulation to the closest possible scale in a commercial finite difference simulation is validated. From the pore network simulation to the field scale practiced in reservoir simulations, a scale-up methodology is proposed, using an optimization process, seeking to be faithful to the original relative permeability curve, on a microporous scale, obtained by simulating phenomenologically the condensation process in the reservoir, using a model that reproduces its dependence on the velocity flow developed by the phases in a porous medium. The three relative permeability curves used were presented by comparing productivities at the field scale and the evolution of condensate saturation in regions close to the wells. The results show that the proposed methodology proves to be more faithful to the influence of condensation in the reservoir on the productivity of the wells when compared to the relative permeability curve input from the laboratory test, which presents the condensate with more mobility.

Grootvlei Power Station’s thermal efficiency had been on a steady declining trend since it was re-commissioned in 2008, which had tremendous financial implications to the company at the time of writing. The main contributory factor to the thermal efficiency losses was identified to be the condenser backpressure losses that the station was experiencing. This loss was responsible for approximately 17% of the total efficiency losses. Therefore an investigation was conducted to determine the potential impact of the condenser backpressure loss on the thermal efficiency and the financial implications thereof. The deliverables were to determine the cause of the condenser backpressure loss and propose possible resolutions, to quantify the financial effect and to produce a cost benefit analysis in order to justify certain corrective actions. Grootvlei Power Station is one of the older power stations in South Africa and it was used as the first testing facility for dry-cooling in South Africa. It consists of six 200MW units, two of which are dry-cooled units. In 1990 it was mothballed and due to rising power demands in South Africa, it was re-commissioned in 2008. Thermal efficiency has been playing a great role due to the power constraints and therefore it was deemed necessary to conduct this study. The approach that was used was one of experimental and quantitative research and analyses, incorporating deductive reasoning in order to test various hypotheses of factors that could have been contributing to the backpressure losses. In order to do so, a logic diagram was designed which could be used to aid in the identification of possible causes of the condenser backpressure losses. The logic diagram was able to identify whether the problem had to do with the cooling tower or the condenser. It was able to identify which area on the condenser was defective i.e. whether the pumps were not performing, or whether the air ejectors were not performing. It was also able to indicate whether the inefficiency was due to air ingress or fouling. Alongside the logic diagram, a condenser efficiency analysis was used in order to strengthen and improve on the investigation. This analysis was able to identify whether the condenser was experiencing fouling conditions, air ingress, passing valves or low cooling water flow. After the investigation commenced, it was decided to focus on the two largest contributing units since the largest contributor was a dry-cooled unit and the second largest contributor was a wet-cooled unit, thus some comparison between the units was incorporated. The condenser efficiency analysis on Unit 3 (wet-cooled unit) indicated a low cooling water flow, fouling as well as air ingress. The logic diagram indicated poor cooling tower performance, high air ingress as well as fouling. Further tests and analyses as well as visual inspections confirmed these phenomena and condenser fouling was identified to be the largest contributor to the backpressure loss on this unit. The condenser efficiency analysis on Unit 6 indicated that air was entering the condenser. The logic diagram indicated that a segment of the backpressure loss was due to poor cooling tower performance. Inspection of the cooling tower indicated damage and leaks. A cooling tower performance test was conducted and the result of the test indicated that the tower was in need of cleaning. Further analyses according to the logic diagram indicated that the condenser was experiencing air ingress which concurred with the condenser efficiency analysis. A helium test, condensate extraction pump pressure test as well as a flood test was conducted on this unit and various air in-leakage points were identified. The financial implications of the backpressure losses were investigated and found to be costing millions each month. The condenser backpressure loss was contributing more than 2% to the thermal efficiency loss. The cost benefit analysis indicated that the cost of cleaning the condenser on Unit 3 would be made up within six months and a return on investment of 16,6% was calculated. The cost benefit analysis motivates for extended outage times for the purpose of cleaning the condensers from a financial perspective. Therefore, it was recommended to clean the condenser on Unit 3 and fix all known defects on the unit as well as on Unit 6. The cooling towers were recommended to be refurbished. Further investigation was recommended to determine the feasibility of installing an online cleaning system on the wet-cooled units’ condensers such as a Taprogge system. Alternative investigation methods were suggested such as smoke stick analyses for air ingress determination. It was also recommended to review the maintenance strategies that were being used since many of the defects were found to be maintenance related. If the identified problem areas are attended to, the condenser backpressure loss will decrease and the condensers transfer heat more efficiently which will lead to financial gains for Grootvlei Power Station as well as efficiency gains, plant reliability and availability gains. / MIng (Development and Management Engineering), North-West University, Potchefstroom Campus, 2015

Grootvlei Power Station’s thermal efficiency had been on a steady declining trend since it was re-commissioned in 2008, which had tremendous financial implications to the company at the time of writing. The main contributory factor to the thermal efficiency losses was identified to be the condenser backpressure losses that the station was experiencing. This loss was responsible for approximately 17% of the total efficiency losses. Therefore an investigation was conducted to determine the potential impact of the condenser backpressure loss on the thermal efficiency and the financial implications thereof. The deliverables were to determine the cause of the condenser backpressure loss and propose possible resolutions, to quantify the financial effect and to produce a cost benefit analysis in order to justify certain corrective actions. Grootvlei Power Station is one of the older power stations in South Africa and it was used as the first testing facility for dry-cooling in South Africa. It consists of six 200MW units, two of which are dry-cooled units. In 1990 it was mothballed and due to rising power demands in South Africa, it was re-commissioned in 2008. Thermal efficiency has been playing a great role due to the power constraints and therefore it was deemed necessary to conduct this study. The approach that was used was one of experimental and quantitative research and analyses, incorporating deductive reasoning in order to test various hypotheses of factors that could have been contributing to the backpressure losses. In order to do so, a logic diagram was designed which could be used to aid in the identification of possible causes of the condenser backpressure losses. The logic diagram was able to identify whether the problem had to do with the cooling tower or the condenser. It was able to identify which area on the condenser was defective i.e. whether the pumps were not performing, or whether the air ejectors were not performing. It was also able to indicate whether the inefficiency was due to air ingress or fouling. Alongside the logic diagram, a condenser efficiency analysis was used in order to strengthen and improve on the investigation. This analysis was able to identify whether the condenser was experiencing fouling conditions, air ingress, passing valves or low cooling water flow. After the investigation commenced, it was decided to focus on the two largest contributing units since the largest contributor was a dry-cooled unit and the second largest contributor was a wet-cooled unit, thus some comparison between the units was incorporated. The condenser efficiency analysis on Unit 3 (wet-cooled unit) indicated a low cooling water flow, fouling as well as air ingress. The logic diagram indicated poor cooling tower performance, high air ingress as well as fouling. Further tests and analyses as well as visual inspections confirmed these phenomena and condenser fouling was identified to be the largest contributor to the backpressure loss on this unit. The condenser efficiency analysis on Unit 6 indicated that air was entering the condenser. The logic diagram indicated that a segment of the backpressure loss was due to poor cooling tower performance. Inspection of the cooling tower indicated damage and leaks. A cooling tower performance test was conducted and the result of the test indicated that the tower was in need of cleaning. Further analyses according to the logic diagram indicated that the condenser was experiencing air ingress which concurred with the condenser efficiency analysis. A helium test, condensate extraction pump pressure test as well as a flood test was conducted on this unit and various air in-leakage points were identified. The financial implications of the backpressure losses were investigated and found to be costing millions each month. The condenser backpressure loss was contributing more than 2% to the thermal efficiency loss. The cost benefit analysis indicated that the cost of cleaning the condenser on Unit 3 would be made up within six months and a return on investment of 16,6% was calculated. The cost benefit analysis motivates for extended outage times for the purpose of cleaning the condensers from a financial perspective. Therefore, it was recommended to clean the condenser on Unit 3 and fix all known defects on the unit as well as on Unit 6. The cooling towers were recommended to be refurbished. Further investigation was recommended to determine the feasibility of installing an online cleaning system on the wet-cooled units’ condensers such as a Taprogge system. Alternative investigation methods were suggested such as smoke stick analyses for air ingress determination. It was also recommended to review the maintenance strategies that were being used since many of the defects were found to be maintenance related. If the identified problem areas are attended to, the condenser backpressure loss will decrease and the condensers transfer heat more efficiently which will lead to financial gains for Grootvlei Power Station as well as efficiency gains, plant reliability and availability gains. / MIng (Development and Management Engineering), North-West University, Potchefstroom Campus, 2015

In this thesis we present solutions of spontaneous compactifications of D=11, N=1 supergravity on parallelizable manifolds S^1, S^3 and S^7. In Freund-Rubin compactifications one usually obtains AdS vacua in 4D, these solutions usually sets the fermionic VEV's to zero. However giving them non zero VEV's allows us to define torsion given by the fermionic bilinears that essentially flattens the geometry giving us a vanishing cosmological constant on M_4. We further give an analysis of the consistent truncation of the bosonic sector of D=11 supergravity on a S^3 manifold and relate this to other known consistent truncation compactifications. We also consider the squashed S^7 where we check for surviving supersymmetries by analyzing the generalised holonomy, this compactification is of interest in phenomenology.

Nesta dissertação são estudados Condensados de Bose-Einstein de átomos com pseudo-spin 1/2 cuja dinâmica orbital está acoplada a estes dois níveis de energia internos. A geração de tal sistema é possível induzindo transições entre os subníveis m_f = -1 e m_f = 0 do estado hiperfino atômico f = 1 usando um arranjo de lasers, os quais também introduzem junto uma dependência espacial dada por suas fases, as quais estão relacionadas a posição do átomo no campo, levando assim à interação acoplando spin e órbita. É considerado então um sistema unidimensional efetivo na mesma direção do acoplamento dos lasers, onde são estudado diferentes observáveis do estado fundamental, para uma varredura dos parâmetros presentes na equação, dando origem a três fases diferenciadas pela distribuição do momento. Foram determinadas estas fases do estado fundamental para interação atrativa, sendo elas modulada(striped), onda plana e de momento nulo, mostrando a localização onde cada uma ocorre no domínio de parâmetros da equação, através de diagramas de fase. São também mostrados, separadamente, observáveis relevantes como momento e desbalanço entre os estados internos nestas transições, os quais apresentaram variações bruscas, ditando valores críticos nos parâmetros, onde ocorrem. Posteriormente é estudado a dinâmica através de soluções do tipo sóliton, as quais não se propagam linearmente e são ditadas por oscilações do centro de massa e das populações, explorando diferentes situações iniciais. / In the present dissertation it has been studied Bose-Einstein Condensation of atoms with 1/2 pseudo-spin whose the orbital dynamics is coupled to these two internal energy levels. The generation of such a system is done by inducing transitions between the sub-levels m_f = -1 and m_f = 0 from the hyperfine atomic state f = 1 using an arrangement of lasers, that also introduce a spacial dependence due to their phases, that changes accordingly the atom\'s position in the light field, conducting in this way to a interaction that couples orbital motion with spin. It is then considered an effective one dimensional system in the same direction of the laser coupling, where it has been studied different ground state observables, making a sweeping in the equation parameters, showing three typical phases based on momentum distribution. So far, it was determined these phases for attractive interactions, named striped, plane wave and zero momentum, determining as well the location where each one occurs in the equation\'s parameters through a phase diagram. It is also reported, separately, a few relevant observables as individual momentum of each population and the unbalance between the internal spin states, in the transition among these phases, whose the values present abrupt variations, dictating critical values for the parameters, where it occurs. Lately is presented a dynamical study with soliton like solutions, that do not linearly propagate and instead, shows a center of mass and unbalance oscillation, probing different initial conditions.

In this thesis, we numerically investigate quantum turbulence in trapped atomic Bose-Einstein condensates (BECs). We first discuss the appropriate qualitative characterization of turbulence in these systems, showing the limitation of analogies with classical hydrodynamics and turbulence in large superfluid Helium experiments. Due to their lack of available length scales, our investigated systems can only fit the ultraquantum (or Vinen) type of quantum turbulence. Secondly, we propose experimentally feasible schemes for more controlled investigations of turbulence making use of dynamical instability of multicharged vortices as an onset for complex vortex dynamics. In two dimensions, our suggested scheme allows control over vortex polarization in the harmonically trapped system. This setup is then used to study how turbulence decays in such a scenario, through the phenomenological modeling of a vortex-number rate equation. As a consequence, we were able to identify that vortex annihilation in these trapped systems happens through a four-vortex process. For three dimensions, we have first provided a study on the decay of a quadruply-charged vortex, also in a harmonically trapped BEC. Having this setting as a comparison point, we propose a quasi-isotropic turbulent system, starting from a phase-imprinted initial state of two doubly-charged, anti-parallel vortices. The vortex turbulence arisen from such configuration was shown to agree with the Vinen turbulent regime, after we characterized specific features of its decay, such as the energy spectrum [E(k) &#8764; k1] and the time evolution of the vortex-line density [L(t) &#8764; t1]. Although these features have been frequently verified in the context of superfluid Helium turbulence, here this identification was for the first time done for realistic, trapped atomic BECs. / Nesta tese, investigamos numericamente a turbulência quântica em condensados de Bose- Einstein (BECs) aprisionados. Discutimos, inicialmente, a caracterização qualitativa apropriada para estes sistemas, mostrando a limitação de analogias tipicamente feitas com hidrodinâmica clássica e turbulência em grandes sistemas com Hélio superfluido. Devido às suas limitadas escalas espaciais, os sistemas investigados somente podem exibir o tipo de turbulência conhecida como ultra-quântica (ou de Vinen). Em seguida, propomos sistemas experimentalmente factíveis que permitem investigações mais controladas da turbulência, fazendo uso da instabilidade dinâmica de vórtices multi-carregados como ponto de partida para geração de dinâmicas complexas. Em duas dimensões, nossa proposta permite controle sobre a polarização de vórtices em sistemas aprisionados em potencial harmônico. Este arranjo é então utilizado no estudo do decaimento da turbulência nesse contexto, através de um modelo fenomenológico para equação que descreve a taxa de variação do número de vórtices. Como consequência, pudemos verificar que a aniquilação de vórtices dá-se através de um processo que envolve quatro vórtices. Em três dimensões, apresentamos um estudo do decaimento de um vórtice de carga topológica quatro, também em potencial harmônico. Mantendo em mente esse sistema a título de comparação, propomos um cenário turbulento, quase-isotrópico, partindo de um estado inicial formado por dois vórtices duplamente carregados, mas orientados anti-paralelamente. Verificamos que a turbulência decorrente desse arranjo coincide com a regime de Vinen analisando características do seu decaimento, especificamente obtendo o espectro de energia [E(k) &#8764; k1] e evolução temporal da densidade de linhas de vórtices [L(t) &#8764; t1]. Apesar de que essas características são comumente encontradas no contexto de Hélio superfluido, apresentamos pela primeira vez essa identificação no cenário realístico de BEC aprisionados.

Nesta dissertação são estudados Condensados de Bose-Einstein de átomos com pseudo-spin 1/2 cuja dinâmica orbital está acoplada a estes dois níveis de energia internos. A geração de tal sistema é possível induzindo transições entre os subníveis m_f = -1 e m_f = 0 do estado hiperfino atômico f = 1 usando um arranjo de lasers, os quais também introduzem junto uma dependência espacial dada por suas fases, as quais estão relacionadas a posição do átomo no campo, levando assim à interação acoplando spin e órbita. É considerado então um sistema unidimensional efetivo na mesma direção do acoplamento dos lasers, onde são estudado diferentes observáveis do estado fundamental, para uma varredura dos parâmetros presentes na equação, dando origem a três fases diferenciadas pela distribuição do momento. Foram determinadas estas fases do estado fundamental para interação atrativa, sendo elas modulada(striped), onda plana e de momento nulo, mostrando a localização onde cada uma ocorre no domínio de parâmetros da equação, através de diagramas de fase. São também mostrados, separadamente, observáveis relevantes como momento e desbalanço entre os estados internos nestas transições, os quais apresentaram variações bruscas, ditando valores críticos nos parâmetros, onde ocorrem. Posteriormente é estudado a dinâmica através de soluções do tipo sóliton, as quais não se propagam linearmente e são ditadas por oscilações do centro de massa e das populações, explorando diferentes situações iniciais. / In the present dissertation it has been studied Bose-Einstein Condensation of atoms with 1/2 pseudo-spin whose the orbital dynamics is coupled to these two internal energy levels. The generation of such a system is done by inducing transitions between the sub-levels m_f = -1 and m_f = 0 from the hyperfine atomic state f = 1 using an arrangement of lasers, that also introduce a spacial dependence due to their phases, that changes accordingly the atom\'s position in the light field, conducting in this way to a interaction that couples orbital motion with spin. It is then considered an effective one dimensional system in the same direction of the laser coupling, where it has been studied different ground state observables, making a sweeping in the equation parameters, showing three typical phases based on momentum distribution. So far, it was determined these phases for attractive interactions, named striped, plane wave and zero momentum, determining as well the location where each one occurs in the equation\'s parameters through a phase diagram. It is also reported, separately, a few relevant observables as individual momentum of each population and the unbalance between the internal spin states, in the transition among these phases, whose the values present abrupt variations, dictating critical values for the parameters, where it occurs. Lately is presented a dynamical study with soliton like solutions, that do not linearly propagate and instead, shows a center of mass and unbalance oscillation, probing different initial conditions.