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Thesis (PhD)--Stellenbosch University, 2012. / ENGLISH ABSTRACT: Gasification provides a proven alternative to the dependence on petroleum for the production of high value products such as liquid fuels and chemicals. Syngas, the main product from gasification can be converted to fuels and chemicals via a number of possible synthesis processes. Coal and natural gas are currently the main feedstock used for syngas production. In South Africa (SA), Sasol operates the largest commercial coal-to-liquids conversion process in the world, based on updraft fixed bed gasification of low grade coal to syngas. Co-utilizing alternative and more sustainable feedstock (such as biomass and wastes) with coal in existing coal-based plants offers a realistic approach to reducing the costs and risks associated with setting up dedicated biomass conversion plants. An experimental and modelling investigation was performed to assess the impacts of co-gasifying two of the most commonly available agricultural wastes in SA (sugarcane bagasse and corn residue) with typical low grade SA coals, on the main products of updraft fixed bed gasification, i.e. liquid condensates and syngas. Condensates are produced in the pyrolysis section of the updraft gasifier, whereas syngas is a result of residual char conversion. An experimental set-up that simulates the pyrolysis section of the gasifier was employed to investigate the yield and composition of devolatilized products at industrially relevant conditions of 26 bars and 400-600°C. The results show that about 15 wt% of coal and 70 wt% of biomass are devolatilized during the pyrolysis process. The biomass derived condensates were determined to comprise of significantly higher quantities of oxygenates such as organic acids, phenols, ketones, and alcohols, whereas coal derived hydrocarbon condensates were dominated by polycyclic aromatic hydrocarbons, creosotes and phenols. Results of investigation into the influence of coal-biomass feedstock mix ratio on yields of products from pyrolysis show limited evidence of non-additive or synergistic behaviour on the overall distribution of solid, liquid and gas yields. On the other hand, in terms of the distribution of specific liquid phase hydrocarbons, there was significant evidence in favour of non-additive pyrolysis behaviour, as indicated by the non-additive yield distribution of specific chemicals. Synergistic trends could also be observed in the thermogravimetric (TGA) study of pyrolysis under kinetically controlled non-isothermal conditions. Model free and model fitting kinetic analysis of the TGA data revealed activation energies ranging between 94-212 kJ mol-1 for the biomass fuels and 147-377 kJ mol-1 for coal. Synergistic interactions may be linked to the increased presence of hydrogen in biomass fuels which partially saturates free radicals formed during earlier stages of devolatilization, thereby preventing secondary recombination reactions that would have produced chars, allowing for the increased formation of volatile species instead. Analysis of char obtained from the co-pyrolysis experiments revealed that the fixed carbon and volatile content of the blended chars is is proportional to the percentage of biomass and coal in the mixture. CO2 reactivity experiments on the chars showed that the addition of biomass to coal did not impose any kinetic limitation on the gasification of blended chars. The blended chars decomposed at approximately the same rate as when coal was gasified alone, even at higher biomass concentrations in the original feedstock blend. Based on these observations, a semi-empirical equilibrium based simulation of syngas production for co-gasification of coalbiomass blends at various mix ratios was developed using ASPEN Plus. The model showed that H2/CO ratio was relatively unaffected by biomass addition to the coal fuel mix, whereas syngas heating value and thermal efficiency were negatively affected. Subsequent evaluation of the production cost of syngas at biomass inputs ranging between 0-20 wt% of coal reflected the significant additional cost of pretreating biomass (3.3% of total capital investment). This resulted in co-gasification derived syngas production costs of ZAR146/tonne (ZAR12.6/GJ) at 80:20 coalbiomass feedstock ratio, compared to a baseline (coal only) cost of ZAR130/tonne (ZAR10.7/GJ). Sensitivity analysis that varied biomass costs from ZAR0 ZAR470 revealed that syngas production costs from co-gasification remained significantly higher than baseline costs, even at low to zero prices of the biomass feedstock. This remained the case even after taking account of a carbon tax of up to ZAR117/tCO2. However, for range of carbon tax values suggested by the SA treasury (ZAR70 tCO2 to ZAR200 tCO2), the avoided carbon tax due to co-feeding biomass can offset between 40-96% of the specific retrofitting cost at 80:20 coal-biomass feedstock mass ratio. In summary, this dissertation has showed that in addition to the widely recognized problems of ash fouling and sintering, co-feeding of biomass in existing coal based updraft gasification plants poses some challenges in terms of impacts on condensates and syngas quality, and production costs. Further research is required to investigate the potential in ameliorating some of these impacts by developing new high value product streams (such as acetic acid) from the significant fraction of condensates derived from biomass. / AFRIKAANSE OPSOMMING: Vergassing bied 'n beproefde alternatief vir die afhanklikheid van petroleum vir die produksie van hoë waarde produkte soos vloeibare brandstof en chemikalieë. Sintese gas, die belangrikste produk van vergassing, kan omgeskakel word na brandstof en chemikalieë deur 'n aantal moontlike sintese prosesse. Steenkool en aardgas is tans die belangrikste grondstowwe wat gebruik word vir sintese gas produksie. In Suid-Afrika (SA) bedryf Sasol die grootste kommersiële steenkool-totvloeistof omskakelingsproses in die wêreld, gebaseer op stygstroom vastebed vergassing van laegraadse steenkool na sintese gas. Die gebruik van alternatiewe en meer volhoubare grondstowwe (soos biomassa en afval) saam met steenkool in die bestaande steenkool-gebaseerde aanlegte bied 'n realistiese benadering tot die vermindering van die koste en risiko's wat verband hou met die oprigting van toegewyde biomassa omskakelingsaanlegte. 'n Eksperimentele en modelleringsondersoek is uitgevoer om die impak van gesamentlike vergassing van twee van die mees algemeen beskikbare landbouafvalprodukte in Suid-Afrika (suikerriet bagasse en mieliereste) met tipiese laegraadse SA steenkool op die vernaamste produkte van stygstroom vastebed vergassing, dws vloeistof kondensate en sintese gas, te evalueer. Kondensate word geproduseer in die piroliese gedeelte van die stygstroomvergasser, terwyl sintese gas 'n resultaat is van die omskakeling van oorblywende houtskool. 'n Eksperimentele opstelling wat die piroliese gedeelte van die vergasser simuleer is gebruik om die opbrengs en die samestelling van produkte waarvan die vlugtige komponente verwyder is by industrie relevante toestande van 26 bar en 400-600°C te ondersoek. Die resultate toon dat ongeveer 15% (massabasis) van die steenkool en 70% (massabasis) van die biomassa verlore gaan aan vlugtige komponente tydens die piroliese proses. Daar is vasgestel dat die kondensate afkomstig van biomassa uit aansienlik hoër hoeveelhede suurstofryke verbindings soos organiese sure, fenole, ketone, en alkohole bestaan, terwyl koolwaterstofkondensate afkomstig uit steenkool oorwegend bectaan uit polisikliese aromatise verbindings, kreosote en fenole. Die resultate van die ondersoek na die invloed van die verhouding van steenkool tot biomassa grondstof op piroliese opbrengste toon beperkte bewyse van nie-toevoegende of sinergistiese gedrag op die algehele verspreiding van soliede, vloeistof en gas opbrengste. Aan die ander kant, in terme van die verspreiding van spesifieke vloeibare fase koolwaterstowwe, was daar beduidende bewyse ten gunste van 'n sinergistiese piroliese gedrag. Sinergistiese tendense is ook waargeneem in die termogravimetriese (TGA) studie van piroliese onder kineties beheerde nieisotermiese toestande. Modelvrye en modelpassende kinetiese analise van die TGA data het aan die lig gebring dat aktiveringsenergieë wissel tussen 94-212 kJ mol-1 vir biomassa brandstof en 147-377 kJ mol-1 vir steenkool. Ontleding van die houtskool verkry uit die gesamentlike piroliese eksperimente het aan die lig gebring dat die onmiddellike kenmerke van die gemengde houtskool die geweegde gemiddelde van die individuele waardes vir steenkool en biomassa benader. CO2 reaktiwiteitseksperimente op die houtskool het getoon dat die byvoeging van biomassa by steenkool nie enige kinetiese beperking op die vergassing van gemengde houtskool plaas nie. Die gemengde houtskool ontbind teen ongeveer dieselfde tempo as wanneer steenkool alleen vergas is, selfs teen hoër biomassa konsentrasies in die oorspronklike grondstofmengsel. Op grond van hierdie waarnemings is 'n semi-empiriese ewewig-gebaseerde simulasie van sintese gas produksie vir gesamentlike vergassing van steenkool-biomassa-mengsels vir verskeie mengverhoudings ontwikkel met behulp van Aspen Plus. Die model het getoon dat die H2/CO verhouding relatief min geraak is deur biomassa by die steenkool brandstofmengsel te voeg, terwyl sintese gas se verhittingswaarde en termiese doeltreffendheid negatief geraak is. Daaropvolgende evaluering van die produksiekoste van sintese gas vir biomassa insette wat wissel tussen 0-20% (massabasis) van die hoeveelheid steenkool het die aansienlike addisionele koste van die vooraf behandeling van biomassa (3.3% van die totale kapitale belegging) gereflekteer. Dit het gelei tot 'n produksiekoste van ZAR146/ton (ZAR12.6/GJ) vir sintese gas afkomstig uit gesamentlike-vergassing van 'n 80:20 steebkool-biomassa grondstof mengesl, in vergelyking met 'n basislyn (steenkool) koste van ZAR130/ton (ZAR10.7/GJ). Sensitiwiteitsanalise wat biomassa koste van ZAR0 - ZAR470 gevarieër het, het aan die lig gebring dat sintese gas produksiekoste van gesamentlike vergassing aansienlik hoër bly as die basislyn koste, selfs teen 'n lae of nul prys van biomassa grondstof. Dit bly die geval selfs nadat koolstof belasting van tot ZAR117/tCO2 in ag geneem is. In opsomming het hierdie verhandeling getoon dat, bykomend tot die wyd-erkende probleme van as besoedeling en sintering, die gesamentlike gebruik van biomassa in bestaande steenkool stygstroom vergassingsaanlegte groot uitdagings inhou in terme van die impak op die kwaliteit van kondensate en sintese gas, asook produksiekoste. Verdere navorsing is nodig om die potensiaal te ondersoek vir die verbetering van sommige van hierdie impakte deur die ontwikkeling van nuwe hoë waarde produkstrome (soos asynsuur) uit die beduidende breukdeel van kondensate wat verkry word uit biomassa.

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Three problems are investigated in the context of quantum collective dynamics. First, we examine the optomechanics of a Bose-Einstein condensate trapped in an optical ring cavity and coupled to counter-propagating light fields. Virtual dipole transitions cause the light to recoil elastically from the condensate and to excite its atoms into momentum side modes. These momentum side modes produce collective density oscillations. We contrast the situation to a condensate trapped in a Fabry-Perot cavity, where only symmetric ("cosine") side modes are excited. In the ring cavity case, antisymmetric ("sine") modes can be excited also. We explore the mean field limit and find that even when the counter-propagating light fields are symmetrically pumped, there are parameter regions where spontaneous symmetry breaking occurs and the sine mode becomes occupied. In addition, quantum fluctuations are taken into account and shown to be particularly significant for parameter values near bifurcations of the mean field dynamics. The next system studied is a hybrid composed of a high quality micromechanical membrane coupled magnetically to a spinor condensate. This coupling entangles the membrane and the condensate and can produce position superposition states of the membrane. Successive spin measurements of the condensate can put the membrane into an increasingly complicated state. It is possible in principle to produce nonclassical states of the membrane. We also examine a model of weaker, nonprojective measurements of the condensate's spin using phase contrast imaging. We find an upper limit on how quickly such measurements can be made without severely disrupting the unitary dynamics. The third situation analyzed is the string breaking mechanism in ultrahigh energy collisions. When quark-antiquark pairs are produced in a collision, they are believed to be linked by a tube of chromoelectric field flux, the color string. The energy of the string grows linearly with quark separation. This energy is converted into real particles by the Schwinger mechanism. Screening of the color fields by new particles breaks the string. By quantizing excitations of the string using the conjugate coordinates of field strength and string cross-section, we recover the observed exponential spectrum of outgoing particles.

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Neste trabalho de mestrado é estudada a estabilidade de vórtices em condensados de Bose-Einstein com interação atrativa entre os átomos através da solução numérica da equação de Gross-Pitaevskii. Inicialmente são reproduzidos resultados da literatura, nos quais são estudados vórtices em condensados bidimensionais atrativos com potencial interatômico homogêneo em todo o condensado. A estabilidade de tais sistemas é inferida através da solução numérica das equações de Bogoliubov-de Gennes e da evolução temporal dos vórtices. Demonstra-se que esses vórtices são estáveis, até um certo número crítico de átomos, apenas para valores de vorticidade S=1. Em seguida foi proposto um modelo no qual a interação entre os átomos é espacialmente modulada. Neste caso é possível demonstrar que vórtices com valores de vorticidade de até S=6, pelo menos, são estáveis. Finalmente é estudada a estabilidade de vórtices em condensados tridimensionais atrativos, novamente com potencial interatômico homogêneo em todo o condensado. Assim como no caso bidimensional mostra-se que tais vórtices são estáveis para valores de vorticidade de S=1. Espera-se em breve estudar a estabilidade de vórtices em condesados tridimensionais com potencial de interação espacialmente modulado. / In this work we study the stability of vortices in attractive Bose-Einstein condensates by solving numerically the Gross-Pitaevskii equation. Initially we reproduce some results from the literature, in which vortices in two-dimensional attractive Bose-Einstein condensates with homogeneous interatomic potential are studied. The stability of these systems is determined by solving numerically the Bogoliubov-de Gennes equations and by studying the time evolution of these vortices. We demonstrate that these vortices are stable, up to a certain critical number of atoms, just for the value of vorticity S=1. After we propose a model in which the interatomic interaction are spatially modulated. In this case it is possible to verify that vortices with values of vorticity up to S=6 , at least, are stable. Finally, we study the stability of vortices in three-dimensional attractive condensates, again with a homogeneous interatomic potential. As in the two-dimensional case, we show that vortices in these systems are stable to values of vorticity S=1. The next step in this work is study the stability of vortices in three-dimensional condensates with spatially modulated interatomic interaction.

The Schrödinger equations have had a profound impact on a wide range of fields of modern science, including quantum mechanics, superfluidity, geometrical optics, Bose-Einstein condensates, and the analysis of dispersive phenomena in the theory of PDE. The main purpose of this thesis is to explore two Schrödinger-type equations appearing in the so-called Bohmian formulation of quantum mechanics and in the study of exciton-polariton condensates. For the first topic, the linear Schrödinger equation is the starting point in the formulation of a phase-space model proposed in [1] for the Bohmian interpretation of quantum mechanics. We analyze this model, a nonlinear Vlasov-type equation, as a Hamiltonian system defined on an appropriate Poisson manifold built on Wasserstein spaces, the aim being to establish its existence theory. For this purpose, we employ results from the theory of PDE, optimal transportation, differential geometry and algebraic topology. The second topic of the thesis is the study of a nonlinear Schrödinger equation, called the complex Gross-Pitaevskii equation, appearing in the context of Bose-Einstein condensation of exciton-polaritons. This model can be roughly described as a driven-damped Gross-Pitaevskii equation which shares some similarities with the complex Ginzburg-Landau equation. The difficulties in the analysis of this equation stem from the fact that, unlike the complex Ginzburg-Landau equation, the complex Gross-Pitaevskii equation does not include a viscous dissipation term. Our approach to this equation will be in the framework of numerical computations, using two main tools: collocation methods and numerical continuation for the stationary solutions and a time-splitting spectral method for the dynamics. After performing a linear stability analysis on the computed stationary solutions, we are led to postulate the existence of radially symmetric stationary ground state solutions only for certain values of the parameters in the equation; these parameters represent the “strength” of the driving and damping terms. Moreover, numerical continuation allows us to show, for fixed parameters, the ground and some of the excited state solutions of this equation. Finally, for the values of the parameters that do not produce a stable radially symmetric solution, our dynamical computations show the emergence of rotating vortex lattices.

Recently the phenomena of Bose-Einstein condensates have been observed in laboratories, and the related problems are extensively studied. In this paper we consider the nonlinear Schrödinger equation in the laser beam rotating magnetic field and compute its corresponding energy functional under the mass conservative condition. By separating time and space variables, factoring real part and image part, and discretizing via finite difference method, the original equation can be transformed to a large scale parametrized polynomial systems. We use continuation method to find the solutions that satisfy the mass conservative condition. We will also explore bifurcation points on the curves and other solutions lying on bifurcation branches. The numerical results show that when the rotating angular momentum is small, we can find the solutions by continuation method along some particular curves and these curves are regular. As the angular momentum is increasing, there will be more bifurcation points on curves.

Turbulence in classical fluids has been the subject of scientific study for centuries, yet there is still no complete general theory of classical turbulence connecting microscopic physics to macroscopic fluid flows, and this remains one of the open problems in physics. In contrast, the phenomenon of quantum turbulence in superfluids has well-defined theoretical descriptions, based on first principles and microscopic physics, and represents a realm of physics that can connect the classical and quantum worlds. Studies of quantum turbulence may thus be viewed as a path for progress on the long-standing problem of turbulence.A dilute-gas Bose-Einstein condensate (BEC) is, in most cases, a superfluid that supports quantized vortices, the primary structural elements of quantum turbulence. BECs are particularly convenient systems for the study of vortices, as standard techniques allow the microscopic structure and dynamics of the vortices to be investigated. Vortices in BECs can be created and manipulated using a variety of techniques, hence BECs are potentially powerful systems for the microscopic study of quantum turbulence.This dissertation focuses on quantized vortices in BECs, specifically experimental and numerical studies of their formation, dynamics, and decay, in an effort to understand the microscopic nature of vortices as elements of quantum turbulence. Four main experiments were performed, and are described in the main chapters of this dissertation, after introductions to vortices, experimental methods, and turbulence are presented. These experiments were aimed at understanding various aspects of how vortices are created and behave in a superfluid system. They involved vortex dipole nucleation in the breakdown of superfluidity, persistent current generation from a turbulent state in the presence of energy dissipation, decay of angular momentum of a BEC due to trapping potential impurities, and exploration of the spontaneous formation of vortices during the BEC phase transition. These experiments represent progress towards enhanced understanding of the formation, dynamics, and decay of vortices in BECs and thus may be foundational to more general studies of quantum turbulence in superfluids.

Phase transitions abound in the physical world, from the subatomic length scales of quark condensation to the decoupling forces in the early universe. In the Bose-Einstein condensation phase transition, a gas of trapped bosonic atoms is cooled to a critical temperature. Below this temperature, a macroscopic number of atoms suddenly starts to occupy a single quantum state; these atoms comprise the Bose-Einstein condensate (BEC). The dynamics of the BEC phase transition are the focus of this dissertation and the experiments described here have provided new information on the details of BEC formation. New theoretical developments are proving to be valuable tools for describing BEC phase transition dynamics and interpreting new experimental results. With their amenability to optical manipulation and probing along with the advent of new microscopic theories, BECs provide an important new avenue for gaining insight into the universal dynamics of phase transitions in general.Spontaneous symmetry breaking in the system's order parameter may be one result of cooling through a phase transition. A potential consequence of this is the spontaneous formation of topological defects, which in a BEC appear as vortices. We experimentally observed and characterized the spontaneous formation of vortices during BEC growth. We attribute vortex creation to coherence length limitations during the initial stages of the phase transition. Parallel to these experimental observations, theory collaborators have used the Stochastic Gross-Pitaevski Equation formalism to simulate the growth of a condensate from a thermal cloud. The experimental and theoretical statistical results of the spontaneous formation of vortex cores during the growth of the condensate are in good quantitative agreement with one another, supporting our understanding of the dynamics of the phase transition. We believe that our results are also qualitatively consistent with the Kibble-Zurek mechanism, a universal model for topological defect formation.Ultimately, our understanding of the dynamics of the BEC phase transition may lead to a broader understanding of phase transitions in general, and provide new insight into the development of coherence in numerous systems.