The gas transfer process across the air-water interface in a buoyant-convective environment has been investigated by Direct Numerical Simulation (DNS) to gain improved understanding of the mechanisms that control the process. The process is controlled by a combination of molecular diffusion and turbulent transport by natural convection. The convection when a water surface is cooled is combination of the Rayleigh-B´enard convection and the Rayleigh-Taylor instability. It is therefore necessary to accurately resolve the flow field as well as the molecular diffusion and the turbulent transport which contribute to the total flux. One of the challenges from a numerical point of view is to handle the very different levels of diffusion when solving the convection-diffusion equation. The temperature diffusion in water is relatively high whereas the molecular diffusion for most environmentally important gases is very low. This low molecular diffusion leads to steep gradients in the gas concentration, especially near the interface. Resolving the steep gradients is the limiting factor for an accurate resolution of the gas concentration field. Therefore a detailed study has been carried out to find the limits of an accurate resolution of the transport for a low diffusivity scalar. This problem of diffusive scalar transport was studied in numerous 1D, 2D and 3D numerical simulations. A fifth-order weighted non-oscillatory scheme (WENO) was deployed to solve the convection of the scalars, in this case gas concentration and temperature. The WENO-scheme was modified and tested in 1D scalar transport to work on non-uniform meshes. To solve the 2D and 3D velocity field the incompressible Navier-Stokes equations were solved on a staggered mesh. The convective terms were solved using a fourth-order accurate kinetic energy conserving discretization while the diffusive terms were solved using a fourth-order central method. The diffusive terms were discretized using a fourth-order central finite difference method for the second derivative. For the time-integration of the velocity field a second-order Adams-Bashworth method was employed. The Boussinesq approximation was employed to model the buoyancy due to temperature differences in the water. A linear relationship between temperature and density was assumed. A mesh sensitivity study found that the velocity field is fully resolved on a relatively coarse mesh as the level of turbulence is relatively low. However a finer mesh for the gas concentration field is required to fully capture the steep gradients that occur because of its low diffusivity. A combined dual meshing approach was used where the velocity field was solved on a coarser mesh and the scalar field (gas concentration and temperature) was solved on an overlaying finer submesh. The velocities were interpolated by a second-order method onto the finer sub-mesh. A mesh sensitivity study identified a minimum mesh size required for an accurate solution of the scalar field for a range of Schmidt numbers from Sc = 20 to Sc = 500. Initially the Rayleigh-B´enard convection leads to very fine plumes of cold liquid of high gas concentration that penetrate the deeper regions. High concentration areas remain in fine tubes that are fed from the surface. The temperature however diffuses much stronger and faster over time and the results show that temperature alone is not a good identifier for detailed high concentration areas when the gas transfer is investigated experimentally. For large timescales the temperature field becomes much more homogeneous whereas the concentration field stays more heterogeneous. However, the temperature can be used to estimate the overall transfer velocity KL. If the temperature behaves like a passive scalar a relation between Schmidt or Prandtl number and KL is evident. A qualitative comparison of the numerical results from this work to existing experiments was also carried out. Laser Induced Fluorescence (LIF) images of the oxygen concentration field and Schlieren photography has been compared to the results from the 3D simulations, which were found to be in good agreement. A detailed quantitative analysis of the process was carried out. A study of the horizontally averaged convective and diffusive mass flux enabled the calculation of transfer velocity KL at the interface. With KL known the renewal rate r for the so called surface renewal model could be determined. It was found that the renewal rates are higher than in experiments in a grid stirred tank. The horizontally averaged mean and fluctuating concentration profiles were analysed and from that the boundary layer thickness could be accurately monitored over time. A lot of this new DNS data obtained in this research might be inaccessible in experiments and reveal previously unknown details of the gas transfer at the air water interface.

For over two decades, mathematicians and cryptologists have evaluated and presented the theoretical performance of Elliptic-curve scalar point-multiplication in projective geometry. Because computation in projective domain is composed of a wide array of formulations and computing optimizations, there is not a comprehensive performance comparison of point-multiplication using projective transformation available to verify its realistic efficiency in 64-bit x86 computing platforms. Today, research on explicit mathematical formulations in projective domain continues to excel by seeking higher computational efficiency and ease of realization. An explicit performance evaluation will help implementers choose better implementation methods and improve Elliptic-curve scalar point-multiplication. This paper was founded on the practical solution that obtaining realistic performance figures should be based on more precise computational cost metrics and specific computing platforms. As part of that solution, an empirical performance benchmark comparison between two approaches implementing projective Elliptic-curve scalar point-multiplication will be presented to provide the selection of, and subsequently ways to improve scalar point-multiplication technology executing in a 64-bit x86 runtime environment.

Thesis (MSc)--Stellenbosch University, 2013. / This work is a thesis regarding the energy scaling of end-pumped Ho:YLF amplifiers. The work includes: a brief review of laser physics and models, the development of a suitable three dimensional time resolved numerical model, a parametric study of double pass ampli ers simulated using the model, comparison between the simulation and the experimental results of a double pass ampli er system, and simulation of a high energy single pass ampli er. A three dimensional time resolved numerical model of an end-pumped ampli er was developed. A rate equation model was used to simulate the absorption and emission of light, energy transfer upconversion, and spontaneous emission within the gain medium. In the traveling wave approximation the propagation of light through the gain medium was modelled with the use of a split step method that included di raction and gain. A parametric study was performed to nd the design parameters for an end-pumped two pass ampli- er. Limited optimisation of several ampli er parameters was performed. The study focused on the optimisation of the energy per pulse through changes to the following parameters: crystal length, laser beam size, pump beam sizes, and pump wavelength. The nal design speci cations for an experimental system were for a 100 mm long 0.5 % (atm.) doped Ho:YLF gain medium, pump and seed beams with spot sizes with e ective beam sizes of 1 mm and 0.95 mm respectively and a pump wavelength of 1892 nm. The simulation predicted pulse energies above 480 mJ when seeded by a 55 mJ pulse at repetition rates of 50 Hz. The experimentally realised system with similar design parameters produced the highest reported energy, 330 mJ, from an end-pumped Ho:YLF ampli er. Comparison between the simulation and the experimental results showed signi cant deviation. The deviation was explained by the e ect of parameters not included previously in the simulation. These parameters were the power of the continuous component of the seed beam, and the energy transfer upconversion rate. Limitations and delity of the numerical model with respect to the experimental system are discussed, notably the model of the highly divergent pump beam was simplistic. Preliminary simulation results of a high energy single pass ampli er predict that energy scaling in Ho:YLF follows linearly with respect to pump power and that in the ideal case, multi-Joule operation is possible at 50 Hz with optical to optical e ciencies of 19%.

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This thesis makes contributions to the solution of Hadamard's problem through an examination of the question of the validity of Huygens'principle for the non-self-adjoint scalar wave equation on a Petrov type D spacetime. The problem is split into five further sub-cases based on the alignment of the Maxwell and Weyl principal spinors of the underlying spacetime. Two of these sub-cases are considered, one of which is proved to be incompatible with Huygens' principle, while for the other, it is shown that Huygens' principle implies that the two principal null congruences of the Weyl tensor are geodesic and shear-free. Furthermore, an unpublished result of McLenaghan regarding symmetric spacetimes of Petrov type D is independently verified. This result suggests the possible existence of counter-examples of the Carminati-McLenaghan conjecture.

Implicatura escalar é uma interpretação upper-bound (limite máximo de informatividade) de um termo escalar fraco. E.g. \'alguns\', o termo fraco da escala semântica <todos, alguns>, pode ter interpretação lower-bound/literal (\"pelo menos alguns e talvez todos\") ou upper-bound/pragmática, de implicatura escalar (\"apenas alguns mas não todos\"). Na primeira parte deste trabalho, investigamos, por vias teóricas e experimentais, a capacidade infantil de interpretação de implicaturas escalares, que entendemos, por influência da Teoria da Relevância, como a negação implicada por um termo fraco de uma pergunta explícita ou contextualmente implícita acerca do termo forte. Nossos resultados indicam domínio de implicatura escalar pelas crianças e sensibilidade capaz de flexibilizar a interpretação dos termos fracos de acordo com contextos lower-bound ou upper-bound. Assim, identificamos na já bem desenvolvida capacidade infantil de inferir intenções comunicativas alheias (mindreading) a função cognitiva central para o sucesso de sua interpretação pragmática. Dedicamos a segunda parte do texto a uma mais abrangente exploração do papel da leitura de intenções na aquisição de linguagem, ainda comprometidos com os paradigmas conceituais da Teoria da Relevância. Ultrapassando o escopo da interpretação pragmática, procuramos reunir evidências favoráveis à adoção da capacidade humana de leitura de intenções como a operação cognitiva motivadora e coesiva do processo de amadurecimento linguístico, de modo que, argumentamos, nenhuma teoria que se proponha a explicar a aquisição de linguagem deve negligenciar em seu modelo a esfera sócio-pragmática da comunicação verbal. / Scalar implicatures happen when an upper-bound interpretation (upper limit of informativeness) is given to a weak scalar term. E.g. \'some\' (the weak term of the scale <all, some>) may receive a lower-bound/literal interpretation (\"at least some and perhaps all\") or an upper-bound/pragmatic scalar implicature interpretation (\"only some but not all\"). In the first part of the work, we investigate children\'s capacity of scalar implicature interpretation through theoretical and experimental research. By influence of Relevance Theory, we assume that such interpretation must infer the negation implicated by the weak term of an explicit or contextually implicit question about the strong term. Our results indicate children\'s mastery of scalar implicature and their sensitivity to adaptation of weak term\'s interpretation according to lower-bound or upper-bound contexts. Thus, we see in the well-developed child capacity of reading other\'s communicative intentions (mindreading) the central cognitive function of their successful pragmatic interpretation. The second part is dedicated to a more embracing analysis of mindreading\'s role in language acquisition, still taking Relevance Theory\'s concepts as references. Beyond the scope of pragmatic interpretation, we sought to gather evidences that support the hypothesis of the human capacity of intentions reading as the cognitive operation that motivates language development and provides cohesion to the parts of the process. Being so, we argue that no theory that intends to explain language acquisition should neglect in its model the social-pragmatics level of verbal communication.

A adequada quantificação do transporte interfacial de escalares em escoamentos turbulentos é de interesse prático para os processos industriais e para a gestão dos problemas ambientais. O fenômeno é matematicamente complexo devido ao uso de equações governantes estatísticas não lineares e não fechadas. Neste estudo, analisam-se detalhes do método de Ondas Quadradas Aleatórias (OQA), o qual fornece uma quantificação estatística que permite fechar as equações e obter um perfil normalizado da grandeza de interesse para a transferência unidimensional turbulenta de escalares, que, num caso idealizado, depende de apenas dois parâmetros adimensionais, A e k (neste caso, k representa um coeficiente de transferência e A depende da interação entre os fenômenos de transporte molecular e turbulento). Simulações numéricas foram realizadas no intuito de se verificar a influência das derivadas de ordem superior para a função normalizada de concentração. A sensibilidade do modelo e a análise de aspectos intrínsecos ao mesmo foram também realizadas. Importante análise das condições de contorno empregadas foi desenvolvida com a inserção de um contorno adicional, com base física, no seio líquido. Como os estudos iniciais tinham se concentrado em exemplos de transferência de massa, uma extensão para o caso de transporte de calor foi considerada. Os resultados obtidos reproduzem o comportamento dos dados experimentais observados na literatura. / The adequate quantification of interfacial scalar transport in turbulent flows is of practical interest for industrial processes and in environmental problems. The phenomenon is mathematically complex due to the use of unclosed nonlinear statistical equations. In this study, we analyze details of the method of Random Square Waves (RSW), which provides a statistical quantification that allows closing the set of equations and getting the normalized scalar profile of the one-dimensional turbulent scalar variable, which, in an idealized case, depends on only two nondimensional parameters, k and A (in this case, k represents a transfer coefficient and A depends on the interaction between the molecular and turbulent transports). Numerical simulations were performed in order to verify the influence of the higher order of derivatives over the normalized concentration function. The sensitivity of the model to the relevant parameters and the analysis of its intrinsic parameters were also performed. An important aspect is the analysis of the boundary conditions, for which an additional condition was proposed and employed in the bulk liquid (with based on physical grounds). Because the initial studies have focused on examples of mass transfer, an extension to the case of heat transport was here considered. The results reproduce the behavior of experimental data reported in the literature.

In the first part of the thesis, we carried out direct two-dimensional (2D) multipoint measurements of the velocity fields in a turbulent Rayleigh-Benard convection cell to study the properties of small-scale convective turbulence. The local homogeneity and isotropy of the velocity field are tested using a number of criteria and are found to hold to an excellent degree. The properties of velocity circulation Gammar are also studied. The results show that the circulation appears to be more effective to capture the effect of local anisotropy than the velocity field itself. The distribution of Gammar is found to depend on the scale r, reflecting strong intermittency. It is further found that velocity circulation has the same anomalous scaling exponents as the longitudinal and transverse structure functions for low-order moments (p &lsim; 5). Whereas, for high-order moments (p &gsim; 5), the anomalous scaling exponents for circulation are found to be systematically smaller than the scaling exponents of the longitudinal and transverse structure functions. / In the second part of the thesis, the simultaneous visualization of the temperature and velocity fields was used to study the properties of thermal plumes. Our visualization reveals the process of the morphological evolution between sheetlike and mushroomlike plumes, which were also quantified by the height dependence of plume numbers and of vorticity fluctuations. A direct connection between the heat transport and coherent structures, i.e. thermal plumes, was established, which shows that it is plume number that primarily determines the Nu-Ra scaling relation. Individual plumes were extracted and their statistical and geometric properties were studied. It is found that the log-normal distribution is universal for thermal plumes and the log-normal statistics may be used to model them. In addition, both our quantitative characteristic and direct 3D spatial visualizations indicate that the previously-believed sheetlike plumes should be reconsidered to be only one-dimensional structures. / In the third part of the thesis, the planar laser-induced fluorescence technique was induced to study the 2D passive scalar mixing in high-Schmidt-number buoyancy-driven turbulence. The passive scalar mixing evolution was studied and various geometric properties, such as shape complexity, fractal dimension and local curvature, were used to characterize the isoconcentration contours of the 2D passive scalar fields. It is found that when the flow gets more turbulent the shape of passive scalar packets becomes closer to a circular shape and the passive scalar mixing becomes more isotropic, indicating the increased mixing and stirring of the turbulent flow. / The objective of this thesis is to address the following three key issues in turbulent thermal convection, i.e. turbulent fluctuations in small scales, coherent structures and passive scalar mixing in buoyancy-driven turbulence. / Zhou, Quan = 對流熱湍流中能量級串, 相干結構和標量場混合的实验研究 / 周全. / Adviser: Ke-Qing Xia. / Source: Dissertation Abstracts International, Volume: 70-06, Section: B, page: 3576. / Thesis (Ph.D.)--Chinese University of Hong Kong, 2008. / Includes bibliographical references (leaves 103-117). / Electronic reproduction. Hong Kong : Chinese University of Hong Kong, [2012] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Electronic reproduction. [Ann Arbor, MI] : ProQuest Information and Learning, [200-] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Abstracts in English and Chinese. / School code: 1307. / Zhou, Quan = Dui liu re tuan liu zhong neng liang ji chuan, xiang gan jie gou he biao liang chang hun he de shi yan yan jiu / Zhou Quan.