For many decades, turbulence has been the subject of extensive numerical research and experimental work. A bottleneck problem in turbulence research has been to detect and characterize the energetic, space and time-dependent structures and give a mathematical definition to each topology. This research presents a fundamental study of coherent structures, embedded in turbulent flows, by use of Proper Orthogonal Decomposition (POD). The target is to detect dominant features which contain the largest fraction of the total kinetic energy and hence contribute more to a turbulent flow. POD is proven to be a robust methodology in multivariate analysis of non-linear problems. This method also helps to obtain a low-dimensional approximation of a high-dimensional process, like a turbulent flow. This manuscript-based dissertation consists of five chapters. The first chapter starts with a brief introduction to turbulence, available simulation techniques, limitations and practical applications. Next, POD is introduced and the step-by-step approach is explained in detail. Three submitted manuscripts are presented in the subsequent chapters. Each chapter starts with introducing the study case and explaining the contribution of the study to the whole topic and also has its topic-relevant literature review. Each article consists of two parts: flow simulation and verification of the results at the onset, followed by POD analysis and reconstruction of the turbulent flow fields. For flow simulation, Large Eddy Simulation (LES) was performed to obtain databases for POD analysis. The simulations were validated by making comparison with available experimental and numerical studies. For each case, coherent topologies are characterized and the contribution of kinetic energy for each structure is determined and compared with previous literature. The first manuscript focused on investigating the large-scale dynamics in the wake of an infinite square cylinder. This case is the first step towards the targeting study case of this research, i.e. flow over rib roughened walls. The main purpose the first step is to establish a benchmark for comparison to the more complicated cases of a square cylinder with a nearby wall and flow over a rib-roughened surface. For POD analysis, the three-dimensional velocity field is obtained from LES of the flow around an infinite square cylinder at a Reynolds number of Re = 500. The POD algorithm is examined and the total energy of the flow is found to be well captured by only a small number of eigenmodes. From the energy spectrum, it is learned that each eigenmode represents a particular flow characteristic embedded in the turbulent wake, and eigenmodes with analogous characteristics can be bundled as pairs. Qualitative analysis of the dominant modes provided insight as to the spatial distribution of dominant structures in the turbulent wake. Another outcome of this chapter is to develop physical interpretations of the energetic structures by examining the temporal coefficients and tracking their life-cycle. It was observed that the paired temporal coefficients are approximately sinusoidal with similar order of magnitude and frequency and a phase shift. Lastly, it was observed that the turbulent flow field can be approximated by a linear combination of the mean flow and a finite number of spatial modes. The second manuscript analyses the influence of a solid wall on the wake dynamics of an infinite square cylinder. Different cases have been studied by changing the distance between the cylinder and the bottom wall. From the simulation results, it is learned that the value of drag and lift coefficients can be significantly affected by a nearby solid wall. From the energy decay spectrum it is observed that the energy decay rate varies for different gap ratios and accordingly a physical explanation is developed. Visualization of coherent structures for each case shows that for larger gaps, although the structures are distorted and inclined away from the wall, the travelling wave characteristic persists. Lastly, it is observed that as the gap ratio gets smaller, energetic structures originated by the wall begin to appear in the lower index modes. The last manuscript presents a numerical study of the structures in turbulent Couette flow with roughness on one wall, which as mentioned earlier, is the targeting study case of this research. Flow over both roughened and smooth surfaces was examined in a single study. Comparison was made with experiments and other numerical studies to verify the LES results. The mean velocity distribution across the channel shows that the rib roughness on the bottom wall has a strong effect on the velocity profile on the opposite wall. The energetic coherent dynamics of turbulent flow were investigated by the use of POD. The energy decay spectrum was analysed and the influence of a roughened wall and each roughness element on formation of those structures was investigated. Coherent POD modes on a spanwise sampling plane are detected. A secondary swirling motion is visualized, for the first two modes and counter-rotating cells are observed in the lower region of the channel above the rough wall for the higher modes. At the end, a quantitative analysis of the POD temporal coefficients was performed, which characterize the life-cycle of each coherent dynamic. A motivating outcome of this analysis is to decompose the time trace curves into quasi-periodic and fluctuations curves and to detect a linkage between these life cycles and physical meaning and location of each energetic pattern. At the end, in a closuring chapter, concluding remarks of this research work are presented in more detail and some potential extensions have been proposed for future researchers.

We study complex analogues on Calabi-Yau manifolds of gauge theories on low dimensional real manifolds. In particular we define a holomorphic analogue of the Casson invariant, counting coherent sheaves on a Calabi-Yau 3-fold.

No description available.

This thesis explores the theory describing wavefunctions and images, both elastic and inelastic, formed in scanning transmission electron microscopy. / A method is presented for calculating the elastic wavefunction based upon a new formulation of the boundary conditions which couples the probe to Bloch states within the crystal in a single step. Though this method is fundamentally equivalent to previous approaches based upon the superposition of wavefunctions corresponding to individual plane wave components in the incident probe, it provides new insight into the some of the dynamics, allows for efficient calculations, and proves useful for demonstrating well known results such as reciprocity relations. A formal inversion technique is also presented that uses a collection of diffraction plane data in scanning transmission electron microscopy to reconstruct the object potential, even in the presence of strong multiple scattering. / The new form of the boundary conditions allows for a generalization of a crosssection expression for calculating inelastic images, making use of the theory of mixed dynamic form factors. This enables the simulation of images for a range of inelastic mechanisms, including thermal scattering, used to simulate high-angle annular dark field imaging, and inner-shell ionization, used to simulate electron energy loss spectroscopy images. A multislice form of this expression is given. Selection between the methods can thus be based on the sample of interest: the Bloch wave method is very efficient when the sample is crystalline; the multislice method is more appropriate if the sample lacks periodicity. / The issue of cross-talk, where dynamical probe spreading may result in a signal containing contributions from several columns and therefore confound direct interpretation, is assessed for high-angle annular dark field imaging. Single atom images are simulated to provide an estimate of the localization of signal in electron energy loss spectroscopy, and confirm that the limitations of probe size generally outweigh those of the nature of the ionization interaction. The feasibility of column-by-column spectroscopic identification is demonstrated through a combination of experimental data and supporting calculations. Data demonstrating the location and spectroscopic identification of a single impurity atom in the bulk are supported by simulation and it is demonstrated that a quantitative comparison can offer further useful information: an estimate for the depth of the impurity. / The contribution to electron energy loss spectroscopy images from electrons which have undergone thermal scattering prior to causing an inner-shell ionization event is assessed. It is concluded that this contribution is significant in strongly scattering specimens imaged using fine probes. It will be necessary to include this contribution if quantitative comparisons are to be made.

The lunar Cherenkov technique is a promising method to resolve the mystery of the origin of the highest energy particles in nature, the ultra-high energy (UHE) cosmic rays. By pointing Earth-based radio-telescopes at the Moon to look for the characteristic nanosecond pulses of radio-waves produced when a UHE particle interacts in the Moon’s outer layers, either the cosmic rays (CR) themselves, or their elusive counterparts, the UHE neutrinos, may be detected. The LUNASKA collaboration aims to develop both the theory and practice of the lunar Cherenkov technique in order to utilise the full sensitivity of the next generation of giant radio telescope arrays in searching for these extreme particles. My PhD project, undertaken as part of the collaboration, explores three key aspects of the technique. In the first three chapters, I describe a Monte Carlo simulation I wrote to model the full range of lunar Cherenkov experiments. Using the code, I proceed to calculate the aperture to, and resulting limits on, a UHE neutrino flux from the Parkes lunar Cherenkov experiment, and to highlight a pre-existing discrepancy between existing simulation programs. An expanded version of the simulation is then used to determine the sensitivity of past and future lunar Cherenkov experiments to UHE neutrinos, and also the expected event rates for a range of models of UHE CR production. Limits on the aperture of the Square Kilometre Array (SKA) to UHE CR are also calculated. The directional dependence of both the instantaneous sensitivity and time-integrated exposure of the aforementioned experiments is also calculated. Combined, these results point the way towards an optimal way utilisation of a giant radio-array such as the SKA in detecting UHE particles. The next section describes my work towards developing accurate parameterisations of the coherent Cherenkov radiation produced by UHE showers as expected in the lunar regolith. I describe a ‘thinning’ algorithm which was implemented into a pre-existing electromagnetic shower code, and the extensive measures taken to check its veracity. Using the code, a new parameterisation for radiation from electromagnetic showers is developed, accurate for the first time up to UHE energies. The existence of secondary peaks in the radiation spectrum is predicted, and their significance for detection experiments discussed. Finally, I present the data analysis from three runs of LUNASKA’s on-going observation program at the Australia Telescope Compact Array (ATCA). The unusual nature of the experiment required both new methods and hardware to be developed, and I focus on the timing and sensitivity calibrations. The loss of sensitivity from finite-sampling of the electric field is modelled for the first time. Timing and dispersive constraints are used to determine that no pulses of lunar origin were detected, and I use my simulation software to calculate limits on an UHE neutrino flux from the experiment. / http://proxy.library.adelaide.edu.au/login?url= http://library.adelaide.edu.au/cgi-bin/Pwebrecon.cgi?BBID=1371947 / Thesis (Ph.D.) - University of Adelaide, School of Chemistry and Physics, 2009.

The lunar Cherenkov technique is a promising method to resolve the mystery of the origin of the highest energy particles in nature, the ultra-high energy (UHE) cosmic rays. By pointing Earth-based radio-telescopes at the Moon to look for the characteristic nanosecond pulses of radio-waves produced when a UHE particle interacts in the Moon’s outer layers, either the cosmic rays (CR) themselves, or their elusive counterparts, the UHE neutrinos, may be detected. The LUNASKA collaboration aims to develop both the theory and practice of the lunar Cherenkov technique in order to utilise the full sensitivity of the next generation of giant radio telescope arrays in searching for these extreme particles. My PhD project, undertaken as part of the collaboration, explores three key aspects of the technique. In the first three chapters, I describe a Monte Carlo simulation I wrote to model the full range of lunar Cherenkov experiments. Using the code, I proceed to calculate the aperture to, and resulting limits on, a UHE neutrino flux from the Parkes lunar Cherenkov experiment, and to highlight a pre-existing discrepancy between existing simulation programs. An expanded version of the simulation is then used to determine the sensitivity of past and future lunar Cherenkov experiments to UHE neutrinos, and also the expected event rates for a range of models of UHE CR production. Limits on the aperture of the Square Kilometre Array (SKA) to UHE CR are also calculated. The directional dependence of both the instantaneous sensitivity and time-integrated exposure of the aforementioned experiments is also calculated. Combined, these results point the way towards an optimal way utilisation of a giant radio-array such as the SKA in detecting UHE particles. The next section describes my work towards developing accurate parameterisations of the coherent Cherenkov radiation produced by UHE showers as expected in the lunar regolith. I describe a ‘thinning’ algorithm which was implemented into a pre-existing electromagnetic shower code, and the extensive measures taken to check its veracity. Using the code, a new parameterisation for radiation from electromagnetic showers is developed, accurate for the first time up to UHE energies. The existence of secondary peaks in the radiation spectrum is predicted, and their significance for detection experiments discussed. Finally, I present the data analysis from three runs of LUNASKA’s on-going observation program at the Australia Telescope Compact Array (ATCA). The unusual nature of the experiment required both new methods and hardware to be developed, and I focus on the timing and sensitivity calibrations. The loss of sensitivity from finite-sampling of the electric field is modelled for the first time. Timing and dispersive constraints are used to determine that no pulses of lunar origin were detected, and I use my simulation software to calculate limits on an UHE neutrino flux from the experiment. / http://proxy.library.adelaide.edu.au/login?url= http://library.adelaide.edu.au/cgi-bin/Pwebrecon.cgi?BBID=1371947 / Thesis (Ph.D.) - University of Adelaide, School of Chemistry and Physics, 2009.

Thesis (Ph. D.)--University of Washington, 1997. / Vita. Includes bibliographical references (leaves [72]-80).

Thesis (Ph. D.)--University of Texas at Austin, 2004. / Supervisors: Tomio Petrosky and E.C.G. Sudarshan. Vita. Includes bibliographical references.

Questões ambientais estão no centro das discussões nas últimas décadas. A poluição atmosférica, causada pela expansão pós-revolução industrial fez surgir a necessidade de aprender a descrever, usando modelos matemáticos, esse fenômeno. Com esse conhecimento pode-se propor soluções que mitiguem a poluição e os danos colaterais causados ao ambiente. A dispersão de poluentes modelada por soluções analíticas, a partir das equações de advecção-difusão oferecem um conhecimento sobre cada componente que constrói a equação, característica inexistente em outras abordagens, como a numérica. Entretanto ela era incapaz de descrever propriedades que se referem à turbulência, as estruturas coerentes, causadas por componentes não-lineares suprimidas por construção das equações governantes do modelo. Este trabalho estudou uma forma de recuperar características associadas à turbulência através de uma componente fundamental em estruturas coerentes, a fase. Essa é incluída no modelo que passa a descrever manifestações da turbulência em processos de dispersão através de flutuações de pequena escala na concentração da solução do modelo sesquilinear, que é determinístico-estocástico. No decorrer do trabalho há um estudo através de variações de parâmetros para compreender os efeitos da fase no modelo. Ele também foi aplicado ao experimento de Copenhagen e a dois cenários reais com a intenção de compreender o modelo frente à variáveis micrometeorológicas assim como aprimorá-lo para simular a dispersão de poluentes oriundos de fontes de forma realística. / Environmental issues have been at the center of discussions in the last few decades. Atmospheric pollution, caused by post-industrial revolution, has increased the necessity to describe, using mathematical models, this phenomenon. With this knowledge is possible to propose solutions mitigating the pollution and collateral damages caused in the environment. The pollutant dispersion modeled by analytical solutions, from advection-diffusion equations, offers a knowledge about each component that constructs the equation, a characteristic that does not exist in other approaches, such as numerical. However it was unable to describe properties that refer to turbulence, coherent structures, caused by nonlinear components suppressed by constructing the model governing equations. This work studied a way to recover characteristics associated with turbulence through a fundamental component in coherent structures, the phase. This is included in the model which describes manifestations of turbulence in the dispersion process through the presence of small-scale concentration fluctuations in the sesquilinear model, which is deterministicstochastic. In the course of this work there is a study through variations of parameters to understand the phase effects in the model. It was also applied to Copenhagen experiment and to two real scenarios with the intention of understanding the model regarding micrometeorological variables as well as improving it to simulate the pollutant dispersion from sources in a realistic way.

xxv, 207 p. ; ill. (some col.) A print copy of this title is available from the UO Libraries, under the call number: SCIENCE QD172.T6 T87 2008 / A growing interest in the physics of complex systems such as in the transition-metal oxide family has exploded recently, especially in the last 20 years or so. One notable effect is the change in electrical resistivity of a system by orders of magnitude in an applied magnetic field, coined the "colossal magnetoresistance effect". In efforts to understand these types of effects, there has been an unveiling of a rich variety of phenomena in the field of strongly correlated electron physics that has come to dominate the current scientific times. Most notable is the competition of myriad types of order: magnetic, lattice, charge and orbital all self-organize to display a fascinating array of phases on a variety of length scales. Furthermore, it has become apparent that new probes are needed to grasp some of this physics that transcends current condensed matter theory, where much of the behavior of these types of systems has remained unexplored. We have developed a new technique to gain more information about the system than with conventional x-ray diffraction. By scattering highly coherent, low energy x-rays, we can measure manganite speckle: a "fingerprint' of the microscopic structure in the bulk. The coherence of the x-rays can further be used to elucidate new insight into the dynamics of these phases. We describe here a number of novel effects near the orbital order phase transition in a half-doped manganite. We observe a small fluctuating component in the scattered signal that is correlated with three effects: both a rapidly decreasing total signal and orbital domain size, as well as an abrupt onset of a broad background intensity that we attribute to the thermal production of correlated polarons. Our results suggest that the transition is characterized by a competition between a pinned orbital domain topology that remains static, and mobile domain boundaries that exhibit slow, spatiotemporal fluctuations. This study opens up a new chapter to the study of manganite physics as coherent x-ray scattering offers a new direction to understand the strange and exotic behavior demonstrated in the multifaceted manganites. / Adviser: Stephen Kevan