Data from present day scientific simulations and observations of physical processes often consist of multiple scalar fields. It is important to study the interactions between the fields to understand the underlying phenomena. A visual representation of these interactions would assist the scientist by providing quick insights into complex relationships that exist between the fields. We describe new techniques for visual analysis of multifield scalar data where the relationships can be quantified by the gradients of the individual scalar fields and their mutual alignment. Empirically, gradients along with their mutual alignment have been shown to be a good indicator of the relationships between the different scalar variables. The Jacobi set, defined as the set of points where the gradients are linearly dependent, describes the relationship between the gradient fields. The Jacobi set of two piecewise linear functions may contain several components indicative of noisy or a feature-rich dataset. For two dimensional domains, we pose the problem of simplification as the extraction of level sets and offset contours and describe a robust technique to simplify and create a multi-resolution representation of the Jacobi set. Existing isosurface-based techniques for scalar data exploration like Reeb graphs, contour spectra, isosurface statistics, etc., study a scalar field in isolation. We argue that the identification of interesting isovalues in a multifield data set should necessarily be based on the interaction between the different fields. We introduce a variation density function that profiles the relationship between multiple scalar fields over isosurfaces of a given scalar field. This profile serves as a valuable tool for multifield data exploration because it provides the user with cues to identify interesting isovalues of scalar fields. Finally, we introduce a new multifield comparison measure to capture relationships between scalar variables. We also show that our measure is insensitive to noise in the scalar fields and to noise in their gradients. Further, it can be computed robustly and efficiently. The comparison measure can be used to identify regions of interest in the domain where interactions between the scalar fields are significant. Subsequent visualization of the data focuses on these regions of interest leading to effective visual analysis. We demonstrate the effectiveness of our techniques by applying them to real world data from different domains like combustion studies, climate sciences and computer graphics.

This thesis investigates some of the properties of a variational approximation to scalar field theories: a trial wavefunctional which has a gaussian form is used as a ground state ansatz for an interacting scalar field theory - the expectation value of the Hamiltonian in this state is then minimized. This we call the Gaussian Approximation; the resulting effective potential we follow others by calling the Gaussian Effective Potential (GEP). An equivalent but more general finite temperature formalism is then reviewed and used for the calculations of the GEP in this thesis. Two scalar field theories are described: ϕ⁴ theory in four dimensions (ϕ⁴₄) and ϕ⁶ theory in three dimensions (ϕ⁶₃). After showing what the Gaussian Approximation does in terms of Feynman diagrams, renormalized GEP's are calculated for both theories. Dimensional Regularization is used in the renormalization and this this is especially convenient for the GEP in ϕ⁶₃ theory because it becomes trivially renor-malizable. It is noted that ϕ⁶₃ loses its infrared asymptotic freedom in the Gaussian Approximation. Finally, it is shown how a finite temperature GEP can be calculated by finding low and high temperature expansions of the temperature terms in ϕ⁶₃ theory. / Science, Faculty of / Physics and Astronomy, Department of / Graduate

The three main parts of this thesis demonstrate our current understanding of certain physics but mostly go beyond our understanding and present novel approaches, both technically and physically. The first part concentrates on the scalar mesons and presents search methodology to enable a better understanding of their existence and structures. The second part discusses one step further on beyond the standard model physics searches. Emphasis is given to discriminating factors between the MSSM and the U(1)' gauge extended models. The last part discusses a specific readout problem in calorimetry together with its solution and presents the digital hadron calorimetry, which will be an essential part of calorimeter systems of future colliders.

Soot is a carbon particulate formed as a result of the combustion of fossil fuels. Due to the health hazard posed by the carbon particulate, government agencies have applied strict regulations to control soot emissions from road vehicles, airplanes, and industrial plants. Thus, understanding soot formation and evolution is critical. Practical combustion devices operate at high pressure and in the turbulent regime. Elevated pressures and turbulence on soot formation significantly and fundamental understanding of these complex interactions is still poor. In this study, the effects of pressure and turbulence on soot formation and growth are investigated numerically. As the first step, the evolution of the particle size distribution function (PSDF) and soot particles morphology are investigated in turbulent non-premixed flames. A Direct Simulation Monte Carlo (DSMC) code is developed and used. The stochastic reactor describes the evolution of soot in fluid parcels following Lagrangian trajectories in a turbulent flow field. The trajectories are sampled from a Direct Numerical Simulation (DNS) of an n-heptane turbulent non-premixed flame. Although individual trajectories display strong bimodality as in laminar flames, the ensemble-average PSDF possesses only one mode and a broad tail, which implies significant polydispersity induced by turbulence. Secondly, the effect of the flow and mixing fields on soot formation at atmospheric and elevated pressures is investigated in coflow laminar diffusion flames. The experimental observation and the numerical prediction of the spatial distribution are in good agreement. Based on the common scaling methodology of the flames (keeping the Reynolds number constant), the scalar dissipation rate decreases as pressure increases, promoting the formation of PAH species and soot. The decrease of the scalar dissipation rate significantly contributes to soot formation occurring closer to the nozzle and outward on the flames wings as pressure increases. The scaling of the scalar dissipation rate is not straightforward due to buoyancy effects. Finally, a new scaling approach of the flame at different pressures is introduced. In this approach, both Reynolds number and Grashof number are kept constant so that the effect of gravity is the same at all pressures. In order to keep Gr constant, this requires the diameter of the nozzle to be changed as pressures vary. This approach guarantees a similar non-dimensional flow field at all pressures and rules out the effect of hydrodynamics and mixing, so that only the effect of chemical kinetics on soot formation can be studied.

PhD / Department of Mathematics and Applied Mathematics

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Stellar structure is investigated within the framework of scalar-tensor gravity. Novel perturbative analytical results are obtained for constant-density stars and for Newtonian polytropes in the quadratic model with coupling function A(Φ) = exp(αΦ+1/2βΦ^2). They are compared to full numerical calculations, and possible applications to main-sequence stars, white dwarfs, and the Chandrasekhar mass are indicated. It is found that Buchdahl's theorem is violated in Brans-Dicke theory for stars with exponentially-decaying density profiles. However, the mass-to-radius ratio M/R tends to the constant-density value in a certain limit. It is observed that for β < 0, there exists a maximum value of η = P0/ρo for constant-density stars, where P0 and ρ0 are the central pressure and density, respectively. It is conjectured that if such a maximum value also exists for other equations of state, and is less than the constant-density maximum value, then knowledge of P/ρ in the centre of a star can be used to constrain β. / Thesis / Master of Science (MSc)

The beta-decay interaction contains two terms which consist of invariant products of two scalars and two tensors respectively. The relative absolute magnitude of these two terms is fairly well established but there has been some controversy over their relative sign. In this thesis the form of the interaction is investigated by means of an analysis of the second-forbidden decay spectrum of Cs137 and it is concluded that the relative sign of the scalar and tensor terms is negative. / Thesis / Master of Science (MS)

In the field of urban planning, environmental psychology studies human relationship to places and settings, which are then categorized as the public's identities, attachments, and dependencies. Of interest to city planning, these findings can also be utilized in a design methodology. By giving particular attention to civic programs, this thesis presents a model for multi-scalar architecture and construction of place meanings. With urban, political, and historic networks contributing to place categories, ecological evolution provides developmental trajectories that can then be manifested through architectural design in civic and cultural institutions within city centers. From site selection through the design and execution of the project, the precedence is led by the people of past, present, and future, and the spaces they celebrate. The following is about the County of Arlington Civic Center, a multi-scalar perspective and design. / Master of Architecture