Thesis (Ph.D)--Materials Science and Engineering, Georgia Institute of Technology, 2008. / Committee Co-Chair: Dr. Hamid Garmestani; Committee Co-Chair: Dr. Rina Tannenbaum; Committee Member: Dr. Kenneth Gall; Committee Member: Dr. Meisha Shofner; Committee Member: Dr. Thomas Sanders. Part of the SMARTech Electronic Thesis and Dissertation Collection.

Thesis (Ph. D.)--Washington State University, May 2009. / Title from PDF title page (viewed on June 3, 2009). "College of Engineering and Architecture." Includes bibliographical references.

Thesis (M.S.)--University of California, Berkeley, 1960. / "Chemistry Distribution" -t.p. "TID-4500 (15th Ed.)" -t.p. Includes bibliographical references (p. 49).

Zugl.: Hannover, Universiẗat, Diss., 1985.

Universiẗat, Diss., 2004--Kiel.

Robust estimators for multivariate location and dispersion should be ãn consistent and highly outlier resistant, but estimators that have been shown to have these properties are impractical to compute. The RMVN estimator is an easily computed outlier resistant robust ãn consistent estimator of multivariate location and dispersion, and the estimator is obtained by scaling the classical estimator applied to the gRMVN subseth that contains at least half of the cases. Several robust estimators will be presented, discussed and compared in detail. The applications for the RMVN estimator are numerous, and a simple method for performing robust principal component analysis (PCA), canonical correlation analysis (CCA) and factor analysis is to apply the classical method to the gRMVN subset.h Two approaches for robust PCA and CCA will be introduced and compared by simulation studies.

The kinetic energy density, k, and lifetime, t, of a turbulent eddy, volume V, are shown to be related to a characteristic length scale, 2, by: 13 =vk= c2/3e2/3 t-C 1/312/3 where c is the energy dissipation rate. A self similar cascade of discrete eddy sizes is derived, each size related to the next larger by: P 22 CC i+l i where C= 81'2. With some simple assumptions as to the turbulent production process the mean logarithmic velocity profile is derived. The relationship between the friction velocity and Reynolds stress is explained in terms of the large eddy intermittency, n. Below a critical free stream velocity, U', n is proportional to the free stream velocity. The dissipation rate, e, is then constant and given by: e U'3/N3L where N is the number of discrete eddy sizes in the boundary layer. When the boundary layer has reached the surface N- 11. The observed turbulent spectral characteristics are derived from the eddy equations without using dimensional reasoning and an explanation of the mechanism behind surface layer similarity scaling is proposed. An experiment was carried out in the North Sea to test the model predictions. Correlations showed that, except at slack water, the largest eddies were approximately cubic, occupying the whole flow depth, and were advected with the mean flow. Frequency spectra provided evidence that the cascade formulation was correct. The turbulent intermittency was proportional to the current speed and the value of c, calculated by several methods, was found to be constant with a value: C=0.3 cm2/s3 The characteristics of the largest eddies were isolated using a spectral cropping technique and plotted as a phase portrait of the turbulent strange attractor. This demonstrated that the boundary layer sat at preferred, discrete energy levels. The levels observed could be related to the discete cascade model. A computer code based on the model equations was tested against a series of large scale oil and dye releases in the North Sea. The observed intermittency, meandering, and dispersion were well simulated with the value of c given above.

The research is concerned with· exploration of the utility of fractal methods for characterising the mixing treatment applied to a rubber compound and also for characterising the microstructure developed during mixing (filler dispersion). Fractal analysis is also used for characterisation of the fracture surfaces generated during tensile testing of vulcanised samples. For these purposes, Maximum Entropy Method and Box Counting Method are developed and they are applied to analyse the mixing treatment and the filler dispersion, respectively. These methods are effectively used and it is found that fractal dimensions of mixer-power-traces and fracture surfaces of vulcanised rubber decrease with the evolution of mixing time while the fractal dimension of the state-of-mix (filler dispersion) also decreases. The relationship of the fractal dimensions thus determined with conventional properties, such as viscosity, tensile strength and heat transfer coefficient are then explored For example, a series of thennal measurements are carried out during vulcanisation process and the data are analysed for determining the heat transfer coefficient Nuclear Magnetic Resonance is used to obtain the properties of bound rubber and a quantitative analysis is also carried out and possible mechanisms for the relationships between the parameters are discussed based on existing interpretations. Fmally, the utility of the fractal methods for establishing mixing-microstructureproperty relationships is compared with more conventional and well established methods. For this purpose, the fractal dimension of the state-of-mix is compared to conventional methods such as the Payne Effect, electrical conductivity and carbon black dispersion (ASTM D2663 Method C). It is found that the characterisation by the fractal concept agrees with the conclusions from these conventional methods. In addition, it becomes possible to interpret the relationships between these conventional methods with the help of the fractal concept.

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Nonlinearity accompanied with stiffness in atmospheric boundary layer physical parameterizations is a well-known concern in numerical weather prediction (NWP) models. Nonlinear diffusion equations, furthermore, are a class of equations which are extensively applicable in different fields of science and engineering. Numerical stability and accuracy is a common concern in this class of equation. In the present research, a comprehensive effort has been made toward the temporal integration of such equations. The main goal is to find highly stable and accurate numerical methods which can be used specifically in atmospheric boundary layer simulations in weather and climate prediction models, and extensively in other models where nonlinear differential equations play an important role, such as magnetohydrodynamics and Navier-Stokes equations. A modified extended backward differentiation formula (ME BDF) scheme is adapted and proposed at the first stage of this research. Various aspects of this scheme, including stability properties, linear stability analysis, and numerical experiments, are studied with regard to applications for the time integration of commonly used nonlinear damping and diffusive systems in atmospheric boundary layer models. A new temporal filter which leads to significant improvement of numerical results is proposed. Nonlinear damping and diffusion in the turbulent mixing of the atmospheric boundary layer is dealt with in the next stage by using optimally stable singly-diagonally-implicit Runge-Kutta (SDIRK) methods, which have been proved to be effective and computationally efficient for the challenges mentioned in the literature. Numerical analyses are performed, and two schemes are modified to enhance their numerical features and stability. Three-stage third-order diagonally-implicit Runge-Kutta (DIRK) scheme is introduced by optimizing the error and linear stability analysis for the aforementioned nonlinear diffusive system. The new scheme is stable for a wide range of time steps and is able to resolve different diffusive systems with diagnostic turbulence closures, or prognostic ones with a diagnostic length scale, with enhanced accuracy and stability compared to current schemes. The procedure implemented in this study is quite general and can be used in other diffusive systems as well. As an extension of this study, high-order low-dissipation low-dispersion diagonally implicit Runge-Kutta schemes are analyzed and introduced, based on the optimization of amplification and phase errors for wave propagation, and various optimized schemes can be obtained. The new scheme shows no dissipation. It is illustrated mathematically and numerically that the new scheme preserves fourth-order accuracy. The numerical applications contain the wave equation with and without a stiff nonlinear source term. This shows that different optimized schemes can be investigated for the solution of systems where physical terms with different behaviours exist.