"In this dissertation we study the so-called “city effect” problem. This effect occurs when earthquakes strike large cities. In earlier studies, seismic wave propagation was evaluated in a separate step and then impacts on man made structures above ground were calculated. The 1985 Michoacan earthquake in Mexico City led Wirgin and Bard (1996) to hypothesize that city buildings may collectively affect the ground motion during an earthquake. Ghergu and Ionescu (2009) proposed a model of this phenomenon and a solution algorithm. Our contribution is to extend their work and to provide a mathematical analysis for proving the existence of preferred frequencies coupling vibrations of buildings to underground seismic waves. Given the geometry and the specific physical constants of an idealized two dimensional city, Ghergu and Ionescu computed a frequency that will couple vibrating buildings to underground seismic waves. This frequency was obtained by increasing the number of buildings at the expense of solving larger and larger systems. Our idea is to use a periodic Green's function and perform computations on a single period. That allows for much faster computations, and makes it possible to consider more complex geometries within a single period. We provide a rather in depth and proof based account of different formulations for the periodic Green's function that we need. We show that they are indeed fundamental solutions to the Helmholtz operator and we analyze their convergence rate. Finally, we give a mathematical proof of existence of preferred frequencies coupling vibrations of buildings to underground seismic waves."

No description available.

Distributed Point Source Method (DPSM) was developed by Placko and Kundu 1, as a technique for modeling electromagnetic and elastic wave propagation problems. DPSM has been used for modeling ultrasonic, electrostatic and electromagnetic fields scattered by defects and anomalies in a structure. The modeling of such scattered field helps to extract valuable information about the location and type of defects. Therefore, DPSM can be used as an effective tool for Non-Destructive Testing (NDT). Anisotropy adds to the complexity of the problem, both mathematically and computationally. Computation of the Green's function which is used as the fundamental solution in DPSM is considerably more challenging for anisotropic media, and it cannot be reduced to a closed-form solution as is done for isotropic materials. The purpose of this study is to investigate and implement DPSM for an anisotropic medium. While the mathematical formulation and the numerical algorithm will be considered for general anisotropic media, more emphasis will be placed on transversely isotropic materials in the numerical example presented in this paper. The unidirectional fiber-reinforced composites which are widely used in today's industry are good examples of transversely isotropic materials. Development of an effective and accurate NDT method based on these modeling results can be of paramount importance for in-service monitoring of damage in composite structures.

The ability to predict and control laminar-to-turbulent transition in high-speed flow has a substantial effect on heat transfer and skin friction, thus improving the design and operation of hypersonic vehicles. The control of transition on blunt bodies is essential to improve the performance of lifting and control surfaces. The objective of this Ph.D. research is to develop efficient and accurate algorithms for the detection of high-frequency heat flux fluctuations supported by hypersonic flow in transitional boundary layers. The focus of this research is on understanding the mathematical properties of the reconstruction such as regularity, sensitivity to noise, multi-resolution, and accuracy. This research is part of an effort to develop small-footprint heat flux sensors able to measure high-frequency fluctuations on test articles in a hypersonic wind tunnel with a small curvature radius. In the present theoretical/numerical study a multi-resolution formulation for the direct and inverse reconstruction of the heat flux from temperature sensors distributed over a multidimensional solid in a hypersonic flow was developed and validated. The solution method determines the thermal response by approximating the system Green's function with the Galerkin method and optimizes the heat flux distribution by fitting the distributed surface temperature data. Coating and glue layers are treated as separate domains for which the Green's function is obtained independently. Connection conditions for the system Green's function are derived by imposing continuity of heat flux and temperature concurrently at all interfaces. The solution heat flux is decomposed on a space-time basis with the temporal basis a multi-resolution wavelet with arbitrary scaling function. Quadrature formulas for the convolution of wavelets and the Green's function, a reconstruction approach based on isoparametric mapping of three-dimensional geometries, and a boundary wavelet approach for inverse problems were developed and verified. This approach was validated against turbulent conjugate heat transfer simulations at Mach 6 on a blunted wedge at 0 angle of attack and wind tunnel experiments of round impinging jet at Mach 0.7 It was found that multidimensional effects were important near the wedge shoulder in the short time scale, that the L-curve regularization needed to be locally corrected to analyze transitional flows and that proper regularization led to sub-cell resolution of the inverse problem. While the L2 regularization techniques are accurate they are also computationally inefficient and lack mathematical rigor. Optimal non-linear estimators were researched both as means to promote sparsity in the regularization and to pre-threshold the inverse heat conduction problem. A novel class of nonlinear estimators is presented and validated against wind tunnel experiments for a flat-faced cylinder also at Mach 6. The new approach to hypersonic heat flux reconstruction from discrete temperature data developed in this thesis is more efficient and accurate than existing techniques. / Doctor of Philosophy / The harsh environment supported by hypersonic flows is characterized by high-frequency turbulent bursts, acoustic noise, and vibrations that pollute the signals of the sensors that probe at high frequencies the state of the boundary layers developing on the walls. This research describes the search for optimal estimators of the noisy signal, i.e., those that lead to the maximum attenuation of the risk of error pollution by non-coherent scales. This research shows that linear estimators perform poorly at high-frequency and non-linear estimators can be optimized over a sparse projection of the signal in a discrete wavelet basis. Optimal non-linear estimators are developed and validated for wind tunnel experiments conducted at Mach 6 in the Advanced Propulsion and Power Laboratory at Virginia Tech.

Interferometry in geosciences uses mathematical techniques to image subsurface properties. This method turns a receiver in to a virtual source through utilizing either random noises or engineered sources. The method in seismology has been discussed extensively. Electromagnetic interferometry at high frequencies with coupled electromagnetic fields was developed in the past. However, the problem was not addressed for diffusive electromagnetic fields where the quasi-static limit holds. One of the objectives of this dissertation was to theoretically derive the impulse response of the Earth for low-frequency electromagnetic fields. Applying the theory of interferometry in the regions where the wavefields are diffusive requires volumetrically distributed sources in an infinite domain. That precondition imposed by the theory is not practical in experiments. Hence, the aim of this study was to quantify the important areas and distribution of sources that makes it possible to apply the theory in practice through conducting numerical experiments. Results of the numerical analysis in double half-space models revealed that for surface-based exploration scenarios sources are required to reside in a region with higher diffusivity. In contrast, when the receivers straddle an interface, as in borehole experiments, there is no universal rule for which region is more important; it depends on the frequency, receiver separation and also diffusivity contrast between the layers and varies  for different scenarios. Time-series analysis of the sources confirmed previous findings that the accuracy of the Green\'s function retrieval is a function of both source density and its width. Extending previous works in homogenous media into inhomogeneous models, it was found that sources must be distributed asymmetrically in the system, and extend deeper into the high diffusivity region in comparison to the low diffusivity area. The findings were applied in a three-layered example with a reservoir layer between two impermeable layers. Bayesian statistical inversion of the data obtained by interferometry was then used to estimate the fluid diffusivity (and permeability) along with associated uncertainties. The inversion results determined the estimated model parameters in the form of probability distributions. The output demonstrated that the algorithm converges closely to the true model. / Ph. D.

The growing fields of spintronics and nanotechnology have created increased interest in developing the means to manipulate the spin of electrons. One such method arises from the combination of the spin-orbit interaction and the broken inversion symmetry that arises at surfaces and interfaces, and has prompted many recent investigations on metallic surfaces. A method by which surface states, in the absence of spin orbit effects, have been successfully investigated is the Green function embedding scheme of Inglesfield. This has been integrated into a self consistent FLAPW density functional framework based on the scalar relativistic K¨olling Harmon equation. Since the spin of the electron is a direct effect of special relativity, calculations involving the spin orbit interaction are best performed using solutions of the Dirac equation. This work describes the extension of Green’s function embedding to include the Dirac equation and how fully relativistic FLAPW surface electronic structure calculations are implemented. The general procedure used in performing a surface calculation in the scalar relativistic case is closely followed. A bulk transfer matrix is defined and used to generate the complex band structure and an embedding potential. This embedding potential is then used to produce a self consistent surface potential, leading to a Green’s function from which surface state dispersions and splittings are calculated. The bulk embedding potential can also be employed in defining channel functions and these provide a natural framework in which to explore transport properties. A relativistic version of a well known expression for the ballistic conductance across a device is derived in this context. Differences between the relativistic and nonrelativistic methods are discussed in detail. To test the validity of the scheme, a fully relativistic calculation of the extensively studied spin orbit split L-gap surface state on Au(111) is performed, which agrees well with experiment and previous calculations. Contributions to the splitting from different angular momentum channels are also provided. The main advantages of the relativistic embedding method are the full inclusion of the spin orbit interaction to all orders, the true semi infinite nature of the technique, allowing the full complex bands of the bulk crystal to be represented and the fact that a only small number of surface layers is needed in comparison to other existing methods.

<p>This Licentiate presents the main results of theoretical study of light propagation in photonic structures, namely lasing disk microcavities and photonic crystals. In the first two papers (Paper I and Paper II) we present the developed novel scattering matrix technique dedicated to calculation of resonant states in 2D disk microcavities with the imperfect surface or/and inhomogeneous refractive index. The results demonstrate that the imperfect surface of a cavity has the strongest impact on the quality factor of lasing modes.</p><p>The generalization of the scattering-matrix technique to the quantum-mecha- nical case has been made in Paper III. That generalization has allowed us to treat a realistic potential of quantum-corrals (which can be considered as nanoscale analogues of optical cavities) and to obtain a good agreement with experimental observations.</p><p>Papers IV and V address the novel effective Green's function technique for studying propagation of light in photonic crystals. Using this technique we have analyzed characteristics of surface modes and proposed several novel surface-state-based devices for lasing/sensing, waveguiding and light feeding applications.</p> / Report code: LIU-TEK-LIC 2006:5

Evaluation of motion characteristics of ships and offshore structures at the early stage of design as well as during operation at the site is very important. Strip theory based programs and 3D panel method based programs are the most popular tools used in industry for vessel motion analysis. These programs use different variations of the Green’s function or Rankine sources to formulate the boundary element problem which solves the water wave radiation and diffraction problem in the frequency domain or the time domain. This study presents the development of a 3D frequency domain Green’s function method in infinite water depth for predicting hydrodynamic coefficients, wave induced forces and motions. The complete theory and its numerical implementation are discussed in detail. An in house application has been developed to verify the numerical implementation and facilitate further development of the program towards higher order methods, inclusion of forward speed effects, finite depth Green function, hydro elasticity, etc. The results were successfully compared and validated with analytical results where available and the industry standard computer program WAMIT v7.04 for simple structures such as floating hemisphere, cylinder and box barge as well as complex structures such as ship, spar and a tension leg platform.

No description available.

Thesis (Ph. D.)--University of Nevada, Reno, 2008. / "May 2008." Includes bibliographical references (leaves 66-76). Online version available on the World Wide Web.