Since the introduction of the Born and Rytov approximations for use in random wave propagation some forty years ago, a controversy has boiled over the regions of validity and relative merits of the methods. Although the methods fail for strong fluctuations and distant path lengths, these two perturbation methods are the only approaches available for weak fluctuations in a random in homogeneous media. The approximations have also been applied to the inverse problem for optical and acoustical tomography. The intent of this thesis is to investigate the work of previous authors and attempt to clarify the distinctions of each method. The conclusion will be reached that neither approximation is necessarily better than the other in general for all applications. A careful consideration of the problem following the points given should point towards the use of one approximation over the other. / Master of Science

In this Thesis the theoretical understanding of oscillations in coronal structures is developed. In particular, coronal loops are modelled as magnetic slabs of plasma. The effect of introducing inhomogeneities on the frequency of oscillation is studied. Current observations indicate the existence of magnetohydrodynamic (MHD) modes in the corona, so there is room for improved modelling of these modes to understand the physical processes more completely. One application of the oscillations, on which this Thesis concentrates, is coronal seismology. Here, the improved theoretical models are applied to observed instances of coronal MHD waves with the aim of determining information regarding the medium in which these waves propagate. In Chapter two, the effect of gravity on the frequency of the longitudinal slow MHD mode is considered. A thin, vertical coronal slab of magnetised plasma, with gravity acting along the longitudinal axis of the slab is studied, and the effect on the frequency of oscillation for the uniform, stratified and structured cases is addressed. In particular, an isothermal plasma, a two-layer plasma and a plasma with a linear temperature profile are studied. Here, a thin coronal loop, with its footpoints embedded in the chromosphere-photosphere is modelled, and the effects introduced by both gravity and the structuring of density at the footpoint layers are studied. In this case, gravity increases the frequency of oscillation and causes amplification of the eigenfunctions by stratification. Furthermore, density enhancements at the footpoints cause a decrease in the oscillating frequency, and can inhibit wave propagation, depending on the parameter regime. In Chapter three, the effects introduced to the transverse fast MHD mode when gravity acts across a thin coronal slab of magnetised plasma are considered. This study concentrates on the modification of the frequency due to the dynamical effect of gravity in the equation of motion, neglecting the effect of stratification. Here, gravity causes a reduction of the oscillating frequency of the fundamental fast mode, and increases the lower cutoff frequency. In effect, for this configuration, gravity allows the transition between body and surface modes, in a slab geometry. It is found, in these two studies, that each harmonic is affected in a unique manner due to structuring or stratification of density. With this knowledge, in Chapter four, a new parameter is derived; P1/2P2, the ratio of the period of the fundamental harmonic of oscillation to twice the period of its first harmonic. This parameter is shown to be a measure of the longitudinal structuring of density along a coronal loop, and the departure of this ratio from unity can yield information regarding the lengthscales of the structure. This process is highlighted using the known observations, indicating that P1/2P2 may prove to be a useful diagnostic tool for coronal seismology. Finally, in Chapter five, outwardly propagating coronal slow MHD modes are observed and are used to infer coronal parameters. The possibility of using these oscillations to infer near-resolution lengthscales in coronal loops -- fine-scale strands -- is also discussed. TRACE observations are used to determine the average period, phase speed, detection length, amplitude and energy flux for the propagating slow MHD mode. The indication is that the source of these oscillations appears very localised in space, and the driver only acts for a few periods, suggesting the perturbations are driven by leaky p-modes (solar surface modes).

In the present dissertation, the hydrodynamic and hydro-elastic characteristics of ship hull and plate vibrations are analyzed using theoretical and numerical methods. The wave forces are determined using a suite of methods which include the Froude-Krylov method for incident wave forces, Wagner's method and ABS rules for the slamming wave force, and numerical methods for nonlinear wave radiation forces. Finite difference methods are developed to determine the wave forced vibrations of ship hull plates which are modeled using a range of plate theories including nonlinear plate theory with and without material damping and orthotropic plate theory for stiffened hull plates. For small amplitude deformation of thin plates, a semi-theoretical superposition method is used to determine the free and forced vibrations. The transient ship hull vibration due to whipping is also analyzed using the finite difference method. Results, in the form of deformations and stress distributions, are obtained for a range of scantling and wave parameters to identify key parameters to consider in ship structural design. / by Fnu Lakitosh. / Thesis (Ph.D.)--Florida Atlantic University, 2012. / Includes bibliography. / Electronic reproduction. Boca Raton, Fla., 2012. Mode of access: World Wide Web.

Fu Sau-chung. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2006. / Includes bibliographical references (leaves 68-71). / Abstracts in English and Chinese. / Abstract --- p.i / Acknowledgement --- p.iii / Chapter 1 --- Introduction --- p.1 / Chapter 1.1 --- Background of Explosion and Implosion Problems --- p.1 / Chapter 1.2 --- Background of the Development of Numerical Schemes --- p.2 / Chapter 1.3 --- Organization of the Thesis --- p.5 / Chapter 2 --- Governing Equations and Numerical Schemes --- p.6 / Chapter 2.1 --- Governing Equations --- p.6 / Chapter 2.2 --- Numerical Schemes --- p.8 / Chapter 2.2.1 --- Splitting Scheme for Partial Differential Equations with Source Terms --- p.8 / Chapter 2.2.2 --- Boundary Conditions --- p.9 / Chapter 2.2.3 --- "Numerical Solvers for the ODEs - The Second-Order, Two-Stage Runge-Kutta Method" --- p.10 / Chapter 2.2.4 --- Numerical Solvers for the Pure Advection Hyperbolic Problem - The Second-Order Relaxed Scheme --- p.11 / Chapter 3 --- Numerical Results --- p.29 / Chapter 3.1 --- Spherical Explosion Problem --- p.30 / Chapter 3.1.1 --- Physical Description --- p.32 / Chapter 3.1.2 --- Comparison with Previous Analytical and Experimental Results --- p.33 / Chapter 3.2 --- Cylindrical Explosion Problem --- p.46 / Chapter 3.2.1 --- Physical Description --- p.46 / Chapter 3.2.2 --- Two-Dimensional Model --- p.49 / Chapter 3.3 --- Spherical Implosion Problem --- p.52 / Chapter 3.3.1 --- Physical Description --- p.52 / Chapter 3.4 --- Cylindrical Implosion Problem --- p.53 / Chapter 3.4.1 --- Physical Description --- p.53 / Chapter 3.4.2 --- Two-Dimensional Model --- p.53 / Chapter 4 --- Conclusion --- p.65 / Bibliography --- p.68

Graduation date: 1992

Accurate modeling and simulation of wave propagation in dispersive dielectrics such as water, human tissue and sand, among others, has a variety of applications. For example in medical imaging, electromagnetic waves are used to interrogate human tissue in a non-invasive manner to detect anomalies that could be cancerous. In non-destructive evaluation of materials, such interrogation is used to detect defects in these materials. In this thesis we present the construction and analysis of two novel operator splitting methods for Maxwell's equations in dispersive media of Debye type which are used to model wave propagation in polar materials like water and human tissue. We construct a sequential and a symmetrized operator splitting scheme which are first order, and second order, respectively, accurate in time. Both schemes are second order accurate in space. The operator splitting methods are shown to be unconditionally stable via energy techniques. Their accuracy and stability properties are compared to established schemes like the Yee or FDTD scheme and the Crank-Nicolson scheme. Finally, results of numerical simulations are presented that confirm the theoretical analysis. / Graduation date: 2012 / Access restricted to the OSU Community at author's request from June 20, 2012 - Dec. 20, 2012

Many hydrocarbon reservoirs have sufficient porosity but low permeability (for example, tight gas sands and coal beds). However, such reservoirs are often naturally fractured. The fracture patterns in these reservoirs can control flow and transport properties, and therefore, play an important role in drilling production wells. On the scale of seismic wavelengths, closely spaced parallel fractures behave like an anisotropic media, which precludes the response of individual fractures in the seismic data. There are a number of fracture parameters which are needed to fully characterize a fractured reservoir. However, seismic data may reveal only certain fracture parameters and those are fracture orientation, crack density and fracture infill. Most of the widely used fracture characterization methods such as Swave splitting analysis or amplitude vs. offset and azimuth (AVOA) analysis fail to render desired results in laterally varying media. I have conducted a systematic study of the response of fractured reservoirs with laterally varying elastic and fracture properties, and I have developed a scheme to invert for the fracture parameters. I have implemented a 3D finite-difference method to generate multicomponent synthetic seismic data in general anisotropic media. I applied the finite-difference algorithm in both Standard and Rotated Staggered grids. Standard Staggered grid is used for media having symmetry up to orthorhombic (isotropic, transversely isotropic, and orthorhombic), whereas Rotated Staggered grid is implemented for monoclinic and triclinic media. I have also developed an efficient and accurate ray-bending algorithm to compute seismic traveltimes in 3D anisotropic media. AVOA analysis is equivalent to the first-order Born approximation. However, AVOA analysis can be applied only in a laterally uniform medium, whereas the Born-approximation does not pose any restriction on the subsurface structure. I have developed an inversion scheme based on a ray-Born approximation to invert for the fracture parameters. Best results are achieved when both vertical and horizontal components of the seismic data are inverted simultaneously. I have also developed an efficient positivity constraint which forbids the inverted fracture parameters to be negative in value. I have implemented the inversion scheme in the frequency domain and I show, using various numerical examples, that all frequency samples up to the Nyquist are not required to achieve desired inversion results.

Tide-topography coupling is important for understanding surface-tide energy loss, the intermittency of internal tides, and the cascade of internal-tide energy from large to small scales. Although tide-topography coupling has been observed and modeled for 50 years, the identification of surface and internal tides over arbitrary topography has not been standardized. Here, we begin by examining five surface/internal-tide decompositions and find that only one is (i) consistent with the normal-mode description of tides over a flat bottom, (ii) produces a physically meaningful depth-structure of internal-tide energy flux, and (iii) results in an established expression for internal-tide generation. Next, we examine the expression for internal-tide generation and identify how it is influenced by remotely-generated shoaling internal tides. We show that internal-tide generation is subject to both resonance and intermittency, and can not always be predicted from isolated regional models. Lastly, we quantify internal-tide generation and scattering on the Oregon Continental slope. First, we derive a previously unpublished expression for inter-modal energy conversion. Then we evaluate it using observations and numerical simulations. We find that the surface tide generates internal tides, which propagate offshore; while at the same time, low-mode internal tides shoal on the slope, scatter, and drive turbulent mixing. These results suggest that internal tides are unlikely to survive reflection from continental slopes, and that continental margins play an important role in deep-ocean tidal-energy dissipation. / Graduation date: 2011

[Truncated abstract] Observations are presented from Lake Biwa (Japan) and Lake Kinneret (Israel) showing the ubiquitous and often periodic nature of high-frequency internal waves in large stratified lakes. In both lakes, high-frequency wave events were observed within two distinct categories: (1) Vertical mode one solitary waves with wavelength ˜100-500 m and frequency near 103 Hz and (2) sinusoidal vertical mode one waves with wavelength ˜5-30 m and frequency just below the local maximum buoyancy frequency near 102 Hz. The sinusoidal waves were associated with shear instability and were shown to dissipate their energy sporadically within the lake interior. Conversely, the solitary waves were found to be capable of propagating to the lake perimeter where they may break upon sloping topography, each releasing ˜1% of the total basin-scale internal wave energy to the benthic boundary layer.

Department of Civil, Surveying and Environmental Engineering. Bibliography: leaves 246-255