Yes / A two-dimensional numerical model is developed to study the propagation of a solitary wave in the presence of a steady current flow. The numerical model is based on the Reynolds-averaged Navier-Stokes (RANS) equations with a k-ε turbulence closure scheme and an internal wave-maker method. To capture the air-water interface, the volume of fluid (VOF) method is used in the numerical simulation. The current flow is initialized by imposing a steady inlet velocity on one computational domain end and a constant pressure outlet on the other end. The desired wave is generated by an internal wave-maker. The propagation of a solitary wave travelling with a following/opposing current is simulated. The effects of the current velocity on the solitary wave motion are investigated. The results show that the solitary wave has a smaller wave height, larger wave width and higher travelling speed after interacting with a following current. Contrariwise, the solitary wave becomes higher with a smaller wave width and lower travelling speed with an opposing current. The regression equations for predicting the wave height, wave width and travelling speed of the resulting solitary wave are for practical engineering applications. The impacts of current flow on the induced velocity and the turbulent kinetic energy (TKE) of a solitary wave are also investigated. / National Natural Science Foundation of China Grant #51209083, #51137002 and #41176073, the Natural Science Foundation of Jiangsu Province (China) Grant #BK2011026, the 111 Project under Grant No. B12032, the Fundamental Research Funds for the Central University, China (2013B31614), and the Carnegie Trust for Scottish Universities

The method of spin projection was examined by developing and applying computer programs to calculate projected semi-empirical and ab initio unrestricted Hartree-Fock (UHF) wavefunctions. The electronic spectra of naphthalene, anthracene, naphthacene and pentacene were calculated using the Pariser-Pople-Parr (PPP) Π-electron approximations and both UHF and configurational interaction (CI) techniques. The results of both techniques were compared with experimentally determined spectra with reasonable agreement between the CI and projected UHF results. While the CI calculations generally produced lower energies for the triplet states than the UHF calculations, the spectra from UHF calculations were in somewhat better agreement with experiment. Anomalies encountered with degeneracies and the presence of open shell ground states are also discussed. The geometry of monohomocyclooctatetraene anion radical (MHCOT) was studied using spin projection of the UHF INDO wavefunction. The theoretical molecular geometry was varied until the experimental hyperfine coupling constants matched hyperfine constants obtained from using both projected and unprojected UHF wavefunctions. The two types of calculations resulted in slightly different energies and geometries with the projected calculations giving a higher energy for the doublet state; essentially no differences were noted in the bond orders obtained from the two types of calculations. The geometry from the projected calculations was a somewhat more strained conformation than the geometry from the unprojected calculation. Ab initio UHF calculations with spin projection were performed on H₂O(+) to compare the energies of pure spin states from ab initio multiconfigurational self-consistent field with CI. (MCSCF/CI) with those from spin projection. The MCSCF/CI calculations are superior to the UHF plus spin projection calculations. This result will always be observed when the UHF wavefunction is very close to a pure spin state before spin projection. The dissociation of CF₂O was studied using ab initio wavefunctions. The energies of the unprojected UHF wavefunctions were examined along with those for the dissociated CF₂ + O fragments. Good agreement exists between the calculated and experimental vertical ionization potentials for CF₂0 at the equilibrium geometry. / Doctor of Philosophy

Coastal regions are vulnerable to various natural processes, ranging from normal waves to extreme events. Given the flourishing development and large population along coastlines, various measures have been taken to mitigate the water-induced damage. Nature-based coastal protection, especially vegetation, has attracted unprecedented studies over the past two decades. To enhance understanding of this subject, this dissertation evaluates the impact of patchy vegetation on wave and runup dynamics along coastlines. Selecting from a prototype in Dalehite Cove, Galveston Bay, TX, results from a Boussinesq model (COULWAVE) showed patchy vegetation reduced up to 75% mean shoreward current in the mound-channel wetland systems. These vegetation patches also reduced the primary circulation around mounds, with a power-form relation between circulation size and various parameters (i.e., bathymetry, incident wave and vegetated roughness). Substituting spectral waves for regular waves in the similar wetlands, more energy was transferred into the higher frequencies. The impact of patchy vegetation on wave energy was frequency- and space-dependent, with increased energy observed in specific harmonics and locations. Comparison with unvegetated horizontal bathymetry demonstrated that mound-channel bathymetry was the dominant factor in transferring and dissipating wave energy, while vegetation patches added a fair contribution. As for extreme events, such as tsunamis, laboratory experiments and numerical simulations were conducted to assess the effectiveness of patchy vegetation with various roughness levels, spacings and sizes. Overall, vegetation patches reduced the most destructive loads onshore by up to 80%. Within-patch roughness variation only caused uncertainty on the hydrodynamics around the seaward patches, while the mitigation of extreme loads was not undermined. A logarithmic relation was observed between the protected area from extreme loads and the vegetated coverage. These findings will fill the knowledge gap of hydrodynamics in the presence patchy vegetation, and improve the engineering practice of coastal protection using nature-based infrastructure. / Ph. D.

The purpose of this thesis is to investigate the properties and wave velocities for an axially symmetric medium. The investigation consists of four parts. In the first part, the physical properties of the medium are defined. Then the stress-strain relations for the case under consideration are obtained from the general case. This is done by imposing the condition of symmetry on the strain energy function. Next the measurable constants are round in terms or the natural constants. This is done by applying simple extensions and shears to the material. After the measurable constants are determined in terms or the natural constants, then the relationship is inverted and the natural constants are found in terms or the measurable constants. Some elastic constants are then determined for an arbitrary direction, as it is not likely that the stresses will always be imposed along an axis of symmetry. Following this major part, the equations of motion for a vibrating medium are determined in terms or the natural constants by substituting the stress-strain relations. This is very straightforward, but must be done. The final step is made by finding the velocities of propagation of the waves by using the equations of motion. This is done by assuming a solution and substituting into the equations of motion. From these equations, a cubic equation defining the three principal velocities arises. The solution of this cubic equation is the culmination of this investigation. / M.S.

The structure of seismic discontinuities at depths of about 410 km and 660 km provides important constraints on mantle convection as the associated mineral phase transformations in the transition zone are sensitive to thermal perturbations. Teleseismic P-to-S receiver functions have been widely used to map the depths of the two discontinuities. In this study, we investigate the resolution of receiver functions in imaging topographic variations of the 410-km and 660-km discontinuities based on wave propagation simulations using a Spectral Element Method (SEM). We investigate finite-frequency effects of direct P waves as well as P-to-S converted waves by varying the length scale of discontinuity topography in the transition zone. We show that wavefront healing effects are significant in broadband receiver functions. For example, at a period of 10 to 20 seconds, the arrivaltime anomaly in P-to-S converted waves is about 50% of what predicted by ray theory when the topography length scale is in the order of 400 km. The observed arrival anomaly further reduces to 10-20% when the topography length scale reduces to about 200 km. We calculate 2-D boundary sensitivity kernels for direct P waves as well as receiver functions based on surface wave mode summation and confirm that finite frequency-effects can be properly accounted for. Three-dimensional wavespeed structure beneath seismic stations can also introduce significant artifacts in transition zone discontinuity topography if time corrections are not applied, and, the effects are dependent on frequency. / Master of Science

In this work, nondispersive wave packet solutions to linear partial differential equations are investigated. These solutions are characterized by infinite energy content; otherwise, they are continuous, nonsingular and propagate in free space without spreading out. Examples of such solutions are Berry and Balazs’ Airy packet, MacKinnon’s wave packet and Brittingham’s Focus Wave Mode (FWM). It is demonstrated in this thesis that the infinite energy content is not a basic problem per se and that it can be dealt with in two distinct ways. First these wave packets can be used as bases to construct highly localized, slowly decaying, time-limited pulsed solutions. In the case of the FWMs, this path leads to the formulation of the bidirectional representation, a technique that provides the most natural basis for synthesizing Brittingham-like solutions. This representation is used to derive new exact solutions to the 3-D scalar wave equation. It is also applied to problems involving boundaries, in particular to the propagation of a localized pulse in an infinite acoustic waveguide and to the launch ability of such a pulse from the opening of a semi-infinite waveguide. The second approach in dealing with the infinite energy content utilizes the bump-like structure of nondispersive solutions. With an appropriate choice of parameters, these bump fields have very large amplitudes around the centers, in comparison to their tails. In particular, the FWM solutions are used to model massless particles and are capable of providing an interesting interpretation to the results of Young’s two slit experiment and to the wave-particle duality of light. The bidirectional representation provides, also, a systematic way of deriving packet solutions to the Klein-Gordon, the Schrodinger and the Dirac equations. Nondispersive solutions of the former two equations are compared to previously derived ones, e.g., the Airy packet and MacKinnon's wave packet. / Ph. D.

Call number: LD2668 .T4 1960 M55

This dissertation presents the research on a novel combination of well proven concepts for passive electromagnetic wave-guiding components. The goal of this work is to overcome and minimize losses occurring in frequency-selective structures. The work aims to contribute to an improvement in the application of conventional and Substrate Integrated Waveguide (SIW). It is proposed to mount conventional waveguide structures on the surface of printed circuit boards containing substrate integrated waveguides. The crossover technology is referred to as Surface Mounted Waveguide (SMW). Theoretical investigations are performed, proving the validity and superiority of the proposed structure focusing on the elimination of losses, while maintaining low space consumption and printed circuit board technology compatible manufacturing processes. Additionally, a mode matching technique is developed and successfully applied to prototype such components. The validation of this method reveals superior computational speed when compared to commercial available electromagnetic field solvers. The proposed structures are validated by measurements of several prototypes, including coupled SMW resonator filters, combined SMW and SIW resonator filters, a SMW triple-layer diplexer and single individual SMW resonator filters. The experimental verification shows good agreement between theory and measurements. Moreover, the comparison to other technologies proves the superiority of the proposed structures. / Graduate

Combined electrical and structural models of five types of permanent magnet linear electrical machines suitable for direct-drive power take-off on wave energy applications are presented. Electromagnetic models were developed using polynomial approximation to finite element analysis results. The structural models are based on simple beam theory, other classical techniques, and automated finite element analysis formulations. The machine models have been integrated with a time-domain model of a wave energy converter based on a heaving buoy. They have then been optimised using a genetic algorithm approach, using a score based primarily on the amortised cost per unit of energy production. The optimised designs have then been used for a comparison of the economic performance of the generator types.

published_or_final_version / Physics / Master / Master of Science