In a laminar model of a collisionless magnetosonic shock wave, ion equations of motion are integrated through shock-like profiles. Conservation relations and Maxwell's equations allow a self-consistent determination of unknown downstream ion distribution functions fᵢ, ion temperature Tᵢ, and electric potential jump ̧›ʺ. Favourable comparison of model Tᵢ, ̧›ʺ. Favourable comparison of model Tᵢ, ̧›ʺ , with experiment establishes (at low ̧›ư ́œø O.3, ̧›ư=8 Ï€ N [sub] l k (T[sub]é‚‚+Tᵢ[sub]l)/B́‚℗ø) importance of laminar ion dynamics. Heating is due to distortion of Maxwellian distributions when entropy is conserved; in particular shock dynamics is dominated by a fast "tail" of reflected ions. The solutions for fᵢ are considered. The "stability" of the model to its assumptions (linear profiles, shock thickness (L[sub]s)) is shown. When reflections occur a self-consistent length emerges. The solutions Tᵢ, ̧›ʺ are extensively studied at various Mach numbers for different values of ̧›ư. Laminar ion heating is very efficient and at high ̧›ư can exceed proper conservation levels due to ion reflections; at high ̧›ư(́œÆ ̧›ư *) the electric potential is unable to slow the ions to conservation levels. The model predicts significant reflected ion currents in the plane of the shock. The boundary ̧›ư * is determined. Then laminar ion dynamics on the scale of the electron heating length (~10 C/w[sub]p ́‚‘) cannot occur for ̧›ư > ̧›ư *. Dependence on L[sub]s and T ́‚‘́‚,/Tᵢ́‚ is considered. The nature of non-laminar ̧›ư >̧›ư* shocks is considered. Collisions are found to be important in laboratory shocks, and are efficient in slowing the reflected ions. In the absence of collisions, ion instabilities must be considered. It is shown that turbulent slowing of the fast ions cannot take place in L[sub]s alone. Further it is shown possible to construct a shock so that non-laminar mechanisms cannot occur significantly. Then the laminar model is re-instated. A decoupling of ion and electron heating lengths is proposed. Reflection heating in the Earth's Bow Shock (̧›ư>̧›ư*) is modelled, and is comparable with experiment.

The main focus of this research was to gain an understanding as to how waves propagate through structures. Lamb's Problem was studied on an isometric half plane, where numerical results were obtained. The calculated wavefronts for this problem were in agreement to the numerical results. When a distributed pressure is applied on an isometric half plane, after a long period of time, the wavefronts look as if a point force was applied on the half plane. Waves propagating through an orthotropic material were obtained numerically; it was found that Huygens' Principle cannot be used to calculate the wavefronts. The impact of spherical and cylindrical projectiles on glass plates was studied next. The waves introduced into the material were calculated using Finite Element Analysis, and compared to calculated wavefronts using Snell's Law, where they were found to be in agreement with one another. The effects of circular and square discontinuities were also studied, where a creeping wave that is produced after a wave propagates past a circular hole is explained. A sandwich beam was also modeled using FEA, where the wavefronts were obtained, and were found to be in agreement with calculated wavefronts. The displacement of the bottom layer of the sandwich beam was obtained numerically; it was found that the bending of the beam occurs at the same time as whether the middle layer is present or not.

Shelf tidal streams are accelerated by coastal features, such as headlands and islands. In the search for sustainable forms of electricity generation, such locations may become attractive for tidal stream power. For many prospective sites, however, little is known about the intricacies of the local tidal dynamics: knowledge which is crucial to understanding the resource and the potential environmental consequences of its extraction. This thesis explores tidal stream energy in the Pentland Firth (Scotland, UK). This channel contains some of the most promising tidal stream energy sites in the world and is set to become host to the first large-scale arrays of tidal stream turbines, but its detailed characteristics were previously unknown. A hydrodynamic model was used to investigate the complex tidal dynamics of the Pentland Firth. This demonstrated, for the first time, the hydrodynamic mechanisms driving the exceptionally fast tidal currents through this channel. The model was then refined at a key site within the Pentland Firth, the Inner Sound. The results provided insight into complex flow characteristics, such as displacement and misalignment of peak flood and ebb tides, which must be considered when contemplating the exploitation of this energy resource. Tidal stream turbines were simulated in the hydrodynamic model. Artificial energy extraction was parameterised at the sub-grid-scale via added seabed drag. Turbine drag of varying magnitude was represented by a novel analytical model based on published characteristics of horizontal axis turbines. This new formulation reflects the non-linear dynamics of tidal turbine operation. Using the new turbine model, arrays of turbines were simulated within the Inner Sound. Complex interactions between the dynamics of energy extraction and flow required individual turbines to be parameterised in-concert with all other turbines in the array. This required extra effort, but offered enhanced insight into the behaviour of turbine arrays. Accounting for nonlinear turbine dynamics at high current speeds limited the magnitude of peak energy dissipation. Tidal stream velocities decreased both upstream and downstream of the extraction zone and were accelerated around it. At peak energy extraction, changes in tidal velocity were detectable several kilometres from the array, but were confined to the shallow waters of the Inner Sound and its environs. Implications for array modelling are discussed in the context of environmental impact assessments.

Progress in integrating microwave circuits depends largely on the development of computationally effective and accurate numerical methods. These methods allow a miniaturization of microwave components and their utilization at higher frequency. In this thesis, the application of the mode matching method is described as well as their modification to different kinds of structure in rectangular and circular waveguides. The task is to design and optimize filters, multiplexers and impedance matching networks. In its most general form, the mode matching method at waveguide discontinuities requires the matching of four field components. However, to improve computational efficiency, the effect of matching only two field components (versus four field components) is investigated and successfully exploited for selected discontinuities. To satisfy space requirements, low loss, compact, and lightweight diplexer, triplexer and quadriplexer structures in rectangular waveguide technology are designed and optimized. The analysis is made possible by decomposing the structure into simple discontinuity sections such as discontinuity in width, height or bi- and tri-furcations. Three different types of discontinuities in coaxial waveguide are investigated: the outer step, the inner step and the gap discontinuities. By cascading such discontinuities, filters or matching networks can be obtained. Finally, a new type of circular waveguide bandpass filter using printed metal inserts is developed and designed in Ka-band. A comparison between theoretical results and measurements shows excellent agreement. / Graduate

No description available.

D.Sc. / Please refer to full text to view abstract

The breakdown of vertically propagating planetary waves in the stratosphere is investigated using an ultra-high horizontal resolution Contour Dynamics with Surgery model. In the model, planetary waves are forced at the tropopause and propagate upwards through the stratosphere and into an absorbing sponge (the first of its kind for such a model). In the context of wave breaking, two aspects of the system are questioned, namely, (1) what is the sensitivity to upper-boundary conditions? and (2) given perfect upper-boundary conditions what controls wave breaking? (1) In a Boussinesq environment. wave breaking is compared using: (a) a rigid upper-boundary condition (as in previous work) and (b) an absorbing sponge (preventing spurious reflections). In (a) both local (to the forcing) and remote breaking is evidenced for weak forcing while only local breaking is observed for sufficiently strong forcing. In (b) remote breaking is absent and local breaking, which occurs for sufficiently strong forcing, has quite a different character to that seen in (a). Compressibility effects are also investigated. (2) A quasi-linear theory is developed which predicts wave breaking if the zonal mean flow decelerates by more than one-half of its initial value (via positive group-velocity/zonal-mean-flow feedbacks). This so-called “one-half” rule for planetary wave breaking is confirmed through fully-nonlinear simulations. Numerical simulations detail the precise sequence of events leading up to and after wave breaking. / Graduate

No description available.

University of Macau / Faculty of Science and Technology / Department of Mathematics

M.Sc. (Theoretical Physics) / Please refer to full text to view abstract