For accurate prediction of tsunami wave propagation, information on the system of PDEs modelling its evolution and full initial and/or boundary data is required. However the latter is not generally fully available, and so the primary objective becomes to find an optimal estimate of these conditions, using available information. Data Assimilation is a methodology used to optimally integrate observed measurements into a mathematical model, to generate a better estimate of some control parameter, such as the initial condition of the wave, or the sea floor bathymetry. In this study, we considered the shallow water equations in both linear and non-linear form as an approximation for ocean wave propagation, and derived a data assimilation scheme based on the calculus of variations, the purpose of which is to optimise some distorted form of the initial condition to give a prediction closer to the exact initial data. We considered two possible forms of distortion, by adding noise to our initial wave, and by rescaling the wave amplitude. Multiple cases were analysed, with observations measured at different points in our spatial domain, as well as variations in the number of observation points. We found that the error between measurements and observation data was sufficiently minimised across all cases. A relationship was found between the number of measurement points and the error, dependent on the choice of where measurements were taken. In the linear case, since the wave form simply translates a fixed form, multiple measurement points did not necessarily provide more information. In the nonlinear case, because the waveform changes shape as it translates, adding more measurement points provides more information about the dynamics and the wave shape. This is reflected in the fact that in the nonlinear case adding more points gave a bigger decrease in error, and much closer convergence of the optimised guess for our initial condition to the exact initial wave profile. / Thesis / Master of Science (MSc) / In ocean wave modelling, information on the system dynamics and full initial and/or boundary data is required. When the latter is not fully available the primary objective is to find an optimal estimate of these conditions, using available information. Data Assimilation is a methodology used to optimally integrate observed measurements into a mathematical model, to generate a better estimate of some control parameter, such as the initial condition of the wave, or the sea floor bathymetry. In this study, we considered the shallow water equations in both linear and non-linear form as an approximation for ocean wave propagation, and derived a data assimilation scheme to optimise some distorted form of the initial condition to generate predictions converging to the exact initial data. The error between measurements and observation data was sufficiently minimised across all cases. A relationship was found between the number of measurement points and the error, dependent on the choice of where measurements were taken.

No description available.

Significant effort in the current technological development of aircraft is aimed at improving engine efficiency, while reducing fuel burn, emissions, and noise levels. One way to achieve these is to better integrate airframe and propulsion system. Tighter integration, however, may also cause adverse effects to the flow entering the engines, such as total pressure, total temperature, and swirl distortions. Swirl distortions are angular non-uniformities in the flow that may alter the functioning of specific components of the turbomachinery systems. To investigate the physics involved in the ingestion of swirl, pre-determined swirl distortion profiles were generated through the StreamVane method in a low-speed wind tunnel and in a full-scale turbofan research engine. Stereoscopic particle image velocimetry (PIV) was used to collect three-component velocity fields at discrete planes downstream of the generation of the distortions with two main objectives in mind: identifying the physics behind the axial development of the distorted flow; and describing the generation of the distortion by the StreamVane and its impact to the flow as a distortion generating device. Analyses of the mean velocity, velocity gradients, and Reynolds stress tensor components in these flows provided significant insight into the driving physics. Comparisons between small-scale and full-scale results showed that swirl distortions are Mach number independent in the subsonic regime. Reynolds number independence was also verified for the studied cases. The mean secondary flow and flow angle profiles demonstrated that the axial development of swirl distortions is highly driven by two-dimensional vortex dynamics, when the flow is isolated from fan effects. As the engine fan is approached, the vortices are axially stretched and stabilized by the acceleration of the flow. The flow is highly turbulent immediately downstream of the StreamVane due to the presence of the device, but that vane-induced turbulence mixes with axial distance, so that the device effects are attenuated for distances greater than a diameter downstream, which is further confirmed by the turbulent length scales of the flow. These results provide valuable insight into the generation and development of swirl distortion for ground-testing environments, and establishes PIV as a robust tool for engine inlet investigations. / Ph. D.

There is a growing demand for the high quality TV programs such as High Definition TV (HDTV). The CATV network is often a suitable solution to address this demand using a CATV modem delivering high data rate digital signals in a cost effective manner, thereby, utilizing a complex digital modulation scheme is inevitable. Exploiting complex modulation schemes, entails a more sophisticated modulator and distribution system with much tighter tolerances. However, there are always distortions introduced to the modulated signal in the modulator degrading signal quality.<p> In this research, the effect of distortions introduced by the RF band pass filter in the modulator will be considered which cause degradations on the quality of the output Quadrature Amplitude Modulated (QAM) signal. Since the RF filter's amplitude/group delay distortions are not symmetrical in the frequency domain, once translated into the base band they have a complex effect on the QAM signal. Using Matlab, the degradation effects of these distortions on the QAM signal such as Bit Error Rate (BER) is investigated.<p> In order to compensate for the effects of the RF filter distortions, two different methods are proposed. In the first method, a complex base band compensation filter is placed after the pulse shaping filter (SRRC). The coefficients of this complex filter are determined using an optimization algorithm developed during this research. The second approach, uses a pre-equalizer in the form of a Feed Forward FIR structure placed before the pulse shaping filter (SRRC). The coefficients of this pre-equalizer are determined using the equalization algorithm employed in a test receiver, with its tap weights generating the inverse response of the RF filter. The compensation of RF filter distortions in base band, in turn, improves the QAM signal parameters such as Modulation Error Ratio (MER). Finally, the MER of the modulated QAM signal before and after the base band compensation is compared between the two methods, showing a significant enhancement in the RF modulator performance.

There is a growing demand for the high quality TV programs such as High Definition TV (HDTV). The CATV network is often a suitable solution to address this demand using a CATV modem delivering high data rate digital signals in a cost effective manner, thereby, utilizing a complex digital modulation scheme is inevitable. Exploiting complex modulation schemes, entails a more sophisticated modulator and distribution system with much tighter tolerances. However, there are always distortions introduced to the modulated signal in the modulator degrading signal quality.<p> In this research, the effect of distortions introduced by the RF band pass filter in the modulator will be considered which cause degradations on the quality of the output Quadrature Amplitude Modulated (QAM) signal. Since the RF filter's amplitude/group delay distortions are not symmetrical in the frequency domain, once translated into the base band they have a complex effect on the QAM signal. Using Matlab, the degradation effects of these distortions on the QAM signal such as Bit Error Rate (BER) is investigated.<p> In order to compensate for the effects of the RF filter distortions, two different methods are proposed. In the first method, a complex base band compensation filter is placed after the pulse shaping filter (SRRC). The coefficients of this complex filter are determined using an optimization algorithm developed during this research. The second approach, uses a pre-equalizer in the form of a Feed Forward FIR structure placed before the pulse shaping filter (SRRC). The coefficients of this pre-equalizer are determined using the equalization algorithm employed in a test receiver, with its tap weights generating the inverse response of the RF filter. The compensation of RF filter distortions in base band, in turn, improves the QAM signal parameters such as Modulation Error Ratio (MER). Finally, the MER of the modulated QAM signal before and after the base band compensation is compared between the two methods, showing a significant enhancement in the RF modulator performance.

Optical wireless communication (OWC) is a promising alternative to radio frequency (RF) communication with a significantly larger and unregulated spectrum. Impairments in the physical layer, such as the non-linear transfer characteristic of the transmitter, the dispersive optical wireless channel and the additive white Gaussian noise (AWGN) at the receiver, reduce the capacity of the OWC system. Single-carrier multi-level pulse position modulation (M-PPM) and multilevel pulse amplitude modulation (M-PAM) suffer from inter-symbol interference (ISI) in the dispersive channel which reduces their capacity even after channel equalization. Multi-carrier modulation such as optical orthogonal frequency division multiplexing (O-OFDM) with multilevel quadrature amplitude modulation (M-QAM) is known to maximize the channel capacity through bit and power loading. There are two general signal structures: bipolar Gaussian signal with a direct current (DC) bias, i.e. DC-biased O-OFDM (DCO-OFDM), or unipolar half- Gaussian signal, employing only the odd subcarriers, i.e. asymmetrically clipped O-OFDM (ACO-OFDM). In this thesis, the signal distortion from the transmitter nonlinearity is minimized through pre-distortion, optimum signal scaling and DC-biasing. The optical front-ends impose minimum, average and maximum optical power constraints, as well as an average electrical power constraint, on the information-carrying signals. In this thesis, the optical signals are conditioned within these constraints through optimum signal scaling and DC-biasing. The presented analysis of the optical-to-electrical (O/E) conversion enables the derivation of the electrical signal-to-noise ratio (SNR) at the receiver, including or excluding the additional DC bias power, which is translated into bit-error rate (BER) performance. In addition, a generalized piecewise polynomial model for the non-linear transfer characteristic of the transmitter is proposed. The non-linear distortion in O-OFDM is translated by means of the Bussgang theorem and the central limit theorem (CLT) into attenuation of the data-carrying subcarriers at the receiver plus zero-mean complex-valued Gaussian noise. The attenuation factor and the variance of the non-linear distortion noise are derived in closed form, and they are accounted towards the received electrical SNR. Through pre-distortion with the inverse of the proposed piecewise polynomial function, the linear dynamic range of the transmitter is maximized, reducing the non-linear distortion to double-sided signal clipping. Finally, the OWC schemes are compared in terms of spectral efficiency and electrical SNR requirement as the signal bandwidth exceeds the coherence bandwidth of the optical wireless channel for a practical 10 dB linear dynamic range. Through optimum signal scaling and DCbiasing, DCO-OFDM is found to achieve the highest spectral efficiency for a target SNR, neglecting the additional DC bias power. When the DC bias power is counted towards the signal power, DCO-OFDM outperforms PAM with linear equalization, approaching the performance of the more computationally intensive PAM with non-linear equalization. In addition, the average optical power in O-OFDM is varied over dynamic ranges of 10 dB, 20 dB and 30 dB. When the additional DC bias power is neglected, DCO-OFDM is shown to achieve the Shannon capacity, while ACO-OFDM exhibits a 3 dB gap which grows with higher SNR targets. When the DC bias power is included, DCO-OFDM outperforms ACO-OFDM for the majority of average optical power levels with the increase of the SNR target or the dynamic range.

A head-mounted-display with an optical combiner may introduce significant amount of distortion to the real world scene. The ability to accurately model the effects of both 2-dimensional and 3-dimensional distortion introduced by thick optical elements has many uses in the development of head-mounted display systems and applications. For instance, the computer rendering system must be able to accurately model this distortion and provide accurate compensation in the virtual path in order to provide a seamless overlay between the virtual and real world scenes. In this paper, we present a ray tracing method that determines the ray shifts and deviations introduced by a thick optical element giving us the ability to generate correct computation models for rendering a virtual object in 3D space with the appropriate amount of distortion. We also demonstrate how a Hartmann wavefront sensor approach can be used to evaluate the manufacturing errors in a freeform optical element to better predict wavefront distortion. A classic Hartmann mask is used as an inexpensive and easily manufacturable solution for accurate wavefront measurements. This paper further suggests two techniques; by scanning the Hartmann mask laterally to obtain dense sampling and by increasing the view screen distance to the testing aperture, for improving the slope measurement accuracy and resolution. The paper quantifies the improvements of these techniques on measuring both the high and low sloped wavefronts often seen in freeform optical-see-through head-mounted displays. By comparing the measured wavefront to theoretical wavefronts constructed with ray tracing software, we determine the sources of error within the freeform prism. We also present a testing setup capable of measuring off-axis viewing angles to replicate how the system would perform when worn by its user.

This thesis describes the effect of placing a phosphorus atom in a sterically strained environment with particular emphasis on the geminal disubstitution of two 2,4,6-tri-tert-butylphenyl (Mes*) groups on a single phosphorus centre and intramolecular sub-van der Waals interactions between peri-substituted atoms on naphthalene and acenaphthene. Chapter 2 outlines the reactive chemistry of a sterically encumbered phosphinic chloride (Mes*)₂P(=O)Cl, which was shown to have extremely low reactivity at the phosphorus centre. It has however, been demonstrated that synthetically significant transformations are possible. The phosphine oxide (Mes*)₂P(=O)H and a secondary phosphine Mes*(2,4-tBu₂C₆H₃)PH were obtained from the reduction of (Mes*)₂P(=O)Cl with hydridic reagents under forcing conditions. The corresponding phosphinite was acquired from the deprotonation of (Mes*)₂P(=O)H, which furnished very crowded tertiary phosphine oxides (Mes*)₂P(=O)R (R = Me and Et) on reactions with electrophiles. We have been unable to chlorinate or deprotonate Mes*(2,4-tBu₂C₆H₃)PH, however the reaction with elemental sulfur afforded the affiliated phosphine sulfide Mes*(2,4-[supercript(t)]Bu₂C₆H₃)P(=S)H, albeit under forcing conditions. Our computations (B3LYP and M06-2X level) show that strain energies of geminally substituted compounds are extremely high (180 to 250 kJ mol⁻¹), the majority of the strain is stored as boat distortions to the phenyl rings in Mes* substituents. Chapter 3 describes the strain inherent with non-bonding atomic distances shorter than the sum of their van der Waals radii, specifically heteroatom substitution of the peri-positions of naphthalene and acenaphthene. It also documents the importance of amine protecting groups in chlorophosphine chemistry. The preparation of Ace[P(Ph)N(ⁱPr)₂]Br (Ace = acenaphthene-5,6-diyl) and Ace[P(Ph)N(ⁱPr)₂]₂, plus the elucidation of the molecular structures of Mes*P[N(CH₃)₂]₂, Ace[P(Mes)N(ⁱPr)₂]Br (Mes = 2,4,6-tri-methylphenyl) and Ace[P([supercript(t)]Bu)N(Et)₂]Br sufficiently demonstrate the ring distorting characteristics of structurally encumbered molecules. The reaction of Ace[P(Ph)N(ⁱPr)₂]Br and Ace[P(Ph)N(ⁱPr)₂]₂ with a methylating agent was also investigated.

Postural distortion of human bite marks on skin occurs when photographing a bite mark in a body position other than the position of the body at the time of biting. Postural distortion in the bite mark may introduce significant changes in both the shape and size of the recorded marks. As a result, the analysis of the marks may be hindered and a proper comparison between the bite mark and the causal dentition may be precluded. Therefore, a method by which postural distortion in a bite mark photographic record can be evaluated and eliminated with minimal operator subjectivity is required. This study describes the development of an objective technique for evaluating postural distortion in bite mark photographic records and for minimising postural distortion during photography of bite marks. The source for developing these techniques was provided by digitally analysing the symmetry of dental arches in a defined population including males and females (236 subjects) whose ages ranged between 20 and 30 years. The analysis resulted in quantifying a mathematical relationship between the biting edges of each homologous pair of the anterior teeth and specified reference lines. The validity of the analytical method of dental arch symmetry is discussed. The developed techniques were applied to posturally distorted (test) bite marks. The results demonstrate the validity of the developed techniques in determining postural distortion and recording correct images (shown to resemble the biters dentition) of the test bites. Suggestions for further work are proposed.

Saab AB Training &amp; Simulation is specialized on military training, including laserbased training. To continue being the world leader in this area, a new generationof laser simulators needs to be developed. To simplify the development of thishighly complex system, this master thesis have resulted in a MATLAB/Simulinkmodel which simulates the electro-opto/mechanical system representing theirlaser based simulation platform. The focus of this master thesis has been to simulateand control the laser beam deflection. To be more precise, the motors usedto rotate the Risley-prisms deflecting the laser beam is modelled. With a goodmodel of the motors, a control system is applied steering the wedges to a referencerotation angle. The reference rotation angle is difficult to calculate though,since the deflection following several rotary wedges is severely nonlinear. Thereare many ways to calculate the rotation angles, but in this master thesis it will bedone by solving optimization problems in MATLAB. / Saab AB Training &amp; Simulation är specialiserade på militär träning, bland annatbaserad på laser och för att fortsätta vara världsledande inom detta områdekrävs utveckling av en ny generation lasersimulatorer. För att underlätta utvecklingsarbetetav detta högst komplexa system, har i detta examensarbete en simulerbarmodell skapats i MATLAB/Simulink för att kunna simulera det elektroopto/mekaniska system som beskriver deras laserbaserade simulatorplattform.Fokus för detta examensarbete har varit att modellera avlänkningen. Mer ingåendeså modelleras de motorer som används för att rotera Risley-prisman så atten laserstråle uppnår önskad avlänkning. Med en bra modell av motorerna applicerasett reglersystem som styr de roterbara kilarna till referensposition. Referenspositionenär dock komplicerad att beräkna eftersom avlänkningen frånflera roterande kilar beter sig högst olinjärt. För att göra detta finns flera tillvägagångssätt,men i detta examensarbete kommer det att göras genom att lösaoptimeringsproblem i MATLAB.