Efficient and accurate solutions of acoustic wave diffraction by a rigid step discontinuity and a curved half-plane are derived by the uniform geometrical theory of diffraction. These solutions can be used in seismic data processing to evaluate and, eventually, to improve the existing data processing procedures. They can also find applications in electromagnetics, microwave antenna design, acoustic design and sound engineering. The rigid step discontinuity solution given in this thesis is more accurate than the existing solutions which are based on Kirchhoff theory of diffraction. This solution removes the previous restriction on the source and the receiver arrangement. It also provides high efficiency by the use of ray theory. This solution is further generalized to two offset half-planes and an inclined wedge. Solutions for more complicated structures can be obtained by superposition of these solutions with added interactions. The complex source position method is used to extend the omnidirectional point source solution to a beam source solution. The effect of changes of the directivity and orientation of the beam source is studied. Time-domain single and double diffraction coefficients are determined through direct Fourier transforming and convolution. An infinite impulse response filter is applied to the time-domain direct computation of single diffraction. This combination achieves a total saving of 75% of computing time over the frequency-domain approach. Diffraction by a curved half-plane is analyzed with the inclusion of creeping wave diffraction and second order edge diffraction. An acoustic model of a curved half-plane is designed to verify the theory. The experimental results obtained by Mellema have verified the existence of the creeping wave diffraction and weak traces of the second order edge diffraction. / Applied Science, Faculty of / Electrical and Computer Engineering, Department of / Graduate

The aim of the study was to compare the effects of the use of interactive computer simulations for cognitive load change of grade 11 learners in the acquisition of knowledge and a science process skill in geometrical optics. Both the use of computer simulations and traditional teaching was teacher centred. The study was done in a rural area in South Africa, in the Limpopo Province in the district of Vhembe. The theoretical framework was based on the information processing model. Within the non-equivalent quasi experimental design a switching replications design study was used whereby 105 learners in four schools took part. This study found that in terms of the acquisition of knowledge, female learners gained more by the use of simulations than their male counterparts. No significant effect was found in the acquisition of the skill when computer simulations were used. Initial reduction of cognitive load was found when simulations were used and with time this increased. Experienced educators reduced the cognitive load through use of their knowledge and expertise and their role needs to be highlighted. Further studies are suggested to study the effect of a learner centred approach on decreasing the cognitive load and its effect on the acquisition of knowledge and skills. / Mathematics, Science and Technology Education / D. Phil. (Mathematics, Science and Technology Education with specialisation in Physics Education)

The aim of the study was to compare the effects of the use of interactive computer simulations for cognitive load change of grade 11 learners in the acquisition of knowledge and a science process skill in geometrical optics. Both the use of computer simulations and traditional teaching was teacher centred. The study was done in a rural area in South Africa, in the Limpopo Province in the district of Vhembe. The theoretical framework was based on the information processing model. Within the non-equivalent quasi experimental design a switching replications design study was used whereby 105 learners in four schools took part. This study found that in terms of the acquisition of knowledge, female learners gained more by the use of simulations than their male counterparts. No significant effect was found in the acquisition of the skill when computer simulations were used. Initial reduction of cognitive load was found when simulations were used and with time this increased. Experienced educators reduced the cognitive load through use of their knowledge and expertise and their role needs to be highlighted. Further studies are suggested to study the effect of a learner centred approach on decreasing the cognitive load and its effect on the acquisition of knowledge and skills. / Mathematics, Science and Technology Education / D. Phil. (Mathematics, Science and Technology Education with specialisation in Physics Education)

QC 351 A7 no. 59 / The optical properties of two prisms combined as a single anamorphic element are discussed. There is a family of solutions for which the angular magnification versus field angle is U-shaped. Thus there are regions for which the angular magnification is almost constant. The distortions associated with these regions are explored. It is shown how distortion can be effectively eliminated over a restricted field by cascading a negative and a positive anamorphic element.

In recent years y-y angular correlations have been very useful in confirming the spins of excited nuclear states. Angular correlation techniques have also been employed to study the electric and magnetic character of excited nuclear states. With these things in mind, it was decided to design, construct, and test a precision angular correlation table.

Student Number : 0006329K - MSc(Eng) Dissertation - School of Electrical and Information Engineering - Faculty of Engineering and the Built Environment / Geometric optimisations are presented for the UTD in SuperNEC which is a commercial electromagnetic software package. Path finding optimisations rapidly find propagation paths of electromagnetic waves by using back face culling to determine the visible plates of polyhedral structures and by using reflection and diffraction zones which use image theory and the law of diffraction to determine illuminated spatial regions. An octree reduces the number of intersections during the shadow tests. Numerical results show that overall the optimisations halve the run time of the software for models which consist of plates and cylinders. The path finding optimisations do not scale with model size, are limited to plates and introduce errors. The mean absolute error due to the path finding optimisations is on average 0:02 dB for first order rays and 0:17 dB for second order rays. The octree optimisation scales with model size, can be used with any geometry and any type of ray and does not cause errors.

by Yuen Wai Ching. / Thesis (M.Phil.)--Chinese University of Hong Kong, 1998. / Includes bibliographical references (leaves 54-55). / Abstract also in Chinese. / Chapter 1 --- Introduction --- p.5 / Chapter 2 --- Group Analysis --- p.9 / Chapter 2.1 --- Groups and Differential Equations --- p.9 / Chapter 2.2 --- Prolongation --- p.11 / Chapter 2.3 --- The Prolongation Formula --- p.14 / Chapter 3 --- Symmetry Group For the Eikonal Equation --- p.17 / Chapter 4 --- An Optimal System For the Eikonal Equation --- p.25 / Chapter 5 --- Group Invariant Solutions --- p.33 / Chapter 5.1 --- Straight Lines --- p.33 / Chapter 5.2 --- Stationary Solutions --- p.33 / Chapter 5.3 --- Traveling Waves --- p.34 / Chapter 5.4 --- Circles --- p.37 / Chapter 5.5 --- Spirals --- p.38 / Chapter 6 --- Appendix --- p.50 / A Group Analysis for some Geometric Evolution Equations --- p.4 / Bibliography

by Ng Pak Hong. / Thesis (M.Phil.)--Chinese University of Hong Kong, 1998. / Includes bibliographical references (leaves 111-112). / Text in English; abstract also in Chinese. / by Ng Pak Hong. / Acknowledgments --- p.i / Abstract --- p.ii / Table of contents --- p.iv / Chapter Chapter 1 --- INTRODUCTION --- p.1 / Chapter 1.1 --- History --- p.2 / Chapter 1.2 --- Airy Theory --- p.4 / Chapter 1.2.1 --- Rainbow angle --- p.4 / Chapter 1.2.2 --- Airy's cubic wave front --- p.4 / Chapter 1.3 --- High-order rainbows --- p.7 / Chapter 1.4 --- Glare points --- p.8 / Chapter 1.5 --- Interference between overlapping rainbows --- p.10 / Chapter Chapter 2 --- HIGH-ORDER RAINBOWS --- p.17 / Chapter 2.1 --- Experiment --- p.17 / Chapter 2.2 --- Results and discussions --- p.19 / Chapter 2.2.1 --- General features --- p.19 / Chapter 2.2.2 --- Angular positions and angular widths of rainbows --- p.21 / Chapter 2.2.3 --- Rainbow intensities as functions of order number --- p.22 / Chapter 2.3 --- Vertical positions of rainbows --- p.24 / Chapter 2.4 --- Vertical spreads of rainbows --- p.26 / Chapter 2.5 --- Rainbow patterns at different values of the refractive index ..… --- p.28 / Chapter 2.6 --- Effect of eccentricity of a droplet's circumference in the equatorial plane on the rainbow angles --- p.30 / Chapter CHAPTER 3 --- GLARE POINTS --- p.56 / Chapter 3.1 --- Experiment --- p.56 / Chapter 3.2 --- Results and discussions --- p.57 / Chapter 3.2.1 --- General features --- p.57 / Chapter 3.2.2 --- Glare point position and intensity --- p.58 / Chapter A. --- Glare point position --- p.58 / Chapter B. --- Glare point intensity --- p.61 / Chapter C. --- Summary of results of glare points --- p.62 / Chapter 3.2.3 --- Fourier transform of rainbow patterns --- p.63 / Chapter Chapter 4 --- INTERFERENCE BETWEEN OVERLAPPING RAINBOWS --- p.90 / Chapter 4.1 --- Experiment --- p.90 / Chapter 4.2 --- Results and discussions --- p.91 / Chapter 4.2.1 --- General features --- p.91 / Chapter 4.2.2 --- Simulation of the interference --- p.91 / Chapter 4.2.3 --- Estimation of the droplet vibration amplitude and frequency --- p.95 / Chapter 4.3 --- Comparison with results of Lock and Woodruff --- p.96 / Chapter Chapter 5 --- CONCLUSION --- p.107 / APPENDIX A --- p.109 / References --- p.111

Chan, Kwan Chung. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2011. / Includes bibliographical references (leaves 63-69). / Abstracts in English and Chinese. / Abstract --- p.v / Acknowledgements --- p.ix / List of Figures --- p.xiii / List of Tables --- p.xv / Chapter 1 --- Introduction --- p.1 / Chapter 1.1 --- Main contributions --- p.4 / Chapter 1.2 --- Overview --- p.4 / Chapter 2 --- Related Work --- p.7 / Chapter 2.1 --- Point cloud processing --- p.7 / Chapter 2.2 --- Model repairing --- p.9 / Chapter 2.3 --- Deformation and reconstruction --- p.10 / Chapter 3 --- Iterative Consolidation on Un-orientated Point Clouds --- p.11 / Chapter 3.1 --- Algorithm overview --- p.12 / Chapter 3.2 --- Down-sampling and outliers removal --- p.14 / Chapter 3.2.1 --- Normal estimation --- p.14 / Chapter 3.2.2 --- Down-sampling --- p.15 / Chapter 3.2.3 --- Particle noise removal --- p.17 / Chapter 3.3 --- APSS based repulsion --- p.19 / Chapter 3.4 --- Refinement --- p.22 / Chapter 3.4.1 --- Adaptive up-sampling --- p.22 / Chapter 3.4.2 --- Selection of up-sampled points --- p.23 / Chapter 3.4.3 --- Sample noise removal --- p.23 / Chapter 3.5 --- Set constraints to sample points --- p.24 / Chapter 4 --- Shape Modeling by Point Set --- p.27 / Chapter 4.1 --- Principle of deformation --- p.27 / Chapter 4.2 --- Selection --- p.29 / Chapter 4.3 --- Stretching and compressing --- p.30 / Chapter 4.4 --- Bending and twisting --- p.30 / Chapter 4.5 --- Inserting points --- p.30 / Chapter 5 --- Results and Discussion --- p.37 / Chapter 5.1 --- Program environment --- p.37 / Chapter 5.2 --- Results of iterative consolidation on un-orientated points --- p.37 / Chapter 5.3 --- Effect of our de-noising based on up-sampled points --- p.44 / Chapter 6 --- Conclusions --- p.49 / Chapter 6.1 --- Advantages --- p.49 / Chapter 6.2 --- Factors affecting our algorithm --- p.50 / Chapter 6.3 --- Possible future works --- p.51 / Chapter 6.3.1 --- Improve on the quality of results --- p.51 / Chapter 6.3.2 --- Reduce user input --- p.52 / Chapter 6.3.3 --- Multi-thread computation --- p.52 / Chapter A --- Finding Neighbors --- p.53 / Chapter A.1 --- k-d Tree --- p.53 / Chapter A.2 --- Octree --- p.54 / Chapter A.3 --- Minimum spanning tree --- p.55 / Chapter B --- Principle Component Analysis --- p.57 / Chapter B.1 --- Principle component analysis --- p.57 / Chapter C --- UI of the program --- p.59 / Chapter C.1 --- User Interface --- p.59 / Chapter D --- Publications --- p.61 / Bibliography --- p.63

Mathematics plays a key role in bolstering a country’s knowledge economy. Australia’s knowledge economy is negatively affected by the underachievement of Australian school students in geometry. Research indicates a continuing decline in student performance in geometry and a distinct lack of geometrical knowledge and understanding on the part of students and teachers. To address this issue a theory of success in geometry that focussed on background variables and attitude, was developed. In the theory it was hypothesised that success in geometry can be understood in terms of predictor variables and that attitude mediates the effects of the variables on success in geometry. A model of success in geometry was developed to systematically determine the relationships of the variables. Trainee teachers from the University of Western Sydney (n = 224) participated in the survey. Using Confirmatory Factor Analysis the use of one or two attitude scales was determined as were the items in the scales. Using Structural Equation Modeling (SEM) the relationships between the background factors (age, education, gender, left/right brain preference) on success in geometry (van Hiele level) mediated by attitude were determined. The evidence, however, suggests that attitude is not only correlated with the measures of success in geometry (van Hiele levels) but that it may also be a predictor of success in geometry. It was also hypothesised that attitude was composed of three analytically distinct factors (affective, cognitive and behavioural). The evidence suggests that this hypothesis cannot be rejected. This is an important finding as previous research has not been empirically able to distinguish these factors. In order to improve the success of Australian school students in geometry and assist teachers to succeed and consequently improve Australia’s knowledge economy, the present research indicates that: all trainee teachers should have their van Hiele level of geometry understanding determined; appropriate geometry courses should be a mandatory part of the curriculum for all pre-service teachers whose van Hiele level is less than three; all trainee teachers should have a van Hiele level of three or four before they commence teaching; appropriate changes to the curriculum of trainee teachers should be made so that their stored general evaluative process produces a positive attitude to geometry, especially in female students; school students who intend to pursue a teaching career should complete mathematics courses with a geometry content. / Doctor of Philosophy (PhD)