The Levitating Ball
This project was inspired by a tournament call the International Young Physicist’ Tournament (IYPT). The problem could be broken into two aims: ‘Investigate the forces that cause a ball to levitate in a titled airstream’ and ‘optimize the system for the maximum angle of tilt that results in a supported ball’. The first stage of the investigation was research and learning. Two fluid mechanics courses online were used to build a basic of knowledge of the subject. Next a force diagram was created to model the forces acting on the ball. The diagram identified a force called the lift force that must be acting on the ball to be supported. There were three contending theories that could explain the lift force: The Bernoulli theory, the Coanda theory and the Magnus theory. A practical investigation was then instigated to differentiate between these three theories. Since the Magnus theory is only applicable if the ball is spinning in the airstream, this theory was isolated by changing the center of mass of the ball but keep everything else constant (this allowed control of how much the ball spun in the airstream). Changing the center of mass didn’t impact on the maximum angle of tilt at all, proving that the spinning of the ball isn’t producing a significant amount of lift, and therefore the Magnus theory couldn’t be a cause for lift. Because further testing couldn’t isolate the Coanda and Bernoulli theories, a solution was developed to explain why the two remaining theories might co-exist. Further testing methods have been designed to investigate this possibility in more depth. To meet the second aim of this project, an investigation was launched to see how parameters affected the maximum angle that the ball could be supported at. The parameters investigated were: Ball radius, ball mass, ball surface, air speed and airstream diameter. A lot of time was spent creating a reliable experimental method. The method could be used to support a ball in an air stream, slowly tilt the air stream, and then measure the angle of tilt the moment that the ball fell out. After experimentation, a table was created to describe how the listed parameters affect the maximum angle of tilt that a ball can be supported at. Explanations were proposed for why each parameter affected this angle. Future experiments have been devised to build a deeper understanding of the effects of a wider range of parameters.
Physical Characterization of a Wide Aperture Segmented Reflector Telescope
Characterization of telescope lenses using physical optics and selection of the optimal physical parameters of a reflecting telescope’s optical units were done to improve the design, cost-efficiency, and quality of the 64-cm telescope (named Oof) housed at the National Institute of Physics. Characterization has been done through numerical modeling of the point spread function (PSF) in Python. The PSF code was based on the method of getting wave vectors by Richards and Wolf. The optimal PSF was established to be the PSF of a large monolithic mirror. The PSF of a single optical lens was compared to its counterpart segmented lenses. Through the comparison of maximum intensity, the normalized mean square error (NMSE) and the Linfoot’s criteria of correlation quality, fidelity, and relative structural content, the study has produced results which proved that highly segmented optical components produce results with less quality compared to less-segmented optical components. It was found that as the segmentation increases, the maximum intensity decreases. Higher values of maximum intensity denote higher light gathering power. The normalized mean square error of the set-ups having one to seven layers had values greater than zero but less than one. This denotes that the PSF of those set-ups are near the PSF of the optimal set-up. Higher values of correlation quality, fidelity, and relative structural content denote higher correlation, higher signal to noise ratio, higher closeness of correspondence between the optimal set-up and the segmented set-up. The number and the size of the optical components of the segmented mirror were manipulated in order to achieve a negligible difference between that of the optimal PSF and the PSF of a segmented mirror. The equivalent single lens radius in terms of maximum intensity of the current set-up of the telescope was determined to be 234.25 mm. If the optimal PSF is achieved, the physical parameters of the optical components generated may be applied to the optical components of the 64-cm telescope. The design that resulted from the study could be used in the future construction of a wide-aperture telescope, which could aid in the acquisition of knowledge about heavenly bodies.
超通用水分子形交換方塊之FPGA設計
本研究提出一個新的超通用、每邊w個端點的四邊形水分子形交換方塊(Water-Molecule-Shaped Switch Block; WMSB)架構，以應用在FPGA之多點連線（multipoint interconnection）和諸多交換網路的設計上。超通用交換方塊(HUSB)的領域中，Fan[2]提出當前唯一一個(4, w)-HUSB，但Fan’s (4, w)-HUSB所需的開關個數大約是6.3w個開關，在接下來的篇幅之中，我們將證明(4, w)-WMSB是只需6w個開關的HUSB；此外，我們還證明沒有(4, w)-HUSB可以使用小於6w個開關。本研究中還使用VPR（一種CAD）及其內建的大量標準線路以證明(4, w)-WMSB不僅是理論上最佳的亦是實用性佳的交換方塊。鑑此，(4, w)-WMSB開關效率高(switch-efficiency)的設計十分適用於其他的交換網路設計，如公共電話網路(Public Switched Telephone Network)。