A semiflexible polymer confined to a spherical surface is used as a basic model for understanding DNA conformation in restricted space. By means of Monte Carlo simulation for a bead-rod chain generated on a spherical surface, we find an ordered helicoidal phase at sufficiently high surface density and determine the critical density of the isotropic-helicoidal phase transition for various persistence lengths. We verify that the excluded volume effect is the key factor to cause the helicoidal state. In addition to Monte Carlo simulations, we utilize the model of wormlike chain with Onsager's excluded volume interaction and examine the Landau expansion of the free energy involving both the orientational and spatial order parameters. We also analytically figure out the critical density and transition gap for various ratios of persistence lengths of the polymer chain and the radius of spherical surface. The results from both simulation and analysis are consistent with each other.

Single crystalline silicon spheres have been used as alternative material for solar cell fabrication. This innovative technology has several advantages over traditional wafer technology. However, the material, process flow and characterization techniques are very different from the planar technology due to the spherical geometry. In material characterization, microwave photoconductivity decay is used to measure carrier lifetime. This technique is analyzed theoretically by mathematical treatment in this thesis. Furthermore, the carrier lifetime is measured in order to investigate rapid thermal grown oxide quality in the role of surface passivation of silicon sphere. A traditional way of making spherical cells is to create a p-n junction by high temperature diffusion of phosphorous dopants into p-type silicon spheres. To further reduce the fabrication cost, a low temperature epitaxial film highly doped with phosphorous is deposited on the sphere surface to form an emitter layer using Plasma Enhanced Chemical Vapour Deposition (PECVD). The process flow of device fabrication is very different from silicon wafer thus a new set of process steps are derived for silicon spheres. Two main device structures, omission of insulating layer and silicon nitride as insulating layer between emitter film and substrate, are proposed. The deposition parameters, pressure, power, and deposition time are optimized for spherical geometry. The quality of the junction is evaluated by its current-voltage characteristic and capacitance-voltage characteristic. The results are also compared to similar device structures in planar technology. To examine the photovoltaic performance, illuminated current-voltage measurement is taken to provide information on short circuit current, open circuit voltage and fill factor. Furthermore, spectral response of quantum efficiency is investigated to assess the ability of carrier collection for a spectrum of wavelength. Limitations on spherical diode performance are concluded from the measurement results.

A semiflexible polymer confined to a spherical surface is used as a basic model for understanding DNA conformation in restricted space. By means of Monte Carlo simulation for a bead-rod chain generated on a spherical surface, we find an ordered helicoidal phase at sufficiently high surface density and determine the critical density of the isotropic-helicoidal phase transition for various persistence lengths. We verify that the excluded volume effect is the key factor to cause the helicoidal state. In addition to Monte Carlo simulations, we utilize the model of wormlike chain with Onsager's excluded volume interaction and examine the Landau expansion of the free energy involving both the orientational and spatial order parameters. We also analytically figure out the critical density and transition gap for various ratios of persistence lengths of the polymer chain and the radius of spherical surface. The results from both simulation and analysis are consistent with each other.

The backlight module is usually used to increase visual angle and brightness of liquid crystal display (LCD). Thus, the design and fabrication of optical films, including light guide plate, diffuser film, and brightness enhancement film (BEF), are critical factors to decide the optical efficiency in a backlight module. In order to improve the optical efficiency for power-saved display with competitiveness, this study presents a new fabrication process combining precision machining, lithography, and hot-embossing techniques to form a two-side-patterned optical film. One side of the optical film is micro triangular-pyramidal array (MTPA) and the other is micro spherical lens array(MSLA). First, the Taguchi method is applied to design the optimal microstructure configuration by the assistance of the optical software, FRED. Second, a tungsten (W) steel mold (as the mold to hot emboss MTPA) is manufactured by precision machining including optical projection grinding, lapping, and polishing processes. Meanwhile, a nickel-cobalt (Ni-Co) mold (as the mold to hot emboss MSLA) is fabricated by electroplating process. Then, polydimethylsiloxane (PDMS) is used to replicate the MTPA and MSLA patterns, on W and Ni-Co metal molds, respectively, and the replicated PDMS films are used as the molds to form a two-side-patterned optical film. In addition, the optical property such as luminance is measured by photo research 650 (PR 650) to evidence the optical function of the two-side-patterned optical film. From the experimental results, both brightness and uniformity can be improved by this film;thus, optical efficiency is successfully increased in this study.

We consider computation of resonances in open systems and acoustic scattering problems. These problems are posed on an unbounded domain and domain truncation is required for the numerical computation. In this paper, a perfectly matched layer (PML) technique is proposed for computation of solutions to the unbounded domain problems. For resonance problems, resonance functions are characterized as improper eigenfunction (non-zero solutions of the eigenvalue problem which are not square integrable) of the Helmholtz equation on an unbounded domain. We shall see that the application of the spherical PML converts the resonance problem to a standard eigenvalue problem on the infinite domain. Then, the goal will be to approximate the eigenvalues first by replacing the infinite domain by a finite computational domain with a convenient boundary condition and second by applying finite elements to the truncated problem. As approximation of eigenvalues of problems on a bounded domain is classical [12], we will focus on the convergence of eigenvalues of the (continuous) PML truncated problem to those of the infinite PML problem. Also, it will be shown that the domain truncation does not produce spurious eigenvalues provided that the size of computational domain is sufficiently large. The spherical PML technique has been successfully applied for approximation of scattered waves [13]. We develop an analysis for the case of a Cartesian PML application to the acoustic scattering problem, i.e., solvability of infinite and truncated Cartesian PML scattering problems and convergence of the truncated Cartesian PML problem to the solution of the original solution in the physical region as the size of computational domain increases.

Cognate mechanisms have been often used in design of linkages. Improper positions of fixed link or transmission angle could be improved effectively. Cognate mechanisms of planar linkages have been developed well, but the research on the spherical cognate is still wild open. There are just only spherical supplement mechanisms that have been presented by Soni(1967) until today. The aim of this thesis is to investigate the existence of spherical four-bar linkages cognate mechanisms. The geometry and properties of planar cognate mechanisms are discussed and a simulation program is written for the planar cognate mechanism. Then, the characteristics of spherical mechanisms are considered and the spherical cognate simulation program is built by using the result of planar cognate as a reference. Three examples are given to demonstrate the existence of pseudo-cognates for spherical mechanisms.

As an alternative to spherical harmonics in modeling the gravity field of the Earth, we built a multiresolution gravity model by employing spherical regularization wavelets in solving the inverse problem, i.e. downward propagation of the gravity signal to the Earth.s surface. Scale discrete Tikhonov spherical regularization scaling function and wavelet packets were used to decompose and reconstruct the signal. We recovered the local gravity anomaly using only localized gravity measurements at the observing satellite.s altitude of 300 km. When the upward continued gravity anomaly to the satellite altitude with a resolution 0.5° was used as simulated measurement inputs, our model could recover the local surface gravity anomaly at a spatial resolution of 1° with an RMS error between 1 and 10 mGal, depending on the topography of the gravity field. Our study of the effect of varying the data volume and altering the maximum degree of Legendre polynomials on the accuracy of the recovered gravity solution suggests that the short wavelength signals and the regions with high magnitude gravity gradients respond more strongly to such changes. When tested with simulated SGG measurements, i.e. the second order radial derivative of the gravity anomaly, at an altitude of 300 km with a 0.7° spatial resolution as input data, our model could obtain the gravity anomaly with an RMS error of 1 ~ 7 mGal at a surface resolution of 0.7° (< 80 km). The study of the impact of measurement noise on the recovered gravity anomaly implies that the solutions from SGG measurements are less susceptible to measurement errors than those recovered from the upward continued gravity anomaly, indicating that the SGG type mission such as GOCE would be an ideal choice for implementing our model. Our simulation results demonstrate the model.s potential in determining the local gravity field at a finer scale than could be achieved through spherical harmonics, i.e. less than 100 km, with excellent performance in edge detection. / text

The theory of interpolation and approximation of solutions to differential and integral equations on spheres has attracted considerable interest in recent years; it has also been applied fruitfully in fields such as physical geodesy, potential theory, oceanography, and meteorology. In this dissertation we study the approximation of linear partial differential equations on spheres, namely a class of elliptic partial differential equations and the heat equation on the unit sphere. The shifts of a spherical basis function are used to construct the approximate solution. In the elliptic case, both the finite element method and the collocation method are discussed. In the heat equation, only the collocation method is considered. Error estimates in the supremum norms and the Sobolev norms are obtained when certain regularity conditions are imposed on the spherical basis functions.

This project explores systematic strategies for establishing a definitive mode of representation in drawing. These strategies are considered in the context of the subjectivities and contingencies of perceptual experience, the mediation of that experience and inherent limitations in representational language. The aim is to explore the possibilities of constructing two-dimensional artworks which serve to define or investigate perceptual processes, perspective devices and spatial relationships.

Thesis (M. Sc.)--University of Hong Kong, 2007. / Title proper from title frame. Also available in printed format.