Fast algorithms for potential evaluation in N-body problems often tend to be extremely abstract and complex. This thesis presents a simple, hierarchical approach to solving the potential evaluation problem in O(n) time. The approach is developed in the field of electrostatics and can be extended to N-body problems in general. Herein, the potential vector is expressed as a product of the potential matrix and the charge vector. The potential matrix itself is a product of component matrices. The potential function satisfies the Laplace equation and is hence expressed as a linear combination of spherical harmonics, which form the general solutions of the Laplace equation. The orthogonality of the spherical harmonics is exploited to reduce execution time. The duality of the various lists in the algorithm is used to reduce storage and computational complexity. A smart tree-construction strategy leads to efficient parallelism at computation intensive stages of the algorithm. The computational complexity of the algorithm is better than that of the Fast Multipole Algorithm, which is one of the fastest contemporary algorithms to solve the potential evaluation problem. Experimental results show that accuracy of the algorithm is comparable to that of the Fast Multipole Algorithm. However, this approach uses some implementation principles from the Fast Multipole Algorithm. Parallel efficiency and scalability of the algorithms are studied by the experiments on IBM p690 multiprocessors.

In indoor environment, the multi-sensor system can be used as an efficient solution for target location process, in terms of lower estimation cost, due to the factor that sensors have the advantages of low power, simple, cheap, and low operation complexity. However, the location methods and the placements of designed multisensor have great impact on the location performance. Based on the time difference of arrival (TDOA), the present research utilizes linear-correction spherical-interpolation (LCSI) method to estimate the location of its targets. The method is a combination of the linear-correction least-squares method and the spherical-interpolation method. Apart from the usual process of iterative, nonlinear minimization, and consequently, under the influence of noise interference and target-sensor geometry, the spherical-interpolation method will produce better results; therefore, SI method is used in place of the LS part of the LCLS method and named as the LCSI method. The objective is to correct the SI method to generate a better estimate performance. In addition to the performance issues, the limitation of the methods will also be examined. The geometric dilution of precision (GDOP) of the TDOA location method in the 3-D scenario is demonstrated with the effects on location performance of both inside and outside of the multi-sensor formation. Programmed 3-D scenario are used in the simulations, where cases with three different multiple sensor formations and two different target heights are investigated. From the simulation results of various location methods, it can be seen that LCSI has has its advantages over other methods in the wireless TDOA location.

This paper presents a method for resampling a sequence of high dynamic range light probe images into a representation of Incident Light Field (ILF) illumination which enables realtime rendering. The light probe sequences are captured at varying positions in a real world environment using a high dynamic range video camera pointed at a mirror sphere. The sequences are then resampled to a set of radiance maps in a regular three dimensional grid before projection onto spherical harmonics. The capture locations and amount of samples in the original data make it inconvenient for direct use in rendering and resampling is necessary to produce an efficient data structure. Each light probe represents a large set of incident radiance samples from different directions around the capture location. Under the assumption that the spatial volume in which the capture was performed has no internal occlusion, the radiance samples are projected through the volume along their corresponding direction in order to build a new set of radiance maps at selected locations, in this case a three dimensional grid. The resampled data is projected onto a spherical harmonic basis to allow for realtime lighting of synthetic objects inside the incident light field.

In this study we investigate the flow of a Boussinesq fluid contained in a rotating, differentially heated spherical shell. Previous work, on the spherical shell of Boussinesq fluid, differentially heated the shell by prescribing temperature on the inner boundary of the shell, setting the temperature deviation from the reference temperature to vary proportionally with -cos 20, from the equator to the pole. We change the model to include an energy balance equation at the earth's surface, which incorporates latitudinal solar radiation distribution and ice-albedo feedback mechanism with moving ice boundary. For the fluid velocity, on the inner boundary, two conditions are considered: stress-free and no-slip. However, the model under consideration contains only simple representations of a small number of climate variables and thus is not a climate model per se but rather a tool to aid in understanding how changes in these variables may affect our planet's climate. The solution of the model is followed as the differential heating is changed, using the pseudo arc-length continuation method, which is a reliable method that can successfully follow a solution curve even at a turning point. Our main result is in regards to hysteresis phenomenon that is associated with transition from one to multiple convective cells, in a dfferentially heated, co-rotating spherical shell. In particular, we find that hysteresis can be observed without transition from one to multiple convective cells. Another important observation is that the transition to multiple convective cells is significantly suppressed altogether, in the case of stress-free boundary conditions on the fluid velocity. Also, the results of this study will be related to our present-day climate. / UOIT

This thesis incorporates an array of Contact Potential Difference (CPD) sensors to measure and monitor the degree of skew in the rolling elements of a spherical roller bearing. Skewing is the motion of a roller as it turns about an axis normal to the roller race interface. Roller skew is generated as part of the kinematic effects of roller bearings. Skew monitoring is important for bearing design as it is an indirect measure of bearing life. For the purpose of this thesis, roller skew was measured utilizing multiple pairs of CPD probes located around the bearings outer raceway at varying points of the loading zone. These CPD probes are not in direct contact with the rollers, but in close proximity to their surface (through the bearing outer ring). The skew angle measured is related to different operating conditions such as applied load, shaft speed, and lubrication. The pair of CPD probes detected a signal as the roller surface passed by and the phase difference between the two distinct signals measured the skew angles in the range of 0.016 to 1.10. The shaft is rotated both clockwise and counterclockwise to capture any probe misalignment which was in the range of 0.5 up to 2.0 . This thesis also provides a model for the probe signal as a spherical roller surface passes the probe surface.

Due to the explosive improvement of micro machining technology, many kinds of meso-scale products and parts are developed. There are two techniques, CMM (Coordinate Measuring Machine) and SPM (Scanning Probe Microscopy), commonly used to measure the profile of meso-scale products. However, both of these methods have their own strengths and weaknesses in that scale. The CMM can¡¦t be precise and accurate; while the SPM measurement system will be a time-consuming process. The micro scale CMM measurement system with micro spherical probes would be suitable for measuring meso-scale objects. In this study, equipments are built to fabricate the micro spherical probes. The glass optical fiber is selected as the material to fabricate the probes. The heating-pulling method and arc fusion method are selected as the fabrication process. The commercial equipments are available for fabricating micropipette and NSOM (Near-field Scanning Optical Microscopy) probes. However, most of these commercial equipments are expensive, and the heating area is too small to fit our study. In this study, the gas heater is used to replace the laser power as a heat source. A vertical pulling mechanism is developed to pull the optical fiber. Moreover, this study uses Taguchi method to reduce the number of experimental runs and find the suitable parameters for fabrication. The straight-circular-cone-type probe and the bent-circular-cone-type probe can be fabricated at the same time. The radius of the probe tip can be smaller than 0.5£gm for NSOM. In addition, the heating-pulling mechanism can reduce the diameter of optical fiber from £p125£gm to less than £p50£gm for different purposes. An arc discharge machine is also developed to melt the cleaved end-face of the prob. The heating-pulling mechanism and arc discharge machine developed in this study are successfully applied in fabricating different types of probe ends, £p20~125£gm hemispherical end-face and £p50~300£gm spherical end-face for example, for different applications.

Since micro machining technologies are dramatically improved, many kinds of meso-to-micro scale products are developed. The Coordinate Measuring Machine(CMM) and the Scanning Probe Microscope(SPM) are the most commonly used instrument for precision measurement. To acquire geometric characteristic of products in meso scale, the CMM is not adequate due to the minimum diameter of ruby-ball head probes are 300 to 500£gm; while the SPM will be a time-consuming process. Thus, proper probes for meso-scale coordinate measuring machines are necessarily developed. The commercial fusion splicers are available to fabricate glass probes with spherical head. However, the commercial fusion splicers are expensive and the fiber clamps can not fit the diameter of probe stylus in this study. Therefore, instruments are implemented to fabricate the glass probe with spherical head for the meso-scale coordinate measuring machine. The

This thesis presents the analysis, design, and fabrication of a spherical inverted-F antenna (SIFA). The SIFA consists of a spherically conformal rectangular patch antenna recessed into a quarter section of a metallic sphere. The sphere acts as a ground plane, and a metal strip shorts the patch to the metallic sphere. The SIFA incorporates planar microstrip design into a conformal spherical geometry to better meet the design constraints for integrated wireless sensors. The SIFA extends a well-established technology into a new application space, including microsatellites, mobile sensor networks, and wireless biomedical implants. The complete SIFA design depends on several parameters, several of which parallel planar design variables. A modified transmission line model determines the antenna input impedance based on the sphere's inner and outer radii, the patch length and width, short length and width, and feed position. The SIFA can be tuned to the desired frequency band by choosing the proper outer radius, after which the antenna can be matched by tuning the short characteristics, patch dimensions, and feed position. The fabricated design was chosen to operate at the MICS band (402-405 MHz), a popular band for biomedically implanted devices. An initial design was constructed with Styrofoam (epsilon r approximately equal to 1) and copper tape. Simulation in HFSS corroborates that SIFA operation incorporates the MICS band, with resonant frequency of 404 MHz and 32 MHz (7.9%) bandwidth. The fabricated prototype performs similarly, with a resonant frequency of 407 MHz and 19 (4.7%) MHz bandwidth. Following fabrication, several modifications were implemented to miniaturize the SIFA and introduce additional functionality. Slot loading and dielectric coating were implemented to achieve SIFA miniaturization. Multiple elements were also introduced to achieve dual band operation and beam steering. A miniaturized SIFA was investigated in several biological media, and a lossy coating implemented to maintain impedance match in several different media, with the goal of retaining a matched impedance bandwidth in the MICS band.

Thermoacoustic tomography (TAT) is a newly emerging modality in biomedical imaging. It combines the good contrast of electromagnetic and good resolution of ultrasound imaging. The mathematical model of TAT is the observability problem for the wave equation: one observes the data on a hyper-surface and reconstructs the initial perturbation. In this dissertation, we consider several mathematical problems of TAT. The first problem is the inversion formulas. We provide a family of closed form inversion formulas to reconstruct the initial perturbation from the observed data. The second problem is the range description. We present the range description of the spherical mean Radon transform, which is an important transform in TAT. The next problem is the stability analysis for TAT. We prove that the reconstruction of the initial perturbation from observed data is not H¨older stable if some observability condition is violated. The last problem is the speed determination. The question is whether the observed data uniquely determines the ultrasound speed and initial perturbation. We provide some initial results on this issue. They include the unique determination of the unknown constant speed, a weak local uniqueness, a characterization of the non-uniqueness, and a characterization of the kernel of the linearized operator.

The spherical inverted-F antenna (SIFA) is a relatively new conformal antenna design that consists of a microstrip patch resonator on a spherical ground. The SIFA resembles a planar inverted-F antenna (PIFA) that has been conformally recessed onto a sphere. The basic design, simulation, and fabrication of a SIFA were recently reported. The aim of this thesis is to provide a three-fold improvement to the study of the SIFA: the fabrication of a dielectric-coated SIFA, a new analytical model based on the cavity method, and the analysis of a randomly oriented SIFA’s operation in a remote networking scenario. A key improvement to the basic SIFA design is the addition of a lossy dielectric coating to the outside of the sphere for purposes of impedance stability, bandwidth control, and physical ruggedization. The first contribution of this thesis is the fabrication of such a dielectric-coated SIFA. Two antennas are fabricated: a coated SIFA operating at 400 MHz, and an uncoated SIFA operating at 1 GHz for comparison. Both SIFAs are constructed of foam and copper tape; the coating is comprised of silicone rubber and carbon fiber. The fabricated designs perform with reasonable agreement to corresponding simulations, providing a basic proof of concept for the coated SIFA. The SIFA was previously studied analytically using a transmission line model. The second task of this thesis is to present a new model using the cavity method, as employed in microstrip patches. The SIFA cavity model uses a curvilinear coordinate system appropriate to the antenna’s unique geometry and is able to predict the antenna’s performance more accurately than the transmission line model. The final portion of this thesis examines the performance of the SIFA in a remote network scenario. Specifically, a line-of-sight link between two SIFAs operating in the presence of a lossy dielectric ground is simulated assuming that each SIFA is randomly oriented above the ground. This analysis is performed for both uncoated and coated SIFAs. A statistical analysis of the impedance match, efficiency, and power transfer between these antennas for all possible orientations is presented that demonstrates a design tradeoff between efficiency and predictability.