FDTD can successfully simulate various kinds of phenomena of electromagnetic waves. Mainly, we use orthogonal Cartesian coordinate in general situations when we deal with the electromagnetic problems, but the curved geometry of the problem makes it difficult to obtain accurate results using conventional FDTD algorithm because of staircasing. To analyze curved geometry using Conformal FDTD can improve this shortcoming. The Conformal FDTD uses the regular FDTD equation for updating the magnetic field by using the electric field values along the distorted contours, that are appropriately weighted with lengths of the contours. The Conformal FDTD technique is well suited for handling such curved geometries. The moment method is used to convert the integral equation into a matrix equation.The major drawback of moment method (MoM) is the full matrix generation and huge computation time. The CFDTD directly approximates the differential operators in the Maxwell curl equation, and avoids using more mathematic formulae. This thesis uses Conformal FDTD to simulate RCS value of the cylinder and sphere and compare Conformal FDTD with Moment Method. We know that Conformal FDTD will save memory requirement and CPU time even more than Moment Method in layered structure.

Let G be a complex semisimple Lie Group with parabolic subgroup P, so that G/P is a generalized flag manifold. An algebraic construction of invariant differential operators between sections of homogeneous bundles over such spaces is given and it is shown how this leads to the classification of all such operators. As an example of a process which naturally generates such operators, the algebraic Penrose transform between generalized flag manifolds is given and computed for several cases, extending standard results in Twistor Theory to higher dimensions. It is then shown how to adapt the homogeneous construction to manifolds with a certain class of tangent bundle structure, including conformal manifolds. This leads to a natural definition of invariant differential operators on such manifolds, and an algebraic method for their construction. A curved analogue of the Penrose transform is given.

As a contribution to increasing the areal density of digital data stored on a magnetic recording medium, this thesis provides mathematical analyses of various magnetic recording heads. Each of the heads considered here is for use in a perpendicular recording system, writing to or reading from a multi-layer medium which includes a high magnetic permeability layer between the data storage layer and the substrate. The exact two-dimensional analysis is performed in each case by one of two methods: either Fourier analysis or conformal mapping. The types of heads analysed include conventional styles but particular emphasis is placed on the effects of the novel idea of potential grading across the pole pieces. Exact head fields are derived for thin film heads with both constant and linearly varying pole potentials, single pole heads with linearly and arbitrarily varying pole potentials and shielded magnetoresistive heads, all in the presence of a magnetic underlayer. These and other published solutions are used to derive output characteristics for perpendicular replay heads, which are compared with published theoretical and experimental results where possible. The Fourier solutions obtained are in the form of infinite series dependent on at least one set of coefficients which are determined by infinite systems of linear equations. Approximations to the potentials in the head face planes, independent of these coefficients, are derived from the exact Fourier solutions. The accuracy of these approximations is demonstrated when they are used to estimate the vertical field components and the spectral response functions. Heads with graded pole potentials are found to have more localised vertical field components than the corresponding constant potential heads. They are also better suited for use with thin media for 'in contact' recording.

Thesis (Ph.D.) in Physics--University of Maine, 2007. / Includes vita. Includes bibliographical references (leaves 109-112).

Thesis (Ph. D.)--Biomedical Engineering, Georgia Institute of Technology, 2006. / Anthony J. Yezzi, Committee Member ; James Gruden, Committee Member ; Allen Tannenbaum, Committee Chair ; May D. Wang, Committee Member ; Oskar Skrinjar, Committee Member. Vita. Includes bibliographical references.

Thesis (M. Phil.)--University of Hong Kong, 2005. / Title proper from title frame. Also available in printed format.

No description available.

Injection molding is one of the most common methods of mass production. After injecting molten plastic into a mold, the heat must leave the plastic material, enter the mold steel, enter the coolant, and exit the mold. This heat flow is critical to producing high quality parts rapidly. As plastic cools, the plastic shrinks. Uneven cooling causes uneven shrinkage which can cause the part to warp from the resulting internal stresses or create sink marks on the part. Thus the effect of uneven cooling is lower part quality, both in appearance and in dimension. Standard or conventional cooling channels are straight-drilled holes arranged such that they intersect and connect to form a loop for coolant, typically water, to flow through. This allows the mold to act as a heat exchanger, transferring heat to the coolant and carrying heated coolant away from the mold. While standard cooling channels have been used widely in the injection molding industry for their manufacturability and proven results, other methods have been developed for creating molds with cooling channels of any desired path or shape. These channels, called conformal due to how they conform to the shape of the part, provide uniform cooling, eliminate or reduce the quality issues of warpage and shrinkage, and provide faster, more economical cycle times. Conformal cooling is cannot be produced only by subtractive manufacturing methods that remove material from raw stock but rather through additive or hybrid manufacturing techniques that add material in layers of powder, sections, or sheets. Bonded sheet layer mold inserts can be made of any size and are currently the only feasible way of making large, conformally-cooled molds. Presented is a Six Sigma approach for implementing conformal cooling in existing molds to achieve the benefits of higher part quality and fast cycle times. Feasibility considerations include existing mold features such as slides and ejectors, choice of channel diameter, and the cooling channel path. Cost justification considerations include assessing part quality cost impact through calculation of the costs of poor quality and assessing machine capacity as relates to cycle time. With the approach presented, an injection molding company should be able to assess feasibility and cost effectiveness of implementing conformal cooling on its molds.

In the first chapter we consider the question of uniqueness of conformal Ricci flow. We use an energy functional associated with this flow along closed manifolds with a metric of constant negative scalar curvature. Given initial conditions we use this functional to demonstrate the uniqueness of the solution to both the metric and the pressure function along conformal Ricci flow. In the next chapter we study backward Ricci flow of locally homogeneous geometries of 4-manifolds which admit compact quotients. We describe the longterm behavior of each class and show that many of the classes exhibit the same behavior near the singular time. In most cases, these manifolds converge to a sub-Riemannian geometry after suitable rescaling.

This master's thesis presents a study on a slot and microstrip patch as the two main types of antennas for the use on Cube Satellite (CubeSat). A study on the fundamentals of the slot antenna is researched and a circularly polarized (CPd) cavity-backed cross slot antenna and its two-element array for the CubeSat are designed and fabricated. Fabricated two-element phased array cross slot antenna has higher radiation gain and steered radiation pattern compared to the fabricated single cross slot antenna. A CPd square microstrip patch antenna for the application of the CubeSat is designed and compared with a commercial CPd microstrip patch antenna. It is concluded that our designed microstrip patch antenna has a better performance compared to the commercial one. The last part of the research focuses on the design of miniaturized slot antennas for the CubeSat working at an ultra high frequency (UHF) band. The different techniques and challenges that we face through the miniaturization are articulated throughout the research and expanded upon in this thesis. The antenna simulations were performed using Ansoft High Frequency System Simula- tor (HFSS) and the final designs for the CPd cavity-backed single and two-element cross slot antennas and CPd microstrip patch antenna were fabricated using a circuit board milling machine. These were then measured inside an anechoic chamber for the radiation pattern. Both antennas had high radiation gain and good CPd radiation quality.