In modern high-speed digital circuits, the space of the traditional single-layered or double-layered circuit board is not enough, therefore multi-layered circuit and stacked distribution technology are widely applied to many applications. The signal via is a vertical interconnection structure to communicate different signal layers, which will be seriously interfere with the simultaneous switching noise by via through the parallel plate cavity that consists of power and ground plane. It is an important issue to minimize the influence from noise. In multi-layered printed circuit boards, shorting vias are usually utilized to interconnect the planes with the same voltage level. The major theme of this thesis is the placement of shorting vias affecting plane cavity mode. And we propose a design rule of the shorting vias to significantly decrease the simultaneous switching noise and improve the power integrity of multi-layered circuit board.

This work presents a method for building a three-dimensional mesh from two- dimensional topologically identical layers, for use in aeroelastic simulations. The method allows modeling of large deformations of the wing in both the span direction and deformations in the cord of the wing. In addition, the method allows for the modeling of wings attached to fuselages. The mesh created is a hybrid mesh, which allows cell clustering in the viscous region. The generated mesh is high quality and allows capturing of nonlinear uid structure interactions in the form of limit cycle oscillation.

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.

Straight cooling channels are the most common method of controlling part temperature in injection molding process. However, straight cooling channels are not enough to manage temperature uniformity of the parts. In this work, a numerical study is conducted to decrease cycle time and cost of the injection molded parts by using conformal cooling channels. For this purpose, the commercial injection molding simulation program Moldflow is used. The governing physical equations for injection molding were derived and presented. The assumptions of the model were checked for simple geometries by comparing analytical results and numerical results of Moldflow. Then, the effect of conformal cooling channels is investigated for injection molding of a half cylinder shell part. It was seen that conformal cooling channels cools part faster and more uniform than straight cooling channels without corruption on the surface appearance. Finally, a real life case study was presented. For this purpose, a refrigerator shelf that is manufactured by the Ar&ccedil / elik Company was studied. The process was simulated using actual process parameters and simulation results were compared with production results. Then, the process was simulated using conformal cooling channels and compared with production results. It is seen that the cycle time of the refrigerator shelf was decreased considerably while preserving surface quality appearance.

In this study, a MATLAB&reg / code based on the Shooting and Bouncing Ray (SBR) algorithm is developed to compute the Radar Cross Section (RCS) of complex targets. SBR is based on ray tracing and combine Geometric Optics (GO) and Physical Optics (PO) approaches to compute the RCS of arbitrary scatterers. The presented algorithm is examined in two parts / the first part addresses a new aperture selection strategy named as &ldquo / conformal aperture&rdquo / , which is proposed and formulated to increase the performance of the code outside the specular regions, and the second part is devoted to testing the multiple scattering and shadowing performance of the code. The conformal aperture approach consists of a configuration that gathers all rays bouncing back from the target, and calculates their contribution to RCS. Multiple scattering capability of the algorithm is verified and tested over simple shapes. Ray tracing part of the code is also used as v a shadowing algorithm. In the first instance, simple shapes like sphere, plate, cylinder and polyhedron are used to model simple targets. With primitive shapes, complex targets can be modeled up to some degree. Later, patch representation is used to model complex targets accurately. In order to test the whole code over complex targets, a Computer Aided Design (CAD) format known as Stereo Lithography (STL) mesh is used. Targets that are composed in CAD tools are imported in STL mesh format and handled in the code. Different sweep geometries are defined to compute the RCS of targets with respect to aspect angles. Complex targets are selected according to their RCS characteristics to test the code further. In addition to these, results are compared with PO, Method of Moments (MoM) and Multilevel Fast Multipole Method (MLFMM) results obtained from the FEKO software. These comparisons enabled us to improve the code as possible as it is.

Conformal map has application in a lot of areas of science, e.g., fluid flow, heat conduction, solidification, electromagnetic, etc. Especially conformal map applied to elasticity theory can provide most simple and useful solution. But finding of conformal map for custom domain is not trivial problem. We used a numerical method for building a conformal map to solve torsion problem. In addition it was considered an infinite system method to solve the same problem. Results are compared.

In this work, two particular orthogonal and conformal decompositions of the 3+1 dimensional Einstein equation and Arnowitt-Deser-Misner (ADM) formalism for general relativity are obtained. In order to do these, the 3+1 foliation of the four-dimensional spacetime, the fundamental conformal transformations and the Hamiltonian form of general relativity that leads to the ADM formalism, de

This thesis study addresses the problem of overconstraint via introduction of conformal polyhedral linkages comprising revolute joints only and investigation of special geometric properties for the mobility of such overconstrained linkages. These linkages are of particular interest as deployable structures. First, planar case is issued and conditions for assembling irregular conformal polygonal linkages composed of regular and angulated scissor elements are derived. These planar assemblies are implemented into faces of polyhedral shapes and radially intersecting planes to obtain two different kind of polyhedral linkages. Rest of the thesis work relates to spatial linkages. Identical isosceles Bennett loops are assembled to obtain regular polygonal linkages and many such linkages are assembled to form polyhedral linkages. Then, Fulleroid-like linkages are presented. After these seemingly independent linkage types, Jitterbug-like linkages are introduced. Based on some observations on present linkages in the literature a definition for Jitterbug-like linkages is given first, and then a set of critical properties of these linkages are revealed. This special type of polyhedral linkages is further classified as being homothetic and non-homothetic, and geometric conditions to obtain mobile homothetic Jitterbug-like polyhedral linkages are investigated. Homohedral linkages, linkages with polyhedral supports with 3- and 4-valent vertices only, tangential polyhedral linkages are detailed as special cases and the degenerate case where all faces are coplanar is discussed. Two types of modifications on Jitterbug-like linkages are presented by addition of links on the faces and radial planes of Jitterbug-like linkages. Finally, a special class of Jitterbug-like linkages - modified Wren platforms are introduced as potential deployable structures.

The central objective of this work is to present an analysis of the asymptotic conformal Killing vectors in asymptotically-flat space-times of general relativity. This problem has been examined by two different methods; in Chapter 5 the asymptotic expansion technique originated by Newman and Unti [31] leads to a solution for asymptotically-flat spacetimes which admit an asymptotically shear-free congruence of null geodesics, and in Chapter 6 the conformal rescaling technique of Penrose [54] is used both to support the findings of the previous chapter and to set out a procedure for solution in the general case. It is pointed out that Penrose's conformal technique is preferable to the use of asymptotic expansion methods, since it can be established in a rigorous manner without leading to the possible convergence difficulties associated with asymptotic expansions. Since the asymptotic conformal symmetry groups of asymptotically flat space-times Are generalisations of the conformal group of Minkowski space-time we devote Chapters 3 and 4 to a study of the flat space case so that the results of later chapters may receive an interpretation in terms of familiar concepts. These chapters fulfil a second, equally important, role in establishing local isomorphisms between the Minkowski-space conformal group, 90(2,4) and SU(2,2). The SO(2,4) representation has been used by Kastrup [61] to give a physical interpretation using space-time gauge transformations. This appears as part of the survey of interpretative work in Chapter 7. The SU(2,2) representation of the conformal group has assumed a theoretical prominence in recent years. through the work of Penrose [9-11] on twistors. In Chapter 4 we establish contact with twistor ideas by showing that points in Minkowski space-time correspond to certain complex skew-symmetric rank two tensors on the SU(2,2) carrier space. These objects are, in Penrose's terminology [91, simple skew-symmetric twistors of valence [J. A particularly interesting aspect of conformal objects in space-time is explored in Chapter 8, where we extend the work of Geroch [16] on multipole moments of the Laplace equation in 3-space to the consideration. of Q tý =0 in Minkowski space-time. This development hinges upon the fact that multipole moment fields are also conformal Killing tensors. In the final chapter some elementary applications of the results of Chapters 3 and 5 are made to cosmological models which have conformal flatness or asymptotic conformal flatness. In the first class here we have 'models of the Robertson-Walker type and in the second class we have the asymptotically-Friedmann universes considered by Hawking [73].

The high-density integrated circuit (IC) gives rise to geometrically complex multiscale chip-package structures whose electromagnetic performance is difficult to predict. This motivates this dissertation to work on an efficient full-wave transient solver that is capable of capturing all the electromagnetic behaviors of such structures with high accuracy and reduced computational complexity compared to the existing methods. In this work, the unconditionally stable Laguerre-FDTD method is adopted as the core algorithm for the transient full-wave solver. As part of this research, skin-effect is rigorously incorporated into the solver which avoids dense meshing inside conductor structures and significantly increases computational efficiency. Moreover, as an alternative to typical planar interconnects for next generation high-speed ICs, substrate integrated waveguide, is investigated. Conductor surface roughness is efficiently modeled to accurately capture its high-frequency loss behavior. To further improve the computational performance of chip-package co-simulation, a novel transient non-conformal domain decomposition method has been proposed. Large-scale chip-package structure can be efficiently simulated by decomposing the computational domain into subdomains with independent meshing strategy. Numerical results demonstrate the capability, accuracy and efficiency of the proposed methods.