This thesis focuses on the structures of plated through holes in organic substrate, and discusses the high-frequency electrical characteristics of various plated through hole structures. This thesis consists of four parts. The first part introduces various kinds of vias in multilayer substrate. This content includes substrate drilling processes and capabilities, and discussions on plated through hole structures and their manufacture concerns. The second part focuses on actual measurement of plated through holes, and introduces high-frequency double-side probing technique. The difference from traditional high-frequency coplanar probing measurement is also discussed. The third part focuses on the high-frequency simulation by full-wave software ¡V Ansoft HFSS, and discusses the effects of various excited source and model structures on simulations. Part4 focuses on developing the broadband equivalent circuit model based on the physical structures, and discusses the electrical characterization of different plated through holes, and provides the related design concept.

The main purpose of this work is to study the collision of two black holes and the energy loss due to the gravitational waves emitted during this collision in the framework of general relativity. For this purpose we first study plane wave geometries and their collisions. More realistic collisions are the pp-wave collisions. As an analytic treatment of this problem, we investigate the head-on collision of two ultra-relativistic black holes. Treating the problem perturbatively, we extract the news function to compute how much energy is radiated in gravitational waves during the process. We show that the news function vanishes for the solutions obtained meaning that there is no mass-loss at the order of approximation.

Thesis (Ph. D.)--University of Texas at Austin, 2002. / Supervisors: Matthew William Choptuik and Philip J. Morrison. Vita. Includes bibliographical references. Available also from UMI Company.

Thesis (Ph. D.)--Rutgers University, 2009. / "Graduate Program in Physics and Astronomy." Includes bibliographical references (p. 75-80).

Thesis (Ph. D.)--University of Washington, 2003. / Vita. Includes bibliographical references (p. 205-211).

Thesis (Ph. D.)--University of Texas at Austin, 1999. / Vita. Includes bibliographical references (leaves 206-219). Available also in a digital version from Dissertation Abstracts.

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An investigation of Hawking radiation and a method for calculating particle creation in Schwarzschild spacetime using a quantum Langevin approach is presented in this thesis. In particular we shall show that an oscillator confined to a free-fall trajectory in Schwarzschild spacetime radiates as a result of such motions, and this radiation can be interpreted as Hawking radiation. In chapter 1 we present a literature review of the underlying concept: the Unruh effect. We also present some introductory material pertinent to the calculations. Chapter 2 is concerned with the case of a thin collapsing shell to form a black hole in Schwarzschild anti-de Sitter spacetime. We determine the temperature of the black hole to be T[subscript H] = h(r[subscript h])/4π = κ/2π where h(r[subscript h]) is the factorization of the conformal factor, r is the radial coordinate with the location of the horizon situated atr = r[subscript h], and κ the surface gravity. We also calculate the stress tensor at early and late spacetimes which allows us to calculate the renormalized stress-tensor {T[subscript μν]} which satisfies the semi-classical Einstien field equations. In chapter 3 we examine the case of a harmonic oscillator in 2D Schwarzschild spacetime and we show that the choice of trajectory is responsible for making the oscillator radiate. In chapter 4 we derive a quantum Langevin equation for the oscillator in the Heisenberg picture. By solving this equation using the Wigner-Weiskopff approximation we show that, in the case of an oscillator confined to a free fall trajectory in Schwarzschild spacetime, the oscillator radiates with respect to the Boulware vacuum. In agreement with Hawking[1] we obtain a temperature of the black hole as T = 1/8πM[subscript B]. In chapter 5 we present our conclusions and recommendations for further work.

This thesis establishes a precise mathematical connection between the Einstein equations of general relativity and the incompressible Navier-Stokes equation of fluid dynamics. We carry out a holographic analysis which relates solutions to the Einstein equations to the behaviour of a dual fluid living in one fewer dimensions. Gravitational systems are found to exhibit Navier-Stokes behaviour when we study the dynamics of the region near an event horizon. Thus, we find non-linear deformations of Einstein solutions which, after taking a suitable near horizon limit and imposing our particular choice of boundary conditions, turn out to be precisely characterised by solutions to the incompressible Navier-Stokes equation. In other words, for any solution to the Navier-Stokes equation, the set-up we present provides a solution to the Einstein equations near a horizon. We consider the cases of fluids flowing on the plane and on the sphere. Fluid dynamics on the plane is analysed foremost in the context of a flat background geometry whilst the spherical analysis is undertaken for Schwarzschild black holes and the static patch of four-dimensional de Sitter space. / Physics