Finite element eigenvalue enclosures for the Maxwell operator

We propose employing the extension of the Lehmann-Maehly-Goerisch method developed by Zimmermann and Mertins, as a highly effective tool for the pollution-free finite element computation of the eigenfrequencies of the resonant cavity problem on a bounded region. This method gives complementary bounds for the eigenfrequencies which are adjacent to a given real parameter. We present a concrete numerical scheme which provides certified enclosures in a suitable asymptotic regime. We illustrate the applicability of this scheme by means of some numerical experiments on benchmark data using Lagrange elements and unstructured meshes.Comment: arXiv admin note: substantial text overlap with arXiv:1306.535

On finding a penetrable obstacle using a single electromagnetic wave in the time domain

The time domain enclosure method is one of analytical methods for inverse obstacle problems governed by partial differential equations in the time domain. This paper considers the case when the governing equation is given by the Maxwell system and consists of two parts. The first part establishes the base of the time domain enclosure method for the Maxwell system using a single set of the solutions over a finite time interval for a general (isotropic) inhomogeneous medium in the whole space. It is a system of asymptotic inequalities for the indicator function which may enable us to apply the time domain enclosure method to the problem of finding unknown penetrable obstacles embedded in various background media. As a first step of its expected applications, the case when the background medium is homogeneous and isotropic, is considered and the time domain enclosure method is realized. This is the second part.Comment: 22 pages, self revision, introduction revised, on page 5 conditions (B.I), (B.II) and (B.III) introduced, Theorem 1.2 revised, on page 6 another indicator function introduced, Corollary 1.1 created, subsection 3.3 revised, Lemma 3.2 together with the proof revised, grant information added, references [2], [25] adde

Study of eddy current probes

The recognition of materials properties still presents a number of problems for nondestructive testing in aerospace systems. This project attempts to utilize current capabilities in eddy current instrumentation, artificial intelligence, and robotics in order to provide insight into defining geometrical aspects of flaws in composite materials which are capable of being evaluated using eddy current inspection techniques

On avoiding cosmological oscillating behavior for S-brane solutions with diagonal metrics

In certain string inspired higher dimensional cosmological models it has been conjectured that there is generic, chaotic oscillating behavior near the initial singularity -- the Kasner parameters which characterize the asymptotic form of the metric "jump" between different, locally constant values and exhibit a never-ending oscillation as one approaches the singularity. In this paper we investigate a class of cosmological solutions with form fields and diagonal metrics which have a "maximal" number of composite electric S-branes. We look at two explicit examples in D=4 and D=5 dimensions that do not have chaotic oscillating behavior near the singularity. When the composite branes are replaced by non-composite branes chaotic oscillatingComment: Corrected typos, published in Phys. Rev. D72, 103511 (2005

Homogenization Relations for Elastic Properties Based on Two-Point Statistical Functions

In this research, the homogenization relations for elastic properties in isotropic and anisotropic materials are studied by applying two-point statistical functions to composite and polycrystalline materials. The validity of the results is investigated by direct comparison with experimental results. In todays technology, where advanced processing methods can provide materials with a variety of morphologies and features in different scales, a methodology to link property to microstructure is necessary to develop a framework for material design. Statistical distribution functions are commonly used for the representation of microstructures and also for homogenization of materials properties. The use of two-point statistics allows the materials designer to consider morphology and distribution in addition to properties of individual phases and components in the design space. This work is focused on studying the effect of anisotropy on the homogenization technique based on two-point statistics. The contribution of one-point and two-point statistics in the calculation of elastic properties of isotropic and anisotropic composites and textured polycrystalline materials will be investigated. For this purpose, an isotropic and anisotropic composite is simulated and an empirical form of the two-point probability functions are used which allows the construction of a composite Hull. The homogenization technique is also applied to two samples of Al-SiC composite that were fabricated through extrusion with two different particle size ratios (PSR). To validate the applied methodology, the elastic properties of the composites are measured by Ultrasonic methods. This methodology is then extended to completely random and textured polycrystalline materials with hexagonal crystal symmetry and the effect of cold rolling on the annealing texture of near- Titanium alloy are presented.Ph.D.Committee Chair: Hamid Garmestani; Committee Co-Chair: Arun Gokhale; Committee Member: David McDowell; Committee Member: Naresh Thadhani; Committee Member: W. Steven Johnso