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This dissertation examines the response of piezoelectric material strain to electron flux influence. A plate of PZT5h is prepared as the specimen. The positive electrode is removed, and the negative electrode is connected to a power amplifier. Sixteen strain gages are attached as the strain sensor. The specimen is placed in a vacuum chamber, then the positive side is illuminated by electron beam. The characteristic of the static strain response is predicted by deriving the equation strain/deflection of the plate. Two methods are used, the Electro-Mechanical Equations and numerical analysis using Finite Element Method. The settings of the electron gun system (energy and emission current), along with the electric potential of the negative electrode (back-pressure), are varied to examine piezoelectric material responses under various conditions. Several material characteristics are examined: current flow to and from the material, time response of material strain, charge and strain distribution, and blooming. Results from these experiments suggest several conditions control the strain development in piezoelectric material. The current flow and strain on the material is stable if the backpressure voltage is positive. As a comparison, the current flow is small and the strain drifts down if the backpressure voltage is significantly negative. The material needs only 1 second to follow a positive step in backpressure voltage, but needs almost 1 minute to respond to a negative step backpressure change. This phenomenon is a result of secondary electron emission change and the energy transfer from the primary electrons to the local electrons on the material. The time needed to achieve steady state condition is also a dependent of emission current. After a period of time the primary electron incidence induces strain throughout the 7.5-cm-by-5-cm plate despite the fact that the beam diameter is only 1 cm2. One possibility is blooming due to electron movement under intense electric fields in the dielectric material.

"The last fifteen years have seen much success in the analysis of quasi-static evolution for Griffith fracture, which is the mathematically natural starting point for studying fracture. At the same time, attempts have been made to show existence for similar models based on cohesive fracture rather than Griffith. These models are generally viewed as physically more realistic than Griffith, in that they are better models for crack nucleation. These attempts at existence proofs have been unsuccessful without very strong additional assumptions, for example, specifying the crack path a priori. The main purpose of this thesis is to characterize as well as possible the mathematical difficulties in cohesive fracture, and to make progress toward an existence result without the prescribed crack path assumption. So far, the most powerful method for existence proofs is to build a sequence of approximate solutions, based on time discretization, and take the limit as the time steps go to zero. We show that there are mainly two complications on the cracks of these approximate solutions that we need to rule out in order to show existence. The first one is due to the potential oscillation of the crack path. The second is due to the potential splitting of a crack into two or more nearby cracks, with the same total jump in displacement. We begin by first constructing an example illustrating how oscillations described above can affect the minimality of the limit. Then we prove that the splitting described above can be ruled out for any sequence of unilateral minimizers. With this result, we show how exactly oscillation affect the minimality on the limit of the sequence. We then move to the evolution problem and show the convergence of energy for almost every t. Based on this result we develop a method that allows us to analyze the problem using only a finite set of times. An application of this method is a proof of absolute continuity. Future work will be aimed at using the tools we developed to rule out oscillation and finally to prove existence results under more general assumptions."

The use of multiple antennas at the transmitter and/or the receiver promises greatly increased capacity. This can be useful to meet the ever growing demand of wireless connectivity, provided we can find techniques to efficiently exploit the advantages of the Multiple-Input Multiple-Output (MIMO) system. This work explores the MIMO system in a flat quasi-static fading scenario. Such a channel occurs, for example, in packet data systems, where the channel fade is constant for the duration of a codeword and changes independently from one transmission to another. We first show why it is hard to compute the true constrained modulation outage capacity. As an alternative, we present achievable lower bounds to this capacity based on existing space-time codes. The bounds we compute are the fundamental limits to the performance of these space-time codes under maximum-likelihood decoding, optimal outer codes and asymptotically long lengths. These bounds also indicate that MIMO systems have different behavior under Gaussian signaling (unconstrained input) and under the finite alphabet setting. Our results naturally suggest the use of concatenated codes to approach near-capacity performance. However, we show that a system utilizing an iterative decoder has a fundamental limit – it cannot be universal and therefore it cannot perform arbitrarily close to its outage limit. Next, we propose two different transceiver structures that have good performance. The first structure is based on a novel BCJR-decision feedback decoder which results in performance within a dB of the outage limit. The second structure is based on recursive realizations of space-time trellis codes and uses iterative decoding at the receiver. This recursive structure has impressive performance even when the channel has time diversity. Thus, it forms the basis of a very flexible and robust MIMO transceiver structure.

General Relativity (GR) is one theory amongst a wider range of plausible descriptions of the Universe. The aim of this thesis is to examine the behaviour of so-called screened theories, which are designed to avoid local tests of modified gravity (MG). We establish that these theories may be treated in a unified manner in the context of halo formation. A prerequisite for this is the clarification that the quasi-static approximation can be applied in cosmologically-plausible scenarios. Amongst the plethora of MG theories, we select three, each of which exhibit a different form of screening. This describes a self-concealing property whereby each theory behaves like GR in the conditions of the local Universe. Only at regions of high energy density (chameleon), large coupling to matter (symmetron) or large derivatives of the scalar field (Vainshtein) does their modified behaviour emerge. We examine f(R), symmetron and DGP gravity in the context of non-linear gravitational collapse for the remainder of the thesis. Relativistic scalar fields are ubiquitous in our modern understanding of structure formation. They arise as candidates for dark energy and are at the heart of many modified theories of gravity. While there has been tremendous progress in calculating their effects on large scales there are still open questions on how to best quantify their effects on smaller scales where non-linear collapse becomes important. In these regimes, it has become the norm to use the quasi-static approximation in which the time evolution of perturbations in the scalar fields are discarded, akin to what is done in the context of non-relativistic fields in cosmology and the corresponding Newtonian limit. We show that considerable care must be taken in this regime by studying linearly perturbed scalar field cosmologies and quantifying the error that arise from taking the quasi-static limit. We focus on f(R) and chameleon models to assess the impact of the quasi-static approximation and discuss how it might affect studying the non-linear growth of structure in N-body numerical simulations. The halo mass function (HMF) n(M) dM is the number of haloes with mass in the range [ M, M+dM ] per unit volume. It has two remarkable properties which render it a useful probe of extensions to general relativity (GR). On the one hand, it is (nearly-)universal, in the sense that it can be written in a form (f(v) which is (practically) insensitive to changes in redshift and cosmological parameters and redshift. We develop a method to generalise fitting functions derived in GR to a variety of screened MG theories, in order to examine whether they are universal in the sense of being insensitive to MG. On the other hand, the HMF is sensitive to both the expansion history of the universe and the non-linear behaviour of spherical collapse via the critical density parameter and the matter power spectrum via the halo resolution. This greatly complicates the theoretical framework required to calculate the HMF, particularly given the sensitivity of chameleon MG to the surrounding environment. We explore a variety of new and existing methods to do so. Finally we re-calibrate the MG halo mass functions with the same rigour as has been done in GR. An important indicator of modified gravity is the effect of the local environment on halo properties. This paper examines the influence of the local tidal structure on the halo mass function, the halo orientation, spin and the concentration-mass relation. We generalise the excursion set formalism to produce a halo mass function conditional on large-scale structure. Our model agrees well with simulations on large scales at which the density field is linear or weakly non-linear. Beyond this, our principal result is that f(R does affect halo abundances, the halo spin parameter and the concentration-mass relationship in an environment-independent way, whereas we find no appreciable deviation from LCDM for the mass function with fixed environment density, nor the alignment of the orientation and spin vectors of the halo to the eigenvectors of the local cosmic web. There is a general trend for greater deviation from LCDM in under-dense environments and for high-mass haloes, as expected from chameleon screening. Given the broad spectrum of MG theories, it is important to design new probes of MG. Despite the fact that we examine only three theories of MG, the techniques and methodology developed in this thesis can be applied to a wide variety of theories and can be extended to improve the results in this work.

Particulate composites are widely used in many aerospace and military applications as energetic materials, armor materials or coatings and their behavior under dynamic loads have gained increasing significance. The addition of modifiers such as alumina nanoparticles generally facilitates the improvement of the mechanical strength to density ratio due to high specific area and particle rigidity. This allows for sufficient particlematrix bonding and therefore improved stiffness and load transfer in the composite. Photo-luminescent α-alumina nanoparticles when embedded in an epoxy matrix allow for the added benefit of in situ measurements at low strain rates to provide stress-sensitive information using the particle piezospectroscopic (PS) property. To investigate the low strain rate behavior, cylindrical specimens of alumina-epoxy composites with varying volume fractions of alumina were fabricated using a casting process to ensure minimal surface finishing and reduced manufacturing time. The results illustrate the capability of alumina nanoparticles to act as diagnostic sensors to measure the stress-induced shifts of the spectral R-line peaks resulting from low compressive strain rates. The range of PS coefficients measured, -3.15 to -5.37 cm−1/GP a for R1 and -2.62 to -5.39 cm−1/GP a for R2, correlate well with static test results of similar volume fractions. Results reveal a general trend of increasing sensitivity of the PS coefficients with increasing strain rate when compared to similar materials under static conditions. In contrast to static results, at a given strain rate, the PS coefficients show varying degrees of sensitivity for each iii volume fraction. This information can be used to determine the time-dependent microscale stresses the nanoparticles sustain during composite loading. Additionally, this work facilitates failure prediction by monitoring upshifts in the PS information. Calibration of the in situ diagnostic stress sensing capabilities of varying volume fractions of alumina nanocomposites under quasi-static strain rates in this work sets the precedent for future studies at high strain rates.

High transmission data rate, spectral efficiency, and reliability are necessary for future wireless communications systems. In a multipath-rich wireless channel, deploying multiple antennas at both the transmitter and receiver achieves high data rate, without increasing the total transmission power or bandwidth. When perfect knowledge of the wireless channel conditions is available at the receiver, the capacity has been shown to grow linearly with the number of antennas. However, the channel conditions must be estimated since perfect channel knowledge is never known a priori. In practice, the channel estimation procedure can be aided by transmitting pilot symbols that are known at the receiver. System performance depends on the quality of channel estimate, and the number of pilot symbols. It is desirable to limit the number of transmitted pilot symbols because pilot symbols reduce spectral efficiency. This thesis analyzes the system performance of coded multiple-input multiple-output (MIMO) systems for the quasi-static fading channel. The assumption that perfect channel knowledge is available at the receiver must be removed, in order to more accurately examine the system performance. Emphasis is placed on developing channel estimation strategies for an iterative Vertical Bell-Labs Layered Space Time (V-BLAST) architecture. The channel estimate can be sequentially improved between successive iterations of the iterative V-BLAST algorithm. For both the coded and uncoded systems, at high signal to noise ratio only a minimum number of pilot symbols per transmit antenna are required to achieve perfect channel knowledge performance. / Master of Science

The issue of eddy currents induced by the rapid switching of magnetic field gradients is a long-standing problem in magnetic resonance imaging. A new method for dealing with this problem is presented whereby spatial harmonic components of the magnetic field are continuously sensed, through their temporal rates of change, and corrected. In this way, the effects of the eddy currents on multiple spatial harmonic components of the magnetic field can be detected and corrections applied during the rise time of the gradients. Sensing the temporal changes in each spatial harmonic is made possible with specially designed detection coils. However to make the design of these coils possible, general relationships between the spatial harmonics of the field, scalar potential, and vector potential are found within the quasi-static approximation. These relationships allow the vector potential to be found from the field – an inverse curl operation – and may be of use beyond the specific problem of detection coil design. Using the detection coils as sensors, methods are developed for designing a negative feedback system to control the eddy current effects and optimizing that system with respect to image noise and distortion. The design methods are successfully tested in a series of proof-of-principle experiments which lead to a discussion of how to incorporate similar designs into an operational MRI.

The issue of eddy currents induced by the rapid switching of magnetic field gradients is a long-standing problem in magnetic resonance imaging. A new method for dealing with this problem is presented whereby spatial harmonic components of the magnetic field are continuously sensed, through their temporal rates of change, and corrected. In this way, the effects of the eddy currents on multiple spatial harmonic components of the magnetic field can be detected and corrections applied during the rise time of the gradients. Sensing the temporal changes in each spatial harmonic is made possible with specially designed detection coils. However to make the design of these coils possible, general relationships between the spatial harmonics of the field, scalar potential, and vector potential are found within the quasi-static approximation. These relationships allow the vector potential to be found from the field – an inverse curl operation – and may be of use beyond the specific problem of detection coil design. Using the detection coils as sensors, methods are developed for designing a negative feedback system to control the eddy current effects and optimizing that system with respect to image noise and distortion. The design methods are successfully tested in a series of proof-of-principle experiments which lead to a discussion of how to incorporate similar designs into an operational MRI.

Herein, we study the contact damage performance of two armour ceramics, alumina and silicon carbide, with varying microstructures and one particle-reinforced ceramic nanocomposite, alumina/silicon carbide, in an attempt to understand the microstructural mechanisms that affect plasticity and cracking under quasi-static and dynamic conditions. Quasi-static contact damage was imitated using Vickers indentation over a varying load regime. Numerical analysis of the indentation size effect, performed using the proportional specimen resistance model, allowed the contributions of plastic deformation and cracking to be separated into two individual values. In all three samples, higher levels of surface energy were found to correlate with increased amounts of cracking per unit area of indentation impression. Analytical modelling of crack initiation during Vickers indentation together with quantitative measurements of surface flaw populations revealed that such an increase in cracking damage was the result of higher densities of larger flaws. The hardness of the monolithic ceramics was found vary based on grain size and porosity levels, a smaller average grain size and lower porosity levels resulting in higher hardness values. In the nanocomposite materials, hardening was found to occur with further additions of silicon carbide nanoparticles. Such an effect has been attributed to the increased dislocation densities, as measured using Cr3+/Al2O3 fluorescence spectroscopy, and the impedance of dislocation movement within the lattice due to the presence of silicon carbide nanoparticles. In order to simulate dynamic contact damage, a low velocity, scaled-down drop-weight test was designed and developed. The dynamic contact damage resistance was determined based on the depth of penetration of a blunt indenter. In the monolithic ceramics, the indenter penetration was found to be shallower in materials of higher hardness. However, the nanocomposite materials displayed an opposing trend, the indenter penetration becoming deeper in the samples of higher hardness. The macro-scale fracture patterns produced during drop-weight impacts were seen to vary based on flaw populations and indenter penetration. In certain microstructures, extensive micro-cracking was also observed.