The directional distributions of gamma rays from oriented nuclei have been used to study the level structures of 132 Xe and 154Gd populated following the decays of 132 I and 154 Eu respectively. The orientation was produced by using the hyperfine field in iron to polarize the spin system of nuclei at a temperature of 15 mK. The low temperature was achieved using a 3He 4He dilution refrigerator. The directional distribution of gamma rays were measured by a high resolution Ge(Li) detector. With these measurements unique spin assignments were made for most of the levels below 3 MeV in 132Xe. The multipole mixing ratios of 28 transitions in 132 Xe and 15 transitions in 154Gd are given. The results have been compared with the predictions based on the generalized collective model of Gneuss and Greiner and with the SU(5), SU(3) and 0(6) groups of the interacting boson approximation (IBA) model and the w dynamic deformation theory based on the pairing plus quadrupole model.

The use of fluorescein and rhodamine as donor and acceptor fluorescent labels in the development of energy transfer immunoassay (ETIA) methods was evaluated by developing an assay for human serum albumin. The sensitivity of the assay was found to depend on (i) the degrees of fluorophore labelling of antibody and antigen, (ii) concentrations of labelled antibody and antigen, (iii) the fluorimeter spectral bandwidth, and (iv) whether the donor (fluorescein) was conjugated to the antigen or the antibody. These results, including those relating to the stability of the labelled immune reactants on storage, lead to the conclusion that fluorescein and rhodamine are far from ideal as donor and acceptor. Nevertheless, the application of the assay to the analysis of test serum samples gave results that compared favourably with those obtained by electroimmunoassay. Other potential donor and acceptor fluorescent labels were also investigated, viz. Ca) fluorescamine and fluorescein, (b) MDPF and fluorescein, (c) dansyl chloride and rhodamine, (d) quinacrine and fluorescein, and (e) quinacrine and rhodamine. Of these, only (a) and (b) were found to be suitable donor-acceptor pairs, and they were applied to the development of a number of assays for both low and high molecular-weight analytes. Comparative studies of fluorescamine and MDPF as donor fluorescent labels together with fluorescein as the acceptor label were performed by developing immunoassay methods for the determination of human serum transferrin in four serum samples including a blood sample from the victim of a road traffic accident. Results obtained were generally in good agreement with those found by the radial immunodiffusion method. An ETIA developed for nortriptyline and related tricyclic antidepressants was capable of detecting nanomolar concentrations of the drugs in pure solution and in spiked sera. Other ETIA's developed include a sandwich assay for the quantitation of human immunoglobulin A, and a direct assay for the determination of human immunoglobulin G. The Fluram as well as the MDPF enhancement phenomena were also studied in detail and applied successfully to the development of fluorescence enhancement immunoassays for nortriptyline, human serum transferrin and immunoglobulin G. Finally, the automation of an energy transfer immunoassay was successfully performed by using the principles of stopped-flow injection analysis with merging zones.

The dynamics of a class of nonlinear delay differential equations (D.D.E's) is studied. We focus attention on D.D.E's with a discrete delay used as models for production/destruction processes. The design of an electronic analog computer simulating an integrable D.D.E is presented. This computer is used to illustrate the presence of bistable solutions in the system. The multistability is investigated numerically with an analytic integration algorithm. Higher order multistability is reported, and the structure of basin boundaries in the space of initial functions is investigated. Pathological dependence of solution behavior on the initial function is shown to be present in large regions of parameter space. A D.D.E obtained as the singular perturbation of the one dimensional "hat map" is studied numerically. Several schemes to undertake a statistical analysis of the equation are presented. We first focus attention on the construction of densities along trajectories, and then on the construction of densities for ensembles of trajectories generated by ensembles of initial functions. A cycling of densities is observed in both cases, and compared to the asymptotic periodicity of the Frobenius-Perron operator for the hat map. Functional analytic techniques used for the analysis of stochastic wave propagation in continuous media and in quantum field theory are extended to the statistical study of D.D.E's, and provide a theoretical framework within which to study D.D.E dynamics in the spirit of ergodic theory and statistical mechanics.

<p> This dissertation reports studies of the internal structure of jammed granular materials and how granular sound propagation and vibrational modes are influenced by disorder in particle positions and contact forces. We investigate the role of particle scale forces on sound amplitude and speed, how to characterize the bulk pressure via the density of states, and force network modularity. We perform our experiments on a vertical, 2D, photoelastic granular material. Acoustic waves are excited from the bottom of the system and observed via particle scale sensors and a high speed camera. This novel combination of spatial and temporal measurements allows us to observe the role of force chains in sound propagation. The sound amplitude is largest through particles with strong contact forces, and we see that sound travels fastest along high force paths, giving rise to multiple sound speeds. Combining acoustic excitations with a method from thermal physics, we developed a new method to measure the density of modes, <i>D</i>(<i>f</i>). From <i>D</i>(<i> f</i>), we define a critical frequency, <i>f_c</i>, that scales with the bulk pressure, and comparing <i>D</i>(<i> f</i>) to Debye scaling, we find an excess of low frequency modes. Disorder in the force chain network and particle configurations plays a crucial role in <i>D</i>(<i>f</i>), as Debye scaling is only recovered for high pressure, hexagonally ordered packings. Finally, we characterize the force network by dividing it into modules of highly connected nodes. These communities become progressively more ordered as the pressure on the system is increased and the force chains become more uniform. Together, these studies illustrate the importance of the force chains in understanding static and dynamic granular properties.</p>

<p> The temperature dependence of the exchange bias effect, a phenomenon due to the interfacial exchange coupling at the antiferromagnetic-ferromagnetic (AFM-FM) interface, is studied experimentally using CoO/Co bilayers with two different methods: magnetic hysteresis loop and magnetotransport. The exchange bias coupling in the CoO/Co gives rise to induce unidirectional anisotropy in the Co layer causing a shift in the magnetic hysteresis loops. The experimental results show that the exchange bias field decreases with increasing temperature and depends on the Co thicknesses. The exchange bias shift is inversely proportional to the ferromagnetic film thickness confirming that it is an interfacial effect. The large training effect in hysteresis loops indicates that the hysteresis loop method underestimates the unidirectional anisotropy induced by the exchange coupling. The exchange bias is also determined by measuring the anisotropic magnetoresistance (AMR). While previous measurements relied on two separate apparati for comparison, this experiment demonstrates that hysteresis loop measurements and AMR measurements can be performed in one system, the automated Physical Property Measurement System by Quantum Design. A greater magnitude in the exchange anisotropy energy is observed for measurements made with AMR compared to that of the hysteresis loop measurements.</p>

<p> Equilibrium sampling is at the core of computational thermodynamics, aiding our understanding of various phenomena in the natural sciences including phase coexistence, molecular solvation, and protein folding. Despite the widespread development of novel sampling strategies over the years, efficient simulation of large complex systems remains a challenge. While the majority of current methods such as simulated tempering, replica exchange, and Monte Carlo methods rely solely on the use of equilibrium techniques, recent results in statistical physics have uncovered the possibility to sample equilibrium states through nonequilibrium simulations. </p><p> In our first study we present a new replica exchange sampling strategy, "Replica Exchange with Nonequilibrium Switches," which uses nonequilibrium simulations to enhance equilibrium sampling. In our method, trial swap configurations between replicas are generated through nonequilibrium switching simulations which act to drive the replicas towards each other in phase space. By means of these switching simulations we can increase an effective overlap between replicas, enhancing the probability that these moves are accepted and ultimately leading to more effective sampling of the underlying energy landscape. Simulations on model systems reveal that our method can be beneficial in the case of low replica overlap, able to match the efficiency of traditional replica exchange while using fewer processors. We also demonstrate how our method can be applied for the calculation of solvation free energies. </p><p> In a second, separate study, we investigate the dynamics leading to the dissociation of Na⁺Cl^&ndash; in water. Here we employ tools of rare event sampling to deduce the role of the surrounding water molecules in promoting the dissociation of the ion pair. We first study the thermodynamic forces leading to dissociation, finding it to be driven energetically and opposed entropically. In further analysis of the system dynamics, we deduce a) the spatial extent over which solvent fluctuations influence dissociation, b) the role of sterics and electrostatics, and c) the importance of inertia in enhancing the reaction probability.</p>

<p> The advent of highly-coherent x-ray light sources, such as those now available world-wide in modern third-generation synchrotrons and increasingly available in free-electron lasers, is driving the need for improved analytical and experimental techniques which exploit the coherency of the generated light. As the light illuminating a sample approaches full coherence, a simple Fourier transform describes the diffraction pattern generated by the scattered light in the far field; because the Fourier transform of an object is unique, coherent scattering can directly probe local structure in the scattering object instead of bulk properties.</p><p> In this dissertation, we exploit the coherence of Advanced Light Source beamline 12.0.2 to build three types of novel coherent scattering microscopes. First, we extend the techniques of coherent diffractive imaging and Fourier transform holography, which uses iterative computational methods to invert oversampled coherent speckle patterns, into reflection geometry. This proof-of-principle experiment demonstrates a method by which reflection Bragg peaks, such as those from the orbitally-ordered phase of complex metal oxides, might eventually be imaged. Second, we apply a similar imaging method to the x-ray beam itself to directly image the mutual coherence function with only a single diffraction pattern.</p><p> This technique supersedes the double-slit experiments commonly seen in the scattering literature to measure the mutual intensity function by using a set of apertures which effectively contains all possible double slit geometries. Third, we show how to evaluate the speckle patterns taken from a labyrinthine domain pattern for "hidden" rotational symmetries. For this measurement, we modify the iterative algorithms used to invert speckle patterns to generate a large number of domain configurations with the same incoherent scattering profile as the candidate pattern and then use these simulations as the basis for a statistical inference of the degree of ordering in the domain configuration. We propose extending this measurement to position-resolved speckle patterns, creating a symmetry-sensitive microscope. The three new techniques described herein may be employed at current and future light sources.</p>

<p> Randomized benchmarking is an experimental procedure intended to demonstrate control of quantum systems. The procedure extracts the average error introduced by a set of control operations. When the target set of operations is intended to be the set of Clifford operators, the randomized benchmarking algorithm is particularly easy to perform and its results have an important interpretation with respect to quantum computation. The aim of the benchmark is to provide a simple, useful parameter describing the quality of quantum control with an experiment that can be performed in a standard way on any prospective quantum computer. This parameter can be used to fairly compare different experiments or to mark improvement in a single experiment. </p><p> In this thesis I discuss first the original randomized-benchmarking procedure and the importance of the Clifford operators for its implementation. I develop the statistical analysis of the results and the physical assumptions that are required for the simplest analysis to apply. The original procedure does not extend in an obvious way to benchmarking of more than one qubit, so I introduce a standardized procedure for randomized benchmarking that applies to any number of qubits. This new procedure also enables the benchmarking of an individual control operation. I describe two randomized-benchmarking experiments I helped to design: one involved a single qubit and utilized a variation of the original procedure and the second involved two qubits and demonstrated the new procedure. I conclude with several potential extensions to the original and new procedures that give them reduced experimental overhead, the ability to describe encoded operations, and fairer comparisons between experiments.</p>

<p> Magnetic nanostructures have widespread applications in many areas of physics and engineering, and nanosphere lithography has recently emerged as promising tool for the fabrication of such nanostructures. The goal of this research is to explore the magnetic properties of a thin film of ferromagnetic material deposited onto a hexagonally close-packed monolayer array of polystyrene nanospheres, and how they differ from the magnetic properties of a typical flat thin film. The first portion of this research focuses on determining the optimum conditions for depositing a monolayer of nanospheres onto chemically pretreated silicon substrates (via drop-coating) and the subsequent characterization of the deposited nanosphere layer with scanning electron microscopy. Single layers of permalloy (Ni80Fe20) are then deposited on top of the nanosphere array via DC magnetron sputtering, resulting in a thin film array of magnetic nanocaps. The coercivities of the thin films are measured using a home-built magneto-optical Kerr effect (MOKE) system in longitudinal arrangement. MOKE measurements show that for a single layer of permalloy (Py), the coercivity of a thin film deposited onto an array of nanospheres increases compared to that of a flat thin film. In addition, the coercivity increases as the nanosphere size decreases for the same deposited layer. It is postulated that magnetic exchange decoupling between neighboring nanocaps suppresses the propagation of magnetic domain walls, and this pinning of the domain walls is thought to be the primary source of the increase in coercivity.</p>

The first experimental realization of a measurement of the weak value of a variable, a concept recently introduced by Aharonov, Albert and Vaidman, is presented. Weak measurements (measurements of a weak value) address the situation in which the separation of the eigenvalues caused by a weakly interacting measurement device is small compared to the width of the distribution of the individual eigenvalues. By appropriate choice of the pre- and post-selected state it is possible that the overlapping eigenvalues will interfere producing a value outside the range of eigenvalues. We demonstrate that the weak value is a practical method of amplifying and resolving the separation between overlapping eigenvalues in an optical experiment proposed by Duck, Stevenson and Sudarshan. In this experiment a birefringent crystal spatially separates two linear polarization components of a Gaussian laser beam by a distance much smaller than the beam waist.