In this thesis, a systematic study has been carried out on the synthesis, characterization and device fabrication of piezoelectric ZnO nanstructures. The achieved results are composed of the following four parts. Firstly, through a systematic investigation on the Sn-catalyzed ZnO nanostructure, an improved understanding of the chemical and physical process occurring during the growth of hierarchical nanostructures has been achieved. Decomposed Sn from SnO2 has been successfully demonstrated and proved to be an effective catalyst guiding the growth of not only aligned ZnO nanowires, but also the hierarchical nanowire-nanoribbon junction arrays and nanopropeller arrays. During the vapor-liquid-solid (VLS) catalyzing growth process at high temperature, Sn in the liquid state has been proved to be able to guide the growth of nanowires and nanoribbons in terms of growth directions, side facets, and crystallographic interfaces between Sn and ZnO nanostructures. Secondly, using pure ZnO as the only source material, by precisely tuning and controlling the growth kinetics, a variety of hierarchical polar surface dominated nanostructures have been achieved, such as single crystal nanorings, nanobows, nanosprings and superlattice nanohelices. High yield synthesis of ZnO nanosprings over 50% has been successfully obtained by mainly controlling the pre-pumping level associated with the partial pressure of residual oxygen during the vapor-solid growth process. The rigid superlattice nanohelices of ZnO have been discovered, which is a result of minimization of the electrostatic energy induced by polar surfaces. The formation process of the nanohelix has been systematically characterized. Thirdly, two new strategies have been successfully developed for fabricating ZnO quantum dots and synthesis of ZnO nanodiskettes and nanotubes. The formation process is based on a common concept of self-assembly. Finally, a series of devices and applications studies based on several piezoelectric ZnO nanostructures, such as nanobelts, nanopropellers and nanohelices, have been carried out utilizing the electro-mechanical resonance, bio-surface functionalization, devices fabrication and electrical characterization. Individual nanobelt and nanohelix based nanodevices have been successfully fabricated for applications in chemical and biological sensing. The study opens a few new areas in oxide nanostructures and applications.

Smoothing is an important part of the pre-processing step in Signal Processing. A signal, which is purified from noise as much as possible, is necessary to achieve our aim. There are many smoothing algorithms which give good result on a stationary data, but these smoothing algorithms don&rsquo / t give expected result in a non-stationary data. Studying Acceleration data is an effective method to see whether the smoothing is successful or not. The small part of the noise that takes place in the Displacement data will affect our Acceleration data, which are obtained by taking the second derivative of the Displacement data, severely. In this thesis, some linear and non-linear smoothing algorithms will be analyzed in a non-stationary dataset.

As humanly engineered materials systems approach the atomic scale, top-down manufacturing approaches breakdown and following nature's example, bottom-up or self-assembly methods have the potential to emerge as the dominant paradigm. Synthesis of one-dimensional nanomaterials takes advantage of such self-assembly manufacturing techniques, but until now most efforts have relied on high temperature vapor phase schemes which are limited in scalability and compatibility with organic materials. The solution-phase approach is an attractive low temperature alternative to overcome these shortcomings. To this end, this thesis is a study of the rationale solution-phase synthesis of ZnO nanowires and applications in photovoltaics. The following thesis goals have been achieved: rationale synthesis of a single ZnO nanowire on a polymer substrate without seeding, design of a wafer-scale technique to control ZnO nanowire array density using layer-by-layer polymers, determination of optimal nanowire field emitter density to maximize the field enhancement factor, design of bridged nanowires across metal electrodes to order to circumvent post-synthesis manipulation steps, electrical characterization of bridged nanowires, rationale solution-phase synthesis of long ZnO nanowires on optical fibers, fabrication of ZnO nanowire dye-sensitized solar cells on optical fibers, electrical and optical characterization of solar cell devices, comparison studies of 2-D versus 3-D nanowire dye-sensitized solar cell devices, and achievement of 6-fold solar cell power conversion efficiency enhancement using a 3-D approach. The thesis results have implications in nanomanufacturing scale-up and next generation photovoltaics.

In this study, transmissivity and storage coefficient of a semi-infinite, confined, homogeneous and isotropic aquifer, where the flow is one-dimensional and linear, are determined using Marquardt algorithm, considering two independent cases: constant drawdown in the adjacent stream / or constant discharge from the aquifer due to pumping at a constant rate. In the first case piezometric head and discharge measurements are utilized. Hydraulic diffusivity, which is the ratio of transmissivity to storage coefficient, is determined from piezometric head measurements / whereas their product is determined from discharge measurements. Then, the two parameters are calculated easily. In the second case piezometric head observations are utilized only and transmissivity and storage coefficient are determined simultaneously. Convergence to true values is very fast for both cases even for poor initial estimates. Three examples, two using synthetic data for both cases and one using actual field data for the second case, are presented. Conventional type-curve matching method is used for comparison of the results. It is observed that the results of Marquardt algorithm are in a reasonable agreement with those of type-curve matching method.

Die magnetischen Eigenschaften von Li2CuO2 sind seit mehr als zwei Jahrzehnten Gegenstand theoretischen und experimentellen Interesses. Über die genaue Natur der magnetischen Wechselwirkungen in diesem Isolator konnte jedoch keine Einigkeit erzielt werden. Während das Material von Seiten theoretischer Untersuchungen als quasi-eindimensionaler Magnet mit starken ferromagnetischen Kopplungen entlang der Kette verstanden wurde, legten experimentelle Studien dominierende dreidimensionale Zwischenkettenkopplungen nahe. Im Rahmen dieser Dissertation werden auf der Grundlage von Untersuchungen des magnetischen Anregungsspektrums mittels inelastischer Neutronenstreuung und dessen Analyse innerhalb eines Spinwellenmodels die führenden magnetischen Wechselwirkungen in Li2CuO2 bestimmt. Es wird zweifelsfrei nachgewiesen, dass das Material eine quasi-eindimensionale Spinkettenverbindung darstellt. Insbesondere kann die Konkurrenz von ferro- und antiferromagnetischen Wechselwirkungen entlang der Ketten nachgewiesen werden. Die Anwendbarkeit einer Spinwellenanalyse dieses niedrigdimensionalen Spin-1=2 Systems wird gezeigt. Das magnetische Phasendiagramm wird mittels Messungen von spezifischer Wärme, thermischer Ausdehnung und Magnetostriktion sowie der Magnetisierung in statischen und gepulsten Magnetfeldern untersucht und im Bezug auf die Austauschwechselwirkungen diskutiert. Aufgrund seiner einfachen kristallographischen und magnetischen Struktur stellt Li2CuO2 ein potentiell wertvolles Modellsystem in der Klasse der Spinkettenverbindungen mit konkurrierenden ferro- und antiferromagnetischen Wechselwirkungen dar. / The magnetic properties of Li2CuO2 have attracted interest since more than two decades, both in theory and experiment. Despite these efforts, the precise nature of the magnetic interactions in this insulator remained an issue of controversial debate. From theoretical studies, the compound was understood as a quasi-one-dimensional magnet with strong ferromagnetic interactions along the chain, while in contrast, experimentally studies suggested dominant three-dimensional inter-chain interactions. In this thesis, the leading magnetic exchange interactions of Li2CuO2 are determined on the basis of a detailed inelastic neutron scattering study of the magnetic excitation spectrum, analyzed within spin-wave theory. It is unequivocally shown, that the material represents a quasi-one-dimensional spin-chain compound. In particular, the competition of ferro- and antiferromagnetic interactions in the chain has been evidenced. The applicability of a spin-wave model for analysis of this low-dimensional spin-1=2 system is shown. The magnetic phase diagram of Li2CuO2 is studied by specific heat, thermal expansion and magnetostriction measurements as well as magnetization measurements in both static and pulsed magnetic fifields. The phase diagram is discussed with respect to the exchange interactions. With its simple crystallographic and magnetic structure, Li2CuO2 may serve as a worthwhile model system in the class of spin-chain compounds with competing ferromagnetic and antiferromagnetic interactions.

In this thesis we used ESR to investigate magnetic properties of low D vandium and copper oxides in which small quantum spins are arranged in 1D chains and 2D layers. The thesis covers five different low dimensional spin systems. They turned out to be experimental reliazation of some of the most intersiting theoritical models in the field of quantum magnetism.

In this thesis we study the physics of quantum many-body systems confined to one-dimensional geometries. The work was motivated by the recent success of experimentalists in developing atom traps, capable of restricting the motion of the individual atoms to a single spatial dimension. Specifically, we look at aspects of the one-dimensional Bose gas including; excitation spectrum, correlation functions, and dynamical behaviour. In Chapter \ref{ch:excitation1D} we consider the Lieb-Liniger model of interacting bosons in one-dimension. We numerically solve the equations arising from the Bethe ansatz solution for the exact many-body wave function in a finite-size system of up to twenty particles for attractive interactions. We discuss novel features of the solutions, including deviations from the well-known string solutions due to finite size effects. We present excited state string solutions in the limit of strong interactions and discuss their physical interpretation, as well as the characteristics of the quantum phase transition that occurs as a function of interaction strength in the mean-field limit. Our results are compared to those obtained via exact diagonalization of the Hamiltonian in a truncated basis. In Chapter \ref{ch:g2} we analytically calculate the spatial nonlocal pair correlation function for an interacting uniform one dimensional Bose gas at finite temperature and propose an experimental method to measure nonlocal correlations. Our results span six different physical realms, including the weakly and strongly interacting regimes. We show explicitly that the characteristic correlation lengths are given by one of four length scales: the thermal de Broglie wavelength, the mean interparticle separation, the healing length, or the phase coherence length. In all regimes, we identify the profound role of interactions and find that under certain conditions the pair correlation may develop a global maximum at a finite interparticle separation due to the competition between repulsive interactions and thermal effects. In Chapter \ref{ch:casimirdrag} we study the drag force below the critical velocity for obstacles moving in a superfluid. The absence of drag is well established in the context of the mean-field Gross-Pitaevskii theory. We calculate the next order correction due to quantum and thermal fluctuations and find a non-zero force acting on a delta-function impurity moving through a quasi-one-dimensional Bose-Einstein condensate at all subcritical velocities and at all temperatures. The force occurs due to an imbalance in the Doppler shifts of reflected quantum fluctuations from either side of the impurity. Our calculation is based on a consistent extension of Bogoliubov theory to second order in the interaction strength, and finds new analytic solutions to the Bogoliubov-de Gennes equations for a gray soliton. In Chapter \ref{ch:solitons} we study the effect of quantum noise on the stability of a soliton. We find the soliton solutions exactly define the reflectionless potentials of the Bogoliubov-de Gennes equations. This results in complete stability of the solitons in a purely one dimensional system. We look at the modifications to the density profile of a black soliton due to quantum fluctuations.

In this thesis we study the physics of quantum many-body systems confined to one-dimensional geometries. The work was motivated by the recent success of experimentalists in developing atom traps, capable of restricting the motion of the individual atoms to a single spatial dimension. Specifically, we look at aspects of the one-dimensional Bose gas including; excitation spectrum, correlation functions, and dynamical behaviour. In Chapter \ref{ch:excitation1D} we consider the Lieb-Liniger model of interacting bosons in one-dimension. We numerically solve the equations arising from the Bethe ansatz solution for the exact many-body wave function in a finite-size system of up to twenty particles for attractive interactions. We discuss novel features of the solutions, including deviations from the well-known string solutions due to finite size effects. We present excited state string solutions in the limit of strong interactions and discuss their physical interpretation, as well as the characteristics of the quantum phase transition that occurs as a function of interaction strength in the mean-field limit. Our results are compared to those obtained via exact diagonalization of the Hamiltonian in a truncated basis. In Chapter \ref{ch:g2} we analytically calculate the spatial nonlocal pair correlation function for an interacting uniform one dimensional Bose gas at finite temperature and propose an experimental method to measure nonlocal correlations. Our results span six different physical realms, including the weakly and strongly interacting regimes. We show explicitly that the characteristic correlation lengths are given by one of four length scales: the thermal de Broglie wavelength, the mean interparticle separation, the healing length, or the phase coherence length. In all regimes, we identify the profound role of interactions and find that under certain conditions the pair correlation may develop a global maximum at a finite interparticle separation due to the competition between repulsive interactions and thermal effects. In Chapter \ref{ch:casimirdrag} we study the drag force below the critical velocity for obstacles moving in a superfluid. The absence of drag is well established in the context of the mean-field Gross-Pitaevskii theory. We calculate the next order correction due to quantum and thermal fluctuations and find a non-zero force acting on a delta-function impurity moving through a quasi-one-dimensional Bose-Einstein condensate at all subcritical velocities and at all temperatures. The force occurs due to an imbalance in the Doppler shifts of reflected quantum fluctuations from either side of the impurity. Our calculation is based on a consistent extension of Bogoliubov theory to second order in the interaction strength, and finds new analytic solutions to the Bogoliubov-de Gennes equations for a gray soliton. In Chapter \ref{ch:solitons} we study the effect of quantum noise on the stability of a soliton. We find the soliton solutions exactly define the reflectionless potentials of the Bogoliubov-de Gennes equations. This results in complete stability of the solitons in a purely one dimensional system. We look at the modifications to the density profile of a black soliton due to quantum fluctuations.

Thesis(M.S.)--Auburn University, 2006. / Abstract. Vita. Includes bibliographic references (p.100-101).

Smoothing is an important part of the pre-processing step in Signal Processing. A signal, which is purified from noise as much as possible, is necessary to achieve our aim. There are many smoothing algorithms which give good result on a stationary data, but these smoothing algorithms don&rsquo / t give expected result in a non-stationary data. Studying Acceleration data is an effective method to see whether the smoothing is successful or not. The small part of the noise that takes place in the Displacement data will affect our Acceleration data, which are obtained by taking the second derivative of the Displacement data, severely. In this thesis, some linear and non-linear smoothing algorithms will be analyzed in a non-stationary data set.