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### A Search for Periodic and Quasi-Periodic Patterns in Select Proxy Data with a Goal to Understanding Temperature Variation

**Date:**May 2016

**Creator:**Otto, James

**Description:**In this work over 200 temperature proxy data sets have been analyzed to determine if periodic and or quasi-periodic patterns exist in the data sets. References to the journal articles where data are recorded are provided. Chapter 1 serves an introduction to the problem of temperature determination in providing information on how various proxy data sources are derived. Examples are given of the techniques followed in producing proxy data that predict temperature for each method used. In chapter 2 temperature proxy data spanning the last 4000 years, from 2,000 BCE to 2,000 CE, are analyzed to determine if overarching patterns exist in proxy data sets. An average of over 100 proxy data sets was used to produce Figure 4. An overview of the data shows that several “peaks” can be identified. The data were then subjected to analysis using a series of frequency modulated cosine waves. This analysis led to a function that can be expressed by equation 3. The literature was examined to determine what mathematical models had been published to fit the experimental proxy data for temperature. A number of attempts have been made to fit data from limited data sets with some degree of success. Some other ...

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### Charged Particle Transport and Confinement Along Null Magnetic Curves and in Various Other Nonuniform Field Configurations for Applications in Antihydrogen Production

**Date:**May 2016

**Creator:**Lane, Ryan Andrew

**Description:**Comparisons between measurements of the ground-state hyperfine structure and gravitational acceleration of hydrogen and antihydrogen could provide a test of fundamental physical theories such as CPT (charge conjugation, parity, time-reversal) and gravitational symmetries. Currently, antihydrogen traps are based on Malmberg-Penning traps. The number of antiprotons in Malmberg-Penning traps with sufficiently low energy to be suitable for trappable antihydrogen production may be reduced by the electrostatic space charge of the positrons and/or collisions among antiprotons. Alternative trap designs may be needed for future antihydrogen experiments. A computational tool is developed to simulate charged particle motion in customizable magnetic fields generated by combinations of current loops and current lines. The tool is used to examine charged particle confinement in two systems consisting of dual, levitated current loops. The loops are coaxial and arranged to produce a magnetic null curve. Conditions leading to confinement in the system are quantified and confinement modes near the null curve and encircling one or both loops are identified. Furthermore, the tool is used to examine and quantify charged particle motion parallel to the null curve in the large radius limit of the dual, levitated current loops. An alternative to new trap designs is to identify the effects ...

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### Nonlinear and Quantum Optics Near Nanoparticles

**Date:**December 2015

**Creator:**Dhayal, Suman

**Description:**We study the behavior of electric fields in and around dielectric and metal nanoparticles, and prepare the ground for their applications to a variety of systems viz. photovoltaics, imaging and detection techniques, and molecular spectroscopy. We exploit the property of nanoparticles being able to focus the radiation field into small regions and study some of the interesting nonlinear, and quantum coherence and interference phenomena near them. The traditional approach to study the nonlinear light-matter interactions involves the use of the slowly varying amplitude approximation (SVAA) as it simplifies the theoretical analysis. However, SVVA cannot be used for systems which are of the order of the wavelength of the light. We use the exact solutions of the Maxwell's equations to obtain the fields created due to metal and dielectric nanoparticles, and study nonlinear and quantum optical phenomena near these nanoparticles. We begin with the theoretical description of the electromagnetic fields created due to the nonlinear wavemixing process, namely, second-order nonlinearity in an nonlinear sphere. The phase-matching condition has been revisited in such particles and we found that it is not satisfied in the sphere. We have suggested a way to obtain optimal conditions for any type and size of material medium. ...

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### Fractional Calculus and Dynamic Approach to Complexity

**Date:**December 2015

**Creator:**Beig, Mirza Tanweer Ahmad

**Description:**Fractional calculus enables the possibility of using real number powers or complex number powers of the differentiation operator. The fundamental connection between fractional calculus and subordination processes is explored and affords a physical interpretation for a fractional trajectory, that being an average over an ensemble of stochastic trajectories. With an ensemble average perspective, the explanation of the behavior of fractional chaotic systems changes dramatically. Before now what has been interpreted as intrinsic friction is actually a form of non-Markovian dissipation that automatically arises from adopting the fractional calculus, is shown to be a manifestation of decorrelations between trajectories. Nonlinear Langevin equation describes the mean field of a finite size complex network at criticality. Critical phenomena and temporal complexity are two very important issues of modern nonlinear dynamics and the link between them found by the author can significantly improve the understanding behavior of dynamical systems at criticality. The subject of temporal complexity addresses the challenging and especially helpful in addressing fundamental physical science issues beyond the limits of reductionism.

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### Variational Calculations of Positronium Scattering with Hydrogen

**Date:**December 2015

**Creator:**Woods, Denton

**Description:**Positronium-hydrogen (Ps-H) scattering is of interest, as it is a fundamental four-body Coulomb problem. We have investigated low-energy Ps-H scattering below the Ps(n=2) excitation threshold using the Kohn variational method and variants of the method with a trial wavefunction that includes highly correlated Hylleraas-type short-range terms. We give an elegant formalism that combines all Kohn-type variational methods into a single form. Along with this, we have also developed a general formalism for Kohn-type matrix elements that allows us to evaluate arbitrary partial waves with a single codebase. Computational strategies we have developed and use in this work will also be discussed.With these methods, we have computed phase shifts for the first six partial waves for both the singlet and triplet states. The 1S and 1P phase shifts are highly accurate results and could potentially be viewed as benchmark results. Resonance positions and widths for the 1S-, 1P-, 1D-, and 1F-waves have been calculated.We present elastic integrated, elastic differential, and momentum transfer cross sections using all six partial waves and note interesting features of each. We use multiple effective range theories, including several that explicitly take into account the long-range van der Waals interaction, to investigate scattering lengths for the 1,3S ...

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### Complex Numbers in Quantum Theory

**Date:**August 2015

**Creator:**Maynard, Glenn

**Description:**In 1927, Nobel prize winning physicist, E. Schrodinger, in correspondence with Ehrenfest, wrote the following about the new theory: “What is unpleasant here, and indeed directly to be objected to, is the use of complex numbers. Psi is surely fundamentally a real function.” This seemingly simple issue remains unexplained almost ninety years later. In this dissertation I elucidate the physical and theoretical origins of the complex requirement. I identify a freedom/constraint situation encountered by vectors when, employed in accordance with adopted quantum representational methodology, and representing angular momentum states in particular. Complex vectors, quite simply, provide more available adjustable variables than do real vectors. The additional variables relax the constraint situation allowing the theory’s representational program to carry through. This complex number issue, which lies at the deepest foundations of the theory, has implications for important issues located higher in the theory. For example, any unification of the classical and quantum accounts of the settled order of nature, will rest squarely on our ability to account for the introduction of the imaginary unit.

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### Synthesis and Characterization of Ion Beam Assisted Silver Nanosystems in Silicon Based Materials for Enhanced Photocurrent Collection Efficiency

**Date:**May 2015

**Creator:**Dhoubhadel, Mangal S.

**Description:**In recent years a great deal of interest has been focused on the synthesis of transitional metal (e.g. Ag, Cu, Fe, Au) nanosystems at the surface to sub-surface regions of Si and SiO2 matrices for fundamental understanding of their structures as well as for development of technological applications with enhanced electronic and optical properties. The applications of the metal nanoparticle or nanocluster (NC) systems range from plasmonics, photovoltaic devices, medical, and biosensors. In all of these applications; the size, shape and distribution of the metallic NCs in the silicon matrix play a key role. Low energy ion implantation followed by thermal annealing (in vacuum or gas environment) is one of the most suitable methods for synthesis of NCs at near surfaces to buried layers below the surfaces of the substrates. This technique can provide control over depth and concentration of the implanted ions in the host matrix. The implanted low energy metal ions initially amorphizes the Si substrates while being distributed at a shallow depth near the substrate surface. When subject to thermal annealing, the implanted ions agglomerate to form clusters of different sizes at different depths depending upon the fluence. However, for the heavier ions implanted with high fluences ...

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### Highly Efficient Single Frequency Blue Laser Generation by Second Harmonic Generation of Infrared Lasers Using Quasi Phase Matching in Periodically Poled Ferroelectric Crystals

**Date:**August 2014

**Creator:**Khademian, Ali

**Description:**Performance and reliability of solid state laser diodes in the IR region exceeds those in the visible and UV part of the light spectrum. Single frequency visible and UV laser diodes with higher than 500 mW power are not available commercially. However we successfully stabilized a multi-longitudinal mode IR laser to 860 mW single frequency. This means high efficiency harmonic generation using this laser can produce visible and UV laser light not available otherwise. In this study we examined three major leading nonlinear crystals: PPMgO:SLN, PPKTP and PPMgO:SLT to generate blue light by second harmonic generation. We achieved record high net conversion efficiencies 81.3% using PPMgO:SLT (~500 mW out), and 81.1% using PPKTP (~700 mW out). In both these cases an external resonance buildup cavity was used. We also studied a less complicated single pass waveguide configuration (guided waist size of ~ 5 um compared to ~60 um) to generate blue. With PPMgO:SLN we obtained net 40.4% and using PPKT net 6.8% (110mW and 10.1 mW respectively).

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### Analysis of Biological Materials Using a Nuclear Microprobe

**Date:**December 2014

**Creator:**Mulware, Stephen Juma

**Description:**The use of nuclear microprobe techniques including: Particle induced x-ray emission (PIXE) and Rutherford backscattering spectrometry (RBS) for elemental analysis and quantitative elemental imaging of biological samples is especially useful in biological and biomedical research because of its high sensitivity for physiologically important trace elements or toxic heavy metals. The nuclear microprobe of the Ion Beam Modification and Analysis Laboratory (IBMAL) has been used to study the enhancement in metal uptake of two different plants. The roots of corn (Zea mays) have been analyzed to study the enhancement of iron uptake by adding Fe (II) or Fe (III) of different concentrations to the germinating medium of the seeds. The Fe uptake enhancement effect produced by lacing the germinating medium with carbon nanotubes has also been investigated. The aim of this investigation is to ensure not only high crop yield but also Fe-rich food products especially from calcareous soil which covers 30% of world’s agricultural land. The result will help reduce iron deficiency anemia, which has been identified as the leading nutritional disorder especially in developing countries by the World Health Organization. For the second plant, Mexican marigold (Tagetes erecta), the effect of an arbuscular mycorrhizal fungi (Glomus intraradices) for the ...

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### Sputtering of Bi and Preferential Sputtering of an Inhomogeneous Alloy

**Date:**December 2014

**Creator:**Deoli, Naresh T.

**Description:**Angular distributions and total yields of atoms sputtered from bismuth targets by normally incident 10 keV -50 keV Ne+ and Ar+ ions have been measured both experimentally and by computer simulation. Polycrystalline Bi targets were used for experimental measurements. The sputtered atoms were collected on high purity aluminum foils under ultra-high vacuum conditions, and were subsequently analyzed using Rutherford backscattering spectroscopy. The Monte-Carlo based SRIM code was employed to simulate angular distributions of sputtered Bi atoms and total sputtering yields of Bi to compare with experiment. The measured sputtering yields were found to increase with increasing projectile energy for normally incident 10 keV - 50 keV Ne+ and Ar+ ions. The shapes of the angular distributions of sputtered Bi atoms demonstrated good agreement between experiment and simulation in the present study. The measured and simulated angular distributions of sputtered Bi exhibited an over-cosine tendency. The measured value of the degree of this over-cosine nature was observed to increase with increasing incident Ne+ ion energy, but was not strongly dependent on incident Ar+ ion energy. The differential angular sputtering yield and partial sputtering yields due to Ar ion bombardment of an inhomogeneous liquid Bi:Ga alloy have been investigated, both experimentally and ...

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### Studies of Charged Particle Dynamics for Antihydrogen Synthesis

**Date:**December 2014

**Creator:**Correa, Jose Ricardo

**Description:**Synthesis and capture of antihydrogen in controlled laboratory conditions will enable precise studies of neutral antimatter. The work presented deals with some of the physics pertinent to manipulating charged antiparticles in order to create neutral antimatter, and may be applicable to other scenarios of plasma confinement and charged particle interaction. The topics covered include the electrostatic confinement of a reflecting ion beam and the transverse confinement of an ion beam in a purely electrostatic configuration; the charge sign effect on the Coulomb logarithm for a two component (e.g., antihydrogen) plasma in a Penning trap as well as the collisional scattering for binary Coulomb interactions that are cut off at a distance different than the Debye length; and the formation of magnetobound positronium and protonium.

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### Electrical Conduction Mechanisms in the Disordered Material System P-type Hydrogenated Amorphous Silicon

**Date:**December 2014

**Creator:**Shrestha, Kiran (Engineer)

**Description:**The electrical and optical properties of boron doped hydrogenated amorphous silicon thin films (a-Si) were investigated to determine the effect of boron and hydrogen incorporation on carrier transport. The a-Si thin films were grown by plasma enhanced chemical vapor deposition (PECVD) at various boron concentrations, hydrogen dilutions, and at differing growth temperatures. The temperature dependent conductivity generally follows the hopping conduction model. Above a critical temperature, the dominant conduction mechanism is Mott variable range hopping conductivity (M-VRH), where p = ¼, and the carrier hopping depends on energy. However, at lower temperatures, the coulomb interaction between charge carriers becomes important and Efros-Shklosvkii variable hopping (ES-VRH) conduction, where p=1/2, must be included to describe the total conductivity. To correlate changes in electrical conductivity to changes in the local crystalline order, the transverse optical (TO) and transverse acoustic (TA) modes of the Raman spectra were studied to relate changes in short- and mid-range order to the effects of growth temperature, boron, and hydrogen incorporation. With an increase of hydrogen and/or growth temperature, both short and mid-range order improve, whereas the addition of boron results in the degradation of short range order. It is seen that there is a direct correlation between the ...

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### Enhancement of Mechanical, Thermal Stability, and Tribological Properties by Addition of Functionalized Reduced Graphene Oxide in Epoxy

**Date:**August 2014

**Creator:**Shah, Rakesh K.

**Description:**The effects of octadecylamine-functionalized reduced graphene oxide (FRGO) on the frictional and wear properties of diglycidylether of bisphenol-A (DGEBA) epoxy are studied using a pin-on-disk tribometer. It was observed that the addition of FRGO significantly improves the tribological, mechanical, and thermal properties of epoxy matrix. Graphene oxide (GO) was functionalized with octadecylamine (ODA), and then reduction of oxygen-containing functional groups was carried out using hydrazine monohydrate. The Raman and x-ray photoelectron spectroscopy studies confirm significant reduction in oxygen-containing functional groups and formation of ODA functionalized reduced GO. The nanocomposites are prepared by adding 0.1, 0.2, 0.5 and 1.0 wt % of FRGO to the epoxy. The addition of FRGO increases by more than an order of magnitude the sliding distance during which the dynamic friction is ≤ 0.1. After this distance, the friction sharply increases to the range of 0.4 - 0.5. We explain the increase in sliding distance during which the friction is low by formation of a transfer film from the nanocomposite to the counterface. The wear rates in the low and high friction regimes are approximately 1.5 x 10-4 mm3/N·m and 5.5 x 10-4 mm3/N·m, respectively. The nanocomposites exhibit a 74 % increase in Young’s modulus with ...

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### Temporal Complexity and Stochastic Central Limit Theorem

**Date:**August 2014

**Creator:**Pramukkul, Pensri

**Description:**Complex processes whose evolution in time rests on the occurrence of a large and random number of intermittent events are the systems under study. The mean time distance between two consecutive events is infinite, thereby violating the ergodic condition and activating at the same time a stochastic central limit theorem that explains why the Mittag-Leffler function is a universal property of nature. The time evolution of these complex systems is properly generated by means of fractional differential equations, thus leading to the interpretation of fractional trajectories as the average over many random trajectories, each of which fits the stochastic central limit theorem and the condition for the Mittag-Leffler universality. Additionally, the effect of noise on the generation of the Mittag-Leffler function is discussed. Fluctuations of relatively weak intensity can conceal the asymptotic inverse power law behavior of the Mittag-Leffler function, providing a reason why stretched exponentials are frequently found in nature. These results afford a more unified picture of complexity resting on the Mittag-Leffler function and encompassing the standard inverse power law definition.

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### Relaxation Time Measurements for Collision Processes in the Surface Layers of Conductors and Semiconductors Near 10 Ghz

**Date:**December 1973

**Creator:**Childress, Larry Wayne

**Description:**This thesis represents one phase of a joint effort of research on the properties of liquids and solids. This work is concerned primarily with the microwave properties of solids. In this investigation the properties exhibited by conductor and semiconductor materials when they are subjected to electromagnetic radiation of microwave frequency are studied. The method utilized in this experiment is the perturbation of a resonant cavity produced by introduction of a cylindrically shaped sample into it.

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### Microwave Line Widths of the Asymmetric Top Formic Acid Molecule

**Date:**August 1974

**Creator:**Maynard, Wayne R.

**Description:**This work consisted of an experimental investigation of the formic acid (HCOOH) molecule's rotational spectrum. Measurements of line widths were obtained for J = 5, 12, 13, 19, and 20 for a pressure range from 1 to 10 microns. A linear behavior between Av and p was observed as predicted by theory. The line width parameter Avp was observed to depend on the quantum number J. Hard sphere collision diameters b1 were calculated using the obtained AvP values. These deduced hard sphere values were found to be larger than the physical size of the molecule. This result was found to be in general agreement with other investigation in which long range forces (dipole-dipole) dominate.

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### Effects of Discharge Tube Geometry on Plasma Ion Oscillations

**Date:**May 1975

**Creator:**Simmons, David Warren

**Description:**This study considers the effect, on plasma ion oscillations, of various lengths of discharge tubes as well as various cross sections of discharge tubes. Four different gases were used in generating the plasma. Gas pressure and discharge voltage and current were varied to obtain a large number of signals. A historical survey is given to familiarize the reader with the field. The experimental equipment and procedure used in obtaining data is given. An analysis of the data obtained is presented along with possible explanations for the observed phenomena. Suggestions for future study are made.

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### Automatic Frequency Control of Microwave Radiation Sources

**Date:**August 1979

**Creator:**Payne, Bobby D.

**Description:**Resonant cavity controlled klystron frequency stabilization circuits and quartz-crystal oscillator frequency stabilization circuits were investigated for reflex klystrons operating at frequencies in the X-band range. The crystal oscillator circuit employed achieved better than 2 parts in 10 in frequency stability. A test of the functional properties of the frequency standard was made using the Stark effect in molecules.

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### The Classical Limit of Quantum Mechanics

**Date:**December 1977

**Creator:**Hefley, Velton Wade

**Description:**The Feynman path integral formulation of quantum mechanics is a path integral representation for a propagator or probability amplitude in going between two points in space-time. The wave function is expressed in terms of an integral equation from which the Schrodinger equation can be derived. On taking the limit h — 0, the method of stationary phase can be applied and Newton's second law of motion is obtained. Also, the condition the phase vanishes leads to the Hamilton - Jacobi equation. The secondary objective of this paper is to study ways of relating quantum mechanics and classical mechanics. The Ehrenfest theorem is applied to a particle in an electromagnetic field. Expressions are found which are the hermitian Lorentz force operator, the hermitian torque operator, and the hermitian power operator.

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### Synthesis, Characterization, Structural, and Optical Properties of Zinc Oxide Nanostructures Embedded in Silicon Based Substrates

**Date:**May 2014

**Creator:**Pandey, Bimal

**Description:**Structural and optical properties of ZnO nanostructures synthesized by low energy ion implantation technique were examined. ZnO molecular ions were implanted into Si/SiO2 substrates at room temperature and then furnace annealed under different temperatures and environments. In all as-implanted samples only Zn nanostructures with varying diameters distributed into the Si/SiO2 matrices were observed. No trace of ZnO was found. The distributions of Zn nanostructures in Si/SiO2 closely matched results from Stopping and Range of Ions in Matter (SRIM) simulations. During annealing at 750 oC, Zn diffused both toward and away from the surface of the substrate and combine with oxygen to form ZnO nanostructures. At higher annealing temperatures ZnO bonding started to break down and transfer to zinc silicate (Zn2SiO4), and at 900 oC the ZnO was completely converted into Zn2SiO4. The average sizes of Zn/ZnO nanostructures depended on the ion fluence. If the fluence increased the average sizes of nanostructures also increased and vice versa. For room temperature photoluminescence (RT-PL), band-edge emission in the ultraviolet (UV) region was observed from all samples annealed at 700 oC/750 oC and were slightly blue shifted as compare to bulk ZnO. Donor-bound exciton (D,X) and acceptor-bound exciton (A,X) transitions were observed in low ...

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### An Electro- Magneto-static Field for Confinement of Charged Particle Beams and Plasmas

**Date:**May 2014

**Creator:**Pacheco, Josè L.

**Description:**A system is presented that is capable of confining an ion beam or plasma within a region that is essentially free of applied fields. An Artificially Structured Boundary (ASB) produces a spatially periodic set of magnetic field cusps that provides charged particle confinement. Electrostatic plugging of the magnetic field cusps enhances confinement. An ASB that has a small spatial period, compared to the dimensions of a confined plasma, generates electro- magneto-static fields with a short range. An ASB-lined volume thus constructed creates an effectively field free region near its center. It is assumed that a non-neutral plasma confined within such a volume relaxes to a Maxwell-Boltzmann distribution. Space charge based confinement of a second species of charged particles is envisioned, where the second species is confined by the space charge of the first non-neutral plasma species. An electron plasma confined within an ASB-lined volume can potentially provide confinement of a positive ion beam or positive ion plasma. Experimental as well as computational results are presented in which a plasma or charged particle beam interact with the electro- magneto-static fields generated by an ASB. A theoretical model is analyzed and solved via self-consistent computational methods to determine the behavior and equilibrium ...

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### The Effects of Residual Gases on the Field Emission Properties of ZnO, GaN, ZnS Nanostructures, and the Effects of Light on the Resistivity of Graphene

**Date:**May 2014

**Creator:**Mo, Yudong

**Description:**In this dissertation, I present that at a vacuum of 3×10-7 Torr, residual O2, CO2, H2 and Ar exposure do not significantly degrade the field emission (FE) properties of ZnO nanorods, but N2 exposure significantly does. I propose that this could be due to the dissociation of N2 into atomic nitrogen species and the reaction of such species with ZnO. I also present the effects of O2, CO2, H2O, N2, H2, and Ar residual gas exposure on the FE properties of GaN and ZnS nanostructure. A brief review of growth of ZnO, GaN and ZnS is provided. In addition, Cs deposition on GaN nanostructures at ultra-high vacuum results in 30% decrease in turn-on voltage and 60% in work function. The improvement in FE properties could be due to a Cs-induced space-charge layer at the surface that reduces the barrier for FE and lowers the work function. I describe a new phenomenon, in which the resistivity of CVD-grown graphene increases to a higher saturated value under light exposure, and depends on the wavelength of the light—the shorter the wavelength, the higher the resistivity. First-principle calculations and theoretical analysis based on density functional theory show that (1) a water molecule close to ...

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### Synthesis Strategies and a Study of Properties of Narrow and Wide Band Gap Nanowires

**Date:**May 2014

**Creator:**Sapkota, Gopal

**Description:**Various techniques to synthesize nanowires and nanotubes as a function of growth temperature and time were investigated. These include growth of nanowires by a chemical vapor deposition (CVD) system using vapor-liquid-solid (VLS) growth mechanism and electro-chemical synthesis of nanowires and nanotubes. Narrow band gap InSb Eg = 0.17 eV at room temp) nanowires were successively synthesized. Using a phase diagram, the transition of the nanowire from metallic- semiconducting- semi-metallic phase was investigated. A thermodynamic model is developed to show that the occurrence of native defects in InSb nanowires influenced by the nanowire growth kinetics and thermodynamics of defect formation. Wide band gap ZnO (Eg = 3.34 eV) and In2O3 (3.7 eV) were also synthesized. ZnO nanowires and nanotubes were successfully doped with a transition metal Fe, making it a Dilute Magnetic Semiconductor of great technological relevance. Structural and electronic characterizations of nanowires were studied for different semiconducting, metallic and semi-metallic nanowires. Electron transport measurements were used to estimate intrinsic material parameters like carrier concentration and mobility. An efficient gas sensing device using a single In2O3 nanowire was studied and which showed sensitivity to reducing gas like NH3 and oxidizing gas like O2 gas at room temperature. The efficiency of the ...

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### How Cooperative Systems Respond to External Forces

**Date:**May 2014

**Creator:**Svenkeson, Adam

**Description:**Cooperative interactions permeate through nature, bringing about emergent behavior and complexity. Using a simple cooperative model, I illustrate the mean field dynamics that occur at the critical point of a second order phase transition in the framework of Langevin equations. Through this formalism I discuss the response, both linear and nonlinear, to external forces. Emphasis is placed on how information is transferred from one individual to another in order to facilitate the collective response of the cooperative network to a localized perturbation. The results are relevant to a wide variety of systems, ranging from nematic liquid crystals, to flocks and swarms, social groups, and neural networks.

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