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Application of the Finite Element Method to Some Simple Systems in One and Two Dimensions.

Description: The finite element method (FEM) is reviewed and applied to the one-dimensional eigensystems of the isotropic harmonic oscillator, finite well, infinite well and radial hydrogen atom, and the two-dimensional eigensystems of the isotropic harmonic oscillator and the propagational modes of sound in a rectangular cavity. Computer codes that I developed were introduced and utilized to find accurate results for the FEM eigensolutions. One of the computer codes was modified and applied to the one-dimensional unbound quantum mechanical system of a square barrier potential and also provided accurate results.
Date: May 2002
Creator: Hunnell, Jason C.
Partner: UNT Libraries

Maxwell's Equations from Electrostatics and Einstein's Gravitational Field Equation from Newton's Universal Law of Gravitation Using Tensors

Description: Maxwell's equations are obtained from Coulomb's Law using special relativity. For the derivation, tensor analysis is used, charge is assumed to be a conserved scalar, the Lorentz force is assumed to be a pure force, and the principle of superposition is assumed to hold. Einstein's gravitational field equation is obtained from Newton's universal law of gravitation. In order to proceed, the principle of least action for gravity is shown to be equivalent to the maximization of proper time along a geodesic. The conservation of energy and momentum is assumed, which, through the use of the Bianchi identity, results in Einstein's field equation.
Date: May 2004
Creator: Burns, Michael E.
Partner: UNT Libraries

A Dynamic and Thermodynamic Approach to Complexity.

Description: The problem of establishing the correct approach to complexity is a very hot and crucial issue to which this dissertation gives some contributions. This dissertation considers two main possibilities, one, advocated by Tsallis and co-workers, setting the foundation of complexity on a generalized, non-extensive , form of thermodynamics, and another, proposed by the UNT Center for Nonlinear Science, on complexity as a new condition that, for physical systems, would be equivalent to a state of matter intermediate between dynamics and thermodynamics. In the first part of this dissertation, the concept of Kolmogorov-Sinai entropy is introduced. The Pesin theorem is generalized in the formalism of Tsallis non-extensive thermodynamics. This generalized form of Pesin theorem is used in the study of two major classes of problems, whose prototypes are given by the Manneville and the logistic map respectively. The results of these studies convince us that the approach to complexity must be made along lines different from those of the non-extensive thermodynamics. We have been convinced that the Lévy walk can be used as a prototype model of complexity, as a condition of balance between order and randomness that yields new phenomena such as aging, and multifractality. We reach the conclusions that these properties must be studied within a dynamic rather than thermodynamic perspective. The second part focuses on the study of the heart beating problem using a dynamic model, the so-called memory beyond memory, based on the Lévy walker model. It is proved that the memory beyond memory effect is more obvious in the healthy heart beating sequence. The concepts of fractal, multifractal, wavelet transformation and wavelet transform maximum modulus (WTMM) method are introduced. Artificial time sequences are generated by the memory beyond memory model to mimic the heart beating sequence. Using WTMM method, the multifratal singular spectrums of the sequences ...
Date: August 2003
Creator: Yang, Jin
Partner: UNT Libraries

The Concept of Collision Strength and Its Applications

Description: Collision strength, the measure of strength for a binary collision, hasn't been defined clearly. In practice, many physical arguments have been employed for the purpose and taken for granted. A scattering angle has been widely and intensively used as a measure of collision strength in plasma physics for years. The result of this is complication and unnecessary approximation in deriving some of the basic kinetic equations and in calculating some of the basic physical terms. The Boltzmann equation has a five-fold integral collision term that is complicated. Chandrasekhar and Spitzer's approaches to the linear Fokker-Planck coefficients have several approximations. An effective variable-change technique has been developed in this dissertation as an alternative to scattering angle as the measure of collision strength. By introducing the square of the reduced impulse or its equivalencies as a collision strength variable, many plasma calculations have been simplified. The five-fold linear Boltzmann collision integral and linearized Boltzmann collision integral are simplified to three-fold integrals. The arbitrary order linear Fokker-Planck coefficients are calculated and expressed in a uniform expression. The new theory provides a simple and exact method for describing the equilibrium plasma collision rate, and a precise calculation of the equilibrium relaxation time. It generalizes bimolecular collision reaction rate theory to a reaction rate theory for plasmas. A simple formula of high precision with wide temperature range has been developed for electron impact ionization rates for carbon atoms and ions. The universality of the concept of collision strength is emphasized. This dissertation will show how Arrhenius' chemical reaction rate theory and Thomson's ionization theory can be unified as one single theory under the concept of collision strength, and how many important physical terms in different disciplines, such as activation energy in chemical reaction theory, ionization energy in Thomson's ionization theory, and the Coulomb logarithm in ...
Date: May 2004
Creator: Chang, Yongbin
Partner: UNT Libraries

A Data Acquisition System Experiment for Gas Temperature and Pressure Measurements on a Liquid-Nitrogen-Powered Vehicle

Description: A data acquisition system was set up to measure gas temperatures and pressures at various points on a liquid-nitrogen-powered vehicle. The experiment was attempted to develop a data acquisition method for applications on engines that use liquid air as the fuel. Two thermocouples and a pressure transducer were connected using data acquisition instruments interfaced to a laptop computer to acquire data.
Date: May 1998
Creator: Lui, Samson Sze-Sang
Partner: UNT Libraries

Temperature Dependency of Some of the Thermodynamical Properties of Aqueous Binary-Mixture Systems

Description: The temperature dependence of the refractive index and the density of aqueous binary mixtures of water and ethyl alcohol (C₂H₅OH) were measured by using a modified Michelson interferometer and a narrow glass capillary tube over the temperature range of 278≤T≤353 K for solutions of 100, 75,65, 50, 25, 10 and 0 volume percent ethyl alcohol. The temperature was cycled over both increasing and decreasing directions to explore hysteresis in the cycling. The data are discussed and compared with the Lorentz-Lorenz (LL) formula. A more accurate formula which fits the experimental data better than the LL relation was derived. An attempt was made to determine the nature of the solvent-solute interaction through any changes that were found in the refractive index for He-Ne laser light and IR diode signals and to analyze the refractive index and density results to test the accuracy of the available mixing rules in predicting the refractive index values and the density of binary systems. Conductivity measurements (d. c.) over the temperature range 278≤T≤353 K of aqueous solutions of NaCl at various concentrations were made and used to establish transport properties of ions in solution. The dynamical properties of the electrolytes were used to establish the nature of hydrogen bonding in aqueous binary mixture systems. Rate equations for ion formation and recombination were used to establish the temperature ranges in which hydrogen bonding dominated in forming polymeric species. From experimental data on the binary mixtures with water, a better understanding of water in its different functions and aggregation is possible. The water molecule itself and its response to the environment are understood when suitable studies are made of the forces in the system. In this work, some qualitative aspects of the interactions and dynamics of the water molecule have been investigated. Classical molecular dynamics simulations were tried ...
Date: August 1996
Creator: Zheng, Yueming
Partner: UNT Libraries

The Stopping Power of Amorphous and Channelled Silicon at All Energies as Computed with the Binary Encounter Approximation

Description: This thesis utilizes the binary encounter approximation to calculate the stopping power of protons penetrating silicon. The main goal of the research was to make predictions of the stopping power of silicon for low-energy and medium-energy channelled protons, in the hope that this will motivate experiments to test the theory developed below. In attaining this goal, different stopping power theories were compared and the binary encounter approach was applied to random (non-channelled) and high-energy channelled protons in silicon, and these results were compared with experimental data.
Date: December 1994
Creator: Bickel, David, 1970-
Partner: UNT Libraries

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

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 of the positron space in existing traps and to find modes of operation where the space charge is beneficial. Techniques are developed to apply the Boltzmann density relation along curved magnetic field lines. Equilibrium electrostatic potential profiles for a positron plasma are computed by solving Poisson's equation using a finite-difference method. Equilibria are computed in a model Penning trap with an axially varying magnetic field. Also, equilibria are computed for a positron plasma in a model of the ALPHA trap. Electric potential wells are found to form self-consistently. The technique is expanded to compute equilibria for a two-species plasma with ...
Date: May 2016
Creator: Lane, Ryan Andrew
Partner: UNT Libraries

Microstructure and Electronic Structures of Er-Doped Si Nano-particles Synthesized by Vapor Phase Pyrolysis

Description: Si nanoparticles are new prospective optoelectronic materials. Unlike bulk Si cry-stals, Si nanoparticles display intriguing room-temperature photoluminescence. A major challenge in the fabrication of Si nanoparticles is the control of their size distribution. The rare-earth element Er has unique photo emission properties, including low pumping power, and a temperature independent, sharp spectrum. The emission wavelength matches the transmission window of optical fibers used in the telecommunications industry. Therefore, the study of Er-doped Si nanoparticles may have practical significance. The goals of the research described in this dissertation are to investigate vapor phase pyrolysis methods and to characterize the microstructure and associated defects, particles size distributions and photoluminescence efficiencies of doped and undoped Si nanoparticles using analytical transmission electron microscopy, high resolution electron microscopy, and optical spectroscopy. Er-doped and undoped Si nanoparticles were synthesized via vapor-phase pyrolysis of disilane at Texas Christian University. To achieve monodisperse size distributions, a process with fast nucleation and slow growth was employed. Disilane was diluted to 0.48% with helium. A horizontal pyrolysis oven was maintained at a temperature of 1000 °C. The oven length was varied from 1.5 cm to 6.0 cm to investigate the influence of oven length on the properties of the nanoparticles. The Si nanoparticles were collected in ethylene-glycol. The doped and undoped Si nanoparticles have a Si diamond cubic crystal structure. Neither Er precipitation, Er oxides or Er silicides were detected in any of the samples. The Er dopant concentration was about 2 atom% for doped samples from the 3.0 and 6.0 cm ovens as determined by quantitative analysis using X-ray energy dispersive spectroscopy. The average Si nanoparticle size increases from 11.3 to 15.2 nm in the doped samples and from 11.1 to 15.7 nm in the undoped samples as the oven length increases from 1.5 to 6.0 cm. HREM data ...
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Date: May 2000
Creator: Chen, Yandong
Partner: UNT Libraries

Nested Well Plasma Traps

Description: Criteria for the confinement of plasmas consisting of a positive and negative component in Penning type traps with nested electric potential wells are presented. Computational techniques for the self-consistent calculation of potential and plasma density distributions are developed. Analyses are presented of the use of nested well Penning traps for several applications. The analyses include: calculations of timescales relevant to the applications, e.g. reaction, confinement and relaxation timescales, self-consistent computations, and consideration of other physical phenomenon important to the applications. Possible applications of a nested well penning trap include production of high charge state ions, studies of high charge state ions, and production of antihydrogen. In addition the properties of a modified Penning trap consisting of an electric potential well applied along a radial magnetic field are explored.
Date: August 2000
Creator: Dolliver, Darrell
Partner: UNT Libraries

Space-Charge Saturation and Current Limits in Cylindrical Drift Tubes and Planar Sheaths

Description: Space-charge effects play a dominant role in many areas of physics. In high-power microwave devices using high-current, relativistic electron beams, it places a limit on the amount of radiation a device can produce. Because the beam's space-charge can actually reflect a portion of the beam, the ability to accurately predict the amount of current a device can carry is needed. This current value is known as the space-charge limited current. Because of the mathematical difficulties, this limit is typically estimated from a one-dimensional theory. This work presents a two-dimensional theory for calculating an upper-bound for the space-charge limited current of relativistic electron beams propagating in grounded coaxial drift tubes. Applicable to annular beams of arbitrary radius and thickness, the theory includes the effect introduced by a finite-length drift tube of circular cross-section. Using Green's second identity, the need to solve Poisson's equation is transferred to solving a Sturm-Liouville eigenvalue problem, which is easily solved by elementary methods. In general, the resulting eigenvalue, which is required to estimate the limiting current, must be numerically determined. However, analytic expressions can be found for frequently encountered limiting cases. Space-charge effects also produce the fundamental collective behavior found in plasmas, especially in plasma sheaths. A plasma sheath is the transition region between a bulk plasma and an adjacent plasma-facing surface. The sheath controls the loss of particles from the plasma in order to maintain neutrality. Using a fully kinetic theory, the problem of a planar sheath with a single-minimum electric potential profile is investigated. Appropriate for single charge-state ions of arbitrary temperature, the theory includes the emission of warm electrons from the surface as well as a net current through the sheath and is compared to particle-in-cell simulations. Approximate expressions are developed for estimating the sheath potential as well as the transition to space-charge ...
Date: August 2000
Creator: Stephens, Kenneth Frank
Partner: UNT Libraries

The Nonadditive Generalization of Klimontovich's S-Theorem for Open Systems and Boltzmann's Orthodes

Description: We show that the nonadditive open systems can be studied in a consistent manner by using a generalized version of S-theorem. This new generalized S-theorem can further be considered as an indication of self-organization in nonadditive open systems as prescribed by Haken. The nonadditive S-theorem is then illustrated by using the modified Van der Pol oscillator. Finally, Tsallis entropy as an equilibrium entropy is studied by using Boltzmann's method of orthodes. This part of dissertation shows that Tsallis ensemble is on equal footing with the microcanonical, canonical and grand canonical ensembles. However, the associated entropy turns out to be Renyi entropy.
Date: August 2008
Creator: Bagci, Gokhan Baris
Partner: UNT Libraries

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

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 conditions of a relaxed plasma. The equilibrium conditions of a relaxed two species plasma are also computed. In such a scenario, space charge based electrostatic confinement is predicted to occur where a second plasma species is confined by the space charge of the first plasma species. An experimental apparatus with cylindrical symmetry that has its interior surface lined with an ASB is presented. This system was developed by using a simulation of the electro- magneto-static fields present within the trap to guide mechanical design. The construction of the full experimental apparatus is discussed. Experimental results that show the characteristics of ...
Date: May 2014
Creator: Pacheco, Josè L.
Partner: UNT Libraries

Studies of Charged Particle Dynamics for Antihydrogen Synthesis

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.
Date: December 2014
Creator: Correa, Jose Ricardo
Partner: UNT Libraries