Physical Sciences and Mathematics Commons^™

A Method For Achieving Analytic Formulas For Three Body Integrals Consisting Of Powers And Exponentials In All Three Interparticle Hyllerass Coordinates, Chris M. Keating

Dissertations and Theses

After an introduction to the variational principle of three body systems via the Helium atom, we present general analytical formulas for the radial parts of integrals that occur when three body systems are described using wave functions that consist of powers and exponentials in all three interparticle Hylleraas coordinates [Hylleraas1929]. This work is an extension of integrals given by Harris, Frolov and Smith, Jr. [Harris2004]. Specifically included are radial integrals encountered in calculations involving the dipole moment matrix element in Hylleraas coordinates that contain a function f(kr₁) (such as a spherical Bessel function) in addition to …

Analysis Of Capillary Flow In Interior Corners : Perturbed Power Law Similarity Solutions, Joshua Thomas Mccraney

Dissertations and Theses

The design of fluid management systems requires accurate models for fluid transport. In the low gravity environment of space, gravity no longer dominates fluid displacement; instead capillary forces often govern flow. This thesis considers the redistribution of fluid along an interior corner. Following a rapid reduction of gravity, fluid advances along the corner measured by the column length z = L(t), which is governed by a nonlinear partial differential equation with dynamical boundary conditions. Three flow types are examined: capillary rise, spreading drop, and tapered corner. The spreading drop regime is shown to exhibit column length growth L ~ …

Pseudocapacitors For Energy Storage, Anuradha Venkataraman

Dissertations and Theses

Fluctuation in the demand for electrical power and the intermittent nature of the supply of energy from renewable sources like solar and wind have made the need for energy storage a dire necessity. Current storage technologies like batteries and supercapacitors fall short either in terms of power output or in their ability to store sufficient energy. Pseudocapacitors combine features of both and offer an alternative to stabilize the power supply. They possess high rates of charge and discharge and are capable of storing much more energy in comparison to a supercapacitor. In the quest for solutions that are economical and …

Improved Gain Stability Of A Digital Imager Using A Charge Feedback Amplifier, Elliot Eckman Mylott

Dissertations and Theses

Digital imagers including Charge-Coupled Devices (CCD) are essential to most forms of modern photographic technologies. The quality of the data produced by digital imagers have made them an invaluable scientific measurement tool. Despite the numerous advantages of digital imagers, there are still factors that limit their performance. One such factor is the stability of the camera's gain, the ratio that dictates the imager's ability to convert incident photons to a measurable output voltage. Variations in gain can affect the linearity of the device and produce inaccurate measurements.

One of the factors that determines the gain of the camera is the …

Modeling The Optical Response To A Near-Field Probe Tip From A Generalized Multilayer Thin Film, A.J. Lawrence

Dissertations and Theses

The contrast mechanism in Kerr imaging is the apparent angle through which the plane of polarization is rotated upon reflection from a magnetic surface. This can be calculated for a well characterized surface given the polarization state of the incident light. As in traditional optical microscopy, the spatial resolution is limited by diffraction to roughly half the wavelength of the illumination light.

The diffraction limit can be circumvented through the use of near-field scanning optical microscopy, in which the illumination source is an evanescent field at the tip of a tapered optical fiber. A novel probe design for near-field optical …

Aberration Corrected Photoemission Electron Microscopy With Photonics Applications, Joseph P. S. Fitzgerald

Dissertations and Theses

Photoemission electron microscopy (PEEM) uses photoelectrons excited from material surfaces by incident photons to probe the interaction of light with surfaces with nanometer-scale resolution. The point resolution of PEEM images is strongly limited by spherical and chromatic aberration. Image aberrations primarily originate from the acceleration of photoelectrons and imaging with the objective lens and vary strongly in magnitude with specimen emission characteristics. Spherical and chromatic aberration can be corrected with an electrostatic mirror, and here I develop a triode mirror with hyperbolic geometry that has two adjacent, field-adjustable regions. I present analytic and numerical models of the mirror and show …

Modifications To A Cavity Ringdown Spectrometer To Improve Data Acquisition Rates, Gregory Alan Bostrom

Dissertations and Theses

Cavity ringdown spectroscopy (CRDS) makes use of light retention in an optical cavity to enhance the sensitivity to absorption or extinction of light from a sample inside the cavity. When light entering the cavity is stopped, the output is an exponential decay with a decay constant that can be used to determine the quantity of the analyte if the extinction or absorption coefficient is known. The precision of the CRDS is dependent on the rate at which the system it acquires and processes ringdowns, assuming randomly distributed errors. We have demonstrated a CRDS system with a ringdown acquisition rate of …