Studies in nuclear reactor dynamics : I. The accuracy of point kinetics. II. The effect of delayed neutrons on the spectrum of the group-diffusion operator

This thesis is a theoretical work on the space-time dynamic behavior of a nuclear reactor without feedback. Diffusion theory with G-energy groups is used.

In the first part the accuracy of the point kinetics (lumped-parameter description) model is examined. The fundamental approximation of this model is the splitting of the neutron density into a product of a known function of space and an unknown function of time; then the properties of the system can be averaged in space through the use of appropriate weighting functions; as a result a set of ordinary differential equations is obtained for the description of time behavior. It is clear that changes of the shape of the neutron-density distribution due to space-dependent perturbations are neglected. This results to an error in the eigenvalues and it is to this error that bounds are derived. This is done by using the method of weighted residuals to reduce the original eigenvalue problem to that of a real asymmetric matrix. Then Gershgorin-type theorems .are used to find discs in the complex plane in which the eigenvalues are contained. The radii of the discs depend on the perturbation in a simple manner.

In the second part the effect of delayed neutrons on the eigenvalues of the group-diffusion operator is examined. The delayed neutrons cause a shifting of the prompt-neutron eigenvalue s and the appearance of the delayed eigenvalues. Using a simple perturbation method this shifting is calculated and the delayed eigenvalues are predicted with good accuracy.

Analyses of planetary atmospheres across the spectrum : from Titan to exoplanets

Planetary atmospheres exist in a seemingly endless variety of physical and chemical environments. There are an equally diverse number of methods by which we can study and characterize atmospheric composition. In order to better understand the fundamental chemistry and physical processes underlying all planetary atmospheres, my research of the past four years has focused on two distinct topics. First, I focused on the data analysis and spectral retrieval of observations obtained by the Ultraviolet Imaging Spectrograph (UVIS) instrument onboard the Cassini spacecraft while in orbit around Saturn. These observations consisted of stellar occultation measurements of Titan's upper atmosphere, probing the chemical composition in the region 300 to 1500 km above Titan's surface. I examined the relative abundances of Titan's two most prevalent chemical species, nitrogen and methane. I also focused on the aerosols that are formed through chemistry involving these two major species, and determined the vertical profiles of aerosol particles as a function of time and latitude. Moving beyond our own solar system, my second topic of investigation involved analysis of infra-red light curves from the Spitzer space telescope, obtained as it measured the light from stars hosting planets of their own. I focused on both transit and eclipse modeling during Spitzer data reduction and analysis. In my initial work, I utilized the data to search for transits of planets a few Earth masses in size. In more recent research, I analyzed secondary eclipses of three exoplanets and constrained the range of possible temperatures and compositions of their atmospheres.

Energy spectrum of fermionized bosonic atoms in optical lattices

We investigate the energy spectrum of fermionized bosonic atoms, which behave very much like spinless noninteracting fermions, in optical lattices by means of the perturbation expansion and the retarded Green's function method. The results show that the energy spectrum splits into two energy bands with single-occupation; the fermionized bosonic atom occupies nonvanishing energy state and left hole has a vanishing energy at any given momentum, and the system is in Mott-insulating state with a energy gap. Using the characteristic of energy spectra we obtained a criterion with which one can judge whether the Tonks-Girardeau (TG) gas is achieved or not.

Energy spectrum of two-component Bose-Einstein condensates in optical lattices

With the method of Green's function, we investigate the energy spectra of two-component ultracold bosonic atoms in optical lattices. We End that there are two energy bands for each component. The critical condition of the superfluid-Mott insulator phase transition is determined by the energy band structure. We also find that the nearest neighboring and on-site interactions fail to change the structure of energy bands, but shift the energy bands only. According to the conditions of the phase transitions, three stable superfluid and Mott insulating phases can be found by adjusting the experiment parameters. We also discuss the possibility of observing these new phases and their transitions in further experiments.

Energy spectrum of ground state and excitation spectrum of quasi-particle for hard-core boson in optical lattices

We investigate the energy spectrum of ground state and quasi-particle excitation spectrum of hard-core bosons, which behave very much like spinless noninteracting fermions, in optical lattices by means of the perturbation expansion and Bogoliubov approach. The results show that the energy spectrum has a single band structure, and the energy is lower near zero momentum; the excitation spectrum gives corresponding energy gap, and the system is in Mott-insulating state at Tonks limit. The analytic result of energy spectrum is in good agreement with that calculated in terms of Green's function at strong correlation limit.

Hit-or-miss representation of a pattern spectrum and its optical implementation

We demonstrate that a pattern spectrum can be decomposed into the union of hit-or-miss transforms with respect to a series of structure-element pairs. Moreover we use a Boolean-logic function to express the pattern spectrum and show that the Boolean-logic representation of a pattern spectrum is composed of hit-or-miss min terms. The optical implementation of a pattern spectrum is based on an incoherent optical correlator with a feedback operation. (C) 1996 Optical Society of America

A generalized treatment of the order-disorder transformation in alloys and its effects on their magnetic properties

A theory of the order-disorder transformation is developed in complete generality. The general theory is used to calculate long range order parameters, short range order parameters, energy, and phase diagrams for a face centered cubic binary alloy. The theoretical results are compared to the experimental determination of the copper-gold system, Values for the two adjustable parameters are obtained.

An explanation for the behavior of magnetic alloys is developed, Curie temperatures and magnetic moments of the first transition series elements and their alloys in both the ordered and disordered states are predicted. Experimental agreement is excellent in most cases. It is predicted that the state of order can effect the magnetic properties of an alloy to a considerable extent in alloys such as Ni₃Mn. The values of the adjustable parameter used to fix the level of the Curie temperature, and the adjustable parameter that expresses the effect of ordering on the Curie temperature are obtained.

Photonic and Device Design Principles for Ultrahigh-Efficiency (>50%), Spectrum-Splitting Photovoltaics

The sun has the potential to power the Earth's total energy needs, but electricity from solar power still constitutes an extremely small fraction of our power generation because of its high cost relative to traditional energy sources. Therefore, the cost of solar must be reduced to realize a more sustainable future. This can be achieved by significantly increasing the efficiency of modules that convert solar radiation to electricity. In this thesis, we consider several strategies to improve the device and photonic design of solar modules to achieve record, ultrahigh (> 50%) solar module efficiencies. First, we investigate the potential of a new passivation treatment, trioctylphosphine sulfide, to increase the performance of small GaAs solar cells for cheaper and more durable modules. We show that small cells (mm2), which currently have a significant efficiency decrease (~ 5%) compared to larger cells (cm2) because small cells have a higher fraction of recombination-active surface from the sidewalls, can achieve significantly higher efficiencies with effective passivation of the sidewalls. We experimentally validate the passivation qualities of treatment by trioctylphosphine sulfide (TOP:S) through four independent studies and show that this facile treatment can enable efficient small devices. Then, we discuss our efforts toward the design and prototyping of a spectrum-splitting module that employs optical elements to divide the incident spectrum into different color bands, which allows for higher efficiencies than traditional methods. We present a design, the polyhedral specular reflector, that has the potential for > 50% module efficiencies even with realistic losses from combined optics, cell, and electrical models. Prototyping efforts of one of these designs using glass concentrators yields an optical module whose combined spectrum-splitting and concentration should correspond to a record module efficiency of 42%. Finally, we consider how the manipulation of radiatively emitted photons from subcells in multijunction architectures can be used to achieve even higher efficiencies than previously thought, inspiring both optimization of incident and radiatively emitted photons for future high efficiency designs. In this thesis work, we explore novel device and photonic designs that represent a significant departure from current solar cell manufacturing techniques and ultimately show the potential for much higher solar cell efficiencies.

Digital holographic interferometry and the angular spectrum method applied to measuring the domain inversion in ferroelectric crystal

The application of digital holographic interferometry on the quantitative measurement of the domain inversion in a RuO2: LiNbO3 crystal wafer is presented. The recorded holograms are reconstructed by the angular spectrum method. From the reconstructed phase distribution we can clearly observe the boundary between the inverted and un-inverted domain regions. Comparisons with the results reconstructed by use of the Fresnel transform method are given. Factors that influence the measurement include the spectrum filter size and the spectrum movement are discussed. The spectrum filter size has an effect on the measurement of the details. Although the spectrum movement affects every single reconstructed image, it has no influence on the final measurement.

Discharge and turbidity of the regulated River Tees. Variance spectrum analysis

High suspended sediment loads may be deleterious to adult salmonids and invertebrates in gravel-bedded streams. Further, the accumulation of fine material in the interstices of the gravel may have an adverse impact on the recruitment of the young stages of salmonids. It is important therefore not only to quantify the rates and degrees of silting but also to identify sediment sources and to determine both, the frequency of sediment inputs to the system and the duration of high sediment concentrations. This report explores the application of variance spectrum analysis to the isolation of sediment periodicities. For the particular river chosen for examination the method demonstrated the essentially undisturbed nature of the catchment. The regulated river chosen for examination is the River Tees in Northern England. Variance spectrum analysis was applied to a series of over 4000 paired daily turbidity and discharge readings.