In this dissertation, we seek to understand prescribed scalar curvature through the gradient flow of conformal metrics. On S^2, we will define a modified Liouville energy and derive a geometric flow equation related to the energy functional. We will prove longtime existence for solutions of this equation with arbitrary data through the methods used by Gursky and Streets. We will then show that Gauss curvature retains its regularity under evolution through the flow assuming bounds on the Gauss curvature. We will finally show that the solution is stable when converging to constant curvature if the initial curvature is close to the geometry of S^2.

Sarasota County is a Florida gulf-coast community working to alleviate growth and development pressures and provide a balanced community of citizen amenities, economic growth, and a healthy natural environment. To meet this end, county government has been pursuing two main objectives: the acquisition and protection of ecologically significant lands and the minimization of roadway impacts in ecologically valuable areas. In 1992, a committee of citizens was appointed to evaluate the ecological value of undeveloped lands and facilitate a land-acquisition program. Subsequently in 1999, Sarasota voters approved a referendum to fund the Environmentally Sensitive Lands Protection Program (ESLPP). This program has since enabled the acquisition of over 15,000 acres of environmentally sensitive habitat for a total of nearly 105,000 acres of protected land throughout the county. In 2003, the land-acquisition agenda was expanded through the development of the Regional Environmental Mitigation Program, which was designed to facilitate the purchase and restoration of natural lands as compensation for unavoidable environmental impacts associated with county infrastructure projects. Despite protections afforded lands acquired by these landprotection programs, fragmentation continues to threaten ecologically intact landscapes in the county. To address this matter, the Board of County Commissioners initiated an investigation of the habitats and wildlife fragmented by transportation infrastructure. Field-investigation methods have involved reviews of aerial photography with local data overlays (e.g. Florida scrub-jay habitat, panther sightings, etc.), evaluation of significant habitats and protected wildlife, use of motion-sensory cameras, creation of animal-track sand pits, and incorporation of mortality surveys. Data collected continue to be used to identify and recommend promising areas for innovative design of infrastructure, land-acquisition priorities, and habitat-restoration measures. As a result of the current initiative, road projects are increasingly scrutinized for alternative alignments, sound ecological improvements, and defragmentation opportunities. Sustainable design is now a bona fide consideration of Sarasota County road-design teams.

A nanopatterning technique, termed femtosecond laser nanomachining, was developed in order to study the effect of clustering, placement, and overall cell adhesive ligand density on cell function. The general patterning strategy was to render a quartz cell culture substrate non-fouling through the grafting of a pEG polymer, followed by femtosecond laser ablation of the polymer to generate regions into which cell adhesive peptides or proteins could be adsorbed. Specifically, a high density ultrathin pEG brush layer was synthesized directly from the surface using surface initiated atom transfer polymerization, (SI-ATRP) a living radical polymerization with a constant growth rate that provides very low polydispersities. As the film thickness varied linearly with time, demonstrated with in situ growth monitoring in a quartz crystal microbalance with dissipation (QCM-D), thickness was easily tunable, and the resulting surfaces had very low roughness (less than 1 nm RMS) as verified by AFM. Surface chemistry was verified with x-ray photoelectron spectroscopy, (XPS) with a notable peak growth for energies associated with carbon-oxygen bonding, expected for a ethylene glycol rich polymer. Exposure of pEG modified quartz oscillators to various peptide solutions resulted in minimal frequency and dissipation changes, reaffirming that our film robustly inhibits protein adsorption.

Our pEG thin film was then ablated with 400 nm wavelength femtosecond laser pulses focused with various far field objectives to elucidate the ablation thresholds of both our film and the underlying quartz substrate. We identified an ideal processing window between fluences of 0.7 J/cm2 (polymer threshold) and 1.5 J/cm2 (quartz threshold), which results in clean film removal without damaging the underlying substrate. The effect of laser fluence on feature diameter for various film thicknesses and objective magnifications was characterized to map processing parameters for patterned sample generation. Protein adsorption into our ablated features was verified by fluorescence microscopy and AFM scanning samples prior to and post protein modification. Cell adhesion on a variety of avidin derivative proteins and biotinylated peptides were quantified using a fluorescence based assay to assess an optimal ligand presentation system from our surface. Neutravidin with biotin-bsp-RGD(15) was identified as an ideal adhesive ligand presentation system, due to maintenance of a high degree of cell adsorption with minimum background adhesion to the neutravidin itself. We used laser ablation to create a variety of substrates that are not easily accessible to other nanopatterning techniques, including one dimensional and two dimensional gradients of feature pitch, patterns designed to isolate single cells in different morphologies, and line patterns to control cell alignment and aspect ration.

To highlight the link between adhesion island size, pitch, and overall surface ligand density to the morphology and cytoskeletal development within the cell, gradient patterns and isometric pitch samples were created to isolate these variables. Gradient patterns of both adhesive island diameter and pitch were created in order to define a critical ligand density for cell adhesion, determined to lie in the range of 0.15-0.3 pmol/cm2 for the human mesenchymal stem cells on these patterned substrates. Patterns consisting of isometric pitch and diameter constrained within a non-fouling border were also created. For these patterns, rat mesenchymal stem cells were found to adhere down to densities of 0.03 pmol/cm2. Nuclear distension was quantified with the nuclear shape index metric (maximum cross sectional area over the high of the nucleus) and a statistically significant difference in NSI (p<0.05) was found for cells adhered surfaces on designed to project ligand densities of 0.03 pmol/cm2 and 1 pmol/cm2, suggesting the underlying surface density modulates intracellular tension and nuclear distension.

Satellite imagery is now being used to estimate the near-surface chlorophyll concentration for large ocean areas. To assess the accuracy and precision of these remote sensing techniques, contemporaneous ship and satellite data for the determination of oceanic chlorophyll concentrations have been collected. Since chlorophyll fluorometry is a widely used technique for the determination of chlorophylls at sea, our analyses have led us to review the literature of fluorometry in order to re-examine the assumptions and approximations made when using this field technique.

This report gives a summary of the general concepts of fluorometry, examines important assumptions, presents an outline of an established fluorometer calibration technique, and estimates the accuracy and precision of this methodology. Also included are field observations of the discrete chlorophyll to fluorescence ratio, of the variability of discrete chlorophyll determinations using various particle collecting filters, and of diurnal fluorescence ratio comparisons.

The launch of the Nimbus-7 satellite in October 1978 carrying the Coastal Zone Color Scanner (CZCS) has made possible optical measurements of the oceans from space. Algorithms are presently being developed to relate these optical spectral measurements to the chlorophyll present in the water. Our purpose is to outline our own consistent methodology of along track shipboard fluorescence for the concurrent comparison with satellite derived values of chlorophyll. This report is not intended as a definitive statement on fluorometric techniques, but rather a working document describing our field techniques. Hence, although the theory is general, the specifics apply to the Turner and Turner Designs fluorometers.