Synthesis and Characterization of Branched Polyelectrolytes: Star-branched NaPSS

In this thesis, we examined the effect of branching on the solution characteristics of polyelectrolytes using a set of star-branched NaPSS. The polystyrene precursors to these polyelectrolytes were synthesized using anionic polymerization allowing for the production of three distinct groups of star-branched polystyrenes with varying functionality and arm length. Following sulfonation, several methods commonly employed in the literature for evaluation of sulfonation degree we established that sulfonation was quantitative. TGA was also demonstrated to reveal important characteristics of the sample. We used aqueous SEC coupled with a multiple angle light scattering detector to determine several molecular characteristics of the star-branched NaPSS samples. Linear NaPSS synthesized via radical polymerization and sulfonation of polystyrene were characterized and important differences between NaPSS synthesized by the two methods were established. Dynamic light scattering experiments established a qualitative link between the presence of a slow diffusive mode and the degree of sulfonation. The branching parameter g was determined for the star-branched NaPSS samples and compared to theoretical predictions. Static light scattering experiments were performed to elucidate the effect of Cs on the Rg, where it was determined that Rg ~ Cs-0.11 for the whole range of samples. The apparent persistence length was determined and relations were established for its variation as a function of Cs, f and degree of arm polymerization. Additionally, no agreement was found between theoretical predictions of g and experimentally determined ones. A method was developed that enabled the determination of molecular dimensions of star-branched NaPSS using AFM with a high degree of agreement with the radii established using scattering methods on solutions of the polymers. The intrinsic viscosity could reliably be determined in solutions with Cs using either a Huggins or Wolf equation. For solutions with no Cs, the Huggins equation fit over the data at low Cp was confirmed by AFM measurements of the dimensions of the polyelectrolyte and comparisons to the radius determined from the intrinsic viscosities calculated using the two equations to be more accurate. The values of g‟ were calculated for solutions of the NaPSS stars in water and compared with theory

Crystal constructions in Number Theory

Weyl group multiple Dirichlet series and metaplectic Whittaker functions can be described in terms of crystal graphs. We present crystals as parameterized by Littelmann patterns and we give a survey of purely combinatorial constructions of prime power coefficients of Weyl group multiple Dirichlet series and metaplectic Whittaker functions using the language of crystal graphs. We explore how the branching structure of crystals manifests in these constructions, and how it allows access to some intricate objects in number theory and related open questions using tools of algebraic combinatorics

Rpl13a small nucleolar RNAs regulate systemic glucose metabolism

Small nucleolar RNAs (snoRNAs) are non-coding RNAs that form ribonucleoproteins to guide covalent modifications of ribosomal and small nuclear RNAs in the nucleus. Recent studies have also uncovered additional non-canonical roles for snoRNAs. However, the physiological contributions of these small RNAs are largely unknown. Here, we selectively deleted four snoRNAs encoded within the introns of the ribosomal protein L13a (Rpl13a) locus in a mouse model. Loss of Rpl13a snoRNAs altered mitochondrial metabolism and lowered reactive oxygen species tone, leading to increased glucose-stimulated insulin secretion from pancreatic islets and enhanced systemic glucose tolerance. Islets from mice lacking Rpl13a snoRNAs demonstrated blunted oxidative stress responses. Furthermore, these mice were protected against diabetogenic stimuli that cause oxidative stress damage to islets. Our study illuminates a previously unrecognized role for snoRNAs in metabolic regulation

Basic Atomic Physics

Contains reports on five research projects.Joint Services Electronics Program Grant DAAH04-95-1-0038National Science Foundation Grant PHY 92-21489U.S. Navy - Office of Naval Research Grant N00014-90-J-1322National Science Foundation Grant PHY95-14795Charles S. Draper Laboratory Contract DL-H-484775U.S. Army Research Office Contract DAAH04-94-G-0170U.S. Army Research Office Contract DAAH04-95-1-0533U.S. Navy - Office of Naval Research Contract N00014-89-J-1207U.S. Navy - Office of Naval Research Contract N000014-96-1-0432David and Lucile Packard Foundation Grant 96-5158National Science Foundation Grant PHY95-01984U.S. Army - Office of ResearchU.S. Navy - Office of Naval Research Contract N00014-96-1-0485U.S. Navy - Office of Naval Research AASERT N00014-94-1-080

Basic Atomic Physics

Contains reports on five research projects.Joint Services Electronics Program Contract DAAL03-92-C-0001Joint Services Electronics Program Grant DAAH04-95-1-0038National Science Foundation Grant PHY 92-21489U.S. Navy - Office of Naval Research Grant N00014-90-J-1322National Science Foundation Grant PHY 92-22768U.S. Army - Office of Scientific Research Grant DAAL03-92-G-0229U.S. Army - Office of Scientific Research Grant DAAL01-92-6-0197U.S. Navy - Office of Naval Research Grant N00014-89-J-1207Alfred P. Sloan FoundationU.S. Navy - Office of Naval Research Grant N00014-90-J-1642U.S. Navy - Office of Naval Research Grant N00014-94-1-080

Massive Black Hole Binaries as LISA Precursors in the Roman High Latitude Time Domain Survey

With its capacity to observe $\sim 10^{5-6}$ faint active galactic nuclei (AGN) out to redshift $z\approx 6$, Roman is poised to reveal a population of $10^{4-6}\, {\rm M_\odot}$ black holes during an epoch of vigorous galaxy assembly. By measuring the light curves of a subset of these AGN and looking for periodicity, Roman can identify several hundred massive black hole binaries (MBHBs) with 5-12 day orbital periods, which emit copious gravitational radiation and will inevitably merge on timescales of $10^{3-5}$ years. During the last few months of their merger, such binaries are observable with the Laser Interferometer Space Antenna (LISA), a joint ESA/NASA gravitational wave mission set to launch in the mid-2030s. Roman can thus find LISA precursors, provide uniquely robust constraints on the LISA source population, help identify the host galaxies of LISA mergers, and unlock the potential of multi-messenger astrophysics with massive black hole binaries.Comment: White Paper for the Nancy Grace Roman Space Telescope's Core Community Surveys (https://roman.gsfc.nasa.gov/science/ccs_white_papers.html

Basic Atomic Physics

Contains reports on five research projects.Joint Services Electronics Program Grant DAAH04-95-1-0038National Science Foundation Grant PHY 92-21489U.S. Navy - Office of Naval Research Grant N00014-90-J-1322National Science Foundation Grant PHY 92-22768Charles S. Draper Laboratory Contract DL-H-4847759U.S. Army - Office of Scientific Research Grant DAAL03-92-G-0229U.S. Army - Office of Scientific Research Grant DAAL01-92-6-0197U.S. Navy - Office of Naval Research Grant N00014-89-J-1207Alfred P. Sloan FoundationNational Science Foundation Grant PHY 95-01984U.S. Army Research Office Contract DAAL01-92-C-0001U.S. Navy - Office of Naval Research Grant N00014-90-J-1642U.S. Navy - Office of Naval Research Grant N00014-94-1-080