Where Tori fear to tread : hypermassive neutron star remnants and absolute event horizons Or topics in computational general relativity

Computational general relativity is a field of study which has reached maturity only within the last decade. This thesis details several studies that elucidate phenomena related to the coalescence of compact object binaries. Chapters 2 and 3 recounts work towards developing new analytical tools for visualizing and reasoning about dynamics in strongly curved spacetimes. In both studies, the results employ analogies with the classical theory of electricity and magnitism, first (Ch. 2) in the post-Newtonian approximation to general relativity and then (Ch. 3) in full general relativity though in the absence of matter sources. In Chapter 4, we examine the topological structure of absolute event horizons during binary black hole merger simulations conducted with the SpEC code. Chapter 6 reports on the progress of the SpEC code in simulating the coalescence of neutron star-neutron star binaries, while Chapter 7 tests the effects of various numerical gauge conditions on the robustness of black hole formation from stellar collapse in SpEC. In Chapter 5, we examine the nature of pseudospectral expansions of non-smooth functions motivated by the need to simulate the stellar surface in Chapters 6 and 7. In Chapter 8, we study how thermal effects in the nuclear equation of state effect the equilibria and stability of hypermassive neutron stars. Chapter 9 presents supplements to the work in Chapter 8, including an examination of the stability question raised in Chapter 8 in greater mathematical detail.

Sequence specific complexation of b DNA at sites containing g,c base pairs

A series of eight related analogs of distamycin A has been synthesized. Footprinting and affinity cleaving reveal that only two of the analogs, pyridine-2- car box amide-netropsin (2-Py N) and 1-methylimidazole-2-carboxamide-netrops in (2-ImN), bind to DNA with a specificity different from that of the parent compound. A new class of sites, represented by a TGACT sequence, is a strong site for 2-PyN binding, and the major recognition site for 2-ImN on DNA. Both compounds recognize the G•C bp specifically, although A's and T's in the site may be interchanged without penalty. Additional A•T bp outside the binding site increase the binding affinity. The compounds bind in the minor groove of the DNA sequence, but protect both grooves from dimethylsulfate. The binding evidence suggests that 2-PyN or 2-ImN binding induces a DNA conformational change.

In order to understand this sequence specific complexation better, the Ackers quantitative footprinting method for measuring individual site affinity constants has been extended to small molecules. MPE•Fe(II) cleavage reactions over a 10^5 range of free ligand concentrations are analyzed by gel electrophoresis. The decrease in cleavage is calculated by densitometry of a gel autoradiogram. The apparent fraction of DNA bound is then calculated from the amount of cleavage protection. The data is fitted to a theoretical curve using non-linear least squares techniques. Affinity constants at four individual sites are determined simultaneously. The distamycin A analog binds solely at A•T rich sites. Affinities range from 10^(6)- 10^(7)M^(-1) The data for parent compound D fit closely to a monomeric binding curve. 2-PyN binds both A•T sites and the TGTCA site with an apparent affinity constant of 10^(5) M^(-1). 2-ImN binds A•T sites with affinities less than 5 x 10^(4) M^(-1). The affinity of 2-ImN for the TGTCA site does not change significantly from the 2-PyN value. At the TGTCA site, the experimental data fit a dimeric binding curve better than a monomeric curve. Both 2-PyN and 2-ImN have substantially lower DNA affinities than closely related compounds.

In order to probe the requirements of this new binding site, fourteen other derivatives have been synthesized and tested. All compounds that recognize the TGTCA site have a heterocyclic aromatic nitrogen ortho to the N or C-terminal amide of the netropsin subunit. Specificity is strongly affected by the overall length of the small molecule. Only compounds that consist of at least three aromatic rings linked by amides exhibit TGTCA site binding. Specificity is only weakly altered by substitution on the pyridine ring, which correlates best with steric factors. A model is proposed for TGTCA site binding that has as its key feature hydrogen bonding to both G's by the small molecule. The specificity is determined by the sequence dependence of the distance between G's.

One derivative of 2-PyN exhibits pH dependent sequence specificity. At low pH, 4-dimethylaminopyridine-2-carboxamide-netropsin binds tightly to A•T sites. At high pH, 4-Me_(2)NPyN binds most tightly to the TGTCA site. In aqueous solution, this compound protonates at the pyridine nitrogen at pH 6. Thus presence of the protonated form correlates with A•T specificity.

The binding site of a class of eukaryotic transcriptional activators typified by yeast protein GCN4 and the mammalian oncogene Jun contains a strong 2-ImN binding site. Specificity requirements for the protein and small molecule are similar. GCN4 and 2-lmN bind simultaneously to the same binding site. GCN4 alters the cleavage pattern of 2-ImN-EDTA derivative at only one of its binding sites. The details of the interaction suggest that GCN4 alters the conformation of an AAAAAAA sequence adjacent to its binding site. The presence of a yeast counterpart to Jun partially blocks 2-lmN binding. The differences do not appear to be caused by direct interactions between 2-lmN and the proteins, but by induced conformational changes in the DNA protein complex. It is likely that the observed differences in complexation are involved in the varying sequence specificity of these proteins.

The development of an asymmetric palladium-catalyzed conjugate addition and its application toward the total syntheses of taiwaniaquinoid natural products

The asymmetric synthesis of quaternary stereocenters remains a challenging problem in organic synthesis. Past work from the Stoltz laboratory has resulted in methodology to install quaternary stereocenters α- or γ- to carbonyl compounds. Thus, the asymmetric synthesis of β-quaternary stereocenters was a desirable objective, and was accomplished by engineering the palladium-catalyzed addition of arylmetal organometallic reagents to α,β-unsaturated conjugate acceptors.

Herein, we described the rational design of a palladium-catalyzed conjugate addition reactions utilizing a catalyst derived from palladium(II) trifluoroacetate and pyridinooxazole ligands. This reaction is highly tolerant of protic solvents and oxygen atmosphere, making it a practical and operationally simple reaction. The mild conditions facilitate a remarkably high functional group tolerance, including carbonyls, halogens, and fluorinated functional groups. Furthermore, the reaction catalyzed conjugate additions with high enantioselectivity with conjugate acceptors of 5-, 6-, and 7-membered ring sizes. Extension of the methodology toward the asymmetric synthesis of flavanone products is presented, as well.

A computational and experimental investigation into the reaction mechanism provided a stereochemical model for enantioinduction, whereby the α-methylene protons adjacent the enone carbonyl clashes with the tert-butyl groups of the chiral ligand. Additionally, it was found that the addition of water and ammonium hexafluorophosphate significantly increases the reaction rate without sacrificing enantioselectivity. The synergistic effects of these additives allowed for the reaction to proceed at a lower temperature, and thus facilitated expansion of the substrate scope to sensitive functional groups such as protic amides and aryl bromides. Investigations into a scale-up synthesis of the chiral ligand (S)-tert-butylPyOx are also presented. This three-step synthetic route allowed for synthesis of the target compound of greater than 10 g scale.

Finally, the application of the newly developed conjugate addition reaction toward the synthesis of the taiwaniaquinoid class of terpenoid natural products is discussed. The conjugate addition reaction formed the key benzylic quaternary stereocenter in high enantioselectivity, joining together the majority of the carbons in the taiwaniaquinoid scaffold. Efforts toward the synthesis of the B-ring are presented.

Observations of nitrogen and oxygen isotopes in the low energy cosmic rays

The isotopic composition of the enhanced low energy nitrogen and oxygen cosmic rays can provide information regarding the source of these particles. Using the Caltech Electron/Isotope Spectrometer aboard the IMP-7 satellite, a measurement of this isotopic composition was made. To determine the isotope response of the instrument, a calibration was performed, and it was determined that the standard range-energy tables were inadequate to calculate the isotope response. From the calibration, corrections to the standard range-energy tables were obtained which can be used to calculate the isotope response of this and similar instruments.

The low energy nitrogen and oxygen cosmic rays were determined to be primarily ^(14)N and ^(16)O. Upper limits were obtained for the abundances of the other stable nitrogen and oxygen isotopes. To the 84% confidence level the isotopic abundances are: ^(15)N/N ≤ 0.26 (5.6- 12.7 MeV/nucleon), ^(17)0/0 ≤ 0.13 (7.0- 11.8 MeV/nucleon), (18)0/0 ≤ 0.12 (7.0 - 11.2 MeV/nucleon). The nitrogen composition differs from higher energy measurements which indicate that ^(15)N, which is thought to be secondary, is the dominant isotope. This implies that the low energy enhanced cosmic rays are not part of the same population as the higher energy cosmic rays and that they have not passed through enough material to produce a large fraction of ^(15)N. The isotopic composition of the low energy enhanced nitrogen and oxygen is consistent with the local acceleration theory of Fisk, Kozlovsky, and Ramaty, in which interstellar material is accelerated to several MeV/nucleon. If, on the other hand, the low energy nitrogen and oxygen result from nucleosynthesis in a galactic source, then the nucleosynthesis processes which produce an enhancement of nitrogen and oxygen and a depletion of carbon are restricted to producing predominantly ^(14)N and ^(16)O.

Neutron-neutron scattering parameters from the ^3He(d,t)2p and ^3H(d,^3He)2n reactions

The energy spectra of tritons and Helium-3 nuclei from the reactions ³He(d,t)2p, ³H(d,³He)2n, ³He(d,³He)pn, and ³H(d,t)pn were measured between 6° and 20° at a bombarding energy of 10.9 MeV. An upper limit of 5 μb/sr. was obtained for producing a bound di-neutron at 6° and 7.5°. The ³He(d,t)2p and ³H(d,³He)2n data, together with previous measurements at higher energies, have been used to investigate whether one can unambiguously extract information on the two-nucleon system from these three-body final state reactions. As an aid to these theoretical investigations, Born approximation calculations were made employing realistic nucleon-nucleon potentials and an antisymmetrized final state wave function for the five-particle system. These calculations reproduce many of the features observed in the experimental data and indicate that the role of exchange processes cannot be ignored. The results show that previous attempts to obtain information on the neutron-neutron scattering length from the ³H(d,³He)2n reaction may have seriously overestimated the precision that could be attained.

Isolation and characteristics of a bacteriophage for bacillus stearothermophilus

A bacteriophage (TØ3) which infects the thermophilic bacterium Bacillus stearothermophilus ATCC 8005 was isolated and characterized. Infection of the bacterium by the bacteriophage was carried out at 60°C, the optimum growth temperature of the host. At 60°C the phage has a latent period of 18 minutes and a burst size of about 200. The phage is comparatively thermostable in broth. The half life of the phage is 400 minutes at 60°C, 120 minutes at 65°C, 40 minutes at 70°C and 12 minutes at 75°C. The activation energy for the heat inactivation of TØ3 is 56,000 cal. The buoyant density of TØ3 in a cesium chloride density gradient is 1.526.

Electron micrographs of TØ3 indicate that the phage has a regular hexagonal shaped head 57 mμ long. The morphology of the head is compatible with icosahedral symmetry. Each edge of the head is 29 mμ long, and there are 6 or 7 subunits along each edge. The tail of TØ3 is 125 mμ long and 10 mμ wide. There are about 30 cross striations that are spaced at 3.9 mμ intervals along the tail.

The DNA of phage TØ3 has a melting temperature of 88.5°C. Heat denatured TØ3 DNA can be extensively annealed in a high ionic strength environment. The buoyant density of TØ3 DNA in a cesium chloride density gradient is 1.695. TØ3 DNA contains: 42.7% guanine plus cytosine, as determined from the melting temperature; 43% guanine plus cytosine, as determined from the buoyant density; and 40.2% guanine plus cytosine, as determined by chromatographic separation and spectrophotometric estimation of the bases. The molecular weight of TØ3 DNA is 16.7 X 10⁶ as determined from the band width of the TØ3 DNA concentration distribution in a cesium chloride density gradient. Electron microscopy of TØ3 DNA revealed a single linear molecule that is 11.7 μ long. This corresponds to a molecular weight of 22.5 X 10⁶.

Heat denatured TØ3 DNA forms two bands in a cesium chloride density gradient, one at a density of 1.707 and the other at a density of 1.715. After the separated bands are mixed and annealed in the centrifuge cell, the renatured TØ3 DNA forms a single band at a density of 1.699. These results indicate that the two complementary strands of TØ3 DNA have different buoyant densities in cesium chloride, presumably because they have different base compositions.

The characteristics of TØ3 are compared with those of other phages. A hypothesis is presented for a relationship between the base composition of one strand of TØ3 DNA and the amino acid composition of the proteins of TØ3.

Finite-Element Simulations of Earthquakes

This thesis discusses simulations of earthquake ground motions using prescribed ruptures and dynamic failure. Introducing sliding degrees of freedom led to an innovative technique for numerical modeling of earthquake sources. This technique allows efficient implementation of both prescribed ruptures and dynamic failure on an arbitrarily oriented fault surface. Off the fault surface the solution of the three-dimensional, dynamic elasticity equation uses well known finite-element techniques. We employ parallel processing to efficiently compute the ground motions in domains containing millions of degrees of freedom.

Using prescribed ruptures we study the sensitivity of long-period near-source ground motions to five earthquake source parameters for hypothetical events on a strike-slip fault (M_w 7.0 to 7.1) and a thrust fault (M_w 6.6 to 7.0). The directivity of the ruptures creates large displacement and velocity pulses in the ground motions in the forward direction. We found a good match between the severity of the shaking and the shape of the near-source factor from the 1997 Uniform Building Code for strike-slip faults and thrust faults with surface rupture. However, for blind thrust faults the peak displacement and velocities occur up-dip from the region with the peak near-source factor. We assert that a simple modification to the formulation of the near-source factor improves the match between the severity of the ground motion and the shape of the near-source factor.

For simulations with dynamic failure on a strike-slip fault or a thrust fault, we examine what constraints must be imposed on the coefficient of friction to produce realistic ruptures under the application of reasonable shear and normal stress distributions with depth. We found that variation of the coefficient of friction with the shear modulus and the depth produces realistic rupture behavior in both homogeneous and layered half-spaces. Furthermore, we observed a dependence of the rupture speed on the direction of propagation and fluctuations in the rupture speed and slip rate as the rupture encountered changes in the stress field. Including such behavior in prescribed ruptures would yield more realistic ground motions.