BCOV invariants of Calabi--Yau manifolds and degenerations of Hodge structures

Calabi--Yau manifolds have risen to prominence in algebraic geometry, in part because of mirror symmetry and enumerative geometry. After Bershadsky--Cecotti--Ooguri--Vafa (BCOV), it is expected that genus 1 curve counting on a Calabi--Yau manifold is related to a conjectured invariant, only depending on the complex structure of the mirror, and built from Ray--Singer holomorphic analytic torsions. To this end, extending work of Fang--Lu--Yoshikawa in dimension 3, we introduce and study the BCOV invariant of Calabi--Yau manifolds of arbitrary dimension. To determine it, knowledge of its behaviour at the boundary of moduli spaces is imperative. We address this problem by proving precise asymptotics along one-parameter degenerations, in terms of topological data and intersection theory. Central to the approach are new results on degenerations of $L^2$ metrics on Hodge bundles, combined with information on the singularities of Quillen metrics in our previous work.Comment: Minor revision. Mainly restructure of the text, minor improvements and corrections. Added information about subdominant terms of $L^2$-norm

Spectral Classification of Galaxies Along the Hubble Sequence

We develop a straightforward and quantitative two-step method for spectroscopically classifying galaxies from the low signal-to-noise (S/N) optical spectra typical of galaxy redshift surveys. First, using \chi^2-fitting of characteristic templates to the object spectrum, we determine the relative contributions of the old stellar component, the young stellar component, and various emission line spectra. Then, we classify the galaxy by comparing the relative strengths of the components with those of galaxies of known morphological type. In particular, we use the ratios of (1) the emission line to absorption line contribution, (2) the young to old stellar contribution, and (3) the oxygen to hydrogen emission line contribution. We calibrate and test the method using published morphological types for 32 galaxies from the long-slit spectroscopic survey of Kennicutt (1992) and for 304 galaxies from a fiber spectroscopic survey of nearby galaxy clusters. From an analysis of a sample of long-slit spectra of spiral galaxies in two galaxy clusters, we conclude that the majority of the galaxies observed in the fiber survey are sufficiently distant that their spectral classification is unaffected by aperture bias. Our spectral classification is consistent with the morphological classification to within one type (e.g. E to S0 or Sa to Sb) for \gtsim 80% of the galaxies. Disagreements between the spectral and morphological classifications of the remaining galaxies reflect a divergence in the correspondence between spectral and morphological types, rather than a problem with the data or method.Comment: 13 pages, uuencoded gzip'ed ps-file that includes 8 of 9 Figures, accepted for publication in A

Climate change vulnerability index for South African aquifers

South Africa is viewed as a water-stressed country with an average annual rainfall of 500 mm and any climatic change could have adverse impacts on water resources of the country. The potential impacts of climate change on water resources and surface hydrology for Africa and Southern Africa have received considerable attention from hydrologists during the past decade. Very little research has been conducted on the future impact of climate change on groundwater resources in South Africa. Climate change can affect groundwater levels, recharge and groundwater contribution to baseflow. To assess these impacts a climate change vulnerability index was developed. This vulnerability-index method is known as the DART index. The parameters considered in the DART method are as follows: depth to water-level change, aquifer type (storativity), recharge and transmissivity. The DART index is used as a regional screening tool to identify areas that could experience possible changes in their groundwater resources as a result of climate change. The current DART index does notaccount for adaptation and migration occurrences

The synthesis of fullerene fragments

In this thesis, a significant amount of curved fullerene fragment chemistry is covered. The excitement created by buckminsterfullerene has spilled over into these fragments and the complete, controlled synthesis of C60 is an enticing goal of this chemistry. Towards this end, a great deal of effort has been expended to synthesize larger buckybowls and that necessarily includes advancing production methodology. The General Introduction explores the evolution of synthetic methods of buckybowl production, from brute force, through flash vacuum pyrolysis, to solution-phase tactics. The history of the synthesis of corannulene is followed through these methods. The schemes that led to corannulene were expanded to produce up to 60% of a buckyball. Chapter 2 deals with the synthesis of an interesting, new polynuclear aromatic hydrocarbon, 7,10-bis(chlorovinyl)fluoranthene-5-ol, a possible precursor to corannulene through a novel solid?phase route. Although the reaction scheme is arduous and the overall yield poor, the solid-phase methodology is so promising that the effort is validated. Therefore, results of the precursor and silica matrix reaction are highly anticipated. Chapter 3 introduces a new buckybowl. Acenaphtho[3,2,1,8-ijklm]diindeno[4,3,2,1-cdef:1\u27,2\u27,3\u27,4\u27-pqra]triphenylene was prepared by means of a unique combination of reaction steps. Solution-phase chemistry was used to create a substituted corannulene and subsequent pyrolysis gave the final C32H14 buckybowl. However, some non-pyrolytic pathways either failed outright, or were found to have limitations. Chapter 4 better defined the limitations of the convenient, corannulene production method. That is, results reported here and in the previous chapter show that o-phenyl groups prohibit dibromination of benzylic methyls. Chapter 3 illustrated this with 1,6-bis(dibromomethyl)-7,10-bis(bromomethyl)-8,9-bis(2-bromophenyl)fluoranthene. The two methyl groups ortho to the phenyls were only monobrominated while the unhindered methyl groups were dibrominated. In the case of 1,6,7,10-tetramethyl-2,5,8,9-tetraphenylfluoranthene, from Chapter 4, all four methyl groups were unable to be dibrominated and the desired ring closures could not be enacted. Although this pathway to large fullerene fragments failed, it has lead to a better understanding of the limitations of a non-pyrolytic method