Asymptotic behavior and interpretation of virtual states: The effects of confinement and of basis sets

A real-space high order finite difference method is used to analyze the effect of spherical domain size on the Hartree-Fock (and density functional theory) virtual eigenstates. We show the domain size dependence of both positive and negative virtual eigenvalues of the Hartree-Fock equations for small molecules. We demonstrate that positive states behave like a particle in spherical well and show how they approach zero. For the negative eigenstates, we show that large domains are needed to get the correct eigenvalues. We compare our results to those of Gaussian basis sets and draw some conclusions for real-space, basis-sets, and plane-waves calculations. (C) 2016 AIP Publishing LLC.

A backward particle interpretation of Feynman-Kac formulae

We design a particle interpretation of Feynman-Kac measures on path spaces based on a backward Markovian representation combined with a traditional mean field particle interpretation of the flow of their final time marginals. In contrast to traditional genealogical tree based models, these new particle algorithms can be used to compute normalized additive functionals "on-the-fly" as well as their limiting occupation measures with a given precision degree that does not depend on the final time horizon. We provide uniform convergence results with respect to the time horizon parameter as well as functional central limit theorems and exponential concentration estimates. Our results have important consequences for online parameter estimation for non-linear non-Gaussian state-space models. We show how the forward filtering backward smoothing estimates of additive functionals can be computed using a forward only recursion.

A field model interpretation of crack initiation and growth behavior in ferroelectric ceramics: change of poling direction and boundary condition

Strain energy density expressions are obtained from a field model that can qualitatively exhibit how the electrical and mechanical disturbances would affect the crack growth behavior in ferroelectric ceramics. Simplification is achieved by considering only three material constants to account for elastic, piezoelectric and dielectric effects. Cross interaction of electric field (or displacement) with mechanical stress (or strain) is identified with the piezoelectric effect; it occurs only when the pole is aligned normal to the crack. Switching of the pole axis by 90degrees and 180degrees is examined for possible connection with domain switching. Opposing crack growth behavior can be obtained when the specification of mechanical stress sigma(infinity) and electric field E-infinity or (sigma(infinity), E-infinity) is replaced by strain e and electric displacement D-infinity or (epsilon(infinity), D-infinity). Mixed conditions (sigma(infinity),D-infinity) and (epsilon(infinity),E-infinity) are also considered. In general, crack growth is found to be larger when compared to that without the application of electric disturbances. This includes both the electric field and displacement. For the eight possible boundary conditions, crack growth retardation is identified only with (E-y(infinity),sigma(y)(infinity)) for negative E-y(infinity) and (D-y(infinity), epsilon(y)(infinity)) for positive D-y(infinity) while the mechanical conditions sigma(y)(infinity) or epsilon(y)infinity are not changed. Suitable combinations of the elastic, piezoelectric and dielectric material constants could also be made to suppress crack growth. (C) 2002 Published by Elsevier Science Ltd.

Interpretation of lunar topography : impact cratering and surface roughness

This work seeks to understand past and present surface conditions on the Moon using two different but complementary approaches: topographic analysis using high-resolution elevation data from recent spacecraft missions and forward modeling of the dominant agent of lunar surface modification, impact cratering. The first investigation focuses on global surface roughness of the Moon, using a variety of statistical parameters to explore slopes at different scales and their relation to competing geological processes. We find that highlands topography behaves as a nearly self-similar fractal system on scales of order 100 meters, and there is a distinct change in this behavior above and below approximately 1 km. Chapter 2 focuses this analysis on two localized regions: the lunar south pole, including Shackleton crater, and the large mare-filled basins on the nearside of the Moon. In particular, we find that differential slope, a statistical measure of roughness related to the curvature of a topographic profile, is extremely useful in distinguishing between geologic units. Chapter 3 introduces a numerical model that simulates a cratered terrain by emplacing features of characteristic shape geometrically, allowing for tracking of both the topography and surviving rim fragments over time. The power spectral density of cratered terrains is estimated numerically from model results and benchmarked against a 1-dimensional analytic model. The power spectral slope is observed to vary predictably with the size-frequency distribution of craters, as well as the crater shape. The final chapter employs the rim-tracking feature of the cratered terrain model to analyze the evolving size-frequency distribution of craters under different criteria for identifying "visible" craters from surviving rim fragments. A geometric bias exists that systematically over counts large or small craters, depending on the rim fraction required to count a given feature as either visible or erased.

An investigation of techniques for the measurement and interpretation of cosmic ray isotopic abundances

An instrument, the Caltech High Energy Isotope Spectrometer Telescope (HEIST), has been developed to measure isotopic abundances of cosmic ray nuclei in the charge range 3 ≤ Z ≤ 28 and the energy range between 30 and 800 MeV/nuc by employing an energy loss -- residual energy technique. Measurements of particle trajectories and energy losses are made using a multiwire proportional counter hodoscope and a stack of CsI(TI) crystal scintillators, respectively. A detailed analysis has been made of the mass resolution capabilities of this instrument.

Landau fluctuations set a fundamental limit on the attainable mass resolution, which for this instrument ranges between ~.07 AMU for z~3 and ~.2 AMU for z~2b. Contributions to the mass resolution due to uncertainties in measuring the path-length and energy losses of the detected particles are shown to degrade the overall mass resolution to between ~.1 AMU (z~3) and ~.3 AMU (z~2b).

A formalism, based on the leaky box model of cosmic ray propagation, is developed for obtaining isotopic abundance ratios at the cosmic ray sources from abundances measured in local interstellar space for elements having three or more stable isotopes, one of which is believed to be absent at the cosmic ray sources. This purely secondary isotope is used as a tracer of secondary production during propagation. This technique is illustrated for the isotopes of the elements O, Ne, S, Ar and Ca.

The uncertainties in the derived source ratios due to errors in fragmentation and total inelastic cross sections, in observed spectral shapes, and in measured abundances are evaluated. It is shown that the dominant sources of uncertainty are uncorrelated errors in the fragmentation cross sections and statistical uncertainties in measuring local interstellar abundances.

These results are applied to estimate the extent to which uncertainties must be reduced in order to distinguish between cosmic ray production in a solar-like environment and in various environments with greater neutron enrichments.

Constraining the interpretation of 2-methylhopanoids through genetic and phylogenetic methods

Hopanoids are a class of sterol-like lipids produced by select bacteria. Their preservation in the rock record for billions of years as fossilized hopanes lends them geological significance. Much of the structural diversity present in this class of molecules, which likely underpins important biological functions, is lost during fossilization. Yet, one type of modification that persists during preservation is methylation at C-2. The resulting 2-methylhopanoids are prominent molecular fossils and have an intriguing pattern over time, exhibiting increases in abundance associated with Ocean Anoxic Events during the Phanerozoic. This thesis uses diverse methods to address what the presence of 2-methylhopanes tells us about the microbial life and environmental conditions of their ancient depositional settings. Through an environmental survey of hpnP, the gene encoding the C-2 hopanoid methylase, we found that many different taxa are capable of producing 2-methylhopanoids in more diverse modern environments than expected. This study also revealed that hpnP is significantly overrepresented in organisms that are plant symbionts, in environments associated with plants, and with metabolisms that support plant-microbe interactions; collectively, these correlations provide a clue about the biological importance of 2-methylhopanoids. Phylogenetic reconstruction of the evolutionary history of hpnP revealed that 2-methylhopanoid production arose in the Alphaproteobacteria, indicating that the origin of these molecules is younger than originally thought. Additionally, we took genetic approach to understand the role of 2-methylhopanoids in Cyanobacteria using the filamentous symbiotic Nostoc punctiforme. We found that hopanoids likely aid in rigidifying the cell membrane but do not appear to provide resistance to osmotic or outer membrane stressors, as has been shown in other organisms. The work presented in this thesis supports previous findings that 2-methylhopanoids are not biomarkers for oxygenic photosynthesis and provides new insights by defining their distribution in modern environments, identifying their evolutionary origin, and investigating their role in Cyanobacteria. These efforts in modern settings aid the formation of a robust interpretation of 2-methylhopanes in the rock record.