Formation of X-waves at fundamental and harmonics by infrared femtosecond pulse filamentation in air

We experimentally observe the formation of X-waves at fundamental, third harmonic, and fifth harmonic wavelengths by infrared (central wavelength at similar to 1500 nm) femtosecond laser pulse filamentation in air. By fitting the angularly resolved spectra of the fundamental and harmonic waves using X-wave relations, we confirm that all the X-waves have nearly the same group velocity, indicating that they are locked in space and time during their propagation in filament.

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.

Pattern formation during Caenorhabditis Elegans vulval development

Pattern formation during animal development involves at least three processes: establishment of the competence of precursor cells to respond to intercellular signals, formation of a pattern of different cell fates adopted by precursor cells, and execution of the cell fate by generating a pattern of distinct descendants from precursor cells. I have analyzed the fundamental mechanisms of pattern formation by studying the development of Caenorhabditis elegans vulva.

In C. elegans, six multipotential vulval precursor cells (VPCs) are competent to respond to an inductive signal LIN-3 (EGF) mediated by LET- 23 (RTK) and a lateral signal via LIN-12 (Notch) to form a fixed pattern of 3°-3°-2°-1°-2°-3°. Results from expressing LIN-3 as a function of time in animals lacking endogenous LIN-3 indicate that both VPCs and VPC daughters are competent to respond to LIN-3. Although the daughters of VPCs specified to be 2° or 3° can be redirected to adopt the 1°fate, the decision to adopt the 1° fate is irreversible. Coupling of VPC competence to cell cycle progression reveals that VPC competence may be periodic during each cell cycle and involve LIN-39 (HOM-C). These mechanisms are essential to ensure a bias towards the 1° fate, while preventing an excessive response.

After adopting the 1° fate, the VPC executes its fate by dividing three rounds to form a fixed pattern of four inner vulF and four outer vulE descendants. These two types of descendants can be distinguished by a molecular marker zmp-1::GFP. A short-range signal from the anchor cell (AC), along with signaling between the inner and outer 1° VPC descendants and intrinsic polarity of 1° VPC daughters, patterns the 1° lineage. The Ras and the Wnt signaling pathways may be involved in these mechanisms.

The temporal expression pattern of egl-17::GFP, another marker ofthe 1° fate, correlates with three different steps of 1° fate execution: the commitment to the 1° fate, as well as later steps before and after establishment of the uterine-vulval connection. Six transcription factors, including LIN-1(ETS), LIN-39 (HOM-C), LIN-11(LIM), LIN-29 (zinc finger), COG-1 (homeobox) and EGL-38 (PAX2/5/8), are involved in different steps during 1° fate execution.

Formation of nanogratings on the surface of a ZnSe crystal irradiated by femtosecond laser pulses

Two collinear femtosecond laser pulses, one at wavelength of 800 nm and the other at 400 nm (double frequency), simultaneously irradiated the surface of ZnSe crystal, which resulted in regular nanograting with period of 180 nm on the whole ablation area. We attribute the formation of the nanograting to be due to the interference between the surface scattered wave of 800 nm lasers and the 400 nm light. The period of the nanograting Lambda is about lambda/2n, where n is refractive index of the sample, and lambda, the laser wavelength. This mechanism is supported by observation of rotation of the nanograting with the polarization of 400 nm light, and by the dependence of Lambda similar to lambda of the nanoripples on the surface of semiconductors and dielectrics.

Demographic studies of extrasolar planets

Uncovering the demographics of extrasolar planets is crucial to understanding the processes of their formation and evolution. In this thesis, we present four studies that contribute to this end, three of which relate to NASA's Kepler mission, which has revolutionized the field of exoplanets in the last few years.

In the pre-Kepler study, we investigate a sample of exoplanet spin-orbit measurements---measurements of the inclination of a planet's orbit relative to the spin axis of its host star---to determine whether a dominant planet migration channel can be identified, and at what confidence. Applying methods of Bayesian model comparison to distinguish between the predictions of several different migration models, we find that the data strongly favor a two-mode migration scenario combining planet-planet scattering and disk migration over a single-mode Kozai migration scenario. While we test only the predictions of particular Kozai and scattering migration models in this work, these methods may be used to test the predictions of any other spin-orbit misaligning mechanism.

We then present two studies addressing astrophysical false positives in Kepler data. The Kepler mission has identified thousands of transiting planet candidates, and only relatively few have yet been dynamically confirmed as bona fide planets, with only a handful more even conceivably amenable to future dynamical confirmation. As a result, the ability to draw detailed conclusions about the diversity of exoplanet systems from Kepler detections relies critically on understanding the probability that any individual candidate might be a false positive. We show that a typical a priori false positive probability for a well-vetted Kepler candidate is only about 5-10%, enabling confidence in demographic studies that treat candidates as true planets. We also present a detailed procedure that can be used to securely and efficiently validate any individual transit candidate using detailed information of the signal's shape as well as follow-up observations, if available.

Finally, we calculate an empirical, non-parametric estimate of the shape of the radius distribution of small planets with periods less than 90 days orbiting cool (less than 4000K) dwarf stars in the Kepler catalog. This effort reveals several notable features of the distribution, in particular a maximum in the radius function around 1-1.25 Earth radii and a steep drop-off in the distribution larger than 2 Earth radii. Even more importantly, the methods presented in this work can be applied to a broader subsample of Kepler targets to understand how the radius function of planets changes across different types of host stars.

Dynamical stability of nascent neutron stars

This thesis presents a study of the dynamical stability of nascent neutron stars resulting from the accretion induced collapse of rapidly rotating white dwarfs.

Chapter 2 and part of Chapter 3 study the equilibrium models for these neutron stars. They are constructed by assuming that the neutron stars have the same masses, angular momenta, and specific angular momentum distributions as the pre-collapse white dwarfs. If the pre-collapse white dwarf is rapidly rotating, the collapsed object will contain a high density central core of size about 20 km, surrounded by a massive accretion torus extending to hundreds of kilometers from the rotation axis. The ratio of the rotational kinetic energy to gravitational binding energy, β, of these neutron stars is all found to be less than 0.27.

Chapter 3 studies the dynamical stability of these neutron stars by numerically evolving the linearized hydrodynamical equations. A dynamical bar-mode instability is observed when the β of the star is greater than the critical value β_d ≈ 0.25. It is expected that the unstable mode will persist until a substantial amount of angular momentum is carried away by gravitational radiation. The detectability of these sources is studied and it is estimated that LIGO II is unlikely to detect them unless the event rate is greater than 10^-6/year/galaxy.

All the calculations on the structure and stability of the neutron stars in Chapters 2 and 3 are carried out using Newtonian hydrodynamics and gravity. Chapter 4 studies the relativistic effects on the structure of these neutron stars. New techniques are developed and used to construct neutron star models to the first post-Newtonian (1PN) order. The structures of the 1PN models are qualitatively similar to the corresponding Newtonian models, but the values of β are somewhat smaller. The maximum β for these 1PN neutron stars is found to be 0.24, which is 8% smaller than the Newtonian result (0.26). However, relativistic effects will also change the critical value β_d. A detailed post-Newtonian stability analysis has yet to be carried out to study the relativistic effects on the dynamical stability of these neutron stars.

Nematic ordering pattern formation in the process of self-organization of microtubules in a gravitational field

Papaseit et al. (Proc. Nati. Acad. Sci. U.S.A. 97, 8364, 2000) showed the decisive role of gravity in the formation of patterns by assemblies of microtubules in vitro. By virtue of a functional scaling, the free energy for MT systems in a gravitational field was constructed. The influence of the gravitational field on MT's self-organization process, that can lead to the isotropic to nematic phase transition, is the focus of this paper. A coupling of a concentration gradient with orientational order characteristic of nernatic ordering pattern formation is the new feature emerging in the presence of gravity. The concentration range corresponding to a phase coexistence region increases with increasing g or NIT concentration. Gravity facilitates the isotropic to nernatic phase transition leading to a significantly broader transition region. The phase transition represents the interplay between the growth in the isotropic phase and the precipitation into the nematic phase. We also present and discuss the numerical results obtained for local NIT concentration change with the height of the vessel, order parameter and phase transition properties.

Formation mechanisms of uniform arrays of periodic nanoparticles and nanoripples on 6H-SiC crystal surface induced by femtosecond laser ablation

Uniform arrays of periodic nanoparticles with 80-nm period are formed on 6H-SiC crystal irradiated by circularly polarized 400-nm femtosecond laser pulses. In order to understand the formation mechanism, the morphology evolvement as a function of laser pulse energy and number is studied. Periodic nanoripples are also formed on the sample surface irradiated by linearly polarized 400-, 510- and 800-nm femtosecond laser pulses. All these results support well the mechanism that second-harmonic generation plays an important role in the formation of periodic nanostructures.

Standing electron plasma wave mechanism of void array formation inside glass by femtosecond laser irradiation

We investigate the mechanism of formation of periodic void arrays inside fused silica and BK7 glass irradiated by a tightly focused femtosecond (fs) laser beam. Our results show that the period of each void array is not uniform along the laser propagation direction, and the average period of the void array decreases with increasing pulse number and pulse energy. We propose a mechanism in which a standing electron plasma wave created by the interference of a fs-laser-driven electron wave and its reflected wave is responsible for the formation of the periodic void arrays.

Functionalization of Si(111) surfaces and the formation of mixed monolayers for the covalent attachment of molecular catalysts in photoelectrochemical devices

The functionalization of silicon surfaces with molecular catalysts for proton reduction is an important part of the development of a solar-powered, water-splitting device for solar fuel formation. The covalent attachment of these catalysts to silicon without damaging the underlying electronic properties of silicon that make it a good photocathode has proven difficult. We report the formation of mixed monolayer-functionalized surfaces that incor- porate both methyl and vinylferrocenyl or vinylbipyridyl (vbpy) moieties. The silicon was functionalized using reaction conditions analogous to those of hydrosilylation, but instead of a H-terminated Si surface, a chlorine-terminated Si precursor surface was used to produce the linked vinyl-modified functional group. The functionalized surfaces were characterized by time-resolved photoconductivity decay, X-ray photoelectron spectroscopy (XPS), electro- chemical, and photoelectrochemical measurements. The functionalized Si surfaces were well passivated, exhibited high surface coverage and few remaining reactive Si atop sites, had a very low surface recombination velocity, and displayed little initial surface oxidation. The surfaces were stable toward atmospheric and electrochemical oxidation. The surface coverage of ferrocene or bipyridine was controllably varied from 0 up to 30% of a monolayer without loss of the underlying electronic properties of the silicon. Interfacial charge transfer to the attached ferrocene group was relatively rapid, and a photovoltage of 0.4 V was generated upon illumination of functionalized n-type silicon surfaces in CH₃CN. The immobilized bipyridine ligands bound transition metal ions, and thus enabled the assembly of metal complexes on the silicon surface. XPS studies demonstrated that [Cp∗Rh(vbpy)Cl]Cl, [Cp∗Ir(vbpy)Cl]Cl, and Ru(acac)₂vbpy were assembled on the surface. For the surface prepared with iridium, x-ray absorption spectroscopy at the Ir L_III edge showed an edge energy and post-edge features virtually identical to a powder sample of [Cp∗Ir(bipy)Cl]Cl (bipy is 2,2 ́-bipyridyl). Electrochemical studies on these surfaces confirmed that the assembled complexes were electrochemically active.

Nonlinear X-wave formation and conical emission at different powers of a femtosecond laser pulse in water

Nonlinear X-wave formation at different pulse powers in water is simulated using the standard model of nonlinear Schrodinger equation (NLSE). It is shown that in near field X-shape originally emerges from the interplay between radial diffraction and optical Kerr effect. At relatively low power group-velocity dispersion (GVD) arrests the collapse and leads to pulse splitting on axis. With high enough power, multi-photon ionization (NIPI) and multi-photon absorption (MPA) play great importance in arresting the collapse. The tailing part of pulse is first defocused by MPI and then refocuses. Pulse splitting on axis is a manifestation of this process. Double X-wave forms when the split sub-pulses are self-focusing. In the far field, the character of the central X structure of conical emission (CE) is directly related to the single or double X-shape in the near field. (c) 2007 Elsevier B.V. All rights reserved.

New insights into the formation and modification of carbonate-bearing minerals and methane gas in geological systems using multiply substituted isotopologues

This thesis describes the use of multiply-substituted stable isotopologues of carbonate minerals and methane gas to better understand how these environmentally significant minerals and gases form and are modified throughout their geological histories. Stable isotopes have a long tradition in earth science as a tool for providing quantitative constraints on how molecules, in or on the earth, formed in both the present and past. Nearly all studies, until recently, have only measured the bulk concentrations of stable isotopes in a phase or species. However, the abundance of various isotopologues within a phase, for example the concentration of isotopologues with multiple rare isotopes (multiply substituted or 'clumped' isotopologues) also carries potentially useful information. Specifically, the abundances of clumped isotopologues in an equilibrated system are a function of temperature and thus knowledge of their abundances can be used to calculate a sample’s formation temperature. In this thesis, measurements of clumped isotopologues are made on both carbonate-bearing minerals and methane gas in order to better constrain the environmental and geological histories of various samples.

Clumped-isotope-based measurements of ancient carbonate-bearing minerals, including apatites, have opened up paleotemperature reconstructions to a variety of systems and time periods. However, a critical issue when using clumped-isotope based measurements to reconstruct ancient mineral formation temperatures is whether the samples being measured have faithfully recorded their original internal isotopic distributions. These original distributions can be altered, for example, by diffusion of atoms in the mineral lattice or through diagenetic reactions. Understanding these processes quantitatively is critical for the use of clumped isotopes to reconstruct past temperatures, quantify diagenesis, and calculate time-temperature burial histories of carbonate minerals. In order to help orient this part of the thesis, Chapter 2 provides a broad overview and history of clumped-isotope based measurements in carbonate minerals.

In Chapter 3, the effects of elevated temperatures on a sample’s clumped-isotope composition are probed in both natural and experimental apatites (which contain structural carbonate groups) and calcites. A quantitative model is created that is calibrated by the experiments and consistent with the natural samples. The model allows for calculations of the change in a sample’s clumped isotope abundances as a function of any time-temperature history.

In Chapter 4, the effects of diagenesis on the stable isotopic compositions of apatites are explored on samples from a variety of sedimentary phosphorite deposits. Clumped isotope temperatures and bulk isotopic measurements from carbonate and phosphate groups are compared for all samples. These results demonstrate that samples have experienced isotopic exchange of oxygen atoms in both the carbonate and phosphate groups. A kinetic model is developed that allows for the calculation of the amount of diagenesis each sample has experienced and yields insight into the physical and chemical processes of diagenesis.

The thesis then switches gear and turns its attention to clumped isotope measurements of methane. Methane is critical greenhouse gas, energy resource, and microbial metabolic product and substrate. Despite its importance both environmentally and economically, much about methane’s formational mechanisms and the relative sources of methane to various environments remains poorly constrained. In order to add new constraints to our understanding of the formation of methane in nature, I describe the development and application of methane clumped isotope measurements to environmental deposits of methane. To help orient the reader, a brief overview of the formation of methane in both high and low temperature settings is given in Chapter 5.

In Chapter 6, a method for the measurement of methane clumped isotopologues via mass spectrometry is described. This chapter demonstrates that the measurement is precise and accurate. Additionally, the measurement is calibrated experimentally such that measurements of methane clumped isotope abundances can be converted into equivalent formational temperatures. This study represents the first time that methane clumped isotope abundances have been measured at useful precisions.

In Chapter 7, the methane clumped isotope method is applied to natural samples from a variety of settings. These settings include thermogenic gases formed and reservoired in shales, migrated thermogenic gases, biogenic gases, mixed biogenic and thermogenic gas deposits, and experimentally generated gases. In all cases, calculated clumped isotope temperatures make geological sense as formation temperatures or mixtures of high and low temperature gases. Based on these observations, we propose that the clumped isotope temperature of an unmixed gas represents its formation temperature — this was neither an obvious nor expected result and has important implications for how methane forms in nature. Additionally, these results demonstrate that methane-clumped isotope compositions provided valuable additional constraints to studying natural methane deposits.