Small scale turbulence in high Karlovitz number premixed flames

The purpose of this thesis is to characterize the behavior of the smallest turbulent scales in high Karlovitz number (Ka) premixed flames. These scales are particularly important in the two-way coupling between turbulence and chemistry and better understanding of these scales will support future modeling efforts using large eddy simulations (LES). The smallest turbulent scales are studied by considering the vorticity vector, ω, and its transport equation.

Due to the complexity of turbulent combustion introduced by the wide range of length and time scales, the two-dimensional vortex-flame interaction is first studied as a simplified test case. Numerical and analytical techniques are used to discern the dominate transport terms and their effects on vorticity based on the initial size and strength of the vortex. This description of the effects of the flame on a vortex provides a foundation for investigating vorticity in turbulent combustion.

Subsequently, enstrophy, ω² = ω • ω, and its transport equation are investigated in premixed turbulent combustion. For this purpose, a series of direct numerical simulations (DNS) of premixed n-heptane/air flames are performed, the conditions of which span a wide range of unburnt Karlovitz numbers and turbulent Reynolds numbers. Theoretical scaling analysis along with the DNS results support that, at high Karlovitz number, enstrophy transport is controlled by the viscous dissipation and vortex stretching/production terms. As a result, vorticity scales throughout the flame with the inverse of the Kolmogorov time scale, τ_η, just as in homogeneous isotropic turbulence. As τ_η is only a function of the viscosity and dissipation rate, this supports the validity of Kolmogorov’s first similarity hypothesis for sufficiently high Ka numbers (Ka ≳ 100). These conclusions are in contrast to low Karlovitz number behavior, where dilatation and baroclinic torque have a significant impact on vorticity within the flame. Results are unaffected by the transport model, chemical model, turbulent Reynolds number, and lastly the physical configuration.

Next, the isotropy of vorticity is assessed. It is found that given a sufficiently large value of the Karlovitz number (Ka ≳ 100) the vorticity is isotropic. At lower Karlovitz numbers, anisotropy develops due to the effects of the flame on the vortex stretching/production term. In this case, the local dynamics of vorticity in the strain-rate tensor, S, eigenframe are altered by the flame. At sufficiently high Karlovitz numbers, the dynamics of vorticity in this eigenframe resemble that of homogeneous isotropic turbulence.

Combined, the results of this thesis support that both the magnitude and orientation of vorticity resemble the behavior of homogeneous isotropic turbulence, given a sufficiently high Karlovitz number (Ka ≳ 100). This supports the validity of Kolmogorov’s first similarity hypothesis and the hypothesis of local isotropy under these condition. However, dramatically different behavior is found at lower Karlovitz numbers. These conclusions provides/suggests directions for modeling high Karlovitz number premixed flames using LES. With more accurate models, the design of aircraft combustors and other combustion based devices may better mitigate the detrimental effects of combustion, from reducing CO₂ and soot production to increasing engine efficiency.

Non-Linear Scale Interactions in a Forced Turbulent Boundary Layer

This thesis explores the dynamics of scale interactions in a turbulent boundary layer through a forcing-response type experimental study. An emphasis is placed on the analysis of triadic wavenumber interactions since the governing Navier-Stokes equations for the flow necessitate a direct coupling between triadically consist scales. Two sets of experiments were performed in which deterministic disturbances were introduced into the flow using a spatially-impulsive dynamic wall perturbation. Hotwire anemometry was employed to measure the downstream turbulent velocity and study the flow response to the external forcing. In the first set of experiments, which were based on a recent investigation of dynamic forcing effects in a turbulent boundary layer, a 2D (spanwise constant) spatio-temporal normal mode was excited in the flow; the streamwise length and time scales of the synthetic mode roughly correspond to the very-large-scale-motions (VLSM) found naturally in canonical flows. Correlation studies between the large- and small-scale velocity signals reveal an alteration of the natural phase relations between scales by the synthetic mode. In particular, a strong phase-locking or organizing effect is seen on directly coupled small-scales through triadic interactions. Having characterized the bulk influence of a single energetic mode on the flow dynamics, a second set of experiments aimed at isolating specific triadic interactions was performed. Two distinct 2D large-scale normal modes were excited in the flow, and the response at the corresponding sum and difference wavenumbers was isolated from the turbulent signals. Results from this experiment serve as an unique demonstration of direct non-linear interactions in a fully turbulent wall-bounded flow, and allow for examination of phase relationships involving specific interacting scales. A direct connection is also made to the Navier-Stokes resolvent operator framework developed in recent literature. Results and analysis from the present work offer insights into the dynamical structure of wall turbulence, and have interesting implications for design of practical turbulence manipulation or control strategies.

Studies in vortex motion

This thesis covers four different problems in the understanding of vortex sheets, and these are presented in four chapters.

In Chapter 1, free streamline theory is used to determine the steady solutions of an array of identical, hollow or stagnant core vortices in an inviscid, incompressible fluid. Assuming the array is symmetric to rotation through π radians about an axis through any vortex centre, there are two solutions or no solutions depending on whether A^(1/2)/L is less than or greater than 0.38 where A is the area of the vortex and L is the separation distance. Stability analysis shows that the more deformed shape is unstable to infinitesimal symmetric disturbances which leave the centres of the vortices undisplaced.

Chapter 2 is concerned with the roll-up of vortex sheets in homogeneous fluid. The flow over conventional and ring wings is used to test the method of Fink and Soh (1974). Despite modifications which improve the accuracy of the method, unphysical results occur. A possible explanation for this is that small scales are important and an alternate method based on "Cloud-in-Cell" techniques is introduced. The results show small scale growth and amalgamation into larger structures.

The motion of a buoyant pair of line vortices of opposite circulation is considered in Chapter 3. The density difference between the fluid carried by the vortices and the fluid outside is considered small, so that the Boussinesq approximation may be used. A macroscopic model is developed which shows the formation of a detrainment filament and this is included as a modification to the model. The results agree well with the numerical solution as developed by Hill (1975b) and show that after an initial slowdown, the vortices begin to accelerate downwards.

Chapter 4 reproduces completely a paper that has already been published (Baker, Barker, Bofah and Saffman (1974)) on the effect of "vortex wandering" on the measurement of velocity profiles of the trailing vortices behind a wing.

CMB as a probe of new physics and old times

Cosmic birefringence (CB)---a rotation of photon-polarization plane in vacuum---is a generic signature of new scalar fields that could provide dark energy. Previously, WMAP observations excluded a uniform CB-rotation angle larger than a degree.

In this thesis, we develop a minimum-variance--estimator formalism for reconstructing direction-dependent rotation from full-sky CMB maps, and forecast more than an order-of-magnitude improvement in sensitivity with incoming Planck data and future satellite missions. Next, we perform the first analysis of WMAP-7 data to look for rotation-angle anisotropies and report null detection of the rotation-angle power-spectrum multipoles below L=512, constraining quadrupole amplitude of a scale-invariant power to less than one degree. We further explore the use of a cross-correlation between CMB temperature and the rotation for detecting the CB signal, for different quintessence models. We find that it may improve sensitivity in case of marginal detection, and provide an empirical handle for distinguishing details of new physics indicated by CB.

We then consider other parity-violating physics beyond standard models---in particular, a chiral inflationary-gravitational-wave background. We show that WMAP has no constraining power, while a cosmic-variance--limited experiment would be capable of detecting only a large parity violation. In case of a strong detection of EB/TB correlations, CB can be readily distinguished from chiral gravity waves.

We next adopt our CB analysis to investigate patchy screening of the CMB, driven by inhomogeneities during the Epoch of Reionization (EoR). We constrain a toy model of reionization with WMAP-7 data, and show that data from Planck should start approaching interesting portions of the EoR parameter space and can be used to exclude reionization tomographies with large ionized bubbles.

In light of the upcoming data from low-frequency radio observations of the redshifted 21-cm line from the EoR, we examine probability-distribution functions (PDFs) and difference PDFs of the simulated 21-cm brightness temperature, and discuss the information that can be recovered using these statistics. We find that PDFs are insensitive to details of small-scale physics, but highly sensitive to the properties of the ionizing sources and the size of ionized bubbles.

Finally, we discuss prospects for related future investigations.

An experimental investigation of the heat transfer from a buoyant gas plume to a horizontal unobstructed ceiling

This thesis presents an experimental investigation of the axisymmetric heat transfer from a small scale fire and resulting buoyant plume to a horizontal, unobstructed ceiling during the initial stages of development. A propane-air burner yielding a heat source strength between 1.0 kW and 1.6 kW was used to simulate the fire, and measurements proved that this heat source did satisfactorily represent a source of buoyancy only. The ceiling consisted of a 1/16" steel plate of 0.91 m. diameter, insulated on the upper side. The ceiling height was adjustable between 0.5 m and 0.91 m. Temperature measurements were carried out in the plume, ceiling jet, and on the ceiling.

Heat transfer data were obtained by using the transient method and applying corrections for the radial conduction along the ceiling and losses through the insulation material. The ceiling heat transfer coefficient was based on the adiabatic ceiling jet temperature (recovery temperature) reached after a long time. A parameter involving the source strength Q and ceiling height H was found to correlate measurements of this temperature and its radial variation. A similar parameter for estimating the ceiling heat transfer coefficient was confirmed by the experimental results.

This investigation therefore provides reasonable estimates for the heat transfer from a buoyant gas plume to a ceiling in the axisymmetric case, for the stagnation region where such heat transfer is a maximum and for the ceiling jet region (r/H ≤ 0.7). A comparison with data from experiments which involved larger heat sources indicates that the predicted scaling of temperatures and heat transfer rates for larger scale fires is adequate.

I. Impact spallation experiments: fracture patterns and spall velocities. II. Craters in carbonate rocks: an electron paramagnetic resonance analysis of shock damage

This work is divided into two independent papers.

PAPER 1.

Spall velocities were measured for nine experimental impacts into San Marcos gabbro targets. Impact velocities ranged from 1 to 6.5 km/sec. Projectiles were iron, aluminum, lead, and basalt of varying sizes. The projectile masses ranged from a 4 g lead bullet to a 0.04 g aluminum sphere. The velocities of fragments were measured from high-speed films taken of the events. The maximum spall velocity observed was 30 m/sec, or 0.56 percent of the 5.4 km/sec impact velocity. The measured velocities were compared to the spall velocities predicted by the spallation model of Melosh (1984). The compatibility between the spallation model for large planetary impacts and the results of these small scale experiments are considered in detail.

The targets were also bisected to observe the pattern of internal fractures. A series of fractures were observed, whose location coincided with the boundary between rock subjected to the peak shock compression and a theoretical "near surface zone" predicted by the spallation model. Thus, between this boundary and the free surface, the target material should receive reduced levels of compressive stress as compared to the more highly shocked region below.

PAPER 2.

Carbonate samples from the nuclear explosion crater, OAK, and a terrestrial impact crater, Meteor Crater, were analyzed for shock damage using electron para- magnetic resonance, EPR. The first series of samples for OAK Crater were obtained from six boreholes within the crater, and the second series were ejecta samples recovered from the crater floor. The degree of shock damage in the carbonate material was assessed by comparing the sample spectra to spectra of Solenhofen limestone, which had been shocked to known pressures.

The results of the OAK borehole analysis have identified a thin zone of highly shocked carbonate material underneath the crater floor. This zone has a maximum depth of approximately 200 ft below sea floor at the ground zero borehole and decreases in depth towards the crater rim. A layer of highly shocked material is also found on the surface in the vicinity of the reference bolehole, located outside the crater. This material could represent a fallout layer. The ejecta samples have experienced a range of shock pressures.

It was also demonstrated that the EPR technique is feasible for the study of terrestrial impact craters formed in carbonate bedrock. The results for the Meteor Crater analysis suggest a slight degree of shock damage present in the β member of the Kaibab Formation exposed in the crater walls.

Damage detection in civil structures using high-frequency seismograms

The dynamic properties of a structure are a function of its physical properties, and changes in the physical properties of the structure, including the introduction of structural damage, can cause changes in its dynamic behavior. Structural health monitoring (SHM) and damage detection methods provide a means to assess the structural integrity and safety of a civil structure using measurements of its dynamic properties. In particular, these techniques enable a quick damage assessment following a seismic event. In this thesis, the application of high-frequency seismograms to damage detection in civil structures is investigated.

Two novel methods for SHM are developed and validated using small-scale experimental testing, existing structures in situ, and numerical testing. The first method is developed for pre-Northridge steel-moment-resisting frame buildings that are susceptible to weld fracture at beam-column connections. The method is based on using the response of a structure to a nondestructive force (i.e., a hammer blow) to approximate the response of the structure to a damage event (i.e., weld fracture). The method is applied to a small-scale experimental frame, where the impulse response functions of the frame are generated during an impact hammer test. The method is also applied to a numerical model of a steel frame, in which weld fracture is modeled as the tensile opening of a Mode I crack. Impulse response functions are experimentally obtained for a steel moment-resisting frame building in situ. Results indicate that while acceleration and velocity records generated by a damage event are best approximated by the acceleration and velocity records generated by a colocated hammer blow, the method may not be robust to noise. The method seems to be better suited for damage localization, where information such as arrival times and peak accelerations can also provide indication of the damage location. This is of significance for sparsely-instrumented civil structures.

The second SHM method is designed to extract features from high-frequency acceleration records that may indicate the presence of damage. As short-duration high-frequency signals (i.e., pulses) can be indicative of damage, this method relies on the identification and classification of pulses in the acceleration records. It is recommended that, in practice, the method be combined with a vibration-based method that can be used to estimate the loss of stiffness. Briefly, pulses observed in the acceleration time series when the structure is known to be in an undamaged state are compared with pulses observed when the structure is in a potentially damaged state. By comparing the pulse signatures from these two situations, changes in the high-frequency dynamic behavior of the structure can be identified, and damage signals can be extracted and subjected to further analysis. The method is successfully applied to a small-scale experimental shear beam that is dynamically excited at its base using a shake table and damaged by loosening a screw to create a moving part. Although the damage is aperiodic and nonlinear in nature, the damage signals are accurately identified, and the location of damage is determined using the amplitudes and arrival times of the damage signal. The method is also successfully applied to detect the occurrence of damage in a test bed data set provided by the Los Alamos National Laboratory, in which nonlinear damage is introduced into a small-scale steel frame by installing a bumper mechanism that inhibits the amount of motion between two floors. The method is successfully applied and is robust despite a low sampling rate, though false negatives (undetected damage signals) begin to occur at high levels of damage when the frequency of damage events increases. The method is also applied to acceleration data recorded on a damaged cable-stayed bridge in China, provided by the Center of Structural Monitoring and Control at the Harbin Institute of Technology. Acceleration records recorded after the date of damage show a clear increase in high-frequency short-duration pulses compared to those previously recorded. One undamage pulse and two damage pulses are identified from the data. The occurrence of the detected damage pulses is consistent with a progression of damage and matches the known chronology of damage.

Oxygen, carbon and hydrogen isotope studies of contact metamorphism

The O¹⁸/O¹⁶, C¹³/C¹², and D/H ratios have been determined for rocks and coexisting minerals from several granitic plutons and their contact metamorphic aureoles in northern Nevada, eastern California, central Colorado, and Texas, with emphasis on oxygen isotopes. A consistent order of O¹⁸/O¹⁶, C¹³/C¹², and D/H enrichment in coexisting minerals, and a correlation between isotopic fractionations among coexisting mineral pairs are in general observed, suggesting that mineral assemblages tend to approach isotopic equilibrium during contact metamorphism. In certain cases, a correlation is observed between oxygen isotopic fractionations of a mineral pair and sample distance from intrusive contacts. Isotopic temperatures generally show good agreement with heat flow considerations. Based on the experimentally determined quartz-muscovite O¹⁸/O¹⁶ fractionation calibration curve, temperatures are estimated to be 525 to 625°C at the contacts of the granitic stocks studied.

Small-scale oxygen isotope exchange effects between intrusive and country rock are observed over distances of 0.5 to 3 feet on both sides of the contacts; the isotopic gradients are typically 2 to 3 per mil per foot. The degree of oxygen isotopic exchange is essentially identical for different coexisting minerals. This presumably occurred through a diffusion-controlled recrystallization process. The size of the oxygen isotope equilibrium systems in the small-scale exchanged zones vary from about 1.5 cm to 30 cm. A xenolith and a re-entrant of country rock projecting into on intrusive hove both undergone much more extensive isotopic exchange (to hundreds of feet); they also show abnormally high isotopic temperatures. The marginal portions of most plutons have unusually high O¹⁸/O¹⁶ ratios compared to "normal" igneous rocks, presumably due to large-scale isotopic exchange with meta-sedimentary country rocks when the igneous rocks were essentially in a molten state. The isotopic data suggest that outward horizontal movement of H₂O into the contact metamorphic aureoles is almost negligible, but upward movement of H₂O may be important. Also, direct influx and absorption of water from the country rock may be significant in certain intrusive stocks.

Except in the exchanged zones, the O¹⁸/O¹⁶ ratios of pelitic rocks do not change appreciably during contact metamorphism, even in the cordierite and sillimanite grades; this is in contrast to regional metamorphic rocks which commonly decrease in O¹⁸ with increasing grade. Low O¹⁸/O¹⁶ and C¹³/C¹² ratios of the contact metamorphic marbles generally correlate well with the presence of calc-silicate minerals, indicating that the CO₂ liberated during metamorphic decarbonation reactions is enriched in both O¹⁸ and C¹³ relative to the carbonates.

The D/H ratios of biotites in the contact metamorphic rocks and their associated intrusions show a geographic correlation that is similar to that shown by the D/H ratios of meteoric surface waters, perhaps indicating that meteoric waters were present in the rocks during crystallization of the biotites.

Extracting material response from simple mechanical tests on hardening-softening-hardening viscoplastic solids

Compliant foams are usually characterized by a wide range of desirable mechanical properties. These properties include viscoelasticity at different temperatures, energy absorption, recoverability under cyclic loading, impact resistance, and thermal, electrical, acoustic and radiation-resistance. Some foams contain nano-sized features and are used in small-scale devices. This implies that the characteristic dimensions of foams span multiple length scales, rendering modeling their mechanical properties difficult. Continuum mechanics-based models capture some salient experimental features like the linear elastic regime, followed by non-linear plateau stress regime. However, they lack mesostructural physical details. This makes them incapable of accurately predicting local peaks in stress and strain distributions, which significantly affect the deformation paths. Atomistic methods are capable of capturing the physical origins of deformation at smaller scales, but suffer from impractical computational intensity. Capturing deformation at the so-called meso-scale, which is capable of describing the phenomenon at a continuum level, but with some physical insights, requires developing new theoretical approaches.

A fundamental question that motivates the modeling of foams is ‘how to extract the intrinsic material response from simple mechanical test data, such as stress vs. strain response?’ A 3D model was developed to simulate the mechanical response of foam-type materials. The novelty of this model includes unique features such as the hardening-softening-hardening material response, strain rate-dependence, and plastically compressible solids with plastic non-normality. Suggestive links from atomistic simulations of foams were borrowed to formulate a physically informed hardening material input function. Motivated by a model that qualitatively captured the response of foam-type vertically aligned carbon nanotube (VACNT) pillars under uniaxial compression [2011,“Analysis of Uniaxial Compression of Vertically Aligned Carbon Nanotubes,” J. Mech.Phys. Solids, 59, pp. 2227–2237, Erratum 60, 1753–1756 (2012)], the property space exploration was advanced to three types of simple mechanical tests: 1) uniaxial compression, 2) uniaxial tension, and 3) nanoindentation with a conical and a flat-punch tip. The simulations attempt to explain some of the salient features in experimental data, like
1) The initial linear elastic response.
2) One or more nonlinear instabilities, yielding, and hardening.

The model-inherent relationships between the material properties and the overall stress-strain behavior were validated against the available experimental data. The material properties include the gradient in stiffness along the height, plastic and elastic compressibility, and hardening. Each of these tests was evaluated in terms of their efficiency in extracting material properties. The uniaxial simulation results proved to be a combination of structural and material influences. Out of all deformation paths, flat-punch indentation proved to be superior since it is the most sensitive in capturing the material properties.

The Madden-Julian Oscillation : observation, modeling, and theory

The Madden-Julian Oscillation (MJO) is a pattern of intense rainfall and associated planetary-scale circulations in the tropical atmosphere, with a recurrence interval of 30-90 days. Although the MJO was first discovered 40 years ago, it is still a challenge to simulate the MJO in general circulation models (GCMs), and even with simple models it is difficult to agree on the basic mechanisms. This deficiency is mainly due to our poor understanding of moist convection—deep cumulus clouds and thunderstorms, which occur at scales that are smaller than the resolution elements of the GCMs. Moist convection is the most important mechanism for transporting energy from the ocean to the atmosphere. Success in simulating the MJO will improve our understanding of moist convection and thereby improve weather and climate forecasting.

We address this fundamental subject by analyzing observational datasets, constructing a hierarchy of numerical models, and developing theories. Parameters of the models are taken from observation, and the simulated MJO fits the data without further adjustments. The major findings include: 1) the MJO may be an ensemble of convection events linked together by small-scale high-frequency inertia-gravity waves; 2) the eastward propagation of the MJO is determined by the difference between the eastward and westward phase speeds of the waves; 3) the planetary scale of the MJO is the length over which temperature anomalies can be effectively smoothed by gravity waves; 4) the strength of the MJO increases with the typical strength of convection, which increases in a warming climate; 5) the horizontal scale of the MJO increases with the spatial frequency of convection; and 6) triggered convection, where potential energy accumulates until a threshold is reached, is important in simulating the MJO. Our findings challenge previous paradigms, which consider the MJO as a large-scale mode, and point to ways for improving the climate models.

Cosmological consequences of dark matter interactions and vacuum fluctuations

This thesis is divided into two parts: interacting dark matter and fluctuations in cosmology. There is an incongruence between the properties that dark matter is expected to possess between the early universe and the late universe. Weakly-interacting dark matter yields the observed dark matter relic density and is consistent with large-scale structure formation; however, there is strong astrophysical evidence in favor of the idea that dark matter has large self-interactions. The first part of this thesis presents two models in which the nature of dark matter fundamentally changes as the universe evolves. In the first model, the dark matter mass and couplings depend on the value of a chameleonic scalar field that changes as the universe expands. In the second model, dark matter is charged under a hidden SU(N) gauge group and eventually undergoes confinement. These models introduce very different mechanisms to explain the separation between the physics relevant for freezeout and for small-scale dynamics.

As the universe continues to evolve, it will asymptote to a de Sitter vacuum phase. Since there is a finite temperature associated with de Sitter space, the universe is typically treated as a thermal system, subject to rare thermal fluctuations, such as Boltzmann brains. The second part of this thesis begins by attempting to escape this unacceptable situation within the context of known physics: vacuum instability induced by the Higgs field. The vacuum decay rate competes with the production rate of Boltzmann brains, and the cosmological measures that have a sufficiently low occurrence of Boltzmann brains are given more credence. Upon further investigation, however, there are certain situations in which de Sitter space settles into a quiescent vacuum with no fluctuations. This reasoning not only provides an escape from the Boltzmann brain problem, but it also implies that vacuum states do not uptunnel to higher-energy vacua and that perturbations do not decohere during slow-roll inflation, suggesting that eternal inflation is much less common than often supposed. Instead, decoherence occurs during reheating, so this analysis does not alter the conventional understanding of the origin of density fluctuations from primordial inflation.

Palladium-Catalyzed Decarboxylative and Decarbonylative Transformations in the Synthesis of Fine and Commodity Chemicals

Decarboxylation and decarbonylation are important reactions in synthetic organic chemistry, transforming readily available carboxylic acids and their derivatives into various products through loss of carbon dioxide or carbon monoxide. In the past few decades, palladium-catalyzed decarboxylative and decarbonylative reactions experienced tremendous growth due to the excellent catalytic activity of palladium. Development of new reactions in this category for fine and commodity chemical synthesis continues to draw attention from the chemistry community.

The Stoltz laboratory has established a palladium-catalyzed enantioselective decarboxylative allylic alkylation of β-keto esters for the synthesis of α-quaternary ketones since 2005. Recently, we extended this chemistry to lactams due to the ubiquity and importance of nitrogen-containing heterocycles. A wide variety of α-quaternary and tetrasubstituted α-tertiary lactams were obtained in excellent yields and exceptional enantioselectivities using our palladium-catalyzed decarboxylative allylic alkylation chemistry. Enantioenriched α-quaternary carbonyl compounds are versatile building blocks that can be further elaborated to intercept synthetic intermediates en route to many classical natural products. Thus our chemistry enables catalytic asymmetric formal synthesis of these complex molecules.

In addition to fine chemicals, we became interested in commodity chemical synthesis using renewable feedstocks. In collaboration with the Grubbs group, we developed a palladium-catalyzed decarbonylative dehydration reaction that converts abundant and inexpensive fatty acids into value-added linear alpha olefins. The chemistry proceeds under relatively mild conditions, requires very low catalyst loading, tolerates a variety of functional groups, and is easily performed on a large scale. An additional advantage of this chemistry is that it provides access to expensive odd-numbered alpha olefins.

Finally, combining features of both projects, we applied a small-scale decarbonylative dehydration reaction to the synthesis of α-vinyl carbonyl compounds. Direct α-vinylation is challenging, and asymmetric vinylations are rare. Taking advantage of our decarbonylative dehydration chemistry, we were able to transform enantioenriched δ-oxocarboxylic acids into quaternary α-vinyl carbonyl compounds in good yields with complete retention of stereochemistry. Our explorations culminated in the catalytic enantioselective total synthesis of (–)-aspewentin B, a terpenoid natural product featuring a quaternary α-vinyl ketone. Both decarboxylative and decarbonylative chemistries found application in the late stage of the total synthesis.

The Pacoima Area

The Pacoima area consists of Miocene (sediments and basalts) rocks underlain by a quartz diorite basement complex of Jurassic age. The stratigranhic units range from 25 feet to more than 600 feet in thickness. The lower sediments are arkosic land- laid deposits while the Modelo formation, shallow marine in origin, consists of thinly bedded sandstones, shales, volcanic ash and calcareous members. An andesitic mass, possibly a volcanic plug, outcrops near the summit of one of the hills.

An anticline, and possibly an associated syncline, has been developed by compressional folding. Small scale contortion is locally exposed. Regional dip is northward, decreasing from south to north in the area. Faulting is common, most faults trending nearly north-south. Movement along these faults ranges from a few feet to several hundred feet.

There are no important mineral deposits in the area. Quarrying of the basement rocks has been abandoned.

Fabrication, Characterization, And Deformation of 3D Structural Meta-Materials

Current technological advances in fabrication methods have provided pathways to creating architected structural meta-materials similar to those found in natural organisms that are structurally robust and lightweight, such as diatoms. Structural meta-materials are materials with mechanical properties that are determined by material properties at various length scales, which range from the material microstructure (nm) to the macro-scale architecture (μm – mm). It is now possible to exploit material size effect, which emerge at the nanometer length scale, as well as structural effects to tune the material properties and failure mechanisms of small-scale cellular solids, such as nanolattices. This work demonstrates the fabrication and mechanical properties of 3-dimensional hollow nanolattices in both tension and compression. Hollow gold nanolattices loaded in uniaxial compression demonstrate that strength and stiffness vary as a function of geometry and tube wall thickness. Structural effects were explored by increasing the unit cell angle from 30° to 60° while keeping all other parameters constant; material size effects were probed by varying the tube wall thickness, t, from 200nm to 635nm, at a constant relative density and grain size. In-situ uniaxial compression experiments reveal an order-of-magnitude increase in yield stress and modulus in nanolattices with greater lattice angles, and a 150% increase in the yield strength without a concomitant change in modulus in thicker-walled nanolattices for fixed lattice angles. These results imply that independent control of structural and material size effects enables tunability of mechanical properties of 3-dimensional architected meta-materials and highlight the importance of material, geometric, and microstructural effects in small-scale mechanics. This work also explores the flaw tolerance of 3D hollow-tube alumina kagome nanolattices with and without pre-fabricated notches, both in experiment and simulation. Experiments demonstrate that the hollow kagome nanolattices in uniaxial tension always fail at the same load when the ratio of notch length (a) to sample width (w) is no greater than 1/3, with no correlation between failure occurring at or away from the notch. For notches with (a/w) > 1/3, the samples fail at lower peak loads and this is attributed to the increased compliance as fewer unit cells span the un-notched region. Finite element simulations of the kagome tension samples show that the failure is governed by tensile loading for (a/w) < 1/3 but as (a/w) increases, bending begins to play a significant role in the failure. This work explores the flaw sensitivity of hollow alumina kagome nanolattices in tension, using experiments and simulations, and demonstrates that the discrete-continuum duality of architected structural meta-materials gives rise to their flaw insensitivity even when made entirely of intrinsically brittle materials.

The astrophysics of strongly interacting systems

This thesis presents investigations in four areas of theoretical astrophysics: the production of sterile neutrino dark matter in the early Universe, the evolution of small-scale baryon perturbations during the epoch of cosmological recombination, the effect of primordial magnetic fields on the redshifted 21-cm emission from the pre-reionization era, and the nonlinear stability of tidally deformed neutron stars.

In the first part of the thesis, we study the asymmetry-driven resonant production of 7 keV-scale sterile neutrino dark matter in the primordial Universe at temperatures T >~ 100 MeV. We report final DM phase space densities that are robust to uncertainties in the nature of the quark-hadron transition. We give transfer functions for cosmological density fluctuations that are useful for N-body simulations. We also provide a public code for the production calculation.

In the second part of the thesis, we study the instability of small-scale baryon pressure sound waves during cosmological recombination. We show that for relevant wavenumbers, inhomogenous recombination is driven by the transport of ionizing continuum and Lyman-alpha photons. We find a maximum growth factor less than ≈ 1.2 in 10⁷ random realizations of initial conditions. The low growth factors are due to the relatively short duration of the recombination epoch.

In the third part of the thesis, we propose a method of measuring weak magnetic fields, of order 10^-19 G (or 10^-21 G if scaled to the present day), with large coherence lengths in the inter galactic medium prior to and during the epoch of cosmic reionization. The method utilizes the Larmor precession of spin-polarized neutral hydrogen in the triplet state of the hyperfine transition. We perform detailed calculations of the microphysics behind this effect, and take into account all the processes that affect the hyperfine transition, including radiative decays, collisions, and optical pumping by Lyman-alpha photons.

In the final part of the thesis, we study the non-linear effects of tidal deformations of neutron stars (NS) in a compact binary. We compute the largest three- and four-mode couplings among the tidal mode and high-order p- and g-modes of similar radial wavenumber. We demonstrate the near-exact cancellation of their effects, and resolve the question of the stability of the tidally deformed NS to leading order. This result is significant for the extraction of binary parameters from gravitational wave observations.