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What Makes a Narrative? Understanding the Portrayals of Hermenegild's Rebellion
Get PDFWhen one studies an event through the perspectives of multiple accounts, one’s first instinct might be to reconcile the sources into a single cohesive narrative. One can try to assign a likelihood that various portions of each story are factually correct, and then reconstruct what happened based upon which parts seem the most trustworthy.However, in doing so, one cannot be certain of the results. Each of us has our own subjectivity and biases, as our experiences can implicitly shape the decisions we make about what is reliable or plausible and what is not. Moreover, when one tries to compile the “truth” of an event from multiple sources, such "truth" comes at the cost of understanding what made the sources different in the first place. An account is not written in a vacuum, and the way that an author chooses to portray an event is determined by their own personal background, circumstances, and purposes for crafting their narratives. In condensing a host of different accounts into a single internally consistent version, one loses sight of how the authors themselves viewed the events. Keeping different accounts of the same event separate, and investigating each individually in its own context, may not provide a simple solution to the question of “what happened?”, but it will teach us more about the authors’ motivations and what they understood to be important about an event. Such an understanding provides more substantial and reliable information than trying to reconcile the accounts would be able to provide
Synthesis of Enantioenriched Heterocycles by Tandem Sakurai Allylation/Intramolecular Cyclization Processes
Get PDFOrganosilanes are advantageous in organic synthesis due to their ability to act as both stable products and reactive intermediates. A stereospecific one-pot cascade reaction that converts chiral allylic silanes into chiral heterocycles was developed using Lewis acid catalysis. We report on the development of this cascade reaction, optimization to benchtop- scale chemistry, and preliminary investigation into the synthetic scope. In our studies, we were successful in varying the cyclization ring size, investigating cyclization preference in the presence of multiple electrophilic leaving groups, and altering the functional groups present on the aldehyde starting material. Ultimately, we envision this method will be useful in the synthesis of a variety of enantioenriched heterocycles found in bioactive natural products, many of which have may find use as potential drug targets
r-Process Nucleosynthesis in Neutron Star Mergers with the New Nuclear Reaction Network SkyNet
Get PDFAt the Big Bang, only the lightest elements, mainly hydrogen and helium, were produced. Stars synthesize heavier elements, such as helium, carbon, and oxygen, from lighter ones through nuclear fusion. Iron-group elements are created in supernovae (both type Ia and core-collapse). It has been known for 60 years that the slow and rapid neutron capture processes (s- and r-process) are each responsible for creating about half of the elements beyond the iron group. The s-process is known to occur in asymptotic giant branch stars, but the astrophysical site of the r-process is still a mystery. Based on observations of heavy elements in old stars, it was theorized that r-process nucleosynthesis takes place in core-collapse supernovae (CCSNe). However, recent CCSN simulations indicate that the conditions required for the r-process are not obtained in CCSN. The focus has thus shifted to neutron star mergers (both binary neutron star and black hole-neutron star mergers), where the r-process easily synthesizes all the known heavy elements. Neutron star mergers are expected to be detected by the Laser Interferometer Gravitational Wave Observatory (LIGO) in the near future, which should either confirm or rule out their proposed association with radioactively powered transients called kilonovae or macronovae that are the observational signatures of r-process nucleosynthesis. To understand how the r-process operates in different astrophysical scenarios and what relative abundance patterns it produces, detailed nuclear reaction network calculations are needed that track thousands of isotopes and tens of thousands of nuclear reactions. In this thesis, I present SkyNet, a new general-purpose nuclear reaction network that can evolve an arbitrary list of nuclear species with an arbitrary set of nuclear reactions. I describe in detail the different physics that is implemented in SkyNet and I perform code tests and comparisons to other nuclear reaction networks. Then I use SkyNet to systematically investigate r-process nucleosynthesis as a function of the initial electron fraction, initial entropy, and expansion timescale of the fluid. Further, I present r-process nucleosynthesis calculations with SkyNet in the dynamical ejecta of a black hole–neutron star merger with varying levels of neutrino irradiation. Finally, I study the r-process in the outflow of a neutron star merger remnant disk as a function of the lifetime of the central hypermassive neutron star (HMNS). SkyNet is easy to use and flexible and it is publicly available as open-source software. Multiple researchers are already using SkyNet for their work, and I hope that SkyNet will be a useful tool for the broader nuclear astrophysics community
The Low-Frequency Frontier: Cosmology with Future 21cm Experiments
Get PDFThis thesis presents theoretical and observational investigations in two areas of cosmology: the detection of inflationary gravitational waves using the circular polarization of the redshifted 21cm line from neutral hydrogen during the Dark Ages, and the study of galactic foregrounds at low-frequencies using the Owens Valley Radio Observatory Long Wavelength Array (OVRO LWA).
In the theoretical part of this thesis, we propose a new method to measure the tensorto-scalar ratio r using the circular polarization of the 21 cm radiation from the Dark Ages. In Chapter II we discuss the basic principles of inflationary physics, which is now accepted as a standard paradigm for the generation of perturbations in the early universe. Along with density (scalar) perturbations, inflation also produces gravitational wave (tensor) modes. In Chapter IV we outline a novel, albeit futuristic method to detect inflationary gravitational waves. Our method relies on the splitting of the F = 1 hyperfine level of neutral hydrogen due to the quadrupole moment of the
CMB during the Dark Ages. We show that unlike the Zeeman effect, where MF = ±1 have opposite energy shifts, the CMB quadrupole shifts MF = ±1 together relative to MF = 0. This splitting leads to a small circular polarization of the emitted 21cm photon, which is in principle observable. Further, we forecast the sensitivity of future radio experiments to measure the CMB quadrupole during the era of first cosmic light (z ~ 20). The tomographic measurement of 21 cm circular polarization allows us to construct a 3D remote quadrupole field. Measuring the B-mode component of this remote quadrupole field can be used to put bounds on the tensor-to-scalar ratio r. We make Fisher forecasts for a future Fast Fourier Transform Telescope (FFTT), consisting of an array of dipole antennas in a compact grid configuration, as a function of array size and observation time. The forecasts are dependent on the evolution of the Lyman-α flux in the pre-reionization era, that remains observationally unconstrained. Finally, we calculate the typical order of magnitudes for circular polarization foregrounds and comment on their mitigation strategies. We conclude that detection of primordial gravitational waves with 21 cm observations is in principle possible, so long as the primordial magnetic field amplitude is small, but would require a very futuristic experiment with corresponding advances in calibration and foreground suppression techniques.
In the observational part of this thesis, we investigate the cross-correlation between low-frequency radio maps from the Owens Valley Radio Observatory Long Wave-length Array (OVRO LWA) and tracers of the ISM: dust, Hα, and HI. Our goal is to search for any anomalous radiative processes at low frequencies (20 − 80 MHz). In Chapter III we discuss the basic principles of 21cm cosmology and provide an overview of current and planned 21cm experiments. Broadband foreground sources pose the greatest challenge to 21cm tomography and need to be characterized carefully before the technique becomes a sensitive probe of the dark ages and the epoch
of reionization. The foregrounds are expected to be predominantly galactic and approximately four orders of magnitude larger than the cosmological signal. In Chapter V, we investigate the nature of the diffuse Galactic radio emission in the 20 − 80MHz frequency range using data from the OVRO-LWA. We cross-correlate LWA maps with tracers of ISM (dust, Hα, HI) from a number of surveys , to investigate galactic foregrounds relevant to detection of 21cm signal from the Dark Ages. We describe a formalism to compute the cross-power spectra between LWA maps and ISM tracers. Our results are consistent with no correlation between tracers of the gas and dust in the ISM at high Galactic latitudes (b > 55°) and low-frequency maps from the LWA, at scales ℓ ~ 10 − 600 at a 99.9% confidence level.</p
A Symphony of Supersymmetry and Geometry: Invariants, Dualities and Chiral Rings
Get PDFThe present dissertation discusses aspects of supersymmetric quantum field theory, whose main themes are two-folded. First, we explore connections between superconformal theories in various dimensions and geometric invariants. Such correspondence arises from compactification of string theory or M-theory, which encodes geometric quantities into physical observables. Second, we study in detail the chiral rings and their quantum corrections in certain supersymmetric gauge theory. The goal is to shed some light on the hitherto mysterious electric-magnetic dualities.
We first consider M5 brane on the product manifold L(k, 1) × M3, where M3 = L(p, 1). Compactification on L(p, 1) gives rise to three dimensional theory T[L(p, 1)] whose partition function, according to 3d-3d correspondence, is equivalent to Chern-Simons invariants with complex gauge group on L(p, 1). We test the statement in Chapter 2 by taking k = 0 and calculating the supersymmetric index. We find a full agreement between two seemingly distinct quantities. In particular, when p = 1, we see the familiar S3 partition function of Chern-Simons theory arises from the index of a free theory.
We then move on in Chapter 3 to consider M3 = S1 × Σ, and twisted compactification on general Riemann surface Σ with tame punctures. The twisted partition function of lens space theory T[L(k, 1)] on S1 × Σ computes the graded dimension of the Hilbert space after geometrically quantizing Hitchin moduli space MH, dubbed as "tame Hitchin characters" or "equivariant Verlinde formula". We show that this quantity can be computed from the "Coulomb branch index" of the class S theory T[Σ] on L(k, 1) × S1. The gauge groups on two sides of the equivalence are naturally G and the Langlands dual group LG. We check explicitly the relation for G = SU(2) or SO(3). We also consider more general case where G is SU(N) or PSU(N) and show that the SU(N) equivariant Verlinde formula can be derived using field theory via (generalized) Argyres-Seiberg duality.
As a further application, in Chapter 4 we use Coulomb branch indices of Argyres-Douglas theories on S1 × L(k, 1) to quantize moduli spaces MH of wild/irregular Hitchin systems. We obtain the "wild Hitchin characters", and observe that the characters can always be written as a sum over fixed points in MH under the U(1) Hitchin action, and a limit of them can be identified with matrix elements of the vii modular transform STkS in certain vertex operator algebras. The appearance of vertex operator algebras, which was known previously to be associated with Schur operators but not Coulomb branch operators, is somewhat surprising.
The BPS spectrum of superconformal theories probe the geometry of Hitchin moduli space. Conversely, physical data of superconformal theories can be read off from Hitchin moduli space as well. We study this dictionary in Chapter 5 for general Argyres-Douglas theories and obtain a refined classification. We also discuss the S-duality of these theories, and find that the weakly coupled descriptions are given by the degeneration limit of auxiliary Riemann sphere with marked points.
Finally, in Chapter 6, we analyze classical and quantum chiral ring relations of four dimensional N = 1 adjoint SQCD with superpotential turned on for the adjoint field. In particular, for the mass deformed theory we obtain the complete on-shell vacuum expectation value for various gauge invariant chiral operators and find non trivial gaugino condensations. We argue that the solution of the chiral ring is in one-to-one correspondence with supersymmetric vacua, provided that an additional Konishi anomaly equation is included.</p
Antiferromagnetic Quantum Phase Transitions: Continuous Tuning and Direct Probes of Competing States
Get PDFAntiferromagnets are choice systems to study quantum critical behavior. Unlike ferromagnets, they can experience continuous quantum phase transitions when tuned by pressure. However, the lack of a net magnetization renders experimental approaches difficult and often indirect. Here I demonstrate that both non-resonant and resonant x-ray magnetic diffraction under pressure provide the highly-desired direct probe for microscopic insights into the disappearance of the magnetic order, as well as the evolution of the charge and structural degrees of freedom. In Mo3Sb7, where spins are itinerant with small magnetic moments, we have discovered the doubling of the superconducting transition temperature under pressure and relate it to a lattice change from tetragonal to cubic structure. In MnP, a spiral magnetic order with tightened pitch was revealed in the high-pressure phase near a superconducting state at ∼7 GPa. As the spiral pitch changes, fluctuations move from antiferromagnetic to ferromagnetic at long and short wavelengths, respectively, thereby potentially pro- moting spin-fluctuation-mediated superconductivity of different symmetries. In the all-in-all-out (AIAO) pyrochlore antiferromagnet Cd2Os2O7, we discovered an anti- ferromagnetic quantum critical point at 35.8 GPa using new techniques for resonant x-ray magnetic diffraction under pressure. The continuous suppression of AIAO antiferromagnetic order to zero temperature is accompanied by inversion symmetry breaking of the lattice, dividing the P − T phase space into three regions of different time reversal and spatial inversion symmetries. While phase lines of opposite curvature indicate a striking departure from a mean-field form at high pressure, the intertwined spin, charge, and phonon fluctuation modes point to a strong-coupled scenario of quantum criticality.</p
Essays on Early-Stage Financing and Firm Behavior
Get PDFThe first chapter of this thesis studies the role of angel finance in the early-stage capital market. Despite anecdotal evidence connecting angel and venture capital (VC) financing, there is little systematic evidence on how the two early-stage capital sources interact. To study this topic, I assemble the first comprehensive dataset on angel financing and characterize its size, scope, and role in the early-stage capital market. I use the population of newly incorporated startups located in California, the largest VC financing state in the United States. Here, the angel capital market is large: approximately 4% of all startups receive angel financing within three years of incorporation. At least five times as many startups receive financing from angels as from VCs in the VC-active industries. Using local individual income as an instrument for angel financing at the zip code level, I show that angels play both supportive and competitive roles in relation to VCs. Angel financing leads to more VC follow-on financing over firms’ life cycles (complement), while it crowds out VC financing from the initial financing round (substitute). My results demonstrate the explicit role of angel financing in the early-stage capital market.
In the second chapter, I develop a game-theoretic model to study information asymmetries in the evolving equity crowdfunding market. I assume (1) there are two types of investors: informed ("insiders") and uninformed ("outsiders"); (2) the insiders invest first; and (3) the outsiders observe the aggregate of insiders' actions and then decide whether to invest. Under these assumptions, I prove that there does not exist a crowdfunding market equilibrium in which the insiders' information is aggregated and high quality startups are funded with higher chances. I then use data from Regulation crowdfunding (Title III equity crowdfunding), and provide evidence that is consistent with the model implications. My results suggest that adverse selection is a primary barrier to equity crowdfunding, and new market designs are required to better develop this market.
The third chapter is joint work with Matt Elliott. We model firms as sets of scarce capabilities, where each capability provides a source of competitive advantage in some markets. Each market is also associated with a set of capabilities that are valued by it. Firm and market hypergraphs represent this information. Our approach provides a new perspective on several industrial organization literatures including merger analysis, strategic alliances and industry dynamics. We argue that merger analysis should be more holistic and that profitable joint ventures increase consumer surplus even when they reduce competition. We also provide formal foundations for a prominent theory of competitive advantage in the management literature.</p
Modeling of Nucleation and Dynamic Rupture on Heterogeneous Frictional Interfaces with Applications to Foreshocks
Get PDFWhile many large earthquakes are preceded by observable foreshocks, the mechanisms responsible for the occurrence of these smaller-scale seismic events remain uncertain. One physical explanation of foreshocks with growing support is that they are produced by the interaction of slow slip, due to the nucleation of the upcoming mainshock, with fault patches of different properties. Having a better understanding of how earthquakes nucleate on heterogeneous faults would increase our capacity to forecast potentially hazardous events.
With this motivation in mind, we seek to understand what conditions produce isolated microseismicity within the nucleating region of the mainshock and to study the mechanics of the resulting events. Inspired by the suggestion from laboratory experiments that foreshocks occur on asperities, i.e., local deviations from planarity that are flattened by the overall compression, we explore the behavior of asperity-type patches of higher compressive stress embedded in the larger seismogenic region of a rate-and-state fault model by conducting 3D numerical simulations of their slip over long-term sequences of aseismic and seismic slip. Our models do produce smaller-scale seismicity during the aseismic nucleation of much larger seismic events, and we explore their properties as well as the separation in length scales needed to produce them. These foreshock-like events have stress drops that are consistent with laboratory and field observations and approximately constant, despite the highly elevated compression assigned to the source patches. Two main factors contributing to the reasonable stress drops are the significant extent of the rupture into the region surrounding the patch and the aseismic stress release just prior to the seismic event.
We also investigate the seismologically-derived properties of the asperity-type events using the spectral analysis commonly applied to natural microseismic events. We find that the seismological methods cannot adequately capture the properties of the simulated events. In part, the seismological estimates of their stress drops are significantly different from the actual stress drops determined from the on-fault stress changes. This is because our sources have more complex features than the standard models from which the current seismological methods have been built, including heterogeneous stress change over the rupture area with much larger initial stress change, and heterogeneous rupture speed. We identify features in the far-field seismograms of the asperity-type sources that differ from the standard models and can be potentially characteristic of the asperity-type sources.
Our asperity-type models of microseismicity sources provide insight into the conditions conducive for generating foreshocks on both natural and laboratory faults and the properties of the resulting events. The conclusions provided jointly by the two perspectives in this study -- dynamically simulating the behavior of seismic sources within heterogeneous fault models and seismologically analyzing their far-field source spectra -- have important implications that warrant further study. Topics for future research include the interaction among smaller-scale seismic events and their role in the mainshock nucleation process, the effect of timing on their source properties, and relation to the so-called seismic nucleation phase of the subsequent mainshock.
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Sparse Array Signal Processing: New Array Geometries, Parameter Estimation, and Theoretical Analysis
Get PDFArray signal processing focuses on an array of sensors receiving the incoming waveforms in the environment, from which source information, such as directions of arrival (DOA), signal power, amplitude, polarization, and velocity, can be estimated. This topic finds ubiquitous applications in radar, astronomy, tomography, imaging, and communications. In these applications, sparse arrays have recently attracted considerable attention, since they are capable of resolving O(N2) uncorrelated source directions with N physical sensors. This is unlike the uniform linear arrays (ULA), which identify at most N-1 uncorrelated sources with N sensors. These sparse arrays include minimum redundancy arrays (MRA), nested arrays, and coprime arrays. All these arrays have an O(N2)-long central ULA segment in the difference coarray, which is defined as the set of differences between sensor locations. This O(N2) property makes it possible to resolve O(N2) uncorrelated sources, using only N physical sensors.
The main contribution of this thesis is to provide a new direction for array geometry and performance analysis of sparse arrays in the presence of nonidealities. The first part of this thesis focuses on designing novel array geometries that are robust to effects of mutual coupling. It is known that, mutual coupling between sensors has an adverse effect on the estimation of DOA. While there are methods to counteract this through appropriate modeling and calibration, they are usually computationally expensive, and sensitive to model mismatch. On the other hand, sparse arrays, such as MRA, nested arrays, and coprime arrays, have reduced mutual coupling compared to ULA, but all of these have their own disadvantages. This thesis introduces a new array called the super nested array, which has many of the good properties of the nested array, and at the same time achieves reduced mutual coupling. Many theoretical properties are proved and simulations are included to demonstrate the superior performance of super nested arrays in the presence of mutual coupling.
Two-dimensional planar sparse arrays with large difference coarrays have also been known for a long time. These include billboard arrays, open box arrays (OBA), and 2D nested arrays. However, all of them have considerable mutual coupling. This thesis proposes new planar sparse arrays with the same large difference coarrays as the OBA, but with reduced mutual coupling. The new arrays include half open box arrays (HOBA), half open box arrays with two layers (HOBA-2), and hourglass arrays. Among these, simulations show that hourglass arrays have the best estimation performance in presence of mutual coupling.
The second part of this thesis analyzes the performance of sparse arrays from a theoretical perspective. We first study the Cramér-Rao bound (CRB) for sparse arrays, which poses a lower bound on the variances of unbiased DOA estimators. While there exist landmark papers on the study of the CRB in the context of array processing, the closed-form expressions available in the literature are not applicable in the context of sparse arrays for which the number of identifiable sources exceeds the number of sensors. This thesis derives a new expression for the CRB to fill this gap. Based on the proposed CRB expression, it is possible to prove the previously known experimental observation that, when there are more sources than sensors, the CRB stagnates to a constant value as the SNR tends to infinity. It is also possible to precisely specify the relation between the number of sensors and the number of uncorrelated sources such that these sources could be resolved.
Recently, it has been shown that correlation subspaces, which reveal the structure of the covariance matrix, help to improve some existing DOA estimators. However, the bases, the dimension, and other theoretical properties of correlation subspaces remain to be investigated. This thesis proposes generalized correlation subspaces in one and multiple dimensions. This leads to new insights into correlation subspaces and DOA estimation with prior knowledge. First, it is shown that the bases and the dimension of correlation subspaces are fundamentally related to difference coarrays, which were previously found to be important in the study of sparse arrays. Furthermore, generalized correlation subspaces can handle certain forms of prior knowledge about source directions. These results allow one to derive a broad class of DOA estimators with improved performance.
It is empirically known that the coarray structure is susceptible to sensor failures, and the reliability of sparse arrays remains a significant but challenging topic for investigation. This thesis advances a general theory for quantifying such robustness, by studying the effect of sensor failure on the difference coarray. We first present the (k-)essentialness property, which characterizes the combinations of the faulty sensors that shrink the difference coarray. Based on this, the notion of (k-)fragility is proposed to quantify the reliability of sparse arrays with faulty sensors, along with comprehensive studies of their properties. These novel concepts provide quite a few insights into the interplay between the array geometry and its robustness. For instance, for the same number of sensors, it can be proved that ULA is more robust than the coprime array, and the coprime array is more robust than the nested array. Rigorous development of these ideas leads to expressions for the probability of coarray failure, as a function of the probability of sensor failure.
The thesis concludes with some remarks on future directions and open problems.</p
Design and Characterization of Dual-Matrix Composite Deployable Space Structures
Get PDFDual-matrix composites are a promising approach to deployable high performance antennas for small satellites. Several techniques exist for packaging large antenna apertures. Assemblies of rigid bars and hinges obtain high deployed precision but are heavy and mechanically complex. Thin shell structures deployed using stored strain energy are a lightweight alternative offering efficient packaging but reduced surface precision. Moreover, elastomer composites shells attain even smaller fold radii upon packaging but are limited by the deployed structure's stiffness. Dual-matrix composites combine the advantages of several of these approaches to enable larger antenna apertures. They consist of a continuous woven fiber reinforcement with an elastomer matrix embedded in localized hinge regions and a stiff epoxy resin elsewhere. Such structures can achieve small fold radii, are strain energy deployable, and promise high deployed stiffness.
This research demonstrates the capabilities of the proposed dual-matrix structures through direct comparison to existing antenna designs. Analytic scaling relations between structural and electromagnetic performance of various deployable antenna designs are developed. These are used to rapidly predict achievable antenna performance as a function of a common set of antenna geometric parameters. Plotting of this data on a coordinated set of 2D design plots enables the direct comparison of antenna concepts and the selection of specific designs meeting all requirements. This methodology was used to design a deployable dual-matrix composite conical log spiral (CLS) antenna for use on CubeSats which outperformed existing off-the-shelf designs through higher gain, higher bandwidth, and more efficient packaging.
Starting from this initial design, the antenna is tuned to maximize performance and an assembly including the CubeSat, dual-matrix antenna, dual-matrix hinge for antenna deployment, and a flexible feeding network is developed. All portions of the assembly are prototyped and tested. The antenna electromagnetic performance is predicted using ANSYS HFSS and verified by testing in an anaechoic chamber with antenna gains predicted within 4% of measured values. Structural stiffness is characterized through the antenna's fundamental frequency with simulated performance in the Abaqus finite element software within 6% of measured values. Comparison of antenna performance before and after packaging and deployment shows the structural frequency, antenna gain, and antenna bandwidth are unaffected by folding, demonstrating that dual-matrix composites are appropriate for use as deployable structures.
Techniques for the quasi-static deployment of dual-matrix composites are presented. An analytic minimum energy method, which accounts for fiber microbuckling in regions of high curvature, is used to predict the folded shape and deployment moments of a dual-matrix hinge. The model shows excellent agreement with LS-Dyna finite element simulations for a variety of material properties. Comparison with experimental characterization demonstrates the capability of the models to predict folded radii and deployment moment of a prototype hinge withing 5% of measured values. The developed analysis tool-set enables a design of deployment restraints and mechanisms.
The woven elastomer composites forming the fold regions in dual-matrix composites have been the subject of very few studies. Existing methods for predicting the stiffness of woven epoxy composites are applied to elastomer composites here and show poor agreement with measurements. A novel approach is presented for the prediction of tow stiffness in elastomer composites using a semi-empirical approach. The reinforcing efficiency parameter in the well-established Halpin-Tsai model for tow homogenization is estimated using experimental measurements of stiffnesses of several laminates. It is shown that for elastomer composites, the parameter values are orders of magnitude higher than the heuristic values used for epoxy composites. The method is used to predict the stiffness of woven epoxy and elastomer composites making up the dual-matrix structures studied in this work showing agreement withing 15% of experimental measurements for arbitrary layups. The method is extended to the prediction of viscoelastic behavior of dual-matrix structures to enable investigation of deployment reliability after long storage times.</p