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Probing the Trojan-Hilda-KBO Connection: An Empirical Test of Dynamical Instability Models of Solar System Evolution
Get PDFIn recent decades, the paradigm of solar system formation has undergone radical change. Many current models posit that a significant reorganization of the outer Solar System occurred after the end of planet formation. Specifically, it is hypothesized that Jupiter and Saturn crossed a mutual mean motion resonance, leading to a chaotic expansion of the ice giants' orbits that disrupted the large population of planetesimals situated further out. While the majority of these bodies were ejected from the Solar System, a fraction of them were retained as the present-day Kuiper Belt, while others were scattered inward and captured into resonances with Jupiter to become the Trojans and Hildas. These dynamical instability models invariably predict that the Trojans, Hildas, and Kuiper Belt objects (KBOs) were sourced from the same primordial body of outer solar system planetesimals. Therefore, a comparative exploration of these minor body populations serves as one of the definitive observational tests of our present understanding of solar system evolution. Over the past four-and-a-half years, I have carried out a diverse series of systematic studies aimed at synthesizing a detailed picture of Trojan, Hildas, and KBOs. By combining novel analyses of archival data with new photometric surveys, I have derived the first debiased color distributions of Trojans and KBOs and expanded our knowledge of their respective size distributions. In addition, I have explored the peculiar color bimodality attested in the all three asteroid populations, which indicates the presence of two sub-populations. Utilizing the full body of observations, I have formulated the first self-consistent hypothesis outlining the formation, composition, and dynamical/chemical evolution of the primordial outer solar system planetesimals, with special attention given to explaining the color bimodality, size distribution shapes, and collisional families. My results lay the groundwork for future studies with next-generation instruments and ultimately, the Trojan flyby mission Lucy.</p
The Fully Nonlocal, Finite-Temperature, Adaptive 3D Quasicontinuum Method for Bridging Across Scales
Get PDFComputational modeling of metallic materials across various length and time scales has been on the rise since the advent of efficient, fast computing machines. From atomistic methods like molecular statics and dynamics at the nanoscale to continuum mechanics modeled by finite element methods at the macroscale, various techniques have been established that describe and predict the mechanics of materials. Many recent technologies, however, fall into a gap between length scales (referred to as mesoscales), with microstructural features on the order of nanometers (thereby requiring full atomistic resolution) but large representative volumes on the order of micrometers (beyond the scope of molecular dynamics). There is an urgent need to predict material behavior using scale-bridging techniques that build up from the atomic level and reach larger length and time scales. To this end, there is extensive ongoing research in building hierarchical and concurrent scale-bridging techniques to master the gap between atomistics and the continuum, but robust, adaptive schemes with finite-temperature modeling at realistic length and time scales are still missing.
In this thesis, we use the quasicontinuum (QC) method, a concurrent scale-bridging technique that extends atomistic accuracy to significantly larger length scales by reducing the full atomic ensemble to a small set of representative atoms, and using interpolation to recover the motion of all lattice sites where full atomistic resolution is not necessary. We develop automatic model adaptivity by adding mesh refinement and adaptive neighborhood updates to the new fully nonlocal energy-based 3D QC framework, which allows for automatic resolution to full atomistics around regions of interest such as nanovoids and moving lattice defects. By comparison to molecular dynamics (MD), we show that these additions allow for a successful and computationally efficient coarse graining of atomistic ensembles while maintaining the same atomistic accuracy.
We further extend the fully nonlocal QC formulation to finite temperature (termed hotQC) using the principle of maximum entropy in statistical mechanics and averaging the thermal motion of atoms to obtain a temperature-dependent free energy using numerical quadrature. This hotQC formulation implements recently developed optimal summation rules and successfully captures temperature-dependent elastic constants and thermal expansion. We report for the first time the influence of temperature on force artifacts and conclude that our novel finite-temperature adaptive nonlocal QC shows minimal force artifacts and outperforms existing formulations. We also highlight the influence of quadrature in phase space on simulation outcomes.
We study 3D grain boundaries in the nonlocal hotQC framework (previously limited to single-crystals) by modeling coarse-grained symmetric-tilt grain boundaries in coincidence site lattice (CSL) based bicrystals. We predict relaxed energy states of various Σ-boundaries with reasonable accuracy by comparing grain boundary energies to MD simulations and outline a framework to model polycrystalline materials that surpasses both spatial and temporal limitations of traditional MD.</p
The Kapustin-Witten Equations with Singular Boundary Conditions
Get PDFWitten proposed a fasinating program interpreting the Jones polynomial of knots on a 3-manifold by counting solutions to the Kapustin-Witten equations with singular boundary conditions.
In Chapter 1, we establish a gluing construction for the Nahm pole solutions to the Kapustin-Witten equations over manifolds with boundaries and cylindrical ends. Given two Nahm pole solutions with some convergence assumptions on the cylindrical ends, we prove that there exists an obstruction class for gluing the two solutions together along the cylindrical end. In addition, we establish a local Kuranishi model for this gluing picture. As an application, we show that over any compact four-manifold with S3 or T3 boundary, there exists a Nahm pole solution to the obstruction perturbed Kapustin-Witten equations. This is also the case for a four-manifold with hyperbolic boundary under some topological assumptions.
In Chapter 2, we find a system of non-linear ODEs that gives rotationally invariant solutions to the Kapustin-Witten equations in 4-dimensional Euclidean space. We explicitly solve these ODEs in some special cases and find decaying rational solutions, which provide solutions to the Kapustin-Witten equations. The imaginary parts of the solutions are singular. By rescaling, we find some limit behavior for these singular solutions. In addition, for any integer k, we can construct a 5|k| dimensional family of C1 solutions to the Kapustin-Witten equations on Euclidean space, again with singular imaginary parts. Moreover, we get solutions to the Kapustin-Witten equation with Nahm pole boundary condition over S3 × (0, +∞).
In Chapter 3, we develop a Kobayashi-Hitchin type correspondence for the extended Bogomolny equations on Σ× with Nahm pole singularity at Σ × {0} and the Hitchin component of the stable SL(2, ℝ) Higgs bundle; this verifies a conjecture of Gaiotto and Witten. We also develop a partial Kobayashi-Hitchin correspondence for solutions with a knot singularity in this program, corresponding to the non-Hitchin components in the moduli space of stable SL(2, ℝ) Higgs bundles. We also prove the existence and uniqueness of solutions with knot singularities on ℂ × ℝ+. This is joint a work with Rafe Mazzeo.
In Chapter 4, for a 3-manifold Y, we study the expansions of the Nahm pole solutions to the Kapustin-Witten equations over Y × (0, +∞). Let y be the coordinate of (0, +∞) and assume the solution convergence to a flat connection at y → ∞, we prove the sub-leading terms of the Nahm pole solution is C1 to the boundary at y → 0 if and only if Y is an Einstein 3-manifold. For Y non-Einstein, the sub-leading terms of the Nahm pole solutions behave as y log y to the boundary. This is a joint work with Victor Mikhaylov.</p
Laboratory Studies of Granular Materials Under Shear: From Avalanches to Force Chains
Get PDFGranular materials reveal their complexity and some of their unique features when subjected to shear deformation. They can dilate, behave like a solid or a fluid, and are known to carry external forces preferentially as force chains. In this dissertation, we employ laboratory experiments to study the complex behavior of granular materials under shear. We introduce a multiscale approach in which the underlying grain-scale mechanics are experimentally measured and homogenized to obtain enriched macroscopic quantities. First, we investigate granular avalanches spontaneously generated by a rotating drum. Measurements of grain kinematics are directly incorporated into a rate-dependent plasticity model that explains and reproduces the life cycle of laboratory avalanches. The results presented here feature dilatancy as the key material parameter governing the triggering of an avalanche. Second, we report a set of experiments performed on a custom-built mechanical device that allows a specimen composed of a two-dimensional analogue granular assembly to be subjected to quasi-static shear conditions. A numerical force inference technique, the Granular Element Method (GEM), provides direct observation and quantitative characterization of force chain structures in assemblies made of realistic grains. Equipped with a complete description of the grain-scale mechanics, we show that shear deformation creates geometrical (fabric) and mechanical (force) anisotropy. Finally, the influence of grain shape on grain-scale processes is studied. We find that grain interlocking is a prominent deformation mechanism for non-circular grains that ultimately promotes a significant increase in macroscopic shear strength. By seamlessly connecting grain-scale information to continuum scale experiments, this dissertation sheds light on the multiscale mechanical behavior of granular assemblies under shear.</p
Scanning Electrical Mobility Methods for Aerosol Characterization
Get PDFThe scanning electrical mobility measurement is the most common tool used to characterize the size distribution of fine particles in the atmosphere. This thesis develops the methods for retrieving the particle size distribution from scanning electrical mobility measurement data for two systems: (1) the scanning electrical mobility spectrometer (SEMS; also known as the scanning mobility particle sizer, SMPS), which measures particle size distribution ranging from 15 - 1000 nm; (2) the scanning radial opposed migration ion and aerosol classifier (ROMIAC) system, which uses a two-stage condensation particle counter as particle detector to complete the 1 - 20 nm particle size distribution measurements.
SEMS / SMPS data have traditionally been inverted to determine the particle size distribution by solving a Fredholm integral equation in which the kernel function is based upon constant-voltage operation of the mobility classifier. The viscous boundary layer within the classifier renders that model invalid. This thesis determines, for the first time, the transfer function for a real differential mobility analyzer (DMA) that is operated in the scanning mode. The flow and electric fields within the instrument were obtained by finite element simulations taking into account its detailed geometry. Brownian dynamics simulations were then used to simulate diffusive particle trajectories within the instrument as the voltage was scanned. There results were coupled with empirically-derived response-time functions for the condensation particle counter that serves as a detector in the SEMS / SMPS to obtain integrated system transfer function that substantially improve the fidelity of the SEMS / SMPS data inversion.
This approach was also applied to adaptation of the radial opposed migration ion/aerosol classifier (ROMIAC) for scanning-mode operation. The transfer function obtained through simulation of the scanning ROMIAC was used in the experimental validation of this new measurement method. This new instrument was then used to measure wall loss rates for 1.6 nm to 20 nm particles in the Caltech environmental chamber.</p
Synthesis, NMR Solution Structure, and Neuritogenic Activity of Chondroitin Sulfate D and E
Get PDFChondroitin sulfate are ubiquitously expressed linear, sulfated polysaccharides that play critical roles in neuronal development and regeneration growth factor signaling, morphogenesis, and virus invasion. The diverse sulfation patterns presented by chondroitin sulfate has been suggested to regulate its activity, but the structural complexity and heterogeneity have hampered the understanding of structure-activity relationship. Therefore, we envisioned that chemically synthesized chondroitin sulfate oligosaccharide may provide a unique opportunity to specifically study the functions of sulfation patterns.
Here, we report the synthesis of a CS-D and CS-E tetrasaccharide in a step-efficient manner. By generating a disaccharide precursor from hydrolysis of polysaccharides, we were able to streamline the synthesis and reduce the number of steps by one-third comparing to the traditional synthesis without losing versatility of the synthetic route and functionality of the final product. With the structurally defined molecules, we were able to determine the NMR solution structure of CS-D and CS-E. In this work, we accomplished the first structural study of CS-D tetrasaccharide and the most thorough study of CS-E to date. Furthermore, we also discovered the existence of a second conformer in CS-D, which is the first time for such behavior to be observed experimentally in chondroitin sulfate. The electrostatic potential surface constructed based on the NMR structure presented unique structural features that may allow proteins to interact specifically.
The CS-D and CS-E tetrasaccharide, along with a CS-D disaccharide, was
investigated for their neuritogenic activity. We discovered that the CS-D tetrasaccharide specifically stimulates dendritic growth whereas the CS-E tetrasaccharide preferentially promoted axonal growth, revealing the potential critical role chondroitin sulfate with specific sulfation patterns may play in the nervous system. The lack of activity of the CS-D disaccharide suggested that the minimum motif required for activity of CS-D is a tetrasaccharide.</p
High-throughput Characterization of Solid Oxide Fuel Cell Cathode Materials
Get PDFSolid oxide fuel cells are electrochemical devices which convert chemical energy directly to electricity. The extreme environments in which these devices operate require the use of expensive components to withstand degradation. To lower operating temperatures and therefore cost, materials discovery efforts have targeted new electrodes with high ionic and electronic conductivity, but these studies often convolute electrode morphology and performance, masking the inherent activity of electrode materials. In this work, a high-throughput experimental technique utilizing a robotic scanning impedance probe is applied to materials libraries to rigorously compare the performance of electrode materials and characterize fundamental electrode properties.
Two cathode materials libraries are studied in-depth: the perovskite material La1-xSrxCo1-yFeyO3-δ (LSCF) and the double perovskite material PrBa0.5Sr0.5Co2-xFexO5+δ (PBSCF). Each materials library is investigated through the entire regime of cobalt and iron doping and results are obtained on both oxide-ion- and proton-conducting electrolyte materials. For LSCF, a four-fold increase in electrochemical resistance is observed from the cobalt-dominant endmember LSC64 to the iron-dominant endmember LSF64 on an oxygen-ion conducting substrate, concurrent with a decrease in chemical capacitance indicating lower oxygen vacancy concentration. For PBSCF, proton conductivity is observed through the bulk of the film, leading to its use in a real proton-conducting ceramic fuel cell that demonstrates exceptional performance at low temperatures (> 500mW/cm2 at 500°C) while remaining stable over hundreds of hours of testing. These results demonstrate the power and robustness of this high-throughput approach in characterizing both well-known and novel materials, and show great promise for future targeted searches of high-performance materials.</p
Engineering Molecular Self-assembly and Reconfiguration in DNA Nanostructures
Get PDFSmart electronics have developed ubiquitously to assist people in everything from navigation to health monitoring. The rise of complex electronics relied on rational design of platforms to build ever larger and more complex circuit networks and for frameworks to test those electronics. Biochemical circuits have also seen dramatic advancement in the last two decades within the field of DNA nanotechnology. As with electronics, DNA nanotechnology applied rational design to DNA molecules to build ever more complex biochemical networks that, beyond current electronics, also retain a significant measure of biological compatibility and plasticity akin to many networks of biological origin. Well situated for promising applications in diagnostics and therapeutics, advancing DNA nanotechnology devices will also rely upon larger platforms and testing frameworks.
In roughly the last decade, researchers have been building upon the invention of DNA origami, a technique allowing the robust construction of biomolecular nano-structures capable of precise nanometer positioning of proteins, nanoparticles, and other molecules. DNA circuits have computed on the nanostructures; DNA robots have moved nanoparticles, made choices, and have even sorted cargo on the surface of a nanostructure. The complexity of circuits and devices continues to rise.
In this thesis, we will discuss our contributions to the field of DNA nanotechnology by developing design rules and systematic approaches to controlling nanostructure complex assembly. These rules and approaches allow for the construction of molecular structures with a tunable diversity, large systems approaching the size of bacteria yet retaining nanometer precision, and biological plasticity inspired dynamic systems for arbitrary reconfiguration.
Using a DNA origami tile tailored for array formation with a high continuous surface area, we create a framework inspired from molecular stochasticity for programming DNA array formation and gaining control over diversity of global properties through simple local rules. Three general forms of planar networks, random loops, mazes, and trees, were manipulated on the micron scale upon the self-assembled DNA arrays. We demonstrate control of several properties of the networks, such as branching rules, growth directions, the proximity between adjacent networks, and size distributions. The large diversity, in principle, allows for a wide, but tunable, testing environment for molecular circuits. By further applying these principles to subunits of finite assemblies, variable components may be mixed with fixed components potentially opening additional applications in high throughput device or drug screening.
Next we turned to expanding the platform size biochemical circuits may be built upon. While DNA origami allows nanometer precise placement, the size remains roughly below 0.05 um2. Toward making large arbitrarily complex structures with only a set of simple tiles, multi-stage self-assembly has been explored in theory and for small DNA tiles. None were successful experimentally with DNA origami. We developed a strategy for DNA origami: a simple rule set applied recursively in each stage of a hierarchical self-assembly process, and to significantly reduce costs, a constant set of unique DNA strands regardless of size. We also developed a software tool to automatically compile a designed surface pattern into experimental protocols. We experimentally demonstrated DNA origami arrays approaching the size of small bacteria, 0.5 um2, with several arbitrary patterns, each consisting of 8,704 specifically chosen pixel locations with nanometer precision, including a bacteria sized portrait of a bacteria. The large platform opens the door to more advanced molecular circuits for applications such as diagnostics.
Finally we demonstrated control over the dynamics of DNA origami reconfiguration in tile arrays. In an approach we call DNA tile displacement, we showed that a DNA origami array may have tiles arbitrarily replaced by another tile, including tiles of another shape or surface pattern. We also demonstrated control over the kinetics of tile displacement and performed several general purpose reconfigurations of DNA nanostructures. Examples include sequential reconfiguration, competitive reconfiguration, cooperative reconfiguration, and finally the scalability of multi-step reconfiguration as demonstrated through a fully playable nano-scale biomolecular tic-tac-toe game. The major ramifications are a plasticity more common to biology than to electronics—molecular platforms with arbitrary patterning that can reconfigure an arbitrary part of the nanostructure in an arbitrary order based on environmental signals. In principle, such reconfiguration can allow advanced circuits with the capacity to adapt to environmental needs or heal damaged components.</p
Essays in Market Design
Get PDFThis thesis investigates the impact of incomplete information and behavioral biases in the context of market design.
In chapter 2, I analyze centralized matching markets and rationalize why the arguably most heavily used mechanism in applications, the deferred acceptance mechanism, has been so successful in practice, despite the fact that it provides participants with opportunities to “game the system.” Accounting for the lack of information that participants typically have in these markets in practice, I introduce a new notion of behavior under uncertainty that captures participants’ aversion to experience regret. I show that participants optimally choose not to manipulate the deferred acceptance mechanism in order to avoid regret. Moreover, the deferred acceptance mechanism is the unique mechanism within an interesting class (quantile stable) to induce honesty from participants in this way.
In chapter 3, co-authored with Leeat Yariv, we study the impacts of incomplete information on centralized one-to-one matching markets. We focus on the commonly used deferred acceptance mechanism (Gale and Shapley, 1962). We characterize settings in which many of the results known when information is complete are overturned. In particular, small (complete-information) cores may still be associated with multiple outcomes and incentives to misreport, selection of equilibria can affect the set of individuals who are unmatched—i.e., there is no analogue for the Rural Hospital Theorem, and agents might prefer to be on the receiving side of the of the algorithm underlying the mechanism. Nonetheless, when either side of the market has assortative preferences, incomplete information does not hinder stability, and results from the complete-information setting carry through.
In chapter 4, co-authored with Tatiana Mayskaya, we present a dynamic model that illustrates three forces that shape the effect of overconfidence (overprecision of consumed information) on the amount of collected information. The first force comes from overestimating the precision of the next consumed piece of information. The second force is related to overestimating the precision of already collected information. The third force reflects the discrepancy between how much information the agent expects to collect and how much information he actually collects in expectation. The first force pushes an overconfident agent to collect more information, while the second and the third forces work in the other direction. We show that under some symmetry conditions, the second and third force unequivocally dominate the first, leading to underinvestment in information.</p
Achieving High Stereoselectivity in Ruthenium-Catalyzed Olefin Metathesis Reactions for Organic and Polymer Synthesis
Get PDFTransition metal-catalyzed olefin metathesis has emerged as a powerful tool for constructing C−C double bonds. This thesis delineates the development of Ru-based catalysts for the stereoselective formation of olefins and mechanistic studies used to examine how catalyst structure influences selectivity and activity.
Chapter 2 details the synthesis of Z-selective, cyclometalated catalysts bearing nitrite X-ligands. The activity and selectivity of these catalysts were examined in an array of ring-opening metathesis polymerization and cross metathesis reactions. Comparison of these catalysts with their nitrate-bound analogues is described.
Chapter 3 describes the examination of several Z-selective, cyclometalated catalysts in ring-opening metathesis polymerizations. The polymerizations of a variety of norbornene and norbornene derivatives were examined to determine the tacticity and microstructure of the resulting polymer. Computational studies were used to examine the mechanism of the polymerization reactions.
Chapter 4 examines the decomposition of Fischer carbene complexes derived from cyclometalated catalysts. In-depth NMR studies are used to determine the identity of the decomposition product, and the decomposition pathway is examined through computational studies.
Chapter 5 describes the first example of highly E-selective cross metathesis through kinetic control using stereoretentive, Ru-based catalysts bearing dithiolate catalysts. The preparation of additional stereoretentive catalysts is described for increasing catalyst activity while maintaining or increasing selectivity. A model for the observed stereoselectivity is proposed.
Chapter 6 delineates the preparation of a series of fast initiating, stereoretentive catalysts. These catalysts are assessed in an array of cross metathesis reactions, and significantly enhanced activity is observed in E-selective reactions. The examination of the relationships between the structure of a catalyst and its selectivity and activity is described.
Chapter 7 examines the use of stereoretentive catalysts in the synthesis of Z-macrocycles from diene starting materials bearing a Z-olefin and a terminal olefin. Initiation rate studies are conducted to examine the activity of these catalysts compared to previously reported cyclometallated catalysts used in this ring-closing metathesis reaction. The synthesis of twelve- to seventeen-membered rings with high Z-selectivity is described.
Chapter 8 explores the use of fast-initiating, stereoretentive catalysts for synthesizing E-macrocycles. The preparation of diene starting materials containing two E-olefins is described. Using these catalysts, twelve- to eighteen-membered rings are constructed with high E-selectivity. </p