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Clouds and Hazes in Planetary Atmospheres
Get PDFClouds and hazes are found in every significant planetary atmosphere in the Solar System, from the sulfuric acid clouds of Venus and the water clouds of Earth and Mars, to the photochemical hazes that pervade the giant planets, ice giants, Titan, and even Pluto. Beyond the Solar System, transmission spectroscopy of exoplanets have found that many are also bound in clouds and hazes, though their higher temperatures give rise to clouds of salts, rocks, and metals, and hazes of soots and sulfurs. Understanding the behavior and role of clouds and hazes in planetary atmospheres is instrumental in understanding atmospheres as a whole, as they are strongly coupled to other atmospheric processes. For example, highly reflective clouds can reduce the effective temperature of a planet, while UV absorbing hazes can increase local atmospheric temperatures. Clouds and hazes also act as reservoirs for important trace species and can be crucial to atmospheric chemical cycles.
In this Ph.D thesis, I use modeling and comparisons to observations to understand cloud and haze processes on multiple worlds within and beyond the Solar System. I use the Community Aerosol and Radiation Model for Atmospheres (CARMA) to simulate the sulfuric acid clouds of Venus in an attempt to find the cause of the spatial and temporal variability in the Venus upper haze, as observed by Venus Express. I show that the variability is likely caused by sustained updrafts lofting large cloud particles into the haze. I then modify CARMA to include fractal aggregate particles to investigate the properties of the photochemical haze on Pluto as observed by New Horizons, and find that the haze particles must be porous, and that they may act as nucleation cites for simple hydrocarbons. Finally, I add exotic condensates to CARMA to model clouds on exoplanets, where their existence has led to difficulties in finding the atmospheric compositions of these worlds. I show that not all species that can condense will, due to their material properties, and that the cloud optical depth is largely controlled by the rate of particle production via homogeneous nucleation. In addition, I investigate the effect a sulfur haze would have on the reflected light spectrum of giant exoplanets to prepare for upcoming direct imaging missions, and find that sulfur hazes significantly brighten these planets at long wavelengths, while darkening them at short wavelengths due to UV absorption. Finally, I retrieve the properties of water ice particles from Cassini observations of the plumes of Enceladus assuming that they are aggregates rather than spheres, and thereby unifying forward scattering observations with in situ measurements. </p
Quasiparabolic Subgroups of Coxeter Groups and Their Hecke Algebra Module Structures
Get PDFIt is well known that the R-polynomial can be defined for the Hecke algebra of Coxeter groups, and the Kazhdan-Lusztig theory can be developed to understand the representations of Hecke algebra. There is also a generalization for the existence of R-polynomial and Kazhdan-Lusztig theory for the Hecke algebra module of standard parabolic subgroups of Coxeter groups. In recent work of Rains and Vazirani, a generalization of standard parabolic subgroups, called quasiparabolic subgroups, are introduced, and the corresponding Hecke algebra module is well-defined. However, the existence of the analogous involution (Kazhdan-Lusztig bar operator) on the Hecke algebra module of quasiparabolic subgroups is unknown in general. Assuming the existence of the bar-operator, the corresponding R-polynomials and Kazhdan-Lusztig polynomials can be constructed. We prove the existence of the bar operator for the corresponding Hecke algebra modules of quasiparabolic subgroups in finite classical Coxeter groups with a case-by-case verification (Chapter 4). As preparation, we classify all quasiparabolic subgroups of finite classical Coxeter groups. The approach is to first find all rotation subgroups of finite classical Coxeter groups (Chapter 2). Then we exclude the non-quasiparabolic subgroups and confirm the quasiparabolic subgroups (Chapter 3)
Earthquake Source Characterization Through Seismic Observations and Numerical Modeling
Get PDFIn this thesis, I present a series of works on the characterization of source properties and physical mechanisms of various small to moderate earthquakes through both observational and numerical approaches. From the results, we find implications on a broader scheme of topics relating to larger earthquakes, shear zone structure, frictional properties of faults, and seismic hazard assessment.
Part I consists of two studies using waveform modeling. In Chapter 2, we present an in-depth study of a series of intraslab earthquakes that occurred in a localized region near the downdip edge of the 2011 Mw Tohoku-Oki megathrust earthquake. By refining source parameters of selected events, simulating their rupture properties and comparing their mechanisms to stress changes caused by the main shock in the region, we are able to identify the true rupture plane and the reactivation of a subducted normal fault, enhancing our understanding on the downdip shear zone. In Chapter 3, based on similar techniques, we further develop a systematic methodology to perform fast assessments on important source properties as an earthquake occurs. For two Mw 4.4 earthquakes in Fontana, moment magnitude and focal mechanism can be accurately estimated with 3 to 6 s after the first P-wave arrival, while focal depth can be constrained upon the arrival of S waves. Rupture directivity can also be determined with as little as 3 seconds of P waves. This study opens the opportunity to predict ground motions ahead of time and can potentially be useful for Earthquake Early Warning.
Part II involves the modeling of seismic source properties and physical mechanisms of interacting earthquakes in dynamic rupture simulations. In particular, we focus on small repeating earthquake sequences that trigger one another. In Chapter 4, we quantify the relative importance of physical mechanisms that contribute to earthquake interaction and identify that the stress change caused by post seismic slip is the dominating factor. Our findings introduce the possibility to constrain frictional properties of the fault based on earthquake interactions. We further apply this working model in Chapter 5 to reproduce the actual interacting repeating sequences in Parkfield. We are able to identify possible physical mechanisms that cause the inferred high stress drops of these repeating events, as well as reproduce their synchronized seismic cycles. Results from our simulations are consistent with the observed scaling relation between the recurrence time interval and the seismic moment of these events. Our findings indicate that the difference between the observed and the theoretical scaling relations can be explained by the significant aseismic slip in the rupture area.</p
First-Principles-Based Simulations for G Protein-Coupled Receptor Activation and for Large-Scale Nonadiabatic Electron Dynamics
Get PDFThis thesis focuses on simulating large molecular systems within and beyond the Born-Oppenheimer framework from first principles. Two approaches have been developed for very different but important applications.
The first one is a hybrid method based on classical force fields that predicts the high-energy ensemble of three-dimensional structures of a class of proteins critical in human physiology: the G protein-coupled receptors (GPCRs). GPCRs' functions rely on their activation marked by a series of conformational changes related to binding of certain ligands, but the short of experimental structures has hampered the study of their activation mechanism and drug discovery. Our method, combining homology modeling, hierarchical sampling, and nanosecond-scale molecular dynamics, is one of the very few computational methods that can predict their active-state conformations and is one of the most computationally inexpensive. It enables the conformational landscape and the first quantitative energy landscape of GPCR activation to be efficiently mapped out.
This method, named ActiveGEnSeMBLE, allows the inactive- and active-state conformations of GPCRs without an experimental structure to be systematically predicted. We have validated the method with one of the most well-studied GPCRs, human β2 adrenergic receptor (hβ2AR), and applied the method on a GPCR without an experimental structure, human somatostatin receptor 5 (hSSTR5). Insights on GPCR activation as well as structure prediction methods are discussed.
The second one is a semiclassical approach for large-scale nonadiabatic dynamics of condensed systems in extreme conditions, termed Gaussian Hartree Approximated Quantum Mechanics (GHA-QM). Many nonadiabatic processes related to important applications (e.g. renewable energy) happen in large systems, but existing excited state dynamics methods are too computationally demanding for their long timescale simulations. GHA-QM is based on the electron force field (eFF) framework where we model electrons as Gaussian wavepackets and nuclei as classical point charges, and obtain a simplified solution to the time-dependent Schrödinger equation as the equation of motion. We employ a force field philosophy approximating the total energy as a sum of electronic kinetic energies, electrostatic energies and a Pauli correction, which corrects for the lack of explicit antisymmetry in the wavefunctions. New designs of the Pauli potential and preliminary results on hydrogen systems are discussed. With the new development, we hope to improve the accuracy and range of applications of eFF to simulate the nonadiabatic dynamics of hundreds of thousands of electrons on nanosecond timescale.</p
Stereoselective Olefin Metathesis Processes Using Cyclometalated Ruthenium Alkylidene Complexes
Get PDFThe recent development of a class of Z-selective ruthenium metathesis catalysts containing a crucial cyclometalated N-heterocyclic carbene (NHC) ligand has extended the applicability of ruthenium-mediated olefin metathesis to the production of a variety of useful Z-olefin-containing small molecules, polymers, and natural products. This thesis explores the synthesis and application of a number of novel Z-selective cyclometalated ruthenium alkylidene complexes displaying enhanced activity and selectivity across a range of metathesis transformations. Mechanistic investigations aimed at understanding and controlling stereoselectivity specifically in ring-opening metathesis polymerization (ROMP) are also detailed.
Chapter 2 describes the preparation of new Z-selective cyclometalated ruthenium metathesis catalysts via an improved method employing sodium carboxylates. Effects of the cyclometalated NHC ligand on catalyst activity and selectivity in several cross metathesis assays, as well as macrocyclic ring-closing metathesis and other industrially relevant transformations, are investigated.
Chapter 3 relates a story in two parts: the first details the synthesis and activity of a series of novel cyclometalated ruthenium alkylidenes displaying unprecedented cis,syndio-selectivity in the ROMP of norbornene- and norbornadiene-derived monomers. The second comprises an extensive study into the origins of stereoselectivity in ROMP in these and related cyclometalated ruthenium initiators. Experimental results are used in conjunction with a computational analysis of propagation transition states to develop a complete stereochemical model for cis,syndio-selctivity in these systems.</p
The Synthesis and Late-Stage Diversification of the Cyanthiwigin Natural Product Core and Synthetic Insights Derived Therein
Get PDFInspired by the therapeutic properties of many natural products and the ever-growing need for novel medicines, research programs for the late-stage diversification of complex molecular scaffolds have risen in popularity over the past few decades. In addition to generating a wide range of non-natural compounds for biological evaluation, these research efforts provide valuable synthetic insights into the preapration and reactivity of structurally intricate molecules. After a brief summary of the various strategies for late-stage diversification, examples of previous studies toward the derivatization of natural product-inspired scaffolds are highlighted.
A second-generation synthesis of the cyanthiwigin natural product core employing recently developed technologies is described. Re-optimization of the key double asymmetric catalytic alkylation transformation facilitates large-scale operations, and application of the aldehyde-selective Tsuji–Wacker oxidation enables productive recycling of an advanced intermediate. Together, these modifications expedite the preparation of the tricyclic cyanthiwigin framework on multi-gram scale.
The aldehyde-selective Tsuji–Wacker reaction is demonstrated to be effective for the oxidation of terminal alkenes bearing quaternary carbons at the allylic or homoallylic position. The synthetic utility of this method is extended through further transformation of the crude aldehyde products, permitting catalytic conversion of hindered terminal olefins to a variety of other synthetically useful functional groups.
With access to large quantities of the cyanthiwigin natural product core, a comparative study of various methods for intermolecular C–H oxidation was conducted. Examination of the reactivity of the cyanthiwigin framework under established conditions for allylic C–H acetoxylation, C–H hydroxylation, C–H amination, C–H azidation, and C–H chlorination reveals significant steric and electronic influences and suggests that functionalization is guided by innate reactivity within the substrate.
Finally, the preparation of several non-natural cyanthiwigin–gagunin hybrid molecules from the cyanthiwigin core is described. Preliminary studies toward the biological activities of synthetic intermediates are presented, and future directions for the synthesis of novel cyanthiwigin–gagunin hybrids are outlined.</p
Distributed Optimization and Data Market Design
Get PDFWe consider algorithms for distributed optimization and their applications. In this thesis, we propose a new approach for distributed optimization based on an emerging area of theoretical computer science – local computation algorithms. The approach is fundamentally different from existing methodologies and provides a number of benefits, such as robustness to link failure and adaptivity to dynamic settings. Specifically, we develop an algorithm, LOCO, that given a convex optimization problem P with n variables and a “sparse” linear constraint matrix with m constraints, provably finds a solution as good as that of the best online algorithm for P using only O(log(n + m)) messages with high probability. The approach is not iterative and communication is restricted to a localized neighborhood. In addition to analytic results, we show numerically that the performance improvements over classical approaches for distributed optimization are significant, e.g., it uses orders of magnitude less communication than ADMM.
We also consider the operations of a geographically distributed cloud data market. We consider design decisions that include which data to purchase (data purchasing) and where to place or replicate the data for delivery (data placement). We show that a joint approach to data purchasing and data placement within a cloud data market improves operating costs. This problem can be viewed as a facility location problem, and is thus NP-hard. However, we give a provably optimal algorithm for the case of a data market consisting of a single data center, and then generalize the result from the single data center setting in order to develop a near-optimal, polynomial-time algorithm for a geo-distributed data market. The resulting design, Datum, decomposes the joint purchasing and placement problem into two subproblems, one for data purchasing and one for data placement, using a transformation of the underlying bandwidth costs. We show, via a case study, that Datum is near-optimal (within 1.6%) in practical settings.</p
Determining Strength of Materials Under Dynamic Loading Conditions Using Hydrodynamic Instabilities
Get PDFHydrodynamic instability experiments allow access to material properties at extreme conditions where the pressure exceeds 100 GPa and the strain rate exceeds 106 1/s. Laser ablation dynamically loads a sample, causing a manufactured initial perturbation to grow due to hydrodynamic instability. The instability growth rate depends on the strength of the sample. Material strength can then be inferred from a measurement of the instability growth. Past experiments relied on in-flight diagnostics to measure the amplitude growth, which are not available at all facilities.
Recovery instability experiments, where the initial and final amplitude of the instability are measured before and after the sample is dynamically loaded, obviate the need for in-flight diagnostics. Recovery targets containing copper and tantalum samples coined with 2D (hill and valley) and 3D (eggcrate) initial perturbations were dynamically loaded using the Janus laser at the Jupiter Laser Facility, Lawrence Livermore National Laboratory. The energy of the laser pulse was varied to cover a range of conditions in the dynamically compressed sample with pressures in the range 10 GPa to 150 GPa and strain rates in the range 105 1/s to 108 1/s.
The coupling of laser energy into a loading wave was studied with a combination of laser-matter interaction simulations (Hyades) and velocity interferometry data (VISAR). Laser ablation of the recovery targets generated a blast wave, loading the coined initial perturbations with a shock wave followed by a release wave. Different ablator materials and variations in the amount of laser energy deposited in the ablator lead to variations in the loading wave and consequently variations in instability growth.
The growth of the initial perturbation amplitude from initial to final conditions was studied with hydrocode simulations (CTH). During dynamic loading of the sample, the shock wave caused amplitude growth due to hydrodynamic instability. The release wave accelerated the perturbed interface and slowed amplitude growth, in some cases reversing growth.
The sensitivity of the instability growth to coarse changes in the strength model was demonstrated. However, uncertainty in modeling the laser ablation loading prevented a definitive comparison between simulation and experiment.</p
Essays on Matching Theory
Get PDFMatching theory is a rapidly growing field in economics that often deals with markets in which monetary transfers are forbidden. Hence, policy makers often use centralized procedures to organize markets and coordinate players' behavior. Three concerns play central roles in designing the procedures: efficiency, fairness, and incentive compatibility. These concerns are also what I focus on in my studies. Specifically, my dissertation consists of three original studies on the allocation of indivisible resources to agents. The first chapter studies school choice, which is a centralized market to assign students to public schools. I compare popular matching mechanisms used in school choice by accommodating the fact that students and their parents often have heterogeneous sophistication in understanding the mechanisms. In the second chapter I study abstract object allocation problem in which objects do not have priority rankings of agents. I want to show that the three objectives of efficiency, fairness, and incentive compatibility can be incompatible with each other: a mechanism that satisfies a minimal efficiency requirement and mild fairness requirements must be manipulable by some group of agents in a strong sense. Since the efficiency requirement is weak enough such that policy makers are likely to pursue, my results suggest that policy makers have to make a choice between fairness and group incentive compatibility. In the third chapter I study same object allocation problems except that some agents have private endowments. I propose a new mechanism that has desirable properties in efficiency, fairness, and incentive compatibility. In the following I provide more details of each chapter.
School choice is a trend in the K-12 public education of US and many other countries that allows children to choose schools across neighborhoods. In Chapter 1, "Level-k Reasoning in School Choice", I compare two matching algorithms that many cities use to assign children to public schools in school choice. The algorithms are called Boston Mechanism and Deferred Acceptance. BM is manipulable, while DA is strategy-proof. Recently several cities decide to switch from BM to DA to avoid manipulation. However, the effect of the switch has not been well understood. In this paper I use the level-k model to study the strategies used by parents in BM by taking account of the fact that parents often have different abilities to manipulate BM, which are due to their heterogeneous sophistication. Interestingly, I find that the level-k reasoning process in BM is analogous to the procedure of DA. This analogy provides a new way to understand how parents may behave in BM. Under some mild assumption it implies that for any school choice problem and any sophistication distribution of parents, the assignment found by BM is never less efficient than the assignment found by DA. I also examine how parents' beliefs about others' sophistication affect their welfare. I find that, in general, a child is guaranteed to benefit from his parent's sophistication in BM only when his parent's level is high relative to others and his parent's belief about others' sophistication levels is accurate. The simulation results of my model exhibit patterns similar to empirical datasets.
Without monetary transfers, the concern of fairness motivates policy makers to use random assignments in objection allocation problems. In Chapter 2, "Efficient and Fair Assignment Mechanism is Strongly Group Manipulable", I study group incentive compatibility in random assignment mechanisms. I show that if a mechanism satisfies the minimal efficiency requirement (ex-post efficiency), then it cannot satisfy some mild fairness requirements and be minimally group incentive compatible simultaneously: by misreporting preferences, a group of agents can obtain lotteries that strictly first-order stochastically dominate the lotteries they obtain in the truth-telling case. Hence, fairness concerns may force policy maker to give up group incentive compatibility. My results hold as long as there are at least three agents and at least three objects, no matter outside option is available or not. Possibility results exist when there are only two objects and outside option is not available.
In some object allocation problems, some players have private endowments and are willing to bring them to the market in exchange for better ones. In Chapter 3, "A New Solution to the Random Assignment Problem with Private Endowment", I propose a new mechanism to solve the problems. Intuitively, in my mechanism the popularity of a private endowment plays the role of "price" in determining his owner's advantage in the market. Formally, the mechanism is a simultaneous eating algorithm, which generalizes Probabilistic Serial, by letting agents obtain additional eating speeds if their private endowments are consumed by others, and letting multiple agents trade their private endowments if they form cycles. This feature can be summarized by the idea of "you request my house - I get your speed". Indifferent preferences often cause difficulty in efficient random assignment mechanisms. Interestingly, I show that the same idea can also be used to deal with indifferent preferences in a straightforward way. It is in contrast to the mainstream method of iteratively solving maximum network flow problems in the literature.</p
Experimental Generation and Modeling of Vortical Gusts and Their Interactions with an Airfoil
Get PDFThis thesis examines two methods of vortical gust generation and the interaction between these gusts and an airfoil. These flows were studied with both experiments at a Reynolds number of 20,000 and with potential-flow based simulations.
The standard method of generating a vortical gust has been to rapidly pitch an airfoil. A novel approach is presented: heaving a plate across the tunnel, and changing direction rapidly to release a vortex. This method is motivated by the desire to limit a test article's exposure to the wake of the gust generator by moving it to the side of the tunnel.
A series of potential flow models were used to examine these flows: steady and unsteady thin airfoil theory, an extension of Tchieu and Leonard's unsteady airfoil model, and an unsteady vortex panel method.
Experiments characterized the generated gusts and verified that the strength of the shed vortices approximately matched the theoretical predictions. The inviscid simulations were unable to predict viscous effects like the wakes of the generators. The pitching airfoil resulted in a persistent wake in the test section, whereas the wake of the heaving plate only temporarily disturbed the flow.
The vortex-wing interaction was examined using both mechanisms. When the wake of the generator was far from the wing, the unsteady simulations provided reasonable estimates for the early variation in lift. This demonstrated that the initial lift peak is due to inviscid effects. Each of the potential flow methods with wake models provided reasonable estimates of this lift. The simplicity of the unsteady thin airfoil theory model recommends its use for examining early vortex-wing interactions.
With the test article mounted at the midline of the tunnel, the wakes had substantial effects when the pitching generator was near the midline of the tunnel, or when the heaving plate passed the midline. The simulations were not able to capture the effects of the wakes or predict the effects of the airfoil's angle of attack. This had the largest effect on the timescale of the post-gust approach to the final forces. With the airfoil at α=0°, this was 5-10 convective time units, which is characteristic of attached flows. The airfoil at α=10° needed double the time to approach its final state after perturbations due to its separated flow. The heaving plate's withdrawal allowed for measurement of the resumption of vortex shedding, which was impossible with the pitching airfoil's persistent wake.</p