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Assembly of Complex Carbocyclic Architectures via Palladium and Nickel-Catalyzed Cyclizations
Get PDFTransition metal catalysis can be leveraged to construct challenging chemical bonds with excellent chemo- and stereoselectivity. Herein we describe the discovery of a novel palladium-catalyzed cascade cyclization and a nickel-catalyzed spirocyclization, enabling the assembly of complex carbocyclic architectures. We begin with an introduction describing notable applications of palladium-catalyzed cascade cyclizations in natural product synthesis, enabling the concurrent formation of C–C and C–N bonds in a single synthetic step.
Next, the development of a palladium-catalyzed oxidative Heck/aza-Wacker cascade cyclization is described. This cascade reaction enabled the construction of an all-carbon quaternary center, a C–C bond, and a C–N bond in a single synthetic step. Furthermore, it was employed to build the carbocyclic core of the natural product noraugustamine.
Then, we outline the discovery and optimization of an enantioselective nickel-catalyzed α-spirocyclization of lactones. The established method efficiently and enantioselectively forges 5-, 6-, and 7-membered rings containing all-carbon quaternary centers. This discovery represents an expansion of the synthetic toolkit for enantioselective spirocyclization, providing access to chiral, pharmaceutically relevant spirocyclic products.
Finally, we describe a collaborative project with the Su lab at the University of Arizona in the area of polymer synthesis and gas sensing, where we designed a sensor for the selective detection of gaseous nitric oxide. The sensor’s excellent specificity and part-per-trillion level sensitivity was enabled by novel ferrocene-containing polymeric coatings.</p
Essays in Behavioral Game Theory Solution Concepts
Get PDFThis dissertation introduces two novel behavioral solution concepts for dynamic games: the cursed sequential equilibrium (CSE) and the dynamic cognitive hierarchy solution (DCH). Chapter 1 offers an overview of these theories and highlights their departure from standard equilibrium theory.
Chapter 2 develops the cursed sequential equilibrium, incorporating the bias where players neglect the correlation between other players’ private types and actions into game theory. This framework extends the analysis of cursed equilibrium proposed by Eyster and Rabin (2005) from games in strategic form to multi-stage games, and applies it to various applications in economics and political economy.
Chapter 3 introduces the dynamic cognitive hierarchy solution, which relaxes the requirement of mutual consistency of beliefs by extending the cognitive hierarchy approach from games in strategic form to the extensive form. An important feature is that the solution can be dramatically different for games that are strategically equivalent from the perspective of standard equilibrium theory.
This property, which I call the “representation effect,” has significant implications for experimental methodology and real-world phenomena. To test this effect, in Chapter 4, I design and conduct a laboratory experiment on the dirty-faces game, a simple multi-stage game of incomplete information. The experiment consists of two treatments, each implementing one of two strategically equivalent versions of the game. The dynamic cognitive hierarchy solution provides precise predictions about the differences in behavior between treatments, and the experimental results align with that prediction.</p
Statistical Foundations of Operator Learning
Get PDFThis thesis studies operator learning from a statistical perspective. Operator learning uses observed data to estimate mappings between infinite-dimensional spaces. It does so at the conceptually continuum level, leading to discretization-independent machine learning methods when implemented in practice. Although this framework shows promise for physical model acceleration and discovery, the mathematical theory of operator learning lags behind its empirical success. Motivated by scientific computing and inverse problems where the available data are often scarce, this thesis develops scalable algorithms for operator learning and theoretical insights into their data efficiency.
The thesis begins by introducing a convergent operator learning algorithm that is implementable on a computer with controlled complexity. The method is based on linear combinations of function-valued random features, enjoys efficient training via convex optimization, and accurately approximates nonlinear solution operators of parametric partial differential equations. A statistical analysis derives state-of-the-art error bounds for the method and establishes its robustness to errors stemming from noisy observations and model misspecification. Next, the thesis tackles fundamental statistical questions about how problem structure, data quality, and prior information influence learning accuracy. Specializing to a linear setting, a sharp Bayesian nonparametric analysis shows that continuum linear operators, such as the integration or differentiation of spatially varying functions, are provably learnable from noisy input-output pairs. The theory reveals that smoothing operators are easier to learn than unbounded ones and that training with rough or high-frequency input data improves sample complexity. When only specific linear functionals of the operator’s output are the primary quantities of interest, the final part of the thesis proves that the smoothness of the functionals determines whether learning directly from these finite-dimensional observations carries a statistical advantage over plug-in estimators based on learning the entire operator. To validate the findings beyond linear problems, the thesis develops practical deep operator learning architectures for nonlinear mappings that send functions to vectors, or vice versa, and shows their corresponding universal approximation properties. Altogether, this thesis advances the reliability and efficiency of operator learning for continuum problems in the physical and data sciences.</p
Novel Reactivity and Applications of Transition Metal-Catalyzed Nucleophilic Substitution Reactions
Get PDFFor more than 20 years, the Fu lab has explored the use of transition metal catalysts to enable novel nucleophilic substitution reactions. However, deficiencies in both fundamental reactivity and useful applications persist in this area. The research detailed in this thesis focuses on the development of reactivity and applications of transition metal-catalyzed nucleophilic substitution reactions
Observation of the Microenvironment Around CO₂ Reduction Electrodes via Fluorescent Confocal Laser-Scanning Microscopy
No full textElectrochemical carbon dioxide reduction (CO₂R) is compelling because it enables the storage of renewable energy in the form of chemical bonds and offers the possibility to make carbon-based chemicals and fuels from a sustainable feedstock. A solid understanding of and control over the local microenvironment in and around CO₂R electrodes is crucial to optimize the device performance.
In this work, we develop and refine a technique to observe the microenvironment around CO₂R electrodes via fluorescent confocal laser scanning microscopy with three-dimensional sub-micrometer spatial as well as temporal resolution. We combine two fluorescent pH probes, DHPDS and APTS, to resolve the local pH value around operando CO₂R electrodes. The pH plays an important role in determining the CO₂R activity and selectivity. In a first step, we image the local pH value in and around CO₂R GDEs with a random pattern of trenches and find that the pH is locally enhanced inside trenches. This effect becomes more pronounced for narrower trenches, reaching a maximum at a trench width of 5 µm. With the help of multiphysics simulations we can show that the high pH inside trenches is closely related to an enhanced C₂₊ Faradaic efficiency. We harness this effect and fabricate CO₂R GDEs with tailored patterns of holes and trenches that allow a more systematic study of the influence of various micromorphology geometry parameters. We confirm experimentally that narrow holes and trenches exhibit a locally enhanced CO₂R selectivity and determine the most beneficial geometry parameters. We further use the developed technique to investigate the influence of a GDE's pore size on the local pH and with it, on the CO₂R selectivity. We observe that CO₂ transport is slower through smaller pores which can lead to switching of the reaction pathway and significantly alter the selectivity. We further investigate the importance of the microenvironment pH for CO₂R in acidic bulk electrolytes with the result that a non-acidic microenvironment pH, that can be reached at sufficiently high current densities, is required for the onset of CO₂R. Finally, we aim to extend the sensing capabilities and detect the local CO concentration in electrochemical devices but identify several challenges, including the probe reduction at the cathode.
Overall, we utilized fluorescent confocal laser-scanning microscopy to observe the microenvironment around CO₂R electrodes and correlate it with the CO₂R performance to gain a better mechanistic understanding of CO₂R and inform the design of future CO₂R electrodes.</p
Deep Learning-Enabled Integrated Measurements of Immune Signaling in Primary Human Macrophages
Get PDFExamination of biological systems at the single-cell level reveals heterogeneity in both time and space. Single-cell temporal and spatial heterogeneity allow communities of cells to process noisy stimuli and perform complex tasks. We leveraged state-of-the-art imaging technologies to characterize cell-to-cell heterogeneity in responses to environmental stimuli to reveal mechanisms of information transmission. Fluorescent live-cell reporters enable real-time visualization of the activity state of cell signaling proteins. Signaling dynamics allow cells to translate information about environmental stimuli into cellular behaviors. Chapter 2 explores the variety of live-cell reporters designed to characterize the dynamic patterns of activity of key signaling pathways, and covers the development of two live-cell reporters. Spatial transcriptomics assays, on the other hand, excel at capturing heterogeneity in spatial gene expression patterns, which is often required to enable a tissue to perform complex functions. Chapter 3 details the development of Polaris, a deep learning-enabled analysis method for spatial transcriptomics data. Polaris is an assay-agnostic, turnkey solution for analyzing images from spatial transcriptomics experiments, minimizing the time and expertise require to extract biological insights. In chapter 4, we pair dynamic measurements of live-cell reporters with a spatial transcriptomics measurement in an integrated imaging assay in primary human macrophages. This imaging assay revealed transcriptional sub-populations of cells with differing distributions of dynamic immune signaling responses and morphological states.
This work contributes a number of methodological developments, including live- cell reporter expression in primary human macrophages and deep learning-enabled spatial transcriptomics image analysis. Expression of live-cell reporters in primary macrophages will enable the investigation of environmental cues shape macrophages’ cell state, which is highly plastic and shaped by external stimuli. Polaris expedites the analysis of this multi-modal imaging data set, extracting single-cell gene expression values without manual parameter tuning. However, Polaris’ impact extends beyond the scope of this work to the broader spatial biology field as its spot detection and gene decoding capabilities generalize to data sets from a variety of sample types and imaging modalities. Finally, our paired dynamics-spatial transcriptomics imaging assay can be generally applied to characterize information transmission from environmental stimuli through signaling dynamics to the expression of downstream genes for a wide variety of signaling pathways in primary and immortalized cell types.</p
Dissipative Dynamics of Stars, Planets, and Black Holes
No full textIn this dissertation, I present a series of theoretical works on two important dissipative mechanisms in the universe, namely dynamical friction and tidal dissipation. I discuss the physics of these processes, and investigate how they will affect the dynamical evolution of stars, planets, and black holes.
I develop a new sub-grid dynamical friction estimator based on the discrete nature of N-body simulations. This estimator avoids the ambiguously defined quantities in Chandrasekhar's dynamical friction formula. I test the estimator in the GIZMO code, and find that it agrees well with high-resolution simulations where dynamical friction is fully captured. The additional computational cost with this estimator is negligible, making it an efficient and implementable solution to sub-grid dynamical friction modeling.
I study the dynamics of massive black hole seeds in high-redshift galaxies. I analyze the direct N-body integration of seed black hole trajectories with high-resolution cosmological simulations, and calculate the dynamics of randomly generated test particles in post-processing with dynamical friction. I find that seed black holes less massive than 100 million solar-masses (i.e. all but the already-supermassive seeds) cannot efficiently sink to the galactic center in typical high-redshift galaxies. This finding provides new constraints on the formation models of super-massive black holes in the most distant galaxies.
I study the effects of tidal resonance locking for exoplanet systems, in which the planet locks into resonance with a tidally excited stellar gravity mode. I find that due to nonlinear mode damping, resonance locking in Sun-like stars likely only operates for low-mass planets, but in stars with convective cores it can likely operate for all planetary masses. The orbital decay timescale with resonance locking is typically comparable to the star's main-sequence lifetime, corresponding to a wide range in effective stellar quality factor, depending on the planet's mass and orbital period. I make predictions for several individual systems and examine the orbital evolution resulting from both resonance locking and nonlinear wave dissipation.
I investigate the tidal spin-up of subdwarf B (sdB) star binaries. I directly calculate the tidal excitation of internal gravity waves in realistic sdB stellar models, and integrate the coupled spin-orbit evolution of sdB binaries. I find that for canonical sdB binaries, the transitional orbital period below which they could reach tidal synchronization in the sdB lifetime is approximately 0.2 days, with weak dependence on the companion masses. This value is very similar to the tidal synchronization boundary evident from observations.
I investigate the scenario of tidal spin-up of Wolf-Rayet-black-hole binaries, which is a possible way to form the fast-rotating black holes observed from gravitational wave events. I directly calculate the tidal excitation of oscillation modes in Wolf-Rayet star models, determining the tidal spin-up rate, and integrating the coupled spin-orbit evolution for Wolf-Rayet-black-hole binaries. I find that for short-period orbits and massive Wolf-Rayet stars, the tidal interaction is mostly contributed by standing gravity modes, in contrast to Zahn's model of traveling waves which is frequently assumed in the literature. I show that tidal synchronization is rarely reached in Wolf-Rayet-black-hole binaries, and the resulting black hole spins are less than 0.4 for all but the shortest period binaries.</p
Understanding the Plasma Universe through Laboratory Experiments and Related Models
Get PDFLaboratory experiments and the models they inspire are powerful tools for studying the plasma universe. This dissertation details possible solutions to two important problems in the plasma universe, namely how solar flares are generated and how accretion disks transport angular momentum and generate astrophysical jets.
Addressing the first problem, solar coronal loop physics is simulated in a laboratory experiment. The loop structure composed of braided strands is replicated. The MHD kink instability and the magnetic Rayleigh Taylor instability (MRTI) are observed to disrupt the loop structure. The dependence of the MRTI wavelength on the axial magnetic field is studied. Transient, localized 7.6-keV X-ray bursts and a several-kilovolt voltage spike are observed to be associated with the breaking of braided magnetic flux ropes containing 2 eV plasma. These spikes occur when the braid strand radius is choked down to be at the kinetic scale by either MHD kink or magnetic Rayleigh–Taylor instabilities. The observed sequence reveals an MHD to non-MHD cross-scale coupling that is likely responsible for generating solar energetic particles and X-ray bursts. All the essential components of this mechanism have been separately observed in the solar corona.
Magnetic flux ropes, the fundamental building block of magnetohydrodynamic plasma configurations, have often been observed to wrap around each other to form a helical braided structure with net axial current as observed from the laboratory experiment and solar coronal loops. Braiding phenomena extend to astrophysical jets, double helix nebula, and fusion plasma experiments. The equilibrium of braided flux ropes is more complicated than familiar axisymmetric systems because it requires balancing forces between the individual braids. A novel method for constructing these equilibria is developed. This method generates a double helix equilibrium with net axial current which is characteristic of observed solar loops and of laboratory-produced braided magnetic flux ropes. To the best of our knowledge, no previous model has been able to describe braided structures with net axial current. The net-axial-current equilibrium presented here reproduces the observed braided structure of the double helix nebula and is expected to be a powerful tool in other contexts.
Addressing the second problem, the dissertation introduces a first-principles angular momentum transport mechanism based only on collisions between neutrals and charged particles in the presence of gravitational and magnetic fields. The mechanism is demonstrated by a 2D N-body simulation of a weakly-ionized system. It is found that ions and electrons drift in opposite radial directions as a result of colliding with Kepler-motion neutrals. This reduces the ordinary angular momentum of neutrals and increases the canonical angular momentum of charged particles in a manner such that the net global canonical angular momentum is conserved. The accumulation of ions at small radius and electrons at large radius produces a radially outward electric field, while current from the separation of ions and electrons is radially inward. Consequently, this process provides a gravitational dynamo converting gravitational energy into the electric energy that powers an astrophysical jet. Because this neutral angular momentum loss depends only on neutrals colliding with charged particles, it should be ubiquitous. The model predicts an accretion rate of 3 × 10−8 solar mass per year in good agreement with observed accretion rates.
Based on the conservation of canonical angular momentum and dynamics of charged particles under collisions with infalling neutrals, the dissertation also investigates the origin of angular momentum in astrophysical systems. A weakly-ionized, initially non-rotating cloud of neutral particles is shown to spontaneously start rotating when infalling. Quantitative scaling predicts an angular momentum generation rate sufficient to convert neutral infall motion into neutral Keplerian rotation in the outer region of a protoplanetary accretion disk.</p
Vortex Fiber Nulling for Exoplanet Observations
Get PDFAs of December 11, 2023, there are just over 5555 confirmed exoplanet detections. Of these exoplanets, only around 200 have been spectroscopically characterized. Spectra are crucial since they provide unique insights into the physical and chemical properties of exoplanets, their atmospheres, and their formation history. Few exoplanet spectra have been obtained because the prevailing spectroscopic techniques, transit spectroscopy and direct imaging, access different physical separations around a star and leave a gap in coverage from about 1 to 10 AU. This gap coincides with the peak of the giant planet occurrence rate such that there is an important population of exoplanets whose spectra cannot be readily obtained with the prevailing techniques. Interferometry can unlock access to these exoplanets and provide spectra for them.
Exoplanet interferometry has seen waves of interest in the past. However new developments, such as the first interferometric detections, have stoked a revived interest. Though VLTI/GRAVITY and other multi-aperture, long-baseline instruments currently dominate the field, there is a push to develop simpler interferometric architectures. Cross-aperture techniques are of particular interest as they can be readily implemented on existing and future direct imaging instruments with few-to-no modifications. Such single-telescope interferometers and nullers can reach well-within the inner working angle of conventional coronagraphs, but require significantly less infrastructure and investment than their long-baseline counterparts.
This thesis presents vortex fiber nulling (VFN), a new cross-aperture technique for detecting and spectroscopically characterizing exoplanets at separations less than one diffraction beamwidth (≾1 λ/D). VFN utilizes the full collecting area of a telescope to efficiently observe within the inner working angle of conventional coronagraphs. The first chapters of this thesis develop the VFN concept and how it can be readily implemented on existing and future instruments. Subsequent chapters present the laboratory demonstrations used to validate the technique and test its limits. Finally, the last chapters cover the design and deployment of a VFN mode to the KPIC instrument at the Keck Telescope. This includes a glimpse into VFN's capabilities with the first direct detection and spectroscopic characterization of three M dwarf companions previously known only from radial velocity and astrometry. This thesis therefore follows the development of VFN from a concept in 2018 to an operating mode with confirmed detections in 2023.</p
Experiments on Separation Shear Layer Instabilities in Hypervelocity Flows
No full textShock-boundary layer interactions (SBLI) are complex fluid dynamic phenomena that occur when shocks are generated near corners and irregular geometries on vehicles flying near or above supersonic speeds, causing external flow distortion and possible boundary layer separation. Accurate prediction of the mean and unsteady SBLI surface interaction is imperative to avoid failure from highly localized aerodynamic and heating loads, and loss of authority near a control surface. For hypersonic flight-enthalpy matched conditions, current SBLI simulations tend to under-predict thermal loads and have significant disagreements with ground-based experiments in separation location, and location and magnitude of peak heating. These discrepancies are potentially largely due to uncertainties in the modeling and recreation of the coupled real-gas (thermochemical) molecular and gas dynamic processes. To address this issue, efforts have been placed on developing and validating thermochemical gas models, which presents a need for off-surface experimental data. The disagreement between simulations and high-enthalpy ground test experiments have also highlighted the need to better characterize the freestream thermodynamic, velocity, and noise conditions.
Extensive freestream characterization of the T5 Free-Piston Reflected Shock Tunnel was performed over the course of numerous experimental campaigns using high-speed shadowgraph/schlieren imaging, static and pitot pressure probes, tunable diode laser absorption spectroscopy (TDLAS), and focused laser differential interferometry (FLDI). Accurate time-resolved static pressure measurements are key to characterizing the operation and freestream thermodynamic state in hypervelocity reflected shock tunnels, through both direct measurement and for interpretation of TDLAS signals. A series of three static pressure probes were built for use in T5 at a range of conditions from 8-16 MJ/kg stagnation enthalpies, and measurements agreed well with TDLAS-inferred pressure and numerical simulations of the static probe response. At higher enthalpy conditions, TDLAS measurements showed a substantial decrease in freestream temperature (~1000 K) while velocity was constant. This finding motivated the need for a method to characterize the arrival time and degree of driver gas contamination in T5. An opposing-wedge detector was designed to leverage the sensitivity of the canonical Mach stem flow to the freestream γ, such that the flow would choke at a prescribed increase in γ corresponding to the arrival of a specific mole fraction of monatomic driver gas. With high-speed schlieren/shadowgraph imaging, driver gas arrival times and mole fractions were obtained for the 8 MJ/kg test condition.
Informed by these freestream characterization experiments, near-surface FLDI measurements of instabilities in a separation shear layer on a 25°-55° double-cone model were performed with simultaneous static pressure and freestream tunnel noise measurements in hypervelocity conditions. Three main frequency regimes were considered: i) low-frequency content associated with Kelvin-Helmholtz instabilities and streamwise acoustic disturbances along the shear layer, ii) a strong medium-frequency (peak ~370-450 kHz) signal associated with shear layer instabilities communicating with the model surface, and iii) high-frequency features associated with Mack (second-mode) disturbances. Length scaling arguments are discussed for each case, informed by axisymmetric simulations of the mean flow over the double-cone. A ray-tracing model was used to simulate the FLDI response to certain disturbances. The low-frequency Kelvin-Helmholtz and streamwise acoustic disturbance frequencies did not vary beyond uncertainty bounds along the shear layer. The medium-frequency content had a clear dependence on the local separation height, with the mean frequency decreasing with streamwise position. The high-frequency Mack mode disturbances were only observed in some experiments, suggesting the disturbance is limited only to within the shear layer, making detection difficult if any bulk shear layer motion occurs relative to the FLDI beam positions. This study provides the first known FLDI data on shear layers in hypervelocity flows, together with simultaneous freestream characterization, with the aim to inform future experiments in hypervelocity ground testing facilities and high-resolution numerical simulations.</p