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Computational Studies of Dendritic Deposition and Trajectory Phase Coexistence
Get PDFMany out-of-equilibrium systems display collective transitions in the behavior of particles akin to phase transitions. The field of nonequilibrium statistical mechanics seeks to develop new theories and methods to characterize these phenomena. In this thesis, we advance this aim by presenting computational studies of two different kinds of nonequilibrium transitions: the compact-to-dendritic (CTD) transition in the deposition of Brownian particles and trajectory phase coexistence (TPC) in stochastic dynamical systems.
The CTD transition occurs when Brownian particles (like ions, colloids, or misfolded proteins) deposit from all sides onto a reactive cluster. While the cluster initially maintains a compact morphology, upon reaching a critical radius, it spontaneously develops dendritic branches. Although the size of the critical radius depends on the deposition conditions, this relationship is not well understood at a mechanistic level. Here, we show that contrary to previous evidence, the critical radius in Brownian dynamics simulations follows the behavior predicted by a continuum analysis. That is, dendrites emerge when the cluster circumference exceeds the length that particles can diffuse in the characteristic reaction timescale. Consequently, our results provide microscopic validation for continuum methods that are widely applied to study dendrite formation in electrodeposition and lithium metal batteries.
Trajectory phase coexistence (TPC) arises when qualitatively different trajectory behaviors interconvert in a stochastic dynamical system. This type of coexistence plays a central role in theories of glassy dynamics. In this work, we focus on two different research areas related to TPC. First, we introduce an importance sampling method, Variational Ansatz for Rare Dynamics (VARD), for characterizing a system's rate function. VARD is technically and conceptually straightforward yet can still sample the large deviations of many-body models found in the literature. We then examine the meaning of kinks in the scaled cumulant generating function (SCGF). Although these singularities are often taken to be proof that TPC occurs, a more precise understanding of the connection between kinks and coexistence remains lacking. By characterizing the dynamics of two kinds of random walkers, we show that kinks actually result from diverging timescales in the dynamics and do not always indicate the presence of TPC.</p
Twisted Heisenberg Central Extensions and the Affine ADE Basic Representation
Get PDFWe study various aspects of the representation theory of loop groups, all with the aim of giving geometric constructions, parameterized by conjugacy classes of the Weyl group, of the basic representation of the affine Lie algebras associated to a simply laced simple Lie algebra as a restriction isomorphism on dual sections of the level 1 line bundle on the affine Grassmannian. Along the way, we obtain various results on the structure of loop tori, the definition of a notion of a Heisenberg Central extension as an alternative for twisted modules over the lattice vertex algebra and the determination of their representation theory, some computations on central extensions of a torus over a field by K2, and a new proof of the classification of the conjugacy classes of the Weyl group by parabolic induction.</p
Correcting Errors in DNA Storage
Get PDFDNA-based storage has potentially unprecedented advantages of high information density and long duration, and is one of the promising techniques to meet the ever-growing demands to keep data in the future. As noise and errors are present in almost every procedure during reading, writing, and storing of information in DNA storage systems, error correction is inevitable to guarantee reliable data storage in DNA. Moreover, it is often required that error correction is done in an efficient manner to reduce the cost and time needed for reading and writing data. Due to the technology constraints and physical limitations, error correction in DNA-based storage poses the following challenges that differ from those in traditional digital data transmission and storage systems.
1. A combination of deletion, insertion, and substitution errors present. The goal is to construct efficient codes correcting these errors. While substitution errors are special cases of deletion and insertion errors, and are well studied under the current theory and practice frameworks, deletion and insertion errors are much more difficult to deal with, and less understanding was gained for deletion and insertion errors.
2. Error correction is over an unordered set of strings, rather than over a single string, which can be regarded as a set of ordered strings. The latter, which includes the above deletion/insertion coding problem, is commonly studied for current digital communication and storage systems. Our goal is to extend the deletion/insertion correction capability for a single string to a set of unordered strings.
3. The decoder observes multiple noisy copies of every coded string. The problem is to deduce a set of strings (or a single string) from a collection of their noisy samples, also studied as the population recovery (or trace reconstruction for a single string) problem. The problem is well answered with substitution errors only and becomes elusive with the introduction of deletion and insertion errors.
This thesis tries to address the above challenges. For the first challenge, we proposed binary codes correct any constant number of deletions and/or insertions with order-wise optimal redundancy, which made a step toward a solution to a longstanding open problem introduced by Levenshtein in 1960s. We also extended it to different settings, in particular, non-binary deletin/insertion correcting codes suitable for DNA storage applications.
For the second challenge, we established lower and upper bounds on the optimal redundancy of codes correcting any number of substitution, deletion, and insertion errors and found that the redundancy needed for coding over an unordered set of strings is order-wise the same as that needed for coding over a ordered set of strings. Using our results for the first challenge, we proposed codes correcting any constant number of deletion/insertion errors with order-wise optimal redundancy under some parametter settings.
For the third challenge, we studied the problem of trace reconstruction, which asks the number of noisy samples needed to reconstruct a single string. While there is a exponential gap between upper and lower bounds on sample complexities in general, we showed that a polynomial number of samples suffice, given a reference string that is within constant edit distance from the target string.
Apart from dealing with the above challenges, we investigated error correction for multi-head racetrack memory applications. The problem can be considered as correcting any constant number of deletions/insertions in a single string with multiple noisy copies, with the help of coding. Different from the settings we considered above in the trace reconstruction problem, where noisy copies are independent given the target string, in racetrack memory, the noisy copies are correlated, and the number of errors is small compared to the trace reconstruction problem. We derived a lower bound on redundancy and proposed a code correcting any number of deletions/insertions with order-wise optimal redundancy.</p
Direct Imaging of Exoplanets Closer to Stars
Get PDFDetecting exoplanets through direct imaging at lower angular separations, where more planets are expected to be, is limited by the variability of the stellar point spread function. Integral field spectrographs like OSIRIS at the Keck Observatory can leverage high spectral resolution to search for new planets at smaller separations (< 0.3 arcseconds) by detecting their distinct spectral signature compared to the diffracted starlight. In this thesis, we present the mid-survey results of a search for planets around 23 targets in the Ophiuchus and Taurus star-forming regions.
We use this pathfinder survey with Keck/OSIRIS to demonstrate our technique and compare the final sensitivities to other classical imaging techniques, particularly at separations of 0.05-0.3 arcseconds. We detect an M dwarf companion around HD 148352 at a ≈ 34σ significance level. We measure this binary star companion to be at an angular separation of roughly milliarcseconds, with a contrast of , effective temperature Teff ≈ 3200 K, and radial velocity RV ≈ 12 km/s. We also present other low-significance objects, along with detection maps and sensitivity limits around these 23 targets.
We use our open-source data analysis pipeline, called the Broad Repository for Exoplanet Analysis, Detection, and Spectroscopy (breads), as the framework for this planet search. breads operates on high spectral resolution data from existing and in-development instruments. Our code is based on a forward-modeling framework, which is statistically more accurate than classical cross-correlation techniques. It includes a built-in optimization and analytical marginalization of linear parameters in the forward model, therefore limiting the number of parameters to be explored by the posterior sampling method. We allow users to select forward models, parameters to detect and analyze, and fitting methods like Markov Chain Monte Carlo sampling, grid optimization, and gradient descent. breads provides a flexible framework to retrieve radial velocity, spin, and atmospheric parameters of high-contrast companions. We also describe wavelength and resolution calibration, transmission and spectra calculation, and bad pixel identification techniques.
Our work will be applicable to future integral field spectrographs like NIRSpec on the James Webb Space Telescope and other first light instruments on the future Extremely Large Telescopes, which are poised to become the next generation of exoplanet detection facilities.</p
Optoelectronic Physics and Engineering of Atomically Thin Photovoltaics
Get PDFMaterials that are atomically thin behave substantially different than those of their bulk counterparts. However, when most materials become thinner, their surface-to-volume ratio increases and the number of unpassivated dangling bonds at the surface approaches the number of internal crystalline bonds, which prevents examining the intrinsic properties of most ultrathin materials. The recent discovery of layered materials, whose crystal structures have naturally passivated basal planes, has enabled the possibility to examine materials’ thicknesses that approach a single atomic layer.
In this thesis, we examine and explore the consequence of this new regime of thickness for active layers in photovoltaic applications. Specifically, we focus on the three aspects that define photovoltaic operation and explore their differences in these ultrathin materials: optical absorption of photons, subsequent carrier generation and transport, and finally, free energy extraction of collected carriers. We first discuss the implications of band-edge abruptness on the maximum efficiency of a solar cell. Then, we show that optical absorption in these ultrathin materials is dominated by cavity wave optics, and design structures that enable near-unity absorption in both ultrathin (~10 nm) and atomically-thin (~7 Å) active layers. Using these optical design rules, we design heterostructures with record incident photon to electron conversion efficiency (>50%). Next, we examine new methods of creating electrical junctions by using thickness to vary the amount of band bending in a material. We spatiotemporally image these 'band-bending junctions' for the first time. Finally, we argue that photoluminescence can be used as a direct readout of the open circuit voltage potential, and motivate examination of monolayer materials which have substantially higher radiative efficiency. We therefore examine the strain tuning of photoluminescence properties of both monolayer TMDC and heterobilayer TMDC systems. This work illustrates that van der Waals materials are an ideal system for examining the novel optoelectronic physics of atomically thin photovoltaics.</p
Understanding and Optimizing the Local Catalyst Environment in CO₂ Reduction Electrodes
Get PDFUnderstanding and managing the local microenvironments in carbon dioxide reduction catalysts is crucial for optimizing device performance. In particular a locally high pH can increase catalyst selectivity and activity, as well as indicate which part of the catalyst is most active. In this thesis we begin by studying how nanoporous catalysts can induce this locally high pH in an aqueous system. We observe an increase in both Faradaic efficiency and partial current density for carbon monoxide in the nanoporous system relative to a planar metal film. We then show that this same nanoporous architecture can be used for improved device performance in a gas diffusion electrode configuration. We also perform copper underpotential deposition and secondary ion mass spectroscopy to show that almost half of the catalyst is not in contact with the electrolyte in this configuration. Then we use confocal fluorescent microscopy to image the local pH in a gas diffusion electrode to determine which parts of the electrode are most active. Through a combination of experiment and simulations we find that the catalyst within thin cracks of the microporous layer is most active for carbon dioxide reduction. While the study of local pH and wetting is the main focus of this thesis, we also explore how light can be used to improve selectivity and activity. In particular we study gold nanoparticles on p-type gallium nitride and copper nanoparticles on p-type nickel oxide. Finally, this thesis also explores how carbon dioxide conversion can actually be deployed. We discuss opportunities for combining carbon dioxide capture and conversion, as well as evaluate different pathways for renewable methane generation.
This thesis gives in depth analysis of electrochemical carbon dioxide reduction catalysts as well as putting this research into the larger context of how such devices can be deployed. We hope that by combining systems level thinking and specific device studies better carbon dioxide conversion systems can be realized.</p
High-Resolution Imaging of Chemistry in Extreme Interstellar Environments
Get PDFAdvancements in imaging technologies have changed the ways in which we see and understand our chemical universe. Given the extreme distances between Earth, from which we observe the wider chemical universe, and the molecular clouds where stars are born, we cannot resolve the chemical structure of these interstellar laboratories on the same scales as we can with samples on Earth. Nevertheless, with the advent of larger and more sophisticated telescopes, such as the Atacama Large Millimeter/submillimeter Array (ALMA) in Chile, we can now look at interstellar chemistry on scales much smaller than the solar system. The research presented here uses ALMA to investigate the chemistry in (massive) star-forming regions in different parts of the Milky Way with high spatial resolution.
This thesis first focuses on the nearby Orion Kleinmann-Low nebula (Orion KL), the closest (at about 400 parsecs away) massive star-forming region to us, at spatial scales smaller than those of typical planetary systems. Using methanol and methyl cyanide as molecular probes, we provide new insight into the physical structure—especially the thermal structure—of the nebula by mapping physical parameters derived from observed spectra. We also use different isotopologues of methanol to understand its chemistry, specifically after it forms on the surfaces of icy dust grains. This work provides a new view of Orion KL by providing high-angular-resolution maps of parameters such as abundance and temperature, whereas much of the existing literature provides a single set of parameters for a region.
However, Orion KL is only one interstellar laboratory, and it is part of a cohort of star-forming regions that are the targets of repeated astrochemical observations. The second part of this thesis ventures into the so-called molecular ring, a region 4-8 kiloparsecs from the galactic center that has remained relatively unexplored in the context of astrochemistry. Using the Atacama Compact Array (ACA) component of ALMA, we observed a slew of millimeter-emitting objects across 11 giant molecular clouds at higher angular resolutions than most previous observations of our sample, and we characterize their chemistry for the first time. This pilot survey establishes a catalogue of interstellar laboratories for future higher-angular-resolution observations. Over time, this catalogue will drive a better understanding of the chemistry in molecular-ring young stellar objects, allowing us to see whether (and if so, how) chemistry varies across distance from the galactic center and significantly increasing the number of targets for astrochemical observations.</p
Light Modulation with Vanadium Dioxide-Based Optical Devices
Get PDFThis thesis focuses on active material-based tunable optical devices. In particular, I have been working on tunable optical devices based on vanadium dioxide (VO2), which can produce tunable optical responses, such as amplitude, phase, thermal emission, and quantum emission. The modulations of light are achieved by coupling the phase-transition material with the precisely designed resonant structures or by placing it close to quantum emitters. This thesis presents three research streams, which aim at experimentally demonstrating the dynamically tunable optical responses using VO2. First, we propose and experimentally demonstrate an electrically tunable VO2-based reflectarray metasurface that exhibits largely tunable optical responses in the near-infrared region. We incorporate VO2 directly into the plasmonic resonator, which undergoes a phase transition triggered by Joule heating. The induced plasmonic resonance modulation is accompanied by a large and continuous modulation in optical responses, such as amplitude, resonance wavelength, and phase. Second, we propose and demonstrate an active tuning of thermal emission from VO2-based metasurfaces. We introduce a thin VO2 film as an absorbing layer on top of a metal reflector. This layer is coupled with a dielectric resonator, with a dielectric spacer placed between them. Upon undergoing a phase transition triggered by heating, the induced absorption tuning of the VO2 layer is accompanied by modulation in the absorption spectra of the coupled structure. We experimentally show narrowband absorption spectra, which can be tuned by controlling the VO2 temperature. Finally, we experimentally demonstrate the axial position of quantum emitters in a multilayered hexagonal boron nitride (hBN) flake with nanoscale accuracy, which is enabled through the modification of a photonic density of states by introducing VO2. Furthermore, we observe a sharp distance-dependent photoluminescence response by modulating the optical environment of an emitter placed close to the hBN/VO2 interface.</p
Topics in Equidistribution and Exponential Sums
Get PDFIn this thesis, we consider a few problems connected to the exponential sums which is one of the most important topics in analytic number theory.
In the first part, we study the distribution of prime numbers in special subsets of integers and, in particular, the distribution of these primes in arithmetic progressions, small gaps between them, the behavior of the corresponding exponential sums over primes, and related questions. Big progress was made on these questions in recent years. The famous works of Zhang and Maynard gave the proof of existence of bounded gaps between consecutive primes. Applying the sieve of Selberg-Maynard-Tao and an analogue of the Bombieri-Vinogradov theorem, we obtain similar results for a large class of subsets of primes and improve some of the previous results. The proof of the analogue of the Bombieri-Vinogradov theorem is also connected to a breakthrough work of Bourgain, Demeter, and Guth on the proof of Vinogradov Mean Value Conjecture via l2-decoupling. Their result, in particular, has led to a significant improvement of the classical van der Corput estimates for a large class of exponential sums.
In the second part, we study the behavior of higher moments of Gauss sum twisted by a Mobius function. The moments of exponential sums are very important in number theory and harmonic analysis as they appear in many other problems. The sum with the Mobius function is of independent interest because of the famous Sarnak Conjecture which is on the edge of number theory, analysis, and dynamical systems. The bound we obtain for Lp-norm of the sum confirms that the Mobius function is uncorrelated with the quadratic phase αn2 for most α ϵ [0; 1].
In the third part, we study the distribution of lattice points on the surface of 3-dimensional sphere, which is known as Linnik problem. It turns out that the variance for such points is closely related to the behavior of certain GL(2) L-functions estimated at the central point 1/2. To evaluate the moments of these L-functions, we apply similar techniques used to evaluate the moments of Riemann zeta function on the critical line in the breakthrough works of Soundararajan and Harper. Their results have led to the sharp upper bounds for all positive moments of zeta function conditionally on Riemann Hypothesis and similar bounds for a broad class of L-functions in families conditionally on the corresponding Grand Riemann Hypothesis. We apply similar methods to get sharp upper bound for the variance of lattice points on the sphere. The connection of Weyl sums on the sphere to the sums of special values of GL(2) L-functions is a big output of the Langlands program, which has also gotten a lot of attention in recent years.</p
The Absorption and Emission of Neutral Hydrogen around High-Redshift Star-Forming Galaxies
Get PDFThe circumgalactic medium (CGM) mediates the interaction between galaxies and their surrounding gas, and ultimately controls the evolutionary trajectory of its host galaxies. Among the CGM gas, neutral hydrogen (H I) constitutes an important component observationally. This thesis focuses on characterizing the circumgalactic H I around z = 2-3 star-forming galaxies using absorption and emission techniques in the Keck Baryonic Structure Survey (KBSS) fields.
Chapter 2 provides a new statistical measurement of the distribution and kinematics of H I in the CGM using Lyman-alpha (Lyα) absorption signatures. We constructed the KBSS Galaxy Pair Sample (KGPS), which contains > 200,000 distinctive foreground-background galaxy pairs with projected distances of 0.02-4 Mpc. We compared the observed H I absorption map with a cosmological zoom-in simulation, and found qualitative agreement. Furthermore, using an analytic model, we show that the observed H I distribution can be explained by a combination of outflow, accretion, and Hubble expansion.
Chapters 3 and 4 explore the Lyα emission, one of the strongest spectral features of H I, from the spatially resolved spectroscopy, by using the new high-sensitivity integral field unit, Keck Cosmic Web Imager (KCWI). We introduce the use of "cylindrically projected 2D (CP2D) spectra," which map the average Lyα spectral profile over a specified range of azimuthal angle, as a function of impact parameter, around galaxies. We find that the averaged CP2D spectrum is most consistent with the expected signatures of Lyα resonant scattering through outflowing gas.
Furthermore, Chapter 3 investigates the statistical relation between Lyα emission and its orientation relative to the galaxy major axis for 59 galaxies that have been observed with both KCWI and high-spatial-resolution imaging instruments. We find that the extended Lyα emission along the galaxy projected major and minor axes are statistically indistinguishable at projected distance ≾ 30 physical kpc, indicating that resonant scattering of Lyα by outflowing H I occurs in a statistically uniform halo, independent of galaxy orientation.
Chapter 4 provides ongoing research on the connection between Lyα emission in the CGM and the host galaxy properties. Our preliminary result from 110 star-forming galaxies at z ≃ 2-3 demonstrates that the host galaxy affects the production and escape of Lyα emission at ≾ 15 kpc as expected. However, the faint envelopes of Lyα emission reach to similar spatial distances (≳ 30 kpc) regardless of their host galaxies.
Finally, we document the standard data reduction procedure and data products of the KBSS-KCWI survey in Appendix A.</p