12023 research outputs found
Sort by
Superconducting Circuit Architectures Based on Waveguide Quantum Electrodynamics
Get PDFQuantum science and technology provides new possibilities in processing information, simulating novel materials, and answering fundamental questions beyond the reach of classical methods. Realizing these goals relies on the advancement of physical platforms, among which superconducting circuits have been one of the leading candidates offering complete control and read-out over individual qubits and the potential to scale up. However, most circuit-based multi-qubit architectures only include nearest-neighbor (NN) coupling between qubits, which limits the efficient implementation of low-overhead quantum error correction and access to a wide range of physical models using analog quantum simulation.
This challenge can be overcome by introducing non-local degrees of freedom. For example, photons in a shared channel between qubits can mediate long-range qubit-qubit coupling arising from light-matter interaction. In addition, constructing a scalable architecture requires this channel to be intrinsically extensible, in which case a one-dimensional waveguide is an ideal structure providing the extensible direction as well as strong light-matter interaction.
In this thesis, we explore superconducting circuit architectures based on light-matter interactions in waveguide quantum electrodynamics (QED) systems. These architectures in return allow us to study light-matter interaction, demonstrating strong coupling in the open environment of a waveguide by employing sub-radiant states resulting from collective effects. We further engineer the waveguide dispersion to enter the topological photonics regime, exploring interactions between qubits that are mediated by photons with topological properties. Finally, towards the goals of quantum information processing and simulation, we settle into a multi-qubit architecture where the photon-mediated interaction between qubits exhibits tunable range and strength. We use this multi-qubit architecture to construct a lattice with tunable connectivity for strongly interacting microwave photons, synthesizing a quantum many-body model to explore chaotic dynamics. The architectures in this thesis introduce scalable beyond-NN coupling between superconducting qubits, opening the door to the exploration of many-body physics with long-range coupling and efficient implementation of quantum information processing protocols.</p
Singularity Formation in the High-Dimensional Euler Equations and Sampling of High-Dimensional Distributions by Deep Generative Networks
Get PDFHigh dimensionality brings both opportunities and challenges to the study of applied mathematics. This thesis consists of two parts. The first part explores the singularity formation of the axisymmetric incompressible Euler equations with no swirl in ℝⁿ, which is closely related to the Millennium Prize Problem on the global singularity of the Navier-Stokes equations. In this part, the high dimensionality contributes to the singularity formation in finite time by enhancing the strength of the vortex stretching term. The second part focuses on sampling from a high-dimensional distribution using deep generative networks, which has wide applications in the Bayesian inverse problem and the image synthesis task. The high dimensionality in this part becomes a significant challenge to the numerical algorithms, known as the curse of dimensionality.
In the first part of this thesis, we consider the singularity formation in two scenarios. In the first scenario, for the axisymmetric Euler equations with no swirl, we consider the case when the initial condition for the angular vorticity is Cα Hölder continuous. We provide convincing numerical examples where the solutions develop potential self-similar blow-up in finite time when the Hölder exponent α < α*, and this upper bound α* can asymptotically approach 1 - 2/n. This result supports a conjecture from Drivas and Elgindi [37], and generalizes it to the high-dimensional case. This potential blow-up is insensitive to the perturbation of initial data. Based on assumptions summarized from numerical experiments, we study a limiting case of the Euler equations, and obtain α* = 1 - 2/n which agrees with the numerical result. For the general case, we propose a relatively simple one-dimensional model and numerically verify its approximation to the Euler equations. This one-dimensional model might suggest a possible way to show this finite-time blow-up scenario analytically. Compared to the first proved blow-up result of the 3D axisymmetric Euler equations with no swirl and Hölder continuous initial data by Elgindi in [40], our potential blow-up scenario has completely different scaling behavior and regularity of the initial condition. In the second scenario, we consider using smooth initial data, but modify the Euler equations by adding a factor ε as the coefficient of the convection terms to weaken the convection effect. The new model is called the weak convection model. We provide convincing numerical examples of the weak convection model where the solutions develop potential self-similar blow-up in finite time when the convection strength ε < ε*, and this upper bound ε* should be close to 1 - 2/n. This result is closely related to the infinite-dimensional case of an open question [37] stated by Drivas and Elgindi. Our numerical observations also inspire us to approximate the weak convection model with a one-dimensional model. We give a rigorous proof that the one-dimensional model will develop finite-time blow-up if ε < 1 - 2/n, and study the approximation quality of the one-dimensional model to the weak convection model numerically, which could be beneficial to a rigorous proof of the potential finite-time blow-up.
In the second part of the thesis, we propose the Multiscale Invertible Generative Network (MsIGN) to sample from high-dimensional distributions by exploring the low-dimensional structure in the target distribution. The MsIGN models a transport map from a known reference distribution to the target distribution, and thus is very efficient in generating uncorrelated samples compared to MCMC-type methods. The MsIGN captures multiple modes in the target distribution by generating new samples hierarchically from a coarse scale to a fine scale with the help of a novel prior conditioning layer. The hierarchical structure of the MsIGN also allows training in a coarse-to-fine scale manner. The Jeffreys divergence is used as the objective function in training to avoid mode collapse. Importance sampling based on the prior conditioning layer is leveraged to estimate the Jeffreys divergence, which is intractable in previous deep generative networks. Numerically, when applied to two Bayesian inverse problems, the MsIGN clearly captures multiple modes in the high-dimensional posterior and approximates the posterior accurately, demonstrating its superior performance compared with previous methods. We also provide an ablation study to show the necessity of our proposed network architecture and training algorithm for the good numerical performance. Moreover, we also apply the MsIGN to the image synthesis task, where it achieves superior performance in terms of bits-per-dimension value over other flow-based generative models and yields very good interpretability of its neurons in intermediate layers.</p
New Physics Tools for Discovery, a New Era of Timing Detector, and Lepton Flavor Universality Test at CMS
Get PDFThe field of particle and fundamental physics finds itself now in a peculiar situation. The established Standard Model accurately predicts most of the observations, but several compelling reasons motivate a need for an extension of the current theory. In this thesis, I focus my research on facing the current situation of the field in a diversified threefold manner.
First, I develop methods based on physics-driven machine learning algorithms, with a particular focus on developing a model-independent tagger for unexpected events using artificial neural networks. This study shows how model-independent new physics triggers, possibly trained on real data, can select a low rate stream of events able to explore new physics processes up to a 10-100 pb cross section and can create a special dataset of rare unexpected events. Other important results from this body of work include the first application of the proposed anomaly detection strategy to real data, the use of graph neural networks to improve current pileup mitigation algorithms, the development of jet taggers based on the interaction network, and analysis-specific fast simulation.
Second, I focus on the methodological and hardware development of the MIP Timing Layer that is expected to upgrade CMS in preparation for HL-LHC. My seminal study demonstrates the possibility of using time-of-flight information to perform particle identification, which has a significant impact on heavy stable charged particle searches. This work introduces how to measure time-of-flight at CMS, a strategy for particle identification, and an algorithm to locate vertices in space and time. I also participated in the sensor testing and test beam operation. In particular, I conducted a study about the design and prototype of the detector modules' thermal behavior that shows how different geometries could lead to cooling differences of a few K.
Last, I direct my attention towards CMS's first lepton flavor universality tests with B meson decays. Using a dataset acquired thanks to a custom design trigger, I independently develop the measurement of the R(D*) ratio, a parameter whose tensions between the predictions and observation have drawn remarkable attentions. I oversaw the complete mature state of the analysis, from the Monte Carlo simulation to the fitting procedure. Further collaboration-wide efforts are still required, but I demonstrate the expected sensitivity of about 15% using an Asimov dataset.</p
Experimental and Theoretical Studies of Unstable Dynamics of Caltech’s Plasma Jet: X-Rays, Ultraviolet, and Visible Light
Get PDFThe Caltech plasma jet experiment launches a laboratory plasma jet that is analogous to an astrophysical jet. Even though the temperature of the plasma jet is around 2 eV, 6 keV X-rays and 20--60 eV extreme ultraviolet (EUV) radiation were detected when the plasma jet was perturbed by magnetohydrodynamic instabilities. How charged particles in a plasma are accelerated to suprathermal energy has been a key question in plasma physics, solar physics, and astrophysics. Studying these surprisingly energetic radiations from Caltech’s plasma jet can help answer this question. Toward this goal, this thesis contains an experimental study of the X-rays and a theoretical study of the EUV radiation.
In the experimental study, a PIN-diode-based 1D X-ray camera has been developed to spatially, temporally, and spectrally resolve the transient, low-intensity, and suprathermal X-rays detected to be simultaneous with magnetohydrodynamic instabilities that disrupt the plasma jet. This X-ray camera has high detection efficiency over the 5–10 keV X-ray band, an over 20-degree field of view (FOV), and the capability to produce more than 50 time-resolved frames with a submicrosecond time resolution. The X-ray images are formed by a pinhole or by a coded aperture placed outside the vacuum chamber in which the plasma jet is launched. The 1D imaging shows that the location of the X-ray source is either a few centimeters away from an inner disk electrode or near a spatially translatable metal frame that is 30–40 cm away from the electrode.
In the theoretical study, we propose a collisional two-fluid model which involves a novel two-stream instability that is indifferent to collisions, even though collisions have been traditionally presumed to damp the two-stream instability. This model is used to explain previously observed localized dimming of visible light and a simultaneous, localized burst of EUV radiation from a plasma jet the cross section of which is constricted by a kink-instigated Rayleigh-Taylor instability. On being triggered by the constriction of the plasma cross section, the proposed two-stream instability produces a region of low density where an electric double layer leads to localized electron heating. The low-density region is consistent with and so likely explains the visible light dimming, and the localized electron heating is consistent with and likely explains the EUV radiation. The numerical solution of the collisional two-fluid model demonstrates good agreement with the apparent electron velocity and density profiles in the plasma jet.</p
On Multiscale and Statistical Numerical Methods for PDEs and Inverse Problems
Get PDF This thesis focuses on numerical methods for scientific computing and scientific machine learning, specifically on solving partial differential equations and inverse problems. The design of numerical algorithms usually encompasses a spectrum that ranges from specialization to generality. Classical approaches, such as finite element methods, and contemporary scientific machine learning approaches, like neural nets, can be viewed as lying at relatively opposite ends of this spectrum. Throughout this thesis, we tackle mathematical challenges associated with both ends by advancing rigorous multiscale and statistical numerical methods.
Regarding the multiscale numerical methods, we present an exponentially convergent multiscale finite element method for solving high-frequency Helmholtz's equation with rough coefficients. To achieve this, we first identify the local low-complexity structure of Helmholtz's equations when the resolution is smaller than the wavelength. Then, we construct local basis functions by solving local spectral problems and couple them globally through non-overlapped domain decomposition and Galerkin's method. This results in a numerical method that achieves nearly exponentially convergent accuracy regarding the number of local basis functions, even when the solution is highly non-smooth. We also analyze the role of a subsampled lengthscale in variational multiscale methods, characterizing the tradeoff between accuracy and efficiency in the numerical upscaling of heterogeneous PDEs and scattered data approximation.
As for the statistical numerical methods, we discuss using Gaussian processes and kernel methods to solve nonlinear PDEs and inverse problems. This framework incorporates the flavor of scientific machine learning automation and extends classical meshless solvers. It transforms general PDE problems into quadratic optimization with nonlinear constraints. We present the theoretical underpinning of the methodology. For the scalability of the method, we develop state-of-the-art algorithms to handle dense kernel matrices in both low and high-dimensional scientific problems. For adaptivity, we analyze the convergence and consistency of hierarchical learning algorithms that adaptively select kernel functions. Additionally, we note that statistical numerical methods offer natural uncertainty quantification within the Bayesian framework. In this regard, our further work contributes to some new understanding of efficient statistical sampling techniques based on gradient flows.</p
Diversity in Notch Ligand-Receptor Signaling Interactions
Get PDFThe ability to understand and predict signaling between different cell types is a major challenge in biology. The Notch pathway enables direct signaling through membrane-bound ligands and receptors, and is used in diverse contexts. While its canonical molecular signaling mechanism is well characterized, its many-to-many interacting pathway components, the complexity of their expression patterns, and the presence of same-cell (cis) as well as inter-cellular (trans) receptor-ligand interactions, have made it difficult to predict how a given cell will signal to others. Here, we use a cell-based approach, with Chinese hamster ovary (CHO-K1) cells and C2C12 mouse myoblasts, to systematically characterize trans-activation, cis-inhibition, and cis-activation efficiencies for the essential receptors (Notch1 and Notch2) and activating ligands (Dll1, Dll4, Jag1, and Jag2), in the presence of Lunatic Fringe (Lfng) or the enzymatically dead Lfng D289E mutant. All ligands trans-activate Notch1 and Notch2, except for Jag1, which competitively inhibits Notch1 signaling, and whose Notch1 binding strength is potentiated by Lfng. For Notch1, cis-activation is generally weaker than trans-activation, but for Notch2, cis-activation by Delta ligands is much stronger than trans-activation, and Notch2 cis-activation by Jag1 is similar in strength to trans-activation. Cis-inhibition is associated with weak cis-activation, as Dll1 and Dll4 do not cis-inhibit Notch2. Lfng expression potentiates trans-activation of both Notch1 and Notch2 by the Delta ligands and weakens trans-activation of both receptors by the Jagged ligands. The map of receptor-ligand-Fringe interaction outcomes revealed here should help guide rational perturbation and control of the Notch pathway
Regularities, Resurgence and R-Matrices in Chern Simons Theory
Get PDFThis thesis aims to address two related but distinct problems in Chern Simons theory:
1. In 2019, Gukov and Manolescu observed that for fixed a knot K, the family of coloured Jones polynomials Jk(K; q) display regularity in colour k and conjectured that this could be captured by a 2 variable series FK(x, q). Over the subsequent few years, Park proved that, for a large family of knots, FK(x, q) could be computed using the R-matrix for a particular Verma module.
We will show that it is possible to extend the work of Park to compute the 2 variable series FNK(x, q) associated to other lie groups, slN, which capture a similar regularity in the quantum invariants PNk(K; q). Following on from this we will further show that in many cases these series FNK(x, q) themselves display a regularity in N, reminiscent of the HOMFLY-PT polynomial, allowing the construction of a 3 variable series FK(x, a, q) interpolating FNK(x, q) for all N.
2. Complex Chern Simons theory is a rare example of Quantum field theory with both interesting non-perturbative behaviour and whose perturbative expansion can be computed to high order. For a nice class of 3-manifolds, namely surgeries on knot complements, we will show how to predict aspects of the non-perturbative behaviour first semi-classically and then, using resurgence, through studying just the perturbative expansion around the trivial flat connection. Finally, we show that contrary to expectation, these families of 3-manifolds display regularity in the surgery coefficient.</p
A Novel Algorithm for Inferring the Vertical Distribution of Trace Gases Using Remote Sensing Measurements
Get PDFRemote sensing is a powerful tool that is used to diagnose sources, sinks, and fluxes of trace gases across different spatial and temporal scales. Ground-based remote sensing measurements of column-averaged dry mole fractions (DMF) of gases such as carbon dioxide (CO₂) and carbon monoxide (CO) made by the Total Carbon Column Observing Network (TCCON) are used to validate space-based measurements and better understand the carbon cycle. Surface signals of gas exchange can be masked in the total column values, however, limiting their use in assessment of local surface fluxes. Retrievals of the vertical distribution of trace gases can be used to obtain gas exchange information that is more directly related to changes at the surface but require high precision measurements with less temporal resolution than the TCCON total column measurements. In this thesis, I develop an algorithm, the Temporal Atmospheric Retrieval Determining Information from Secondary Scaling (TARDISS), that infers vertical information, or ‘partial columns’, from existing, quality-controlled total column data. The TARDISS algorithm does not fit the solar spectra but rather begins with trace gas column retrievals obtained from different spectral bands using the standard TCCON retrievals. TARDISS takes advantage of the fact that different bands have different sensitivities to the same trace gas as a function of altitude and solar zenith angle. We use the TARDISS partial column data to examine estimated surface fluxes in the North American boreal forest and compare them to surface fluxes estimated from tall tower in situ measurements. We also outline changes in air quality from the sudden change in traffic behavior from the COVID-19 lockdown which serves as motivation for the use of the TARDISS-derived lower partial column CO data to examine recent changes in air quality in the South Coast Air Basin
Essays in Behavioral Economics
Get PDFThis dissertation contains three essays in three chapters. Chapter 1 contributes to the literature on reference dependent preferences, chapter 2 introduces a new solution concept for games played by teams of players, and chapter 3 analyzes a model of biased beliefs in law enforcement.
In Chapter 1, I study the role of reference dependent preferences in motivating effort in online chess. In online chess, players are assigned ratings that measure chess skill and update after every game. I find evidence of bunching above round numbers in the distribution of ratings, suggesting that players care about their rating and that round numbers serve as reference points. I estimate a dynamic discrete choice model of the decision to end a playing session that nests both loss aversion and an alternative 'aspiration' specification involving a discrete jump in utility at reference points. I reject loss aversion in favor of aspirational preferences. I show that higher skilled players are significantly more aspirational, and that aspiration does not diminish with experience.
In Chapter 2, coauthored with Jeongbin Kim and Thomas R. Palfrey, we develop a general framework for the analysis of games where each player is a team and members of the same team all receive the same payoff. The framework combines standard non-cooperative game theory with collective choice theory, and is developed for both strategic form and extensive form games. We introduce the concept of team equilibrium and identify conditions under which it converges to Nash equilibrium with large teams. We identify conditions on the collective choice rules such that team decisions are stochastically optimal: the probability the team chooses an action is increasing in its equilibrium expected payoff. The theory is illustrated with some binary action games.
In Chapter 3, I model a social welfare maximizing law enforcement agency that does not know the supply of crime, that may have incorrect beliefs about its ability to detect crime, and that only observes the quantity of crime that it detects. An equilibrium is defined in which the enforcement agency is not surprised by the crime data it observes, and believes itself to be maximizing social welfare. Sufficient conditions for existence are provided. The model is shown to capture the intuition of crime-policing 'feedback loops' in which inefficient overpolicing or underpolicing is supported in equilibrium.</p
Habitability Through Time: Photochemistry and Aerosols of Planetary Atmospheres
Get PDFThe unique geologic preservation of much of Mars’ ancient surface provides a window into its earliest history, and hence the early history of the solar system. Extensive geological and mineralogical evidence suggest that ancient Mars once had large volumes of surface liquid water, which likely persisted over timescales of 10⁵ - 10⁷ years during the Noachian era (e.g., Carr et al., 2003; Clifford et al., 2001; Barnhart et al., 2009; Schon et al., 2012). Explaining this evidence for surface liquid water is challenging, however, because of Mars’s distant orbit and the lower luminosity of the young Sun 3-4 billion years ago. The faint young Sun paradox is an important problem in planetary science that challenges our ability to understand atmospheric evolution in general, including Earth, Mars, and rocky exoplanets (e.g., Sagan 1972).
The precise composition and climate of the early atmosphere overtime largely remains an open question. In 2014, it was first recognized that early Mars could have been episodically warmed by the greenhouse effects of H₂ in a CO₂ atmosphere (e.g., Wordsworth et al., 2017); however, no sustained source of H₂ was identified in the literature (noting that volcanism would have been short lived). Chapter 2 presents a solution: crustal hydration (the loss of surface water to reduced iron and hydrated minerals) likely supplied large fluxes of H₂. Over a timescale of 10⁷ years (the upper limit for the duration of large volumes of surface liquid water), crustal hydration provides a flux of H₂ into the atmosphere large enough to sustain a surface temperature >273 K in a ≥ 1 bar Noachian atmosphere. Importantly, Mars was likely warm over only a fraction of its early history, and cold early atmospheres likely also existed during early Mars’ history. In cool climates, I find that a loss of atmospheric oxidants to the ground (to oxidize surface reduced iron) caused CO₂ to convert to CO in agreement with the results of Zahnle et al. (2008). Furthermore, a warm and wet climate suggests early Mars may have been similar to early Earth; however, the climate alone is not enough to suggest that early Mars may have been habitable. In Chapters 3 and 4, I investigate whether Mars may have had a nitrogen cycle, which would be important for nitrogen fixation. I used KINETICS, the Caltech-JPL 1D photochemical model, to explain present day deposits in Mars’ soil samples. The Sample Analysis at Mars instrument onboard Mars Science Laboratory (MSL) has baked several volatile species out of the unique rock record at Mars, including nitrate (e.g., Sutter et al., 2017). The formation of these species would originate in the atmosphere as a result of photochemistry. In Chapter 3, I discover that nitrogen fixation in a warm and wet climate with lightning is able to explain the weight percent of nitrate measured by the MSL; lightning-induced NOx forms nitric acid in the atmosphere, and this nitric acid may dissolve in water, rain out to the surface, and undergo photoreduction in shallow surface waters. In Chapter 4, I discover a comparable amount of pernitric acid may be explained from formation in an icy climate; SEP-induced N(2D) attacks CO₂ to form NOx which reacts with HO₂ to form HO₂NO₂.
The relatively new subfield of comparative planetology between Mars’ evolution and exoplanet evolution (specifically, close-in super-Earths) will soon open, in the new era of the James Webb Space Telescope (JWST). I have prepared for this subfield by working with a suite of established numerical models to investigate the formation of prebiotic species in the reduced atmospheres of super-Earths (in Chapter 5) and the aerosols at warm gas Giants. In Chapter 6, I discover that aggregate hazes at warm sub-Neptunes, which result from methane photolysis, can explain the observed flat exoplanet spectra and muted spectral features, including the observations of GJ 1214b. In Chapter 7, I discover that the atmospheric dynamics of hot Jupiters cause patchy clouds of forsterite, iron, and titanium dioxide, and the 3D structure of the clouds helps explain the phase-integrated albedos of six worlds observed by HST.</p