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Topological Invariants of Interacting Gapped Quantum Materials and Transport Phenomena
Get PDFIn this thesis we study transport properties of interacting lattice system focusing, on those which become topologically protected at low temperatures for gapped Hamiltonians.
We prove the vanishing of the net energy currents in
equilibrium states of lattice systems as well as systems of nonrelativistic particles with finite-range potential interactions. We derive Kubo-like formulas for the thermal and thermoelectic Hall conductances of arbitrary 2d lattice systems which are free from
ambiguities associated with the definition of magnetizations. We use these formulas to define a relative topological invariant of gapped 2d lattice systems at zero temperature.
We define and study analogs of the Thouless charge pump and Berry Curvature for many-body gapped systems in spatial dimension D. We show how to attach a topological invariant to a D-dimensional family of such systems. For a large class of families we argue that this topological invariant is an integer.</p
Probing the Buckling of Thin-Shell Space Structures
Get PDFThe overarching goal of the research presented in this dissertation is to apply and extend a newly developed methodology to understand the buckling of complex thin shell structures. This methodology enables the determination of tighter buckling criteria and paves the way to the development of more efficient structures, used closer than ever to their buckling load and even beyond. It would result in dramatically lighter structures to be built and has the potential to enable new applications, such as extremely large aperture satellites.
We first analyze the stability of open section thin shell structures under a pure bending moment, through simulations. These structures are composed of longitudinal thin-shell elements connected transversely by thin rods, and inspired by real spacecraft structures. The present study applies and extends recent work on the stability of cylindrical and spherical shells. The role of localization in the buckling of these structures is investigated and early transitions into the post-buckling regime are unveiled using a probe that locally displaces the structure. The probing method enables the computation of the energy input needed to transition early into a post-buckling state, which is central to determining the critical buckling mechanism for the structure. We show that the structure follows stability landscapes also found in cylindrical and spherical shell buckling problems. This initial computational study is the basis for the first ever probing experiment on a complex structure.
In order to test these new structures under bending, a new bending apparatus is designed and implemented. The boundary conditions are chosen such that the apparatus is statically determinate (isostatic), and no state of self stress can develop in the sample during its mounting and testing. This feature is especially desirable in the study of thin shell structures and their elastic instabilities, for which imperfection sensitivity plays a crucial role in the buckling transition and the post-buckling regime. The accuracy of the isostatic bending machine is first assessed through the testing of rods, and its imperfection insensitive behavior is then highlighted in experiments on tape springs, and through numerical studies of the same structures.
The new bending machine is complemented by a probing apparatus, and the stability of the open section thin-shell structures subjected to a pure bending moment is studied experimentally. The experiment confirms that localization of deformations plays a paramount role in the structure's nonlinear post-buckling regime and is extremely sensitive to imperfections. This characteristic is investigated through probing experiments. The range of moments for which the early buckling of the structure can be triggered using this probe perturbation is determined, as well as the energy barrier separating the pre-buckling and post-buckling states. The stability of the local buckling mode is then illustrated by an experimental stability landscape of shell buckling, and probing is then extended to the entire structure to reveal alternate buckling modes disconnected from the structure's fundamental path. These results can be used to elaborate efficient buckling criteria for this type of structures, through the use of transition diagrams determined experimentally.
Finally, the buckling and post-buckling behavior of ultralight ladder-type coilable structures is investigated. These specific structures are used in the Space Solar Power Project at Caltech and are referred to as strips. Similarly to the previous studies, the stability of strip structures loaded by normal pressure is computationally studied by applying controlled perturbations through localized probing. The probing technique is generalized to higher-order bifurcations along the post-buckling path, and low-energy escape paths into buckling that cannot be predicted by a classical eigenvalue formulation are identified. It is shown that the stability landscape for a pressure-loaded strip is similar to the landscape for classical shells, and the open section thin shell structure studied initially in this thesis. While classical shell structures buckle catastrophically, strip structures feature a large stable post-buckling range. Probing enables the full characterization of the structure's unstable behavior, which paves the way to extend its operation closer than ever to the buckling load, and even in the post-buckling regime. It would enable the design of more efficient structures by dramatically reducing their mass, therefore enabling new large spacecraft to be built.</p
Messy Definitions and Blurred Lines: Marriage, Autonomy, and Reconciliation in Shakespeare’s Measure for Measure
No full text[Introduction] “The tempter or the tempted, who sins the most?” (2.2.200) – Angelo’s question of sin represents the overall tension between violence and reconciliation in Measure for Measure. But why does Shakespeare create tensions between the Latin lex talionis, “eye for an eye” and the biblical consideration of “measure for measure”? What do the different forms of reconciliation mean for the different characters in the play? And are they effective forms of justice? An answer, perhaps, lies in Shakespeare’s presentation of marriage. Measure for Measure depicts marriage specifically as a form of reparation for violence: the characters in the play do not repent for their various sins through jail time or death, only through potentially unhappy marriages. In doing so, Shakespeare constructs his own set of terms in which the reader must consider the concept of a late medieval marriage: marriage in the play does not always take the form of a conventual, consensual relationship, instead Shakespeare uses forced marriage to challenge the Catholic tradition of marriage as a sacrament and the growing Puritan ideal of marriage for companionship. Through the marriages of Claudio and Juliet, Mariana and Angelo, and the ambiguous silence of the Duke’s proposal to Isabella, Shakespeare compares and contrasts different foundations for marriage, making an appeal to the audience to interpret their purpose. Shakespeare plays with the ideals of consent, companionship, and the law to create several competing implementations of a “measure for measure.” The audience must decide which, if any of these marriages are satisfying, and to what extent that, in light of the violence of the play, they can constitute their own form of justice, and their own “measure for measure.
Online Convex Optimization and Predictive Control in Dynamic Environments
Get PDFWe study the performance of an online learner under a framework in which it receives partial information from a dynamic, and potentially adversarial, environment at discrete time steps. The goal of this learner is to minimize the sum of costs incurred at each time step and its performance is compared against an offline learner with perfect information of the environment.
We are interested in the scenarios where, in addition to some costs at each time step, there are some penalties or constraints on the learner's successive decisions. In the first part of this thesis, we investigate a Smoothed Online Convex Optimization (SOCO) setting where the cost functions are strongly convex and the learner pays a squared ℓ₂ movement cost for changing decision between time steps. We shall present a lower bound on the competitive ratio of any online learner in this setting and show a series of algorithmic ideas that lead to an optimal algorithm matching this lower bound. And in the second part of this thesis, we investigate a predictive control problem where the costs are well-conditioned and the learner's decisions are constrained by a linear time-varying (LTV) dynamics but has exact prediction on the dynamics, costs and disturbances for the next k time steps. We shall discuss a novel reduction from this LTV control problem to the aforementioned SOCO problem and use this to achieve a dynamic regret of O(λkT) and a competitive ratio of 1 + O(λk) for some positive constant λ < 1.</p
Electro-Optically Tunable Metasurfaces for a Comprehensive Control of Properties of Light
Get PDFThe ability to control electromagnetic wavefront is a central key in optics. Conventional optical components rely on the gradual accumulation of the phase of light as it passes through an optical medium. However, since the accumulated phase is limited by the permittivity of naturally existing materials, such a mechanism often results in bulky devices that are much thicker than the operating wavelength.
During the last several years, metasurfaces (quasi-2D nanophotonic structures) have attracted a great deal of attention owing to their promise to manipulate constitutive properties of electromagnetic waves such as amplitude, phase, and polarization. Metasurfaces are ultrathin arrays of subwavelength resonators, called meta-atoms, where each meta-atom imposes a predefined change on the properties of the scattered light. By precisely designing the optical response of these meta-atoms to an incident wave, metasurfaces can introduce abrupt changes to the properties of the transmitted, reflected, or scattered light, and hence, can flexibly shape the out-going wavefront at a subwavelength scale. This enables metasurfaces to replace conventional bulky optical components such as prisms or lenses by their flat, low-profile analogs. Furthermore, a single metasurface can perform optical functions typically attained by using a combination of multiple bulky optical elements, offering tremendous opportunities for flat optics.
The optical response of a metasurface is typically dictated by the geometrical parameters of the subwavelength scatterers. As a result, most of the reported metasurfaces have been passive, namely have functions that are entirely fixed at the time of fabrication. By making the metasurfaces reconfigurable in their phase, amplitude, and polarization response, one can achieve real-time control of optical functions, and indeed, achieve multi-functional characteristics after fabrication. Dynamical control of the properties of the scattered light is possible by using external stimuli such as electrical biasing, optical pumping, heating, or elastic strain that can give rise to changes in the dielectric function or physical dimensions of the metasurface elements.
In this dissertation, we present the opportunities and challenges towards achieving reconfigurable metasurfaces. We introduce a paradigm of active metasurfaces for real-time control of the wavefront of light at a subwavelength scale by investigating different modulation mechanisms and possible metasurface designs and material platforms that let us effectively employ the desired modulation mechanism. We will present multiple electro-optically tunable metasurface platforms. These electronically-tunable schemes are of great interest owing to their robustness, high energy-efficiency, and reproducibility. We will also show the design and experimental demonstration of active metasurfaces for which the tunable optical response can be tailored in a pixel-by-pixel configuration.
The ability to individually control the optical response of metasurface elements has made active optical metasurfaces to be progressively ubiquitous by enabling a wide range of optical functions such as dynamic holography, light fidelity (Li-Fi), focusing, and beam steering. As a result, reconfigurable metasurfaces can hold an extraordinary promise for optical component miniaturization and on-chip photonic integration. Such compact and high-performance devices with reduced size, weight, and power (SWaP) can be used in future free-space optical communications or light detection and ranging (LiDAR) systems.</p
Chirped Pulse Microwave and Single-Shot Terahertz Spectroscopy Studies of Intermolecular Interactions
Get PDFWhile the glow of a sodium vapor lamp or the crisp reds in autumn leaves are eye-catching examples of transitions between atomic and molecular energy levels (hv ~2-3 eV), it is arguably the much lower energy, thermally populated intermolecular "bath" states (hv ~10⁻⁵-10⁻² eV) that contribute most directly to the physical properties of matter. Although invisible to the human eye, in this thesis we study fundamentals of these low-energy interactions with two complementary techniques: chirped pulse microwave spectroscopy and nonlinear single-shot terahertz (THz) Kerr effect spectroscopy.
In the first section, we apply chirped pulse-Fourier transform microwave (CP-FTMW) spectroscopy from 8-16 GHz to study fundamental hydrogen bonding motifs in gas phase alcohol water dimers. Hydrogen bonding is ubiquitous in nature and directly contributes to a range of phenomena from phase transitions in water to solvation of ions to enzymatic activity. Our focus on gas phase dimers reduces the spectral ambiguity arising in condensed phase samples, where inhomogeneous and homogeneous broadening can hamper observation of conserved intermolecular interaction motifs. The hydrogen bonding conformation of two alcohol-water dimers, n-propanol-water and isopropanol-water, were characterized. Both were found to adopt a shared water donor-alcohol acceptor conformation.
The following sections use nonlinear THz spectroscopy from 0.1-10 THz to investigate molecular dynamics in the condensed phase. We focus on halogenated methane liquids, whose intense intramolecular vibrational modes are commensurate in energy to the intermolecular bath states. One central goal of this section was developing a technique to more rapidly collect nonlinear, multi-dimensional data from liquid systems. To that end, we developed a single-shot measurement approach using a reflective nickel echelon mirror and a high frame rate camera. With this new device we achieved an order of magnitude reduction in experimental integration times. High resolution, nonlinear multi-dimensional THz studies of several halogenated methane liquids and materials were produced as a result. From these data, we identified important spectral contributions from the experimental instrument response function.</p
Planetary Atmospheres: Astrobiologically Relevant Icy Worlds and Earth as a Proxy Exoplanet
Get PDF"How did we get here?" is a long-standing question in planetary science. Characterizing the pre-biotic atmospheric environment in which life may emerge is critical and increasingly urgent. Given the fact that the Earth provides the only ground truth of habitable worlds, most of the characterizations are based on the current Earth. However, life did not emerge on the modern Earth. It instead took place in a prebiotic environment, which includes a nitrogen-dominated, methane-abundant and oxygen-negligible reducing atmosphere. Therefore, this type of planetary atmospheres has great significance in the context of astrobiology and the search for life. Despite that real time observations can not be obtained for Early-Earth, spacecraft observations of the atmospheres of two icy worlds in the solar system, Titan and Pluto, can provide such valuable constraints. The theme of Chapter 2 and 3 of this thesis focus on this topic of investigating the atmospheres of Titan and Pluto using spectroscopic analysis. Chapter 4 studies the search for life also across the spectrum from a prospective the other way. It characterizes the Earth, the only known inhabited planet, as an exoplanet proxy, to derive observational benchmarks for habitability assessment.
Chapter 2 studies Titan. It retrieves the hydrocarbon and nitrile species in Titan’s upper atmosphere using stellar occultation observations obtained by Cassini UltraViolet Imaging Spectrograph (UVIS) during its Titan flybys. An innovative method is introduced to consider the pointing issue of the instrument, which prevents most of the previous spectral analyses. Combing an instrument simulator for handling the pointing motion and the Markov-Chain Monte Carlo (MCMC) method for parameter searching, species abundances in Titan’s atmosphere are successfully retrieved during occultations with large pointing motions. The method also obtains the altitude range where the abundance of each species could be constrained.
Chapter 3 studies Pluto. It investigates the morphology and microphysical processes of Pluto’s haze particles in the lower 50km of its atmosphere using observations obtained by multiple instruments onboard the New Horizons spacecraft during its Pluto flyby in 2015. It suggests that Pluto’s haze particles have a bimodal distribution: a large-size population of ~1μm fractal aggregates, which consists of ~20nm monomers, and a small-size one of ~80nm. This result successfully addresses the disagreement among the instruments, and provides important constraints on transport and dimensional transition of haze particles in Pluto’s atmosphere.
Chapter 4 studies exoplanets. It evaluates the observational baseline for Earth-like exoplanets using the Earth as a proxy. Observations of the Earth’s images obtained by the Deep Space Climate ObserVatoRy (DSCOVR) are integrated to one single point to generate light curves of the "proxy" planet. Using the singular value decomposition (SVD) method, we found that the surface information of the "proxy" planet is in the second principal component (PC) of its light curves, while the first PC mainly consists of that of clouds. Using the strong linear correlation between the time series of the second PC and the corresponding land fraction, we constructed the first two-dimensional surface map of the Earth seen from a hypothetical distant observer, an observer who treats the Earth as an exoplanet.</p
Computational Investigation of Nanoscale Electrocatalysts for Clean Energy Conversion
Get PDFElectrocatalysis provides a practical solution to the increasing global energy demand while maintaining a sustainable environment. Recently nanoscale catalysts (nanoparticles, nanowires, and dealloyed surfaces) have been shown to have experimentally far superior performance than metallic crystals at sustainable energy conversion. However, the surface feature of these improved catalysts is still unknown, as the detection of the active sites directly from experiment has not been possible.
In this thesis work, we discuss using the quantum mechanics based muitiscale simulations and machine learning to understand the nature of these superior materials. We first studied jagged Pt nanowire (J-PtNW), which was shown to have performance at oxygen reduction reactions (ORR) 50 times better than Pt/C. We used multiscale simulations (reactive force field, and density functional theory) to explain this remarkably accelerated ORR activity from an atomistic perspective. Next, we looked into the irregular gold surfaces and copper surfaces (nanoparticles and dealloyed surfaces), which showed dramatically improved performance at CO2 reduction reactions (CO2RR) and CO reduction reactions (CORR). We developed the strategy to combine the reactive force field, density functional theory, and machine learning to identify the active sites responsible for their improved performance. This approach provided the possibility to understand the highly irregular and disordered surface, which is impossible with surface science experiments or with quantum mechanics. The identification of the active sites provides insights into new design concepts (alloys, NP, NW, and electrolytes such as ionic liquids) aimed at increasing product selectivity and rates simultaneously with reducing energy requirements.</p
Understanding Pattern Formation and Improving Fidelity in Phototropic Growth
Get PDFPhototropic growth of Se-Te yields highly anisotropic lamellar nanostructures and is achieved photoelectrochemically from an isotropic solution of oxidized Se and Te precursors deposited onto isotropic conductive substrates under conformal illumination. In contrast to other spontaneous patterning processes, phototropic growth has no requirement for illumination source coherency and can be performed under mild conditions using low illumination power. Furthermore, as a bottom-up, solution-based synthesis, phototropic growth is scalable and demonstrates high tunability via optical input (i.e. control of wavelength and polarization). However, relative to more traditional lithographic patterning methods, phototropically grown films exhibit defective patterns which may impede their application in devices requiring high pattern fidelities.
Chapter I investigates the role of the growth substrate and its effect on pattern fidelity in phototropically grown Se-Te films, quantified by peak-fitting and analysis of frequency modes in 2D Fourier transform spectra. The work function or Fermi level of the substrate was determined to be the major factor in determining pattern fidelity. Substrates that had work functions closely aligned with Se-Te (p⁺-Si and Au) demonstrated higher fidelity patterns than those that had misaligned work functions (n⁺-Si and Ti). In cases of both nominally identical illumination conditions and nominally identical growth rates, phototropically grown Se-Te films on p⁺-Si exhibited a higher degree of anisotropy and higher pattern fidelity than phototropically grown Se-Te films on n⁺-Si, attributed to energetics and charge conduction at the junction formed by the substrate and growing Se-Te film.
Chapter II follows up on the analysis performed in Chapter I by investigating the role of nucleation and the earliest levels of mass addition to growth substrates in the phototropic growth of Se-Te films. In particular, the relationship between the inter-nucleate spacing of the initial dark electrodeposited material and the pattern formation pathways during the phototropic growth process is described. Conditions that produced small nucleate spacings resulted in phototropically grown films with a higher pattern fidelity and a pattern period that more strongly agreed with the theoretical trend (λ/2n). Furthermore, on substrates that generally produced low pattern fidelity films, use of an applied striking potential during the initial nucleation stage demonstrated both smaller nucleate spacings and improved pattern fidelity of resulting phototropically grown films.
Finally, Chapter III investigates the effect of extrinsic (i.e. lithographically patterned) optical scattering elements on the phototropic growth process. Relative to non-templated substrates, substrates with templated ridges demonstrated higher pattern fidelities, confined pattern periods, and enforced pattern orientation. Full-wave electromagnetic modeling and Monte Carlo growth simulations of Se-Te onto simulated templated substrates resulted in simulated films demonstrating good agreement with the patterns observed experimentally. In simulation, for a given set of illumination conditions that produced a single pattern period on non-templated substrates, films grown on templated substrates were able to attain a much wider range of periods (~80% to ~160% vs. the non-templated pattern period). Additionally, the orientation of phototropically grown patterns (usually dependent on the axis polarization) were enforced to the orientation of the templates to an angular offset tolerance of up to ~40°.</p
Fabrication of Pristine and Doped Graphene Nanostripes and their Application in Energy Storage
Get PDFFossil fuel usage causing rising CO2 levels and leading to climate change is, perhaps, the most pressing issue of our time. However, our economic dependence on energy necessitates its usage such that reducing energy usage is not possible leaving transitioning to renewable energy technologies as the only sustainable option. Currently, the largest barrier to large scale incorporation of renewable energy sources (e.g., solar, wind) is the high cost of energy storage technologies. Electrochemical energy storage technologies (e.g., lithium-ion batteries and supercapacitors) have been identified as a key approach for enabling the transition to renewable energy technologies.
Graphene is a material with exceptional properties that is receiving much attention for application in various energy storage technologies and could help reduce the cost of energy storage technologies. This thesis describes a novel fabrication procedure for low-cost and efficient synthesis of high-quality graphene nanostripes (GNSPs) and their application in lithium-ion battery and supercapacitor electrodes.
This thesis is structured as follows. Chapter 1 outlines the motivation and technical background of this research. Chapter 2 describes the instrumentation and procedures for fabricating GNSPs. Chapter 3 describes in situ exfoliation of GNSPs as electrodes in supercapacitors to increase the capacitance. Chapter 4 describes synthesis and application of pyridinic-type nitrogen-doped GNSPs as a lithium-ion battery anode. Chapter 5 describes the synthesis and application of silicon-, germanium-, and tin-doped GNSPs and their application in lithium-ion battery anodes. Chapter 6 concludes and synthesizes the findings of the thesis holistically. Additionally, future outlook and potential research objectives are presented.</p