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Effective Field Theory Topics in the Modern S-Matrix Program
Get PDFQuantum field theory is the most predictive theory of nature ever tested, yet the scattering amplitudes produced from the standard application of Lagrangians and Feynman rules belie the simplicity of the underlying physics, obscuring the physical answers behind off-shell actions and gauge redundant descriptions. The aim of the modern S-matrix program (or the "amplitudes" subfield) is to reformulate specific field theories and manifest underlying structures in order to make high multiplicity and/or high loop scattering calculations tractable.
Many of the systems amenable to amplitudes techniques are actually intimately related to each other through the double-copy relations. We argue that conformal invariance is common thread linking several of the scalar effective field theories appearing in the double copy. For a derivatively coupled scalar with a quartic O(p⁴) vertex, classical conformal invariance dictates an infinite tower of additional interactions that coincide exactly with Dirac-Born-Infeld theory analytically continued to spacetime dimension D = 0. For the case of a quartic O(p⁶) vertex, classical conformal invariance constrains the theory to be the special Galileon in D = -2 dimensions. We also verify the conformal invariance of these theories by showing that their amplitudes are uniquely fixed by the conformal Ward identities. In these theories, conformal invariance is a much more stringent constraint than scale invariance.
Although many of the theories in the double-copy admit a high degree of space-time symmetry, amplitudes tools can be applied to non-relativistic theories as well. We explore the scattering amplitudes of fluid quanta described by the Navier-Stokes equation and its non-Abelian generalization. These amplitudes exhibit universal infrared structures analogous to the Weinberg soft theorem and the Adler zero. Furthermore, they satisfy on-shell recursion relations which together with the three-point scattering amplitude furnish a pure S-matrix formulation of incompressible fluid mechanics. Remarkably, the amplitudes of the non-Abelian Navier-Stokes equation also exhibit color-kinematics duality as an off-shell symmetry, for which the associated kinematic algebra is literally the algebra of spatial diffeomorphisms. Applying the double copy prescription, we then arrive at a new theory of a tensor bi-fluid. Finally, we present monopole solutions of the non-Abelian and tensor Navier-Stokes equations and observe a classical double copy structure.</p
Control of Wall-Bounded Turbulence Through Closed-Loop Wall Transpiration
Get PDFMany wall-bounded flows of practical relevance are turbulent, including the flows past airplanes and ships. The turbulent motions enhance momentum mixing and, as a result, the drag force on the engineering surface increases, for transportation vessels typically by at least a factor of two compared to laminar flow. Turbulent flow control aimed at drag reduction therefore has the potential to deliver enormous energetic and economic savings, but many challenges remain despite active research for well over a century. The present thesis aims to contribute towards two open questions of the field: first, what are suitable controller design tools for high Reynolds number flows? And second, how does actuation through closed-loop wall transpiration change the flow physics? We investigate aspects of these questions through direct numerical simulation (DNS) and modal analyses of an example control scheme, which is applied to a low Reynolds number turbulent channel flow. The controller is a generalization of the opposition control scheme, and introduces a phase shift between the Fourier transformed sensor measurement and actuator response.
The first part of the thesis demonstrates that a low-order model based on the resolvent framework is able to approximate the drag reduction results of DNS over the entire parameter space considered. The model is about two orders of magnitude cheaper to evaluate than DNS at low Reynolds numbers, and we present a strategy based on subsampling of the wave number space and analytical scaling laws that enables model-based flow control design at technologically relevant Reynolds numbers. The second part of the thesis shows that the physics of the controlled flow can be understood from two distinct families of spatial scales, termed streamwise-elongated and spanwise-elongated scales, respectively. Wall transpiration with streamwise-elongated scales attenuates or amplifies the near-wall cycle and therefore leads to drag reduction or increase, depending on the phase shift. In contrast, wall transpiration with spanwise-elongated scales only leads to drag increase, which occurs at positive phase shifts and is due to the appearance of spanwise rollers which largely enhance momentum mixing. Both patterns are robust features of flows with closed-loop wall transpiration, and the present study offers a simple explanation of their origin in terms of phase relations at distinct spatial scales. The findings of this study may set the stage for a unifying framework for various forms of wall transpiration, and implications for future flow control design are discussed.</p
Dynamic Bipedal Locomotion: From Hybrid Zero Dynamics to Control Lyapunov Functions via Experimentally Realizable Methods
Get PDFRobotic bipedal locomotion has become a rapidly growing field of research as humans increasingly look to augment their natural environments with intelligent machines. In order for these robotic systems to navigate the often unstructured environments of the world and perform tasks, they must first have the capability to dynamically, reliably, and efficiently locomote. Due to the inherently hybrid and underactuated nature of dynamic bipedal walking, the greatest experimental successes in the field have often been achieved by considering all aspects of the problem; with explicit consideration of the interplay between modeling, trajectory planning, and feedback control.
The methodology and developments presented in this thesis begin with the modeling and design of dynamic walking gaits on bipedal robots through hybrid zero dynamics (HZD), a mathematical framework that utilizes hybrid system models coupled with nonlinear controllers that results in stable locomotion. This will form the first half of the thesis, and will be used to develop a solid foundation of HZD trajectory optimization tools and algorithms for efficient synthesis of accurate hybrid motion plans for locomotion on two underactuated and compliant 3D bipeds. While HZD and the associated trajectory optimization are an existing framework, the resulting behaviors shown in these preliminary experiments will extend the limits of what HZD has demonstrated is possible thus far in the literature. Specifically, the core results of this thesis demonstrate the first experimental multi-contact humanoid walking with HZD on the DURUS robot and then through the first compliant HZD motion library for walking over a continuum of walking speeds on the Cassie robot.
On the theoretical front, a novel formulation of an optimization-based control framework is introduced that couples convergence constraints from control Lyapunov functions (CLF)s with desirable formulations existing in other areas of the bipedal locomotion field that have proven successful in practice, such as inverse dynamics control and quadratic programming approaches. The theoretical analysis and experimental validation of this controller thus forms the second half of this thesis. First, a theoretical analysis is developed which demonstrates several useful properties of the approach for tuning and implementation, and the stability of the controller for HZD locomotion is proven. This is then extended to a relaxed version of the CLF controller, which removes a convergence inequality constraint in lieu of a conservative CLF cost within a quadratic program to achieve tracking. It is then explored how this new CLF formulation can fully leverage the planned HZD walking gaits to achieve the target performance on physical hardware. Towards this goal, an experimental implementation of the CLF controller is derived for the Cassie robot, with the resulting experiments demonstrating the first successful realization of a CLF controller for a 3D biped on hardware in the literature. The accuracy of the robot model and synthesized HZD motion library allow the real-time control implementation to regularize the CLF optimization cost about the nominal walking gait. This drives the controller to choose smooth input torques and anticipated spring torques, as well as regulate an optimal distribution of feasible ground reaction forces on hardware while reliably tracking the planned virtual constraints. These final results demonstrate how each component of this thesis were brought together to form an effective end-to-end implementation of a nonlinear control framework for underactuated locomotion on a bipedal robot through modeling, trajectory optimization, and then ultimately real-time control.</p
p-Converse to a Theorem of Gross-Zagier, Kolyvagin, and Rubin for Small Primes
Get PDFLet E be a CM elliptic curve over the rationals and p a good, ordinary prime. We show the implication: corank(Zp)Sel(p∞)(E/Q) = 1 ⟹ ord(s=1)L(s,E/Q) = 1 for the p∞-Selmer group Sel(p∞)(E/Q) and the complex L-function L(s,E/QQ) in the case of p = 2, 3
Contract-Based Design: Theories and Applications
Get PDFMost things we know only exist in relation to one another. Their states are strongly coupled due to dependencies that arise from such relations. For a system designer, acknowledging the presence of these dependencies is as crucial to guaranteeing performance as studying them. As the roles played by technology in fields such as transportation, healthcare, and finance continue to be more profound and diverse, modern engineering systems have grown to be more reliant on the integration of technologies across multiple disciplines and their requirements. The need to ensure proper division of labor, integration of system modules, and attribution of legal responsibility calls for a more methodological look into co-design considerations. Originally conceived in computer programming, contract-based reasoning is a design approach whose promise of a formal compositional paradigm is receiving attention from a broader engineering community. Our work is dedicated to narrowing the gap between the theory and application of this yet nascent framework.
In the first half of this dissertation, we introduce a model interface contract theory for input/output automata with guards and a formalization of the directive-response architecture using assume-guarantee contracts and show how these may be used to guide the formal design of a traffic intersection and an automated valet parking system respectively. Next, we address a major drawback of assume-guarantee contracts, i.e., the problem of a void contract due to antecedent failure. Our proposed solution is a reactive version of assume-guarantee contracts that enables direct specification at the assumption and guarantee level along with a novel synthesis algorithm that exposes the effects of failures on the contract structure. This is then used to help optimize, adapt, and robustify our design against an uncertain environment.
In light of ongoing development of autonomous driving technologies and its potential impact on the safety of future transportation, the second half of this work is dedicated to the application of the design-by-contract framework to the distributed control of autonomous vehicles. We start by defining and proving properties of "assume-guarantee profiles," our proposed approach to transparent distributed multi-agent decision making and behavior prediction. Next, we provide a local conflict resolution algorithm in the context of a quasi-simultaneous game which guarantees safety and liveness to the composition of autonomous vehicle systems in this game. Finally, to facilitate the extension of these frameworks to real-life urban driving settings, we also supply an effective method to predict agent behavior that utilizes recent advances in machine learning research.</p
Serotonergic Circuits: Role in Sleep and Enhanced Genetic Tools for Access and Optical Recording
Get PDFOverall, this thesis encompasses three main directions: the study of neural circuits in sleep (Chapter 2), the development and testing of tools for measuring neuromodulator release (Chapter 3), and methods for in vivo characterization of gene delivery vehicles (Chapter 5).
The role of the neuromodulator serotonin in sleep has been debated for over 60 years. Until recently, the serotonergic system was widely thought to be part of the arousal system and promote wakefulness. In Chapter 2, we investigate the function of serotonin-producing neurons in murine and zebrafish sleep with tools featuring superior specificity and precision compared to previously employed techniques. Our results demonstrate that the serotonergic raphe are sleep-promoting and required for sleep homeostasis. Intriguingly, serotonergic neurons in mice can have opposing effects on sleep depending on the firing mode.
The release of serotonin from neurons can be regulated by the frequency of neuronal firing and can occur at classical synapses, varicosities, soma, and dendrites. Further examination of the complex signaling mechanism of serotonin would benefit from tools capable of measuring the release of serotonin in vivo with long-term stability and high spatiotemporal resolution. To this end, we developed and characterized iSeroSnFR, an intensity-based genetically encoded serotonin indicator. In Chapter 3, we demonstrate that iSeroSnFR can detect serotonin release in freely behaving mice during fear conditioning, social interaction, and sleep-wake transitions.
Adeno-associated viruses (AAVs) have been extensively used as gene delivery vehicles in basic neuroscience and gene therapy. However, optimization of transduction efficiency and target specificity remain a key challenge to overcome. Several AAV vector engineering approaches have been devised for this purpose and yield large collections of candidates that require further in vivo characterization. However, conventional characterization methods fall short with regard to in-depth cell type tropism analysis and/or high-throughput capabilities. In Chapter 5, we address this shortcoming with single-cell RNA sequencing technologies based on the Drop-seq method. We established an experimental and computational pipeline that allows us to profile the viral tropism of multiple AAV variants in parallel across numerous complex cell types.</p
Signal Amplification in Synthetic Bacterial Communication
Get PDFSynthetic biology will one day enable embedded control of a variety of chemical and biological contexts, from the human gastrointestinal tract to crop roots. Groups of engineered organisms, also known as synthetic consortia, can inhabit niches of interest while monitoring and intervening according to their genetic design. However, the spatial structure of the deployment environments can obstruct coordination between cosortia members. The mechanisms engineered bacteria use to communicate must contend with these adversarial conditions to maximize group performance.
Coordination between synthetic bacteria is typically achieved using small molecules that can traverse cell membranes through passive transport. Cell communicate by producing and sensing these small molecules. In cell-cell signaling relationships composed of a sender population and a receiver population, the concentration of signaling molecule sensed by the receiver cells depends on the spatial patterning of the two groups, the geometry of the diffusive environment, and the sender population’s signal secretion rate.
To make sender-receiver communication more robust to these environmental features, we introduce a third consortium strain that transiently amplifies local signaling molecule concentrations. These amplifier cells employ a synchronized pulse-generating circuit built using Lux-type quorum sensing components and an IFFL transcriptional architecture. When applied to sender-receiver consortia growing on semi-solid media, these amplifier cells respond to sender-secreted signaling molecules by contributing a small amount themselves. The support of amplifier cells enables communication over longer distances than can be achieved by sender cells alone and can partially recover coordination in small consortia where the sender population is too small to successfully signal its receiver population alone. We extend these results using simulation to investigate the benefit that amplifier cells confer to consortia of varying complexity.</p
The Limits of The Quasi-Harmonic Approximation: Anharmonicity in Germanium and the Entropy of Melting
Get PDFInelastic Neutron Scattering (INS) measurements were made at the Wide Angular-Range Chopper Spectrometer (ARCS) on Germanium at temperatures higher than what has been done before, from 296 K to 1203 K. Raw data was used to calculate the dynamic structure factor. Multi-phonon and multiple scattering events were accounted for and subtracted. These dynamic structure factors were then used to calculate single phonon density of states (DOS) for temperatures throughout the said temperature range. Thermal softening of the phonon modes was observed. The softening was quantitatively characterized with several Gruneisen parameters to better understand the effects phonon anharmonicity in Germanium. We find the quasi-harmonic approximation alone cannot explain the large phonon softening. The vibrational entropy contribution to the total entropy was also determined. We find that the vibrational entropy makes up almost all of the total entropy in Germanium, even at elevated temperatures.
We also conduct melting experiments to ensure containment of Si, Bi, and Pb in quartz ampules. These metals will be heated through their melting points at ARCS in the near future in order to determine the vibrational entropy contribution to the latent heat of melting. Furthermore, we write an algorithm based on the work of Sivia to determine the number of phonon modes there is the maximum evidence for in any given phonon DOS.</p
Stimuli Responsive Micro-Architected Materials
Get PDFShape memory polymers (SMPs) respond to heat by generating programmable movement useful in devices that require substantial deformation and operate at transient temperatures, including stents, embolization coils, and robotic grippers. Transitioning these materials to the microscale can result in expanded potential applications, such as clot removal from retinal vasculature, neural probe delivery, and responsive metamaterials. To achieve these goals, shape transformation must occur in SMPs with complex 3D geometries and nanoscale features.
This thesis describes the synthesis and sculpting of a benzyl methacrylate-based SMP into 3D structures with <800nm characteristic critical dimensions via two photon lithography. The glass transition based shape memory mechanism of these materials is explored through dynamic nanomechanical analysis of 8µm-diameter cylindrical pillars, which revealed the initiation of a tunable glass transition at 60°C not present in highly crosslinked materials. Shape memory programming of the characterized pillars as well as complex 3D architectures, including flowers with 500nm thick petals and cubic lattices with 2.5µm unit cells and overall dimensions of 4.5µm x 4.5µm x 10µm, demonstrated an 86 +/- 4% characteristic shape recovery ratio. These results reveal a pathway towards SMP devices with nanoscale features and arbitrary 3D geometries changing shape in response to temperature.
This thesis subsequently focuses on a particular potential application for such materials: neural probes designed for deployment in primate brains. Architected shape memory structures have the potential to create favorable long-term recording environments through softening triggered by biological conditions, deployment to beyond tissue damage during initial electrode positioning, and architectural features designed for optimal scaffold-tissue interactions. This thesis addresses one of the barriers to the deployment of such structures: the high loading during centimeter scale insertions required for primate brain targeting is incompatible with buckling free-insertion of low stiffness and/or cross sectional area probes required for minimizing the foreign body response.
Lamb brain tissue model experiments with 280µm diameter platinum coated carbon fiber probes demonstrate that 59+/- 3% of the work during 3cm probe insertion is attributable to friction, suggesting that friction reduction is a favorable approach to load minimization. A phosphorylcholine-based ~100nm low friction coating is used to reduce the shear stress at the probe-brain interface by 20+/-7 %, demonstrating a facile method for friction reduction that has minimal impacts on probe cross sectional area. Surgical validation of probe insertion in a porcine head model reveals that these probes are suitable for whole brain penetration of brains at the primate scale (~10²g). These results show that loading requirements during whole brain penetration can be reduced through addressing the contribution of friction and introduce a viable vehicle for recording electrode delivery to large scale brains.
In summary, this thesis provides the foundation for developing stimuli responsive microscale devices and materials and, in the case of deep brain neural recording, the building blocks for the design of an integrated shape memory/ low friction carbon fiber electrode delivery device. Future research on the scalable fabrication of architected shape memory polymers could enable the widespread application of such materials.</p
Understanding the Electronic Structures of First-Row Transition Metal Complexes for Solar Energy Conversion and Catalysis
Get PDFChapter 1 discusses the major findings and themes of the studies presented in this thesis. Chapter 2 presents a DFT-based methodology for quantifying entatic states. Here it is applied to Cu-based photosensitizers used for solar electricity generation, solar fuels synthesis, organic light emitting diodes (OLEDs), and photoredox catalysis. The methodology can be used to decouple the steric and electronic contributions to excited state dynamics and, in turn, can be used to guide the design of future photosensitizers. The computed entatic energies in some of the photosensitizers were the largest quantified to date: ~20 kcal mol-1 relative to the conformationally flexible [Cu(phen)2]+. Of course, considering typical chemical barriers and driving forces, these values are significant.
Chapter 3 is an investigation of the ground and excited spin state energetics of a free carbene and several of its iron porphyrin carbene (IPC) analogs. Here it is shown that for the IPC models, multireference ab initio wave function methods give results most consistent with experiment. Specifically, the predicted, mixed singlet ground state is mostly dominated by the closed-shell singlet (Fe(II)←{:C(X)Y}0) configuration, with a small contribution from an Fe(III)–{C(X)Y}–• open-shell singlet configuration (hole in d(xz)). This description differs from that obtained by using DFT. Also, using the multireference ab initio wave methods, elongation of the IPC Fe–C(carbene) bond increases the weighting of this particular open-shell configuration within the ground state singlet.
Chapter 4 also deals with a system where DFT and multireference ab initio results diverge: the light-induced Ni(II)–C homolytic bond dissociation in Ni 2,2'-bipyridine photoredox catalysts. DFT calculations give a barrier of ~30 kcal mol-1 while multireference ab initio calculations giving a barrier of ~70 kcal mol-1. Thus, within the latter description, a previously proposed mechanism of thermally assisted dissociation from the lowest energy triplet ligand field excited state is unfavorable. Instead, the mechanism given by the multireference description is initial population of a singlet Ni(II)-to-bpy metal-to-ligand charge transfer (1MLCT) excited state followed by intersystem crossing and aryl-to-Ni(III) charge transfer. From accessible repulsive triplet excited states, homolytic bond dissociation can occur.</p