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Nonlinear Dynamics of Transition Waves in Multi-Stable Discrete and Continuous Media
Get PDFThe concept of phase transitions, i.e., switching between two or more different equilibrium states of a system, is commonly encountered in many physical, chemical and biological phenomena. The exact mechanism of this switching is a highly nonlinear dynamical process that is accommodated by the propagation of a localized wave. The characteristics of the nonlinear wave such as its profile, velocity, energy, and width of transition are governed by the type and specifics of the system that it is propagating through which may be conservative, dissipative, or diffusive in nature. The goal of this thesis is to develop a fundamental understanding of the dynamics of such processes in general nonlinear systems capable of undergoing phase transitions and the application of new theories to elucidate the kinetic and energetic properties of transition waves in different scenarios. In conservative systems, we show that there are three different modes of stable wave propagation that we analytically solve for and validate computationally. In contrast, dissipative and diffusive systems allow the stable propagation of only the strongly nonlinear kink mode whose kinetic energy and propagation velocity are linked through a linear relation. We further validate our results in dissipative systems experimentally by fabricating and testing a strongly nonlinear lattice and show that transition waves are unidirectional in nature, as predicted by theory. Finally, as an application, we devise a strategy of using the physics of dissipative phase transitions to propagate stable mechanical signals in highly dissipative media such as soft polymers which effectively damp out small-amplitude linear waves
Methodological Developments and Synthetic Applications of Strained Rings and Allylic C-H Functionalization of Hindered Substrates
Get PDFFormal dipolar cycloadditions of cyclopropanes and aziridines are useful methods for the formation of carbo- and heterocycles. Given our group’s previous interest in this area, we sought to expand the scope of strained ring cycloadditions by employing heterocumulenes as dipolarophiles. This thesis describes our development of Lewis acid catalyzed formal (3 + 2) cycloadditions between donor–acceptor cyclopropanes and isocyanates, isothiocyanates, and carbodiimides to furnish various five-membered heterocycles. Enantioenriched cycloadducts can be accessed through a stereospecific reaction if enantiopure substrates are employed. We also present a method to access more highly nitrogenated heterocycles by replacing donor–acceptor cyclopropanes with activated aziridines. These aziridines react smoothly with isothiocyanates and carbodiimides in the presence of zinc Lewis acids to afford iminothiazolidine and iminoimidazolidine products in good yields. Our efforts to apply a cyclopropane cycloaddition toward the total synthesis of the indole alkaloid calophyline A are also described.
In addition, a method for the activation of sterically hindered allylic C–H bonds is presented. Despite numerous recent advances in the functionalization of allylic C–H bonds and the general utility of these transformations, reactions of sterically hindered substrates remain challenging. In this thesis we describe the development of a novel system for the palladium(II)-catalyzed allylic C–H acetoxylation of α-allyl lactams. We believe the lactam moiety may act as a directing group to aid in the palladation of these generally unreactive substrates. During optimization, we also discovered enal products were formed if water was added. These conditions represent the first example of a transition metal catalyzed C–H oxidation system with tunable selectivity over the extent of oxidation.</p
Redox Kinetics of Nonstoichiometric Oxides
Get PDFCerium oxide (CeO2-δ) and its derivatives are the most attractive materials under consideration for solar-driven thermochemical production of chemical fuels. Understanding the rate-limiting factors in fuel production is essential for maximizing the efficacy of the thermochemical process.
The rate of response of the porous ceria structured with architectural features typical of those employed in solar reactors was measured via electrical conductance relaxation methods. A transition from behavior controlled by material surface reaction kinetics to that controlled by sweep-gas supply rates is observed on increasing temperature, increasing volume specific surface area, and decreasing normalized gas flow rate. The transition behavior is relevant not only for optimal reactor operation and architectural design of material, but also for accurate measurement of material properties.
The redox kinetics of undoped ceria, CeO2-δ at extreme high temperature (1400 °C) was investigated using the electrical conductivity relaxation method, and those of 10% Pr doped ceria at low temperature (700 °C) were done using the mass relaxation method. It was demonstrated under sufficiently high gas flow rates relative to the mass of the oxide, which is required in order to overcome gas phase limitations and access the material kinetic properties. Furthermore, the surface reaction rate constant of undoped ceria, ,kChem, was investigated at high temperature (1400 °C) in humidified gas atmosphere, in consideration of the operating conditions in thermochemical fuel production system. It was demonstrated that H2O potentially plays a role of oxidants as increasing temperature and/or decreasing oxygen partial pressure; thus in such thermodynamic conditions, pH2O, besides temperature and pO2, needs to be carefully considered in surface reaction study.
In addition to relaxation experiments under small driving force for redox reaction, the kinetics of surface related oxidation reaction under large chemical driving force (large ΔpO2 change) was investigated by mass relaxation method. Based on the normalized reaction rates of several possible rate determining steps, the relaxation behavior in oxygen concentration for all possible rate determining steps was computed. On the comparison with the experimental results, the most probable rate determining step was suggested (reduction of diatomic oxygen from neutral oxygen molecule to superoxide), and the oxidation kinetics under large driving force was explained.</p
Living with Sisyphus
Get PDFMy aim in this paper will be to get a grip on the absurdist reply to, "What is the meaning of life? How should we live well?". Absurdism, related to pessimism, holds that the world is generally meaningless or purposeless. Specifically, I will provide a detailed exposition of Albert Camus' absurdist philosophy as detailed in The Myth of Sisyphus. I will then aim to present three arguments against Camus' existentialist methodology by examining his principle assumptions, pointing out contradictions in his account, and finally rejecting his normative recommendations. Finally, I will briefly advocate for some accounts that allow us to create meaning in our lives following a combination of subjective well being and eudaimonia
Constraints on Cosmology and Quantum Gravity from Quantum Mechanics and Quantum Field Theory
Get PDFTypical cosmological states have structure, obey to very good approximation the laws of classical physics on large scales, and are far from equilibrium. Typical quantum-mechanical states have none of these properties. If the universe is described by a state in a Hilbert space, the state and its Hilbert space must therefore obey a number of constraints to describe realistic cosmological spacetimes. In particular, they must admit a quantum-to-classical transition via decoherence that allows for the emergence of classical spacetimes, and such spacetimes must obey gravitational constraints, in particular on the entanglement entropy of subsystems within them. The papers collected in this thesis are concerned with these constraints. We investigate two holographic correspondences inspired by AdS/CFT, the AdS-MERA correspondence, which suggests that anti-de~Sitter space may be given a discretized description as a tensor network, and the ER=EPR duality, which identified entangled qubits with wormholes connecting them. In the former case, we use holographic entropy bounds to severely constrain the properties of any such tensor network; in the latter case we prove a new general-relativistic area theorem which states that an area corresponding to the entanglement entropy in wormhole geometries is exactly conserved. We use information-theoretic constraints to show that under mild assumptions about the black hole interior an observer falling beyond the horizon is unable to verify the claimed cloning of information in the firewall paradox before reaching the singularity. Finally, we analyze the decoherence structures of late-time de~Sitter space and early-time slow-roll eternal inflation. We show that in the former case a universe with an infinite-dimensional Hilbert space and a positive cosmological constant inevitably reaches a maximum-entropy state from which no further branching or decoherence is possible, forbidding the existence of dynamical quantum fluctuations at late time. In the latter case, gravitational-strength interaction among inflaton modes leads to decoherence of sufficiently super-Hubble modes, which we argue backreacts to cause different histories of cosmological evolution on different branches and hence creates the conditions necessary for eternal inflation.</p
Localization and Stimulation Techniques for Implantable Medical Electronics
Get PDFImplantable medical devices (IMDs) are emerging as one of the keystones of tomorrow’s medical technology. Although they have enabled a revolution in medicine, from research to diagnosis to treatment, most of today’s devices have critical limitations. They are bulky, have low resolution, and, in some cases, are limited to basic functionality. Miniaturization of IMDs will have an enormous impact not only on the technology itself and the medical procedures they enable, but also on the lives of patients, who will be more comfortable, have greater confidence in their medical treatments, and enjoy an overall improvement in their quality of life. The path towards miniaturized bioelectronic devices requires a reevaluation of existing paradigms to reach a seamless integration of electronics and biology. Miniaturization of medical electronics then involves an exploration of advanced integrated circuit processes and novel circuit and system level architectures. In this dissertation, we provide an overview of implantable medical devices and present novel circuit and system level techniques for the miniaturization of medical electronics.
The function of wireless miniaturized medical devices such as capsule endoscopes, biosensors, and drug delivery systems depends critically on their location inside the body. However, existing electromagnetic, acoustic, and imaging-based methods for localizing and communicating with such devices with spatial selectivity are limited by the physical properties of tissue or imaging modality performance. In the first part of this dissertation, we introduce a new approach for microscale device localization by embodying the principles of nuclear magnetic resonance in a silicon integrated circuit. By analogy to the behavior of nuclear spins, we engineer miniaturized RF transmitters that encode their location in space by shifting their output frequency in proportion to the local magnetic field. The application of external field gradients then allows each device’s location to be determined precisely from the frequency of its signal. We demonstrate the core capabilities of these devices, which we call addressable transmitters operated as magnetic spins (ATOMS), in an integrated circuit smaller than 0.7 mm^3, manufactured through a standard 180 nm complementary metal-oxide-semiconductor (CMOS) process. We show that ATOMS are capable of sub-millimeter localization in vitro and in vivo. As a technology that is inherently robust to tissue properties and scalable to multiple devices, ATOMS localization provides an enabling capability for the development of microscale devices to monitor and treat disease.
In neuroprosthetics, retinal prostheses aim to restore vision in patients suffering from advanced stages of retinal degeneration (e.g., retinitis pigmentosa) by bypassing the damaged photoreceptors and directly stimulating the remaining healthy neurons. In the second part of this dissertation, we describe a fully intraocular self-calibrating epiretinal prosthesis that reduces area and power consumption, and increases the functionality and resolution of traditional implementations. We introduce a novel novel digital calibration technique that matches the biphasic stimulation currents of each channel independently while sharing the calibration circuitry among every 4 channels. The system-on-chip presents dual-band telemetry for power and data with on-chip rectifier and clock recovery. These techniques reduce the number of off-chip components and achieve a power conversion efficiency >80% and supporting data rates up to 20 Mb/s. The system occupies an area of 4.5 x 3.1 mm2 and is implemented in 65 nm CMOS . It features 512 independent channels with a pixel size of 0.0169 mm2 and arbitrary waveform generation per channel. The chip is integrated with flexible MEMS origami coils and parylene substrate to provide a fully intraocular implant.</p
Fuels and Materials from Sunlight and Water
Get PDFThe urgency to develop new technologies that harness energy and natural feedstocks in a sustainable fashion has never been more apparent. With global power consumption growing at an exponential rate, only one resource is truly capable of powering the planet: the sun. Sunlight is reliable, clean, and free.
Significant resources have been pledged to develop and refine solar energy devices that convert photons into electricity (i.e. photovoltaics), but the sun’s intermittency and the poor overlap of solar irradiance with global power demand a different strategy. In light of these limitations, we have proposed a device which converts solar energy into reduced chemical fuels (e.g. dihydrogen or methane) that can be indefinitely stored and easily transported. In principle, the only required inputs are sunlight, an earth-abundant feedstock such as carbon dioxide, protons (H+), and reducing equivalents (e-). The source of these protons and electrons must be abundant and ubiquitous—we chose water.
Despite the 2-billion-year history of plants performing water oxidation to produce molecular oxygen, protons, and electrons (Photosystem II), our understanding of this complex 4H+/4e- process has been severely limited. Only recently have high-performing, earth-abundant heterogeneous electrocatalysts been reported that can be scaled up to make functioning devices.
This dissertation describes progress on both the synthetic and mechanistic fronts in developing earth-abundant heterogeneous water oxidation catalysts for solar-driven water splitting. We have synthesized nanoparticulate Ni-Fe catalysts with the highest measured activity on flat electrodes to date. We carefully characterized these materials spectroscopically to determine that edge-site iron was active in catalysis. We then undertook novel in-situ spectroelectrochemical techniques in non-aqueous media to identify the active iron species, which is surprisingly a cis-dioxo-iron(VI) corner site. The data also indicate that geminal iron-oxo coupling may be the operative mechanism of O-O bond formation, a new scheme with potential biological relevance.
Finally, we have expanded our goal to include sustainably reducing other feedstocks, such as carbon dioxide and hydrocarbons. In doing so, we aim to make pharmaceuticals, polymers, and other high-value products from sunlight and water.</p
Essays on the Impact of Information Asymmetry
Get PDFThis dissertation consists of three essays focusing on how information asymmetry affects agents’ behavior across different environments. The first essay characterizes the optimal contract when a firm can employ two incentive schemes, promotion and pay for performance, simultaneously (Chapter 2). In the second essay, I study how information asymmetry can lead a firm to choose a less profitable short-term over a more profitable long-term project (Chapter 3). The other essay analyzes a career choice problem when agents have private information about their ability (Chapter 4).
Chapter 2 presents the effect of information asymmetry on executive pay structure to examine the cause of the rise in CEO compensation and wage inequality between CEO and other executives. To analyze the effect of the interaction of two incentive schemes, promotion and pay for performance, on CEO compensation and within-firm wage inequality, I embed a pay for performance framework into a tournament structure. The model shows that when CEO and managers contribute to a firm’s output independently, it is optimal for the firm to provide the CEO a compensation far beyond her reservation value in order to provide promotion incentives for managers. However, I find that the promotion incentive motive can disappear if there is interdependency between the CEO’s and managers’ outputs. In this case, the main purpose of a high CEO compensation is to induce the CEO to exert effort. The tension between incentives for CEO and managers makes it difficult to interpret the meaning of within-firm wage gap. As a possible solution, this paper suggests the use of CEO’s base salary to identify which incentive factor is driving the pay gap.
In Chapter 3, I study the optimal contract problem when a firm faces a long-term project. I consider a long-term project as one that requires an indefinite amount of time to complete its objective. I assume that the long-term project generates profits once it is accomplished. Using a continuous-time moral hazard model, I characterize the incentive compatibility condition in a relatively general contracting space. Moreover, I find a unique optimal contract under a restricted contracting space which consists of the two components: the termination level and the completion payment. The firm might invest in a short-term project: one that generates an instantaneous profit to the firm without any effect on the future, as analyzed by DeMarzo and Sannikov (2006). Comparison of optimal contracts for long and short-term projects provides an interesting insight to managerial short-termism: the firm, not the agent, could prefer a short-term project to a long-term project if there is a moral hazard problem.
Chapter 4 analyzes the role of asymmetry information on one’s career choice. I examine how people choose their career when they do not know ability of the rest of the applicant pool. The goal is to understand labor supply in the markets where ability is widely distributed. In particular, I consider a situation where there are two exclusive labor markets and the upper and lower bounds of one market’s payoffs are both higher than those of the other market. Under the market setting, agents decide which market to participate in. I find that the symmetric Bayesian Nash equilibrium of this problem is unique. In the equilibrium, agents are divided into two groups according to their ability. Members of the high ability group use a pure strategy and only apply to the more desirable market. Members of the low ability group apply to both markets with positive probability.</p
Dipolar Liquids and Their Mixtures: Equilibrium and Nonequilibrium Properties with Field-Theoretic Approaches
Get PDFLiquid is a state of matter that is intermediate between the gas state and the solid state. Though it is an ordinary state of matter, the application of statistical mechanics for understanding its properties is far from complete. Compared to the solid state, the liquid state has molecules that can move around freely, and yet, unlike that in the gas state, the intermolecular correlations are significant in the liquid state. Therefore, the distance dependent correlations in a liquid need to be taken into account to properly describe a liquid. In particular, all molecules are polarizable. The polarizable nature allows the molecules to induce polarization in surrounding molecules, giving rise to van der Waals interactions that have important consequences on the properties of a liquid. In addition to polarizability, many molecules are intrinsically polar. The long-ranged dipole-dipole correlations contribute to the complexity of interactions and lead to a myriad of interesting properties special to a liquid.
In recent years, field-theoretic technique has emerged as a convenient and systematic tool for deriving coarse-grained theories for a wide range of complex-fluid and soft-matter systems while preserving the essential physics. In this thesis, we present the application of field-theoretic approaches to two problems of liquids and their mixtures. The first problem is to describe the dielectric properties of an ordinary liquid or liquid mixture under equilibrium condition, where current field-theoretic methods are inadequate. In this problem, we apply a variational field-theoretic approach to develop a statistical field theory of the liquid, and predict the dielectric constant and the miscibility of liquids using the variational free energies derived. The second problem involves the nonequilibrium solvent composition and orientational polarization surrounding some charged solute in the context of electron transfer reactions. Using a self-consistent-field theory with constrained coarse-grained fields, we derive expressions for the nonequilibrium solvation energy, and apply it to compute the reorganization energy of electron transfer reactions. The theories presented in this thesis lead to simple analytical expressions for the equilibrium and the nonequilibrium free energies, making it possible to theoretically survey a wide range of liquids. In addition, our models involve only a few readily-available molecular parameters and avoid the use of any adjustable parameters, allowing one to make a priori predictions on the properties of liquids and their mixtures. </p
A Study of Communication Networks through the Lens of Reduction
Get PDFA central goal of information theory is to characterize the capacity regions of communication networks. Due to the difficulty of the general problem, research is primarily focused on families of problems defined by various classifiers. These classifiers include the channel transition function (i.e., noisy, deterministic, network coding), demand type (i.e., single-source, 2-unicast), network topology (i.e. acyclic network coding, index coding). To date, the families of networks that are fully solved remain limited. Moreover, results derived for one specific family often do not extend easily to other families of problems.
Our work shifts from the traditional focus on solving example networks to one that builds connections between problem solutions so that we can say where and when solving a problem in one domain would also solve a corresponding problem in another domain. Central to our approach is a technique called "reduction", in which we connect the solutions and results of communication problems. We say that problem A reduces to problem B when A can be solved by first transforming it to B and then applying a solution for B. We focus on two notions of reduction: reduction in code design and reduction in capacity region.
Our central results demonstrate reductions with respect to a variety of classifiers. We show that finding multiple multicast network capacity regions reduces to finding multiple unicast network capacity regions both when capacity is defined as the maximal rate over all possible codes and when capacity is defined as the optimal rate over linear codes. As a corollary to this result, we show that the same capacity reduction holds for when network types are limited to either network coding networks or index coding networks. In several instances, we show that a reduction in code design extends to a reduction in capacity region if and only if the edge removal conjecture holds. Here, the edge removal conjecture states that removing an edge of negligible capacity from a network does not change its capacity region.
One of the key challenges in network coding research is how to handle networks containing cycles. As a result, many papers on network coding restrict attention to acyclic networks and some results derived for acyclic networks do not extend to networks containing cycles. We consider a streaming model for network communication where information is streamed to its destination under a constraint on maximal delay at the decoder. Restricting our attention to this scenario enables us to prove a code reduction from network coding to index coding in both acyclic and cyclic networks. Since index coding networks are acyclic, a consequence of this reduction is that under the streaming model, there is no fundamental difference between acyclic and cyclic networks.</p