12023 research outputs found
Sort by
Sedimentary Processes on Earth and Mars: Canyon Erosion, Sand-Ripple Formation, and Mineral Composition
Get PDFOver the past few decades, orbiters, landers, and rovers have significantly expanded our understanding of Mars’ hydrology and climate; however, significant knowledge gaps stand in the way of our quest for martian life. In particular, the global drying of the planet remains one of the grandest unsolved mysteries in planetary science. To help unravel this puzzle, we develop new quantitative theories for sedimentary processes with implications for both Earth and Mars. This thesis revolves around three main sedimentary processes – erosion, deposition, and sediment transport. First, we focus on the erosion of bedrock canyons by water on Earth and Mars. After showing that groundwater seepage erosion is only efficient at carving canyons in restricted conditions, we develop a new hydraulic theory for flow focusing upstream of horseshoe-shaped waterfalls and combine it with waterfall-erosion mechanics to constrain the discharge, duration, and volume of canyon-carving floods on Earth and Mars. We show that martian Hesperian floods were large but short-lived. Second, we investigate fluid and sediment controls on the equilibrium size of bedforms. We develop a comprehensive scaling relation to predict the size of ripples forming in various sedimentary environments, including martian brines and methane flows on Titan, and show that the scaling relation predicts the size of large wind ripples forming under a thin martian atmosphere. This new theory, combined with observations of large-ripple cross-strata in wind-blown sandstones of the Burns formation at Victoria crater, suggests that Mars had a thin atmosphere around the Noachian-Hesperian boundary. Finally, we use orbiter-based inferences of the mineralogy of sands of the Bagnold dunes of Gale crater to disentangle the magnitude of wind sorting and local sediment sources. We develop a new probabilistic framework to invert for surface mineralogy, groundtruth our predictions with compositional datasets provided by the Curiosity rover, and discuss the implications of our findings for mineral sorting by martian winds and paleoenvironmental interpretations of martian wind-blown sandstones. Collectively, these results provide new mechanistic and quantitative constraints on the past hydrology and climate of Mars that are key to assess Mars’ astrobiological potential through space and time
Dynamics and Stability of Spinning Membranes
Get PDFMany future space missions require large structures subject to stringent shape accuracy requirements. Spinning membrane-like structures are a cost effective solution for these applications. However, any small deflection of a spinning structure, due to maneuvers or solar radiation pressure, leads to geometrically nonlinear effects on its stability and dynamics. Accurate experiments, simulation tools, and models are required to ensure that buckling and vibrations will not affect mission objectives.
We first focus on the influence of transverse uniform loads on the dynamics and stability of spinning isotropic uniform membranes. A transverse uniform load models the effect of a transverse light beam on flat membranes with small deflections. We present experimental measurements of the angular velocities at which various membranes become wrinkled, and of the wrinkling mode transitions that occur upon spin down. A theoretical formulation to predict the critical angular velocities and critical transverse loads is also presented. The transition between bending dominated and in-plane dominated behavior is identified, and the wrinkling modes are obtained. Next, deflected, non-buckled membranes are further analyzed. Axisymmetric nonlinear oscillations are studied analytically, and a reduced-order model is presented. This model predicts that the deflection of the membrane introduces a hardening behavior at low angular velocities and a softening behavior at high angular velocities. This model is validated through experiments and FEM simulations.
Then, we relax the assumption of uniform membranes loaded by transverse light beams. We present an Abaqus model of foldable membranes and show that for particular types of hinges and at high angular velocities, these structures behave like uniform membranes. Finally, we derive an FEM model for solar radiation pressure for quadrilateral surface elements and 3D problems and present its implementation in Abaqus. We show that this follower load introduces an unsymmetric stiffness matrix and that instabilities known as solarelastic flutter can develop. This new FEM capability enables equilibrium and frequency-based stability analyses for a wide range of spacecraft.</p
Approximation and Classification in the Ergodic Theory of Nonamenable Groups
Get PDFThis thesis is a contribution to the theory of measurable actions of discrete groups on standard probability spaces. The focus is on nonamenable acting groups. It is organized into two parts. The first part deals with a notion called weak equivalence, which describes a sense in which such actions can approximate each other. The second part deals with the concept of entropy for measure preserving actions of sofic groups.</p
Iron-bearing Oxides, Silicate Glasses and Carbonates at Lower Mantle Pressures
Get PDFIron is the fourth most abundant element in Earth’s mantle and it affects geophysically observable properties, such as the density, sound velocities, viscosity and transport properties of mantle phases. Additionally, the concentration of iron in minerals and melts of the lower mantle dictates their structure and stability. Thus, understanding the effect of iron is important to interpret seismically observable complexities and understand their effect on processes in the deep Earth. In this thesis, I use experimental and theoretical methods to improve our understanding of the high-pressure behavior of iron-bearing periclase (“ferropericlase”), silicate glasses and carbonates.
Ferropericlase is thought to represent a significant fraction of Earth’s lower mantle, and may explain the slow compressional and shear sound velocities of ultra-low velocity zones at the core-mantle boundary. To understand the effect of iron concentration on the (Mg,Fe)O solid solution, the equation of state and hyperfine parameters of (Mg,Fe)O with 48 mol% FeO were measured using X-ray powder diffraction and time-domain Mössbauer spectroscopy, respectively, and the spin crossover behavior was compared to that of (Mg,Fe)O with 10 to 60 mol% FeO. I find that iron-rich ferropericlase at core-mantle boundary pressures likely contains a significant fraction of high-spin iron, contributing a positive buoyancy to promote topographic relief of ultra-low velocity zones in the lowermost mantle.
Some ultra-low velocity zones, particularly those at the base of the central parts of large low shear velocity provinces, may be best explained by the presence of iron-bearing silicate melts. The behavior of iron in silicate melts is poorly understood, but may be approximated by iron-bearing silicate glasses. I measured the hyperfine parameters of iron-bearing rhyolitic glass up to ~120 GPa and basaltic glasses up to ~90 GPa using time-domain Mössbauer spectroscopy. Iron within these glasses experiences changes in coordination environment with increasing pressure without undergoing a high-spin to low-spin transition. Thus, ferrous iron in chemically–complex silicate melts likely exists in a high-spin state throughout most of Earth’s mantle.
Decomposition of carbonates may be responsible for creating silicate melts within the lower mantle by lowering the melting temperature of surrounding rock. Identifying and characterizing the stability of carbonate phases is therefore a necessary step towards understanding the transport and storage of carbon in Earth’s interior. Dolomite is one of the major mineral forms in which carbon is subducted into the Earth’s mantle. Although iron-free dolomite is expected to break down upon compression into single-cation carbonates, high-pressure polymorphs of iron-bearing dolomite may resist decomposition. Using a genetic algorithm that predicts crystal structures (USPEX), I have found a monoclinic phase with space group C2/c that has a lower energy than all previously reported dolomite structures at pressures above 15 GPa, and the substitution of iron for magnesium stabilizes monoclinic dolomite with respect to decomposition at certain pressures of the lower mantle.
In this thesis, I demonstrate that iron undergoes a spin transition in (Mg,Fe)O, (Mg,Fe)CO3 and Ca(Mg,Fe)(CO3)2, while iron in basaltic and silicate glasses likely does not experience a spin transition up to lowermost mantle pressures. Additionally, I find that the amount of iron in (Mg,Fe)O and Ca(Mg,Fe)(CO3)2 dictates the dynamic and thermodynamic stabilities of those phases within Earth’s lower mantle.</p
Diffusion and Molecular Association in Artificial Protein Hydrogels
Get PDFArtificial proteins may be programmed to reversibly self-assemble into water-soluble networks, or “hydrogels”, by encoding them with terminal coiled-coil forming domains. Such networks are model viscoelastic materials. The well-defined molecular structures adopted by proteins, combined with their facile preparation by recombinant synthesis, invite a careful exploration of the relationship between protein sequence and the resulting network properties.
This work explores the relationship between network reorganization and diffusion from the perspective of single chains, using artificial elastin-like proteins as a model system. We make use of fluorescence recovery after photobleaching (FRAP), a classic biophysical technique, to measure chain mobilities as a function of network structure and probe architecture. Reversible network association is demonstrated to control the effective diffusivity of network-bound chains, and a novel mechanism of chain transport is proposed: the chains naturally partition into various bound states, and move by “hopping” from site to site in between binding events.
A careful analysis of the equilibrium constants that control this partioning leads to the conclusion that the sequential binding of identical chain ends to the network is inherently asymmetric: the first association is always stronger than the second. This binding asymmetry is shown to arise from a strong entropic penalty for chain entry into the fully bound state due to local network structure. We derive a simple equation predicting the degree of binding asymmetry as a function of network geometry from equilibrium statistical mechanics. A large set of self-diffusivity measurements on a series of model telechelic proteins finds good agreement with this new theory. Generalized binding asymmetry for chains with many associative domains also holds.
Finally, the inherent viscoelasticity of the elastin-like network is found to couple with an entropically driven phase separation above a critical temperature set point. Relaxation of the viscoelastic stress throughout the process of phase domain segregation is found to induce highly dynamic phase patterns. The time evolution of these patterns illustrates that a delicate balance of surface tension and viscoelastic stress controls pattern formation in viscoelastic materials.</p
The Deformations of Thin Nematic Elastomer Sheets
Get PDFThin structures exhibit a broad range of mechanical responses as the competition between stretching and bending in these structures can result in buckling and localized deformations like folding and tension wrinkling. Active materials also exhibit a broad range of mechanical responses as features that manifest themselves at the microscale in these materials result in mechanical couplings at the engineering scale (thermal/electrical/dissipative) and novel function (e.g., the shape memory effect and piezoelectricity in select metal alloys and the immense fracture toughness of hydrogels). Given this richness in behaviors, my research broadly aims to address the following questions: What happens when active materials are incorporated into thin structures? Do phenomena inherent to these materials compete with or enhance those inherent to thin structures? Does this interplay result in entirely new and unexpected phenomena? And can all this be exploited to design new functions in engineering systems?
In this thesis, we explore these questions in the context of a theoretical study of thin sheets of nematic liquid crystal elastomer. These materials are active rubbery solids made of cross-linked polymer chains that have liquid crystals either incorporated into the main chain or pendent from them. Their structure enables a coupling between the mechanical elasticity of the polymer network and the ordering of the liquid crystals, and this in turn results in fairly complex mechanical behavior including large spontaneous distortion due to temperature change, soft-elasticity and fine-scale microstructure.
We study thin sheets of nematic elastomer. First, we show that thin of sheets of a particular class of nematic elastomer can resist wrinkling when stretched. Second, we show that thin sheets of another class of nematic elastomer can be actuated into a multitude of complex shapes. In order to obtain these results, we systematically develop two dimensional theories for thin sheets starting from a well-accepted first principles theory for nematic elastomers. These characterize (i) the mechanical response due to instabilities such as structural wrinkling and fine-scale material microstructure, and (ii) thermal actuation of heterogeneously patterned sheets. For the latter, we show that the theory, which comes in the form of a two dimensional metric constraint, admits two broad classes of designable actuation in nonisometric origami and lifted surface. For the former, we show that taut and appreciably stressed sheets of nematic elastomer are capable of suppressing wrinkling by modifying the expected state of stress through the formation of microstructure.</p
Computational Methods for Bayesian Inference in Complex Systems
Get PDFBayesian methods are critical for the complete understanding of complex systems. In this approach, we capture all of our uncertainty about a system’s properties using a probability distribution and update this understanding as new information becomes available. By taking the Bayesian perspective, we are able to effectively incorporate our prior knowledge about a model and to rigorously assess the plausibility of candidate models based upon observed data from the system. We can then make probabilistic predictions that incorporate uncertainties, which allows for better decision making and design. However, while these Bayesian methods are critical, they are often computationally intensive, thus necessitating the development of new approaches and algorithms.
In this work, we discuss two approaches to Markov Chain Monte Carlo (MCMC). For many statistical inference and system identification problems, the development of MCMC made the Bayesian approach possible. However, as the size and complexity of inference problems has dramatically increased, improved MCMC methods are required. First, we present Second-Order Langevin MCMC (SOL-MC), a stochastic dynamical system-based MCMC algorithm that uses the damped second-order Langevin stochastic differential equation (SDE) to sample a desired posterior distribution. Since this method is based on an underlying dynamical system, we can utilize existing work in the theory for dynamical systems to develop, implement, and optimize the sampler's performance. Second, we present advances and theoretical results for Sequential Tempered MCMC (ST-MCMC) algorithms. Sequential Tempered MCMC is a family of parallelizable algorithms, based upon Transitional MCMC and Sequential Monte Carlo, that gradually transform a population of samples from the prior to the posterior through a series of intermediate distributions. Since the method is population-based, it can easily be parallelized. In this work, we derive theoretical results to help tune parameters within the algorithm. We also introduce a new sampling algorithm for ST-MCMC called the Rank-One Modified Metropolis Algorithm (ROMMA). This algorithm improves sampling efficiency for inference problems where the prior distribution constrains the posterior. In particular, this is shown to be relevant for problems in geophysics.
We also discuss the application of Bayesian methods to state estimation, disturbance detection, and system identification problems in complex systems. We introduce a Bayesian perspective on learning models and properties of physical systems based upon a layered architecture that can learn quickly and flexibly. We then apply this architecture to detecting and characterizing changes in physical systems with applications to power systems and biology. In power systems, we develop a new formulation of the Extended Kalman Filter for estimating dynamic states described by differential algebraic equations. This filter is then used as the basis for sub-second fault detection and classification. In synthetic biology, we use a Bayesian approach to detect and identify unknown chemical inputs in a biosensor system implemented in a cell population. This approach uses the tools of Bayesian model selection.</p
Aspects of Effective Field Theories from Scattering Amplitudes
Get PDFOn-shell methods offer an alternative definition of quantum field theory at tree-level. We first determine the space of constructible theories solely from dimensional analysis, Lorentz invariance, and locality. We show that all amplitudes in a renormalizable theory in four dimensions are constructible, but only a subset of amplitudes is constructible in non-renormalizable theories. The obstructions to effective field theories (EFTs) are then lifted for the non-linear sigma model, Dirac-Born-Infeld theory, and the Galileon, using the enhanced soft limits of their amplitudes.
We then systematically explore the space of scalar EFTs based on the soft lim- its and power counting of amplitudes. We prove that EFTs with arbitrarily soft behavior are forbidden by on-shell momentum shifts and recursion relations. The exceptional EFTs like the non-linear sigma model, Dirac-Born-Infeld theory, and the special Galileon lie precisely on the boundary of allowed theory space. Our results suggest that the exceptional theories are the natural EFT analogs of gauge theory and gravity because they are one-parameter theories whose interactions are strictly dictated by properties of the S-matrix.
Next, a new representation of the nonlinear sigma model is proposed to manifest the duality between flavor and kinematics. The action consists of only cubic interactions, which define the structure constants of an underlying kinematic algebra. The action is invariant under a combination of internal and spacetime symmetries whose conservation equations imply flavor-kinematics duality, ensuring that all Feynman diagrams satisfy kinematic Jacobi identities. Substituting flavor for kinematics, we derive a new cubic action for the special Galileon. The vanishing soft behavior of amplitudes is shown as a byproduct of the Weinberg soft theorem.
Finally, we derive a class of one-loop non-renormalization theorems that strongly constrain the running of higher dimension operators in four-dimensional quantum field theory. Our derivation combines unitarity and helicity selection rules at tree level. These results explain and generalize the surprising cancellations discovered in the renormalization of dimension six operators in the standard model.</p
Understanding the Symbiosis in Anaerobic Oxidation of Methane Through Metabolic, Biosynthetic and Transcriptomic Activities
Get PDFMicroorganisms provide essential ecological services to our planet. Their combined activities control and shape our environment as we know today. In the deep sea, a microbial mediated process known as anaerobic oxidation of methane (AOM) consumes large amounts of methane, a potent greenhouse gas and a valuable energy resource. How this symbiosis works is poorly understood.
In this thesis, I tested current hypotheses on the symbiotic mechanisms in AOM microbial consortia, consisting of a partnership between anaerobic methanotrophic archaea (ANME) and sulfate-reducing bacteria (SRB). Sediments collected from methane seeps offshore Oregon and California and dominated by AOM consortia were used in these investigations. A range of compounds were amended to sediment microcosms, and their effects on the metabolic activities of ANME or SRB were monitored by tracking the rates of methane oxidation or sulfate reduction on timescales varying from hours to months. A lack of stimulation or inhibition on the AOM consortia, combined with long-term community profiles, suggest that diffusible compounds are unlikely to be involved in the symbiosis in AOM. I further examine ANME genomes, focusing the role of sulfur in methane seep ecosystems. Phylogenetic analyses revealed multiple poorly characterized genes in the sulfur pathway, and comparisons with methanogenic archaea related to ANME provided a better understanding of their roles in the cell. Transcriptional responses combined with protein modeling were used to predict the potential substrate of a sulfite reductase related enzyme. These predictions were validated using genetics, and together point to an assimilatory rather than dissimilatory sulfur pathway in methane-utilizing archaea in general. Then, the AOM symbiosis was decoupled for the first time using soluble electron acceptors. ANME remained metabolically and biosynthetically active without their SRB partner, suggesting that the electrons are transferred directly in this partnership. This observation was investigated to a greater depth with transcriptomics. Membrane proteins and multiheme cytochromes critical in extracellular electron transfer in ANME and SRB were expressed. These results together illuminate the path electrons may take to exit or enter the AOM consortia. Overall, multiple activity analyses used here piece together a clearer view on how the symbiosis in AOM works, with potential applications in future energy generation from methane.</p
Electromagnetic Field Manipulation: Biosensing to Antennas
Get PDFWe will explore how understanding and controlling electromagnetic fields can provide significant impact across a multitude of applications throughout the whole frequency spectrum from DC to daylight. Starting from the DC end of the electromagnetic spectrum, we motivate the design of a new integrated magnetic biosensing design as well as various improvements to the initial design based on spatial and temporal manipulations of the magnetic fields. Next, we look into the RF domain and develop maximal performance bounds for antennas and other electromagnetic structures. We develop rapid simulation techniques which when coupled with heuristic optimization algorithms can quickly and effectively produce new antenna structures with little to no manual intervention. We demonstrate the efficacy of these techniques in the context of on-chip antenna designs and a 3D printed coupling antenna for a dielectric waveguide communication link. We present the design of a 120GHz dual-channel 100Gbps QPSK/64QAM transceiver IC developed in a standard 28nm bulk CMOS process. Finally, we explore the higher THz regime in the context of photonic device optimization. We optimize compact photonic multiplexer devices which are fabricated in a standard foundry process and evaluate their performance against simulation results