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A Continuum Model for Slip-Twinning Interactions in Magnesium and Magnesium Alloys
Get PDFDue to their high specific strength and low density, magnesium and magnesium-based alloys have gained great technological importance in recent years. However, their underlying hexagonal crystal structure furnishes Mg and its alloys with a complex mechanical behavior because of their comparably smaller number of energetically favorable slip systems. Besides the commonly studied slip mechanism, another way to accomplish general deformation is through the additional mechanism of deformation-induced twinning. The main aim of this thesis research is to develop an efficient continuum model to understand and ultimately predict the material response resulting from the interaction between these two mechanisms.
The constitutive model we present is based on variational constitutive updates of plastic slips and twin volume fractions and accounts for the related lattice reorientation mechanisms. The model is applied to single- and polycrystalline pure magnesium. We outline the finite-deformation plasticity model combining basal, pyramidal, and prismatic dislocation activity as well as a convexification based approach for deformation twinning. A comparison with experimental data from single-crystal tension-compression experiments validates the model and serves for parameter identification. The extension to polycrystals via both Taylor-type modeling and finite element simulations shows a
characteristic stress-strain response that agrees well with experimental observations for polycrystalline magnesium. The presented continuum model does not aim to represent the full details of individual twin-dislocation interactions, yet it is sufficiently efficient to allow for finite element simulations while qualitatively capturing the underlying microstructural deformation mechanisms.</p
Small Scale Turbulence in High Karlovitz Number Premixed Flames
Get PDFThe purpose of this thesis is to characterize the behavior of the smallest turbulent scales in high Karlovitz number (Ka) premixed flames. These scales are particularly important in the two-way coupling between turbulence and chemistry and better understanding of these scales will support future modeling efforts using large eddy simulations (LES). The smallest turbulent scales are studied by considering the vorticity vector, ω, and its transport equation.
Due to the complexity of turbulent combustion introduced by the wide range of length and time scales, the two-dimensional vortex-flame interaction is first studied as a simplified test case. Numerical and analytical techniques are used to discern the dominate transport terms and their effects on vorticity based on the initial size and strength of the vortex. This description of the effects of the flame on a vortex provides a foundation for investigating vorticity in turbulent combustion.
Subsequently, enstrophy, ω2 = ω • ω, and its transport equation are investigated in premixed turbulent combustion. For this purpose, a series of direct numerical simulations (DNS) of premixed n-heptane/air flames are performed, the conditions of which span a wide range of unburnt Karlovitz numbers and turbulent Reynolds numbers. Theoretical scaling analysis along with the DNS results support that, at high Karlovitz number, enstrophy transport is controlled by the viscous dissipation and vortex stretching/production terms. As a result, vorticity scales throughout the flame with the inverse of the Kolmogorov time scale, τη, just as in homogeneous isotropic turbulence. As τη is only a function of the viscosity and dissipation rate, this supports the validity of Kolmogorov’s first similarity hypothesis for sufficiently high Ka numbers (Ka ≳ 100). These conclusions are in contrast to low Karlovitz number behavior, where dilatation and baroclinic torque have a significant impact on vorticity within the flame. Results are unaffected by the transport model, chemical model, turbulent Reynolds number, and lastly the physical configuration.
Next, the isotropy of vorticity is assessed. It is found that given a sufficiently large value of the Karlovitz number (Ka ≳ 100) the vorticity is isotropic. At lower Karlovitz numbers, anisotropy develops due to the effects of the flame on the vortex stretching/production term. In this case, the local dynamics of vorticity in the strain-rate tensor, S, eigenframe are altered by the flame. At sufficiently high Karlovitz numbers, the dynamics of vorticity in this eigenframe resemble that of homogeneous isotropic turbulence.
Combined, the results of this thesis support that both the magnitude and orientation of vorticity resemble the behavior of homogeneous isotropic turbulence, given a sufficiently high Karlovitz number (Ka ≳ 100). This supports the validity of Kolmogorov’s first similarity hypothesis and the hypothesis of local isotropy under these condition. However, dramatically different behavior is found at lower Karlovitz numbers. These conclusions provides/suggests directions for modeling high Karlovitz number premixed flames using LES. With more accurate models, the design of aircraft combustors and other combustion based devices may better mitigate the detrimental effects of combustion, from reducing CO2 and soot production to increasing engine efficiency.</p
Computational Microscopy: Breaking the Limit of Conventional Optics
Get PDFComputational imaging is flourishing thanks to the recent advancement in array photodetectors and image processing algorithms. This thesis presents Fourier ptychography, which is a computational imaging technique implemented in microscopy to break the limit of conventional optics. With the implementation of Fourier ptychography, the resolution of the imaging system can surpass the diffraction limit of the objective lens's numerical aperture; the quantitative phase information of a sample can be reconstructed from intensity-only measurements; and the aberration of a microscope system can be characterized and computationally corrected. This computational microscopy technique enhances the performance of conventional optical systems and expands the scope of their applications
Microscopic Origin of Macroscopic Strength in Granular Media: A Numerical and Analytical Approach
Get PDFConstitutive modeling in granular materials has historically been based on macroscopic experimental observations that, while being usually effective at predicting the bulk behavior of these type of materials, suffer important limitations when it comes to understanding the physics behind grain-to-grain interactions that induce the material to macroscopically behave in a given way when subjected to certain boundary conditions.
The advent of the discrete element method (DEM) in the late 1970s helped scientists and engineers to gain a deeper insight into some of the most fundamental mechanisms furnishing the grain scale. However, one of the most critical limitations of classical DEM schemes has been their inability to account for complex grain morphologies. Instead, simplified geometries such as discs, spheres, and polyhedra have typically been used. Fortunately, in the last fifteen years, there has been an increasing development of new computational as well as experimental techniques, such as non-uniform rational basis splines (NURBS) and 3D X-ray Computed Tomography (3DXRCT), which are contributing to create new tools that enable the inclusion of complex grain morphologies into DEM schemes.
Yet, as the scientific community is still developing these new tools, there is still a gap in thoroughly understanding the physical relations connecting grain and continuum scales as well as in the development of discrete techniques that can predict the emergent behavior of granular materials without resorting to phenomenology, but rather can directly unravel the micro-mechanical origin of macroscopic behavior.
In order to contribute towards closing the aforementioned gap, we have developed a micro-mechanical analysis of macroscopic peak strength, critical state, and residual strength in two-dimensional non-cohesive granular media, where typical continuum constitutive quantities such as frictional strength and dilation angle are explicitly related to their corresponding grain-scale counterparts (e.g., inter-particle contact forces, fabric, particle displacements, and velocities), providing an across-the-scale basis for better understanding and modeling granular media.
In the same way, we utilize a new DEM scheme (LS-DEM) that takes advantage of a mathematical technique called level set (LS) to enable the inclusion of real grain shapes into a classical discrete element method. After calibrating LS-DEM with respect to real experimental results, we exploit part of its potential to study the dependency of critical state (CS) parameters such as the critical state line (CSL) slope, CSL intercept, and CS friction angle on the grain's morphology, i.e., sphericity, roundness, and regularity.
Finally, we introduce a first computational algorithm to ``clone'' the grain morphologies of a sample of real digital grains. This cloning algorithm allows us to generate an arbitrary number of cloned grains that satisfy the same morphological features (e.g., roundness and aspect ratio) displayed by their real parents and can be included into a DEM simulation of a given mechanical phenomenon. In turn, this will help with the development of discrete techniques that can directly predict the engineering scale behavior of granular media without resorting to phenomenology.</p
Cosmic Explosions: Observations Of Infant Hydrogen-Free Supernovae Towards An Understanding Of Their Parent Systems
Get PDFRadiation in the first days of supernova explosions contains rich information about physical properties of the exploding stars. In the past three years, I used the intermediate Palomar Transient Factory to conduct one-day cadence surveys, in order to systematically search for infant supernovae. I show that the one-day cadences in these surveys were strictly controlled, that the realtime image subtraction pipeline managed to deliver transient candidates within ten minutes of images being taken, and that we were able to undertake follow-up observations with a variety of telescopes within hours of transients being discovered. So far iPTF has discovered over a hundred supernovae within a few days of explosions, forty-nine of which were spectroscopically classified within twenty-four hours of discovery.
Our observations of infant Type Ia supernovae provide evidence for both the single-degenerate and double-degenerate progenitor channels. On the one hand, a low-velocity Type Ia supernova iPTF14atg revealed a strong ultraviolet pulse within four days of its explosion. I show that the pulse is consistent with the expected emission produced by collision between the supernova ejecta and a companion star, providing direct evidence for the single degenerate channel. By comparing the distinct early-phase light curves of iPTF14atg to an otherwise similar event iPTF14dpk, I show that the viewing angle dependence of the supernova-companion collision signature is probably responsible to the difference of the early light curves. I also show evidence for a dark period between the supernova explosion and the first light of the radioactively-powered light curve. On the other hand, a peculiar Type Ia supernova iPTF13asv revealed strong near-UV emission and absence of iron in the spectra within the first two weeks of explosion, suggesting a stratified ejecta structure with iron group elements confined to the slow-moving part of the ejecta. With its total ejecta mass estimated to exceed the Chandrasekhar limit, I show that the stratification and large mass of the ejecta favor the double-degenerate channel.
In a separate approach, iPTF found the first progenitor system of a Type Ib supernova iPTF13bvn in the pre-explosion HST archival mages. Independently, I used the early-phase optical observations of this supernova to constrain its progenitor radius to be no larger than several solar radii. I also used its early radio detections to derive a mass loss rate of 3e-5 solar mass per year for the progenitor right before the supernova explosion. These constraints on the physical properties of the iPTF13bvn progenitor provide a comprehensive data set to test Type Ib supernova theories. A recent HST revisit to the iPTF13bvn site two years after the supernova explosion has confirmed the progenitor system.
Moving forward, the next frontier in this area is to extend these single-object analyses to a large sample of infant supernovae. The upcoming Zwicky Transient Facility with its fast survey speed, which is expected to find one infant supernova every night, is well positioned to carry out this task.</p
Modeling the Effect of Vapor Wall Deposition on the Formation of Secondary Organic Aerosol in Chamber Studies
Get PDFLaboratory chamber experiments are used to investigate formation of secondary organic aerosol (SOA) from biogenic and anthropogenic precursors under a variety of environmental conditions. Simulations of these experiments test our understanding of the prevailing chemistry of SOA formation as well as the dynamic processes occurring in the chamber itself. One dynamic process occurring in the chamber that was only recently recognized is the deposition of vapor species to the Teflon walls of the chamber. Low-volatility products formed from the oxidation of volatile organic compounds (VOCs) deposit on the walls rather than forming SOA, decreasing the amount of SOA formed (quantified as the SOA yield: mass of SOA formed per mass of VOC reacted). In this work, several modeling studies are presented that address the effect of vapor wall deposition on SOA formation in chambers.
A coupled vapor-particle dynamics model is used to examine the competition among the rates of gas-phase oxidation to low volatility products, wall deposition of these products, and mass transfer to the particle phase. The relative time scales of these rates control the amount of SOA formed by affecting the influence of vapor wall deposition. Simulations show that an effect on SOA yield of changing the vapor-particle mass transfer rate is only observed when SOA formation is kinetically limited. For systems with kinetically limited SOA formation, increasing the rate of vapor-particle mass transfer by increasing the concentration of seed particles is an effective way to minimize the effect of vapor wall deposition.
This coupled vapor-particle dynamics model is then applied to α-pinene ozonolysis SOA experiments. Experiments show that the SOA yield is affected when changing the oxidation rate but not when changing the rate of gas-particle mass transfer by changing the concentration of seed particles. Model simulations show that the absence of an effect of changing the seed particle concentration is consistent with SOA formation being governed by quasi-equilibrium growth, in which gas-particle equilibrium is established much faster than the rate of change of the gas-phase concentration. The observed effect of oxidation rate on SOA yield arises due to the presence of vapor wall deposition: gas-phase oxidation products are produced more quickly and condense preferentially onto seed particles before being lost to the walls. Therefore, for α-pinene ozonolysis, increasing the oxidation rate is the most effective way to mitigate the influence of vapor wall deposition.
Finally, the detailed model GECKO-A (Generator for Explicit Chemistry and Kinetics of Organics in the Atmosphere) is used to simulate α-pinene photooxidation SOA experiments. Unexpectedly, α-pinene OH oxidation experiments show no effect when changing either the oxidation rate or the vapor-particle mass transfer rate, whereas GECKO-A predicts that changing the oxidation rate should drastically affect the SOA yield. Sensitivity studies show that the assumed magnitude of the vapor wall deposition rate can greatly affect conclusions drawn from comparisons between simulations and experiments. If vapor wall loss in the Caltech chamber is of order 10-5 s-1, GECKO-A greatly overpredicts SOA during high UV experiments, likely due to an overprediction of second-generation products. However, if instead vapor wall loss in the Caltech chamber is of order 10-3 s-1, GECKO-A greatly underpredicts SOA during low UV experiments, possibly due to missing autoxidation pathways in the α-pinene mechanism.</p
Molecular and Geochemical Insights into Microbial Life Centimeters to Kilometers Below the Seafloor
Get PDFAt the broadest scale, this thesis is an investigation of how life modulates the movement of essential elements (carbon, sulfur, nitrogen, and silicon) on modern and geologic timescales. Chapters 1 and 2 explore carbon and sulfur cycling microbial communities found centimeters below the seafloor in hydrocarbon-rich methane seep ecosystems. At the Hydrate Ridge methane seep, we investigated how microbial partnerships direct the flow of methane and sulfide in these benthic oases by using identity-based physical separation methods developed in our lab (Magneto-FISH) in conjunction with community profiling and metagenomic sequencing. This method explores the middle ground between single cell and bulk sediment analysis by separating target microbes and their physically associated community for downstream sequencing applications. Magneto-FISH captures were done at a range of microbial taxonomic group specificities and sequenced with both clone library and next-gen iTag 16S rRNA gene methods. Chapter 1 provides a demonstration of how FISH probe taxonomic specificity correlates to resultant Archaeal taxonomic diversity in Magneto-FISHed seep sediments, with specific attention to preparation of Archaea-enriched samples for downstream metagenomic sequencing. In Chapter 2, a Bacteria-focused parallel environmental isolation and sequencing effort was subjected to co-occurrence analyses which suggested there may be far more microbial associations in methane seep systems than are currently appreciated, including partnerships that do not involve the canonical anaerobic methane oxidizing archaea and sulfate reducing bacteria. With samples from IODP Expedition 337 Shimokita coalbed biosphere, Chapter 3 provides evidence for an active microbial assemblage kilometers below the sea floor in the deepest samples ever collected by marine scientific ocean drilling. Using in situ temperature Stable Isotope Probing (SIP) incubations and NanoSIMS, we investigated whole community activity (with the passive tracer D2O) and substrate specific activity with C1-carbon compounds methylamine and methanol. We found deuterium-based turnover times to be faster (years) than previous deep biosphere estimates (hundreds to thousands of years), but methylotrophy rates to be slower than previous carbon metabolic rates.</p
Sediment Mobility in Steep Channels and the Transition to Landsliding
Get PDFThe mobility of sediment in steep mountain rivers controls the denudation rate and height of mountain ranges worldwide. Sediment movement within the steepest terrain often occurs as catastrophic shallow landsliding, posing significant hazards to those living downstream. Despite the importance of steep channels, our observations of sediment transport are mostly limited to rivers with slopes of less than 2°. This prevents us from predicting the runoff required to transport sediment throughout most of the drainage network and from knowing the mode of transport that should dominate (dilute river transport vs. landsliding). I performed a series of laboratory experiments in an artificial river with an adjustable slope to test the flow depths required to transport sediment on slopes up to the dry angle of repose. Counterintuitively, sediment becomes harder to move on steeper slopes by dilute river processes. Laboratory observations of flow hydraulics and field observations of cobble stability reveal that this reduced mobility is a hydraulic effect resulting from the shallow flows that are inherent to steep channels. In experiments that were conducted at slopes steeper than half of the dry angle of repose, sediment was more easily transported by shallow landsliding than dilute river processes. Within this landsliding regime, sediment was again observed to be more stable than predicted by traditional theory. Documentation of these experimental failures with high-speed video revealed that failures occur with a characteristic length scale that is shorter than predicted, and that these short failures experience a strong buttressing force at their downstream margin. These results suggest that landslide length scales consistently with width, and also provides new expectations for the saturation level required to initiate failures. Ultimately, these experiments provide us with expectations of the flow depth required to transport sediment throughout the entire drainage network, and also allow us to partition the drainage network into river-dominated and landslide-dominated regimes
Origin of the Earth and Moon
Get PDFAccording to the giant impact hypothesis, the Moon formed from a disk created by an impact between the proto-Earth and an impactor. Three major models for this hypothesis are (a) standard model: a Mars-sized impactor hit the Earth; (b) fast-spinning Earth model: a small impactor hit a rapidly spinning Earth; and (c) sub-Earths model: two half-Earth sized planets collided. These models have been supported because they can explain several observed features of the Earth-Moon system, such as the Moon's mass, angular momentum, and potentially geochemical measurements that suggest that the Earth and Moon have nearly identical isotopic ratios.
However, it is uncertain if these models are consistent with other geochemical constraints. For example, isotopic measurements of Earth's rocks indicate that the early Earth's mantle was chemically heterogeneous and this signature was preserved for billions of years. However, it is not clear if the giant impact hypothesis is consistent with this geochemical constraint because the giant impact could have been so energetic that the Earth's mantle could have completely mixed and homogenized. Furthermore, the fraction of the Earth's mantle that became molten by the impact is not well known, even though it is known to have significantly affected the subsequent evolutions of the Earth's interior and atmosphere. Additionally, the water and volatile content of the Moon may have an important implication for the lunar origin. Since the Moon-forming disk formed through a giant impact process, it must have been hot and partially vaporized. From this disk, a significant amount of water and volatiles may have escaped to space. However, this idea may contradict recent geochemical studies that indicate that Moon may not be as dry as previously thought.
Furthermore, moons of other planets may provide comprehensive pictures of the origin and evolution of the moons. For example, the Pluto-Charon system could have formed via a giant impact. Recent studies also suggest that Mars' satellites Phobos and Deimos could have formed in the same way. In contrast, satellites around the gas giants could have formed in situ from their proto-satellite disks and by gravitational capture. One of the Saturnian satellites, Enceladus has very unique geological and dynamical features. Cassini spacecraft observed that water plumes are emanating from cracks on the surface (so-called ``tiger stripes''). These plumes may originate from a few kilometer deep subsurface liquid ocean. Along the cracks, strong thermal emissions have been observed and these are thought to be related to the plume activities, but the connection has been still unclear.
In my Ph.D. thesis, I aim to understand the origin and evolution of the Earth, Moon, and the Saturnian moon Enceladus.
In order to understand the initial state of the Earth's mantle and the Moon-forming disk, I perform giant impact simulations with a method called smoothed particle hydrodynamics (SPH). I show that the Earth's mantle becomes mostly molten by the impact and that the mantle remains unmixed in (a), but it may be at least partly mixed in (b) and (c). Therefore, (a) is most consistent with the preservation of the mantle heterogeneity. As for the Moon-forming disk, my calculations show that the disk of the standard model has a relatively low temperature (up to 4500 K) and low vapor mass fraction (~20-30%) while the disk formed by other models could be much hotter (6000-7000 K) and has a higher vapor mass fraction (80-90 %). Furthermore, I investigate the structure of the Moon-forming disk and estimated the extent of water escape. I show that escape is in the diffusion-limited regime and water escape from the disk to space is minor. This result could explain recent measurements on lunar water abundance. Furthermore, I develop a dynamical model that includes flow dynamics and flow-ice wall interaction that explains the Enceladus plume mass flux, heat flux, and several observed signatures. These studies will deepen comprehensive understanding of the origin of the moons in the solar system.</p
l-adic Cohomology of the Dual Lubin-Tate Tower via the Exterior Power
Get PDFWe study the l-adic cohomology of the dual Lubin-Tate tower by using the exterior power of a pi-divisible O-module to relate it to the cohomology of the Lubin-Tate tower. By using a result of Harris-Taylor on the cohomology of the Lubin-Tate tower, we show that the supercuspidal part of the cohomology of the dual Lubin-Tate tower realizes the local Langlands and the Jacquet-Langlands correspondences, up to certain twists