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Chaos and Randomness in Strongly-Interacting Quantum Systems
Get PDFQuantum chaos entails an entropic and computational obstruction to describing a system and thus is intrinsically difficult to characterize. An understanding of quantum chaos is fundamentally related to the mechanism of thermalization in many-body systems and the quantum nature of black holes. In this thesis we adopt the view that quantum information theory provides a powerful framework in which to elucidate chaos in strongly-interacting quantum systems.
We first push towards a more precise understanding of chaotic dynamics by relating different diagnostics of chaos, studying the time-evolution of random matrix Hamiltonians, and quantifying random matrix behavior in physical systems. We derive relations between out-of-time ordered correlation functions, spectral quantities, and frame potentials to relate the scrambling of quantum information, decay of correlators, and Haar-randomness. We give analytic expressions for these quantities in random matrix theory to explore universal aspects of late-time dynamics. Motivated by our random matrix results, we define k-invariance in order to capture the onset of random matrix behavior in physical systems.
We then refine our diagnostics in order to study chaotic systems with symmetry by considering Haar-randomness with respect to quotients of the unitary group, and in doing so we generalize our quantum information machinery. We further consider extended random matrix ensembles in the context of strongly-interacting quantum systems dual to black holes. Lastly, we study operator growth in classes of random quantum circuits.</p
Towards a priori Models for Differential Diffusion in Turbulent Non-Premixed Flames
Get PDFIn this work, progress is made towards the correct modeling of differential diffusion, both for resolved simulations, and for reduced-order combustion models. For resolved simulations, the validity and the limitations of the constant non-unity Lewis number approach in the description of molecular mixing in laminar and turbulent flames is studied. Three test cases are selected, including a lean, highly unstable, premixed hydrogen/air flame, a lean turbulent premixed n-heptane/air flame, and a laminar ethylene/air coflow diffusion flame. For the hydrogen flame, both a laminar and a turbulent configuration are considered. The three flames are characterized by Lewis numbers which are less than unity, greater than unity, and close to unity, respectively. For each flame, mixture-averaged transport simulations are carried out and used as reference data. The analysis suggests that, for numerous combustion configurations, the constant non-unity Lewis number approximation leads to small errors when the set of Lewis numbers is chosen properly. For the selected test cases and our numerical framework, the reduction of computational cost is found to be minimal. Two different methods of evaluating the Lewis numbers are tested, with both performing well, and neither consistently better than the other.
The flamelet-based chemistry tabulation technique is a popular reduced-order chemical model for non-premixed turbulent flames. In this approach, the correct choice of the species Lewis numbers in the flamelet equations plays an important role. Experimental results have highlighted that, in turbulent non-premixed jet flames, turbulent transport becomes gradually dominant over molecular mixing with (i) increasing axial distance from the burner exit plane, and (ii) increasing jet Reynolds number. In the current work, this transition is characterized and a priori models for the effective species Lewis numbers in turbulent non-premixed flames are assessed.
First, a flamelet-based methodology is proposed to extract these effective Lewis numbers from data sets of turbulent non-premixed flames. This methodology is then applied to the Sandia non-premixed methane/air jet flames B, C, D, and E (R. Barlow, Int. Work. Meas. Comput. Turb. Non-Prem. Flames, 2003). The effective Lewis numbers are found to transition from their laminar values, close to the burner exit plane, to unity further downstream. Previously-suggested scalings for the effective Lewis numbers are then assessed.
To overcome the limitations associated with the experimental data, a campaign of Direct Numerical Simulations (DNS) of Sandia flame B is carried out. A baseline grid is carefully designed, and grid independence is assessed through simulations using refined grids in the axial, radial and azimuthal directions. Radiation and differential diffusion effects are systematically isolated by considering radiating and unity Lewis number cases, respectively. The DNS database is then validated using available measured statistics for flame B, and comparisons to the higher Reynolds number flames are carried out. Effective Lewis numbers extracted from the DNS data are found to transition to unity with increasing downstream distance. Finally, the scalings for the effective Lewis numbers are re-computed from the DNS data base, and compared to the higher Reynolds number flames.</p
Single-Neuron Correlates of Visual Object Representation in the Human Brain: Effects of Attention, Memory, and Choice
Get PDFNeurons in the medial temporal lobe (amygdala and hippocampus) are known to respond selectively to specific object categories, such as faces. This dissertation investigates two novel extensions of this work: (1) how are such neuronal responses influenced by where we attend; (2) how is category information used by the brain to make decisions.
The first question evaluated the representation of faces in the primate amygdala during naturalistic conditions, by recording from both human and macaque amygdala neurons during free viewing of arrays of images with concurrent eye tracking. We found that category-selective responses were very strongly modulated by where people, or monkeys, fixated (overt attention). Subsequent experiments in humans only further demonstrated that this effect holds even when people allocate visual attention while keeping central fixation (covert attention). In both monkeys and humans, the majority of face-selective neurons preferred faces of conspecifics, a bias also seen behaviorally in first fixation preferences. Response latencies, relative to fixation onset, were shortest for conspecific-selective neurons. Response latencies were also notably shorter in monkeys than in humans. To answer the second question, we investigated how visual representations in the medial temporal lobe are subsequently used to make two types of decisions: a recognition memory choice ("have you seen this image before?"), and a stimulus categorization choice ("Is this a face?"). We show that (i) there are distinct populations of cells in the medial frontal cortex (including anterior cingulate cortex, and supplementary motor cortex) encoding recognition memory or categorization-based choices; (ii) category-selective cells in the medial temporal lobe are insensitive to such task conditions; and (iii) spike-field coherence between field potentials in the medial temporal lobe and action potentials in the medial frontal cortex is enhanced during recognition memory choices. This suggests that inter-areal communication between these two brain regions may be facilitated selectively in tasks that rely on recognition memory-based information. Taken together these two components of this dissertation provide novel insights into how visual object representations in the human brain are gated by attention, and how they are used in decisions. This work thus for the first time provides a comprehensive characterization of how single neurons in the human brain participate in the cycle from perception to action.</p
The Study of the Stepwise Hydroxyl Radical-Mediated Oxidation of Alkyl Surfactants at the Air-Water Interface
Get PDFThis thesis presents work on the heterogeneous chemistry of surfactant monolayers adsorbed at the air-water interface with gas phase hydroxyl radicals (OH). A novel hydroxyl radical source utilizing a low-temperature plasma known as the dielectric barrier discharge source (DBDS) is designed, characterized, and implemented as a high concentration OH generator (approximately 1000 fold higher than ambient conditions) in these experiments. Millimeter-sized water droplets containing a monolayer of surface-adsorbed species are exposed to this OH source until a designated level of oxidation. Field-induced droplet ionization mass spectrometry (FIDI-MS), which has been previously proven to be a surface-selective ionization technique, is used as an analytical method to determine the identity and relative quantity of oxidation products at the interface by sampling progeny droplets expelled upon the application of a pulsed electric field. Chapter 2 establishes the utility of the DBDS and FIDI-MS setup by oxidizing the 12-carbon n-alkyl surfactant dodecyltrimethylammonium (DTA+). Mechanistic details can be determined through the evolution of high mass oxidation products through a nearly complete conversion of the parent monolayer. Carbonyl, hydroxyl, peroxyl, and small amounts of fragmentation products can be discerned from the collision-induced dissociation mass spectra and through hydrogen-deuterium exchange experiments. Psuedo-first order kinetics can also be observed in this system, suggesting a Langmuir-Hinshelwood mechanism of OH-initiated oxidation. Chapter 3 extends the study of oxidation of hydrocarbon surfactants by looking at neighbor chain competition among a bis-quaternary ammonium gemini surfactants, a species that contains two long alkyl chains. Specifically, the experiment assesses the ability of two non-identical alkyl chains to compete with each other for the impinging gas phase hydroxyl radical. The increased reactivity of singly oxidized chains is evaluated by the oxidation of a gemini surfactant parent with identical alkyl chains. Chapter 4 investigates the oxidation of α,ω-surfactants, those that contain polar functional group separated by methylene spacers, discussing deviations of this class of surfactants with those that contain only one head group (i.e. DTA+). Chapter 5 demonstrates the DBDS and FIDI-MS system for use as a peptide footprinting technique for the amphiphilic species substance P. Localization of the site of oxidation can be done through FIDI-MS/MS analysis.</p
Online Algorithms: From Prediction to Decision
Get PDFMaking use of predictions is a crucial, but under-explored, area of sequential decision problems with limited information. While in practice most online algorithms rely on predictions to make real time decisions, in theory their performance is only analyzed in simplified models of prediction noise, either adversarial or i.i.d. The goal of this thesis is to bridge this divide between theory and practice: to study online algorithm under more practical predictions models, gain better understanding about the value of prediction, and design online algorithms that make the best use of predictions.
This thesis makes three main contributions. First, we propose a stochastic prediction error model that generalizes prior models in the learning and stochastic control communities, incorporates correlation among prediction errors, and captures the fact that predictions improve as time passes. Using this general prediction model, we prove that Averaging Fixed Horizon Control (AFHC) can simultaneously achieve sublinear regret and constant competitive ratio in expectation using only a constant- sized prediction window, overcoming the hardnesss results in adversarial prediction models. Second, to understand the optimal use of noisy prediction, we introduce a new class of policies, Committed Horizon Control (CHC), that generalizes both popular policies Receding Horizon Control (RHC) and Averaging Fixed Horizon Control (AFHC). Our results provide explicit results characterizing the optimal use of prediction in CHC policy as a function of properties of the prediction noise, e.g., variance and correlation structure. Third, we apply the general prediction model and algorithm design framework to the deferrable load control problem in power systems. Our proposed model predictive algorithm provides significant reduction in variance of total load in the power system. Throughout this thesis, we provide both average-case analysis and concentration results for our proposed online algorithms, highlighting that the typical performance is tightly concentrated around the average-case performance.</p
Revealing the Mechanism of Xist-mediated Silencing
Get PDFXist initiates XCI by spreading across the future inactive X-chromosome, excluding RNA polymerase II, recruiting the polycomb repressive complex and its associated repressive chromatin modifications, and repositioning active genes into a transcriptionally silenced nuclear compartment. While much is known about the events that occur during XCI, the mechanism by which Xist carries out these various roles remains unclear. Here we identify ten proteins that directly associate with Xist, and we further show that three of these proteins are required for Xist-mediated transcriptional silencing. One of these proteins, SHARP, which is known to interact with the SMRT co-repressor that activates HDAC3, is not only essential for silencing, but is also required for the exclusion of PolII from the inactive X. We show that both SMRT and HDAC3 are required for Xist-mediated silencing and RNA polymerase II exclusion. Another of these proteins, LBR, is required for repositioning actively transcribed genes into the Xist-silenced compartment. We further show that Xist, through its interaction with LBR, a protein that is anchored in the inner nuclear membrane, would effectively reposition Xist-coated DNA to the nuclear lamina, thereby changing the accessibility of other genes on the X-chromosome to enable Xist to spread to active genes across the entire chromosome to silence chromosome-wide transcription. Together, these results present an integrative picture of how Xist can scaffold multiple proteins to orchestrate the complex functions required for the establishment of the inactive X-chromosome.</p
Investigations of Incompressible Variable-Density Turbulence in an External Acceleration Field
Get PDFOf interest to turbulence modeling is the behavior of variable-density flow at high Reynolds numbers - a flow difficult to model. This thesis provides insight into variable-density flow behavior by examining the dynamics and mixing of variable-density turbulence subject to an externally imposed acceleration field. The flow is studied in the zero-Mach-number limit with a series of direct numerical simulations. The flow configuration consists of alternating slabs of high- and low-density fluid in a triply periodic domain. Density ratios in the range of 1.005 to 10 are investigated. The flow produces temporally evolving shear layers.
A perpendicular mean density–pressure gradient is maintained as the flow evolves, with multi-scale baroclinic torques generated in the turbulent flow that ensues. For all density ratios studied, the simulations attain Reynolds numbers at the beginning of the fully developed turbulence regime.
An empirical relation for the convection velocity predicts the observed entrainment-ratio and dominant mixed-fluid composition statistics. Two mixing-layer temporal evolution regimes are identified: an initial diffusion-dominated regime with a growth rate with the square-root of time followed by a turbulence-dominated regime with a cubic growth rate in time. In the turbulent regime, composition probability density functions within the shear layers exhibit a slightly tilted ('non-marching') hump, corresponding to the most probable mole fraction. The shear layers preferentially entrain low-density fluid by volume at all density ratios, which is reflected in the mixed-fluid composition.
The mixed-fluid orientations of vorticity, baroclinic torques, density gradients, and pressure gradients are presented. Baroclinic torques, the cross product of the density and pressure gradients, tend to be aligned with positive or negative vorticity direction, with vorticity preferentially aligning with the intermediate eigenvector of the local strain-rate tensor, with some variance.</p
Nanoscale Field Emission Devices
Get PDFThis thesis outlines work done to produce in-plane nanoscale field emission devices. Field emission, the process of quantum tunneling electrons from a conductor into a vacuum, has been theorized as a device concept for almost as long as integrated circuits have existed. This is because the micro- and nanoscale dimensions of integrated circuits make field emission possible at modest voltages, and because the physics of field emission and conduction in a vacuum channel suggest that field emission devices can operate at extremely high frequencies and in harsh environments where CMOS devices face challenges. Yet despite many attempts to make practical field emission devices none have risen to the level of commercial products. These attempts were stymied by short lifetimes, high operating voltages, and the necessity for vacuum enclosure. In this thesis work, I outline how new fabrication technologies like high resolution electron beam lithography, atomic layer deposition, and refinement in reactive ion etching make lateral field emission devices with extremely short vacuum channels practical. The demonstrated devices can operate at near CMOS voltages and at atmospheric pressures, and are robust to emitting tip destruction. These devices are prime candidates for integration into demonstration circuits.
The second part of this thesis outlines work done in an emerging field to combine field emission with plasmonics for practical devices. The tunneling process in field emission depends exponentially on the magnitude of the instantaneous electric field, either static or time-varying, at the emitting surface. While it has long been known that using extremely powerful pulsed lasers one can field emit electrons from a metallic surface, the combination of plasmonics into a field emitting device has the potential to dramatically lower the incident optical power needed to produce field emission. This could enable extremely fast opto-electronic devices. This thesis presents work in progress to realize a plasmonically enhanced field emission opto-electronic modulator that is designed to operate at 1550 nm and is integratable with existing silicon photonics platforms.</p
Three-Dimensional Nano-Architected Materials as Platforms for Designing Effective Bone Implants
Get PDFThe growing world population coupled with longer human life expectancy warrants the need for better medical implant development. Recent advances in lithographic techniques have opened the door to a variety of approaches to tackle the aforementioned issue. However, several scientific hurdles must be overcome before patients can use fully synthetic and effective implants.
Identifying the optimal material, porosity, and mechanical properties of the scaffold to induce cell functionality are key obstacles. Limitations in established fabrication techniques have hindered the ability to fully understand cell behavior on 3D substrates. 3D printing is limited to feature sizes that are at least one order of magnitude larger than a single cell (~10μm); electrospinning is able to yield features that are on the same scale as cells, but its stochastic nature leads to scaffolds with poor mechanical properties; salt leeching doesn’t allow for control of pore size and distribution which have detrimental effects on nutrient diffusion and cell ingrowth, thereby thwarting the formation of functional tissue.
Much effort has been made to create a suitable platform for regenerating a relatively less complex organ, such as bone, yet the inability to fully understand cell mechanics on 3D scaffolds has curbed the fabrication of effective bone implants.
The first part of this thesis focuses on the suitability of nanoarchitected materials as 3D platforms for bone-tissue growth. We employed two-photon lithography to create polymeric and hydroxyapatite-coated 3D nanolattices to explore scaffold biocompatibility and material effects on osteoblast attachment and growth. Our experiments showed that the unit cell geometry, tetrakaidekahedron, and size, 25μm, were adequate for cell attachment and infiltration, which are hallmark signs of biocompatibility. Our study also corroborated previous findings that mammalian cells respond differently to different materials that they come in contact with. To isolate structural effects, we fabricated nanolattices coated with a uniform 20nm-thick outermost layer of TiO2. These nanolattices, which had fixed porosity and unit cell size (25μm) while they varied in structural stiffness (~2-9MPa) were used to explore the influence of scaffold properties on the viability of osteoblasts in a microenvironment similar to that of natural bone. Upon growing osteogenic cells on the nanolattices, significant cell attachment and presence of various calcium phosphate species, which are commonly found in natural bone, were observed. These findings suggest that 3-dimensional nano-architected materials can be used as effective scaffolds for bone cell growth and proliferation.
The second part of the thesis investigates the effects of nanolattice structural stiffness and loading conditions on osteoblast behavior. We fabricated nanolattices with stiffness ranging from ~0.7MPa to 100MPa. Experiments done by seeding osteoblast-like cells on these nanolattices revealed that both stress fiber concentration and bioapatite deposition were higher on the most compliant nanolattice, (0.7 MPa) by ~20% and ~40% respectively. These results provide insights into cell behavior in 3D microenvironments which can lead to a better understanding of stress shielding at the cellular level. Preventing stress shielding by creating scaffolds with structural stiffness and porosity that enhances osteoblasts activity could lead to the creation of effective implants with improved mechanical stability which ultimately improves osteointegration.
In addition to investigating static cell-scaffold interactions we took advantage of the nanolattices tunability to study the effects of dynamic loading on cell behavior. Bone adaptation is driven by dynamic, rather than static loading, however there is still wide controversy on whether stress, strain or loading frequency plays the most significant role in bone remodeling, which drives bone healing.
In order to understand cell sensitivity to varying loads, displacements and frequencies, we fabricated hollow TiO2 nanolattices with stiffness ranging from ~0.7-35MPa which were populated with osteoblast-like cells and subjected to cyclic compression to either a constant stress or strain. After seeding SAOS-2 cells on the nanolattices for 12 days different dynamic loading conditions were tested: (1) cyclic uniaxial compressions to strains ranging from ~0.3-2% strain were carried out to investigate the effects of strain magnitude on cell behavior. (2) Cyclic uniaxial compressions to stresses spanning from ~0.02-1MPa were performed to explore the role of stress magnitude on the cells’ stress fibers formation. (3) The nanolattices were cyclically loaded at different frequencies, ~0.1-3Hz, while maintaining stress and strain constant, which provided insights into how loading frequency affects osteoblasts behavior.
Cell activity, which was measured by monitoring f-actin and vinculin fluorescence intensity, revealed increased fluorescence in those cells that were mechanically stimulated as opposed to those that were statically grown on the nanolattices regardless of loading condition. Cell response was most drastically affected by varying the loading frequency. A ~30% increase in f-actin fluorescence was observed in the cells grown on the nanolattices that were loaded at ~3Hz compared to those that were grown on the nanolattices that were cyclically compressed at ~0.1Hz.
The last part of this thesis is focused on developing a three-dimensional architected capacitor that could be used as a strain gauge to further our understanding of cell mechanics in 3D. We took advantage of the mechanical tunability of the nanolattices to fabricate a 3D parallel-plate capacitor with a basal capacitance of ~280fF and able to sense forces as low as ~30μN. This work points to nano-architected materials as promising candidates for ideal platforms to investigate more realistic cellular conditions which can immensely benefit the field of tissue engineering.</p
New Capabilities of the Notch Signaling Pathway
Get PDFAnimal cells use a conserved repertoire of signaling pathways to exchange information during and after development. The constituent molecules of these pathways and their individual interactions are now well-characterized. However, it is becoming clear that pathways often possess unexpected signal-processing capabilities, which are typically collective, systems-level, features. Recent work shows that these capabilities are best investigated using quantitative, single-cell, dynamic analyses of pathway behavior. Here, we used this approach to study Notch signaling pathway, which is widely utilized for juxtacrine signaling during the development and maintenance of most tissues. Our work reveals two new capabilities of this pathway. First, the receptor Notch1 is capable of discriminating between two similar ligands, Dll1 and Dll4, and can use this ability to enact ligand-specific developmental programs. To enable this, the pathway encodes ligand identity in the dynamics of Notch1 signaling, and later decodes it for controlling gene expression. We show that dynamic encoding by Dll1 and Dll4 results from different requirements for ligand-receptor clustering during activation. Second, the pathway is capable of cell-autonomous signaling (cis-activation). This mode of signaling is general to multiple ligand-receptor combinations, and possesses many attributes of intercellular signaling. We show that cis-activation occurs in natural stem-cell contexts, where it could be important for self-renewal and prevents premature differentiation. These new capabilities of this central signaling pathway have implications for understanding the role of Notch in development and homeostasis, diagnosing and treating its misregulation in disease, and controlling it for tissue engineering and regeneration.</p