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Predicting Microstructural Pattern Formation Using Stabilized Spectral Homogenization
Get PDFInstability-induced patterns are ubiquitous in nature, from phase transformations and ferroelectric switching to spinodal decomposition and cellular organization. While the mathematical basis for pattern formation has been well-established, autonomous numerical prediction of complex pattern formation has remained an open challenge. This work aims to simulate realistic pattern evolution in material systems exhibiting non-(quasi)convex energy landscapes. These simulations are performed using fast Fourier spectral techniques, developed for high-resolution numerical homogenization. In a departure from previous efforts, compositions of standard FFT-based spectral techniques with finite-difference schemes are used to overcome ringing artifacts while adding grid-dependent implicit regularization.
The resulting spectral homogenization strategies are first validated using benchmark energy minimization examples involving non-convex energy landscapes. The first investigation involves the St. Venant-Kirchhoff model, and is followed by a novel phase transformation model and finally a finite-strain single-slip crystal plasticity model. In all these examples, numerical approximations of energy envelopes, computed through homogenization, are compared to laminate constructions and, where available, analytical quasiconvex hulls.
Subsequently, as an extension of single-slip plasticity, a finite-strain viscoplastic formulation for hexagonal-closed-packed magnesium is presented. Microscale intragranular inelastic behavior is captured through high-fidelity simulations, providing insight into the micromechanical deformation and failure mechanisms in magnesium. Studies of numerical homogenization in polycrystals, with varying numbers of grains and textures, are also performed to quantify convergence statistics for the macroscopic viscoplastic response.
In order to simulate the kinetics of pattern evolution, stabilized spectral techniques are utilized to solve phase-field equations. As an example of conservative gradient-flow kinetics, phase separation by anisotropic spinodal decomposition is shown to result in cellular structures with tunable elastic properties and promise for metamaterial design. Finally, as an example of nonconservative kinetics, the study of domain wall motion in polycrystalline ferroelectric ceramics predicts electromechanical hysteresis behavior under large bias fields. A first-principles approach using DFT-informed model constants is outlined for lead zirconate titanate, producing results showing convincing qualitative agreement with in-house experiments. Overall, these examples demonstrate the promise of the stabilized spectral scheme in predicting pattern evolution as well as effective homogenized response in systems with non-quasiconvex energy landscapes.</p
Novel Light Emitting Mechanisms Originating from Graphene Plasmons Near and Far from Equilibrium
Get PDFGraphene supports surface plasmons bound to an atomically thin layer of carbon, characterized by tunable propagation characteristics and distinctly strong spatial confinement of the electromagnetic energy. Such collective excitations in graphene enable the strong interactions of massless Dirac fermions with light. In this work, I explore fundamental properties and applications of graphene plasmons both near and far from equilibrium. I discuss the ability of graphene plasmons to interact with its local environment in various forms of mid-infrared, optically active excitations, demonstrated by tunable graphene plasmon dispersions and an emergence of a new mode via addition of a monoatomic dielectric layer. Furthermore, the viability of graphene for optics-based applications and large-scale integration is epitomized by the experimental demonstration of perfect tunable absorption in a large-area chemically grown graphene by using a noble-metal-graphene metasurfaces. Using these properties of graphene plasmons, electronically tunable thermal radiation is demonstrated. Finally, I present theoretical predictions and experimental validations of nonequilibrium graphene plasmon excitations via ultrafast optical excitation, originating from a previously unobserved decay channel: hot plasmons generated from optically excited carriers. These studies reveal novel infrared light emitting processes, both spontaneous and stimulated, and provide a platform for achieving ultrafast, ultrabright mid-infrared light sources.</p
Two Holomorphic Extremal Problems in Teichmüller Theory
Get PDFIn this thesis, we study the complex geometry of the Teichmüller space of conformal structures on a finite-type Riemann surface. We give partial answers to two structural questions: (1) Which holomorphic disks in Teichmüller space are holomorphic retracts of Teichmüller space? (2) What are the holomorphic and Kobayashi-isometric submersions between Teichmüller spaces? In both cases, the answers have to do with the geometry of the underlying surfaces, while the methods require developing and applying novel analytic tools.
Question (1) is equivalent to asking the following: on which pairs of points in Teichmüller space do the Carathéodory and Teichmüller metrics coincide? Markovic showed that the Carathéodory and Teichmüller metrics on Teichmüller space are not the same. On the other hand, Kra earlier showed that the metrics coincide when restricted to a Teichmüller disk generated by a differential with no odd-order zeros. We conjecture the converse: the Carathéodory and Teichmüller metrics agree on a Teichmüller disk if and only if the Teichmüller disk is generated by a differential with no odd-order zeros. We prove this conjecture for the Teichmüller spaces of the five-times punctured sphere and the twice-punctured torus. As a key analytic step in the proof, we study the family of holomorphic retractions from the polydisk onto its diagonal. In particular, we analyze the asymptotics of the orbit of such a retraction under the conjugation action of a unipotent subgroup of PSL2(ℝ).
Question (2) concerns holomorphic and isometric submersions between Teichmüller spaces of finite-type surfaces. We prove that, with potential exceptions coming from low-genusphenomena, any such map is a forgetful map τg,n → τg,m obtained by filling in punctures. This generalizes a classical result of Royden and Earle-Kra asserting that biholomorphisms between finite-type Teichmüller spaces arise from mapping classes. As a key step in the argument, we prove that any ℂ-linear embedding Q(X) ↪ Q(Y) between spaces of holomorphic integrable quadratic differentials is, up to scale, pull-back by a holomorphic map. We accomplish this step by adapting methods developed by Markovic to study isometries of infinite-type Teichmüller spaces. The main analytic tool used is a theorem of Rudin on isometries of Lp spaces.</p
A Fully-Nonlocal Quasicontinuum Method to Model the Nonlinear Response of Periodic Truss Lattices
Get PDFWe present a framework for the efficient, yet accurate description of general periodic truss networks based on concepts of the quasicontinuum (QC) method. Previous research in coarse-grained truss models has focused either on simple bar trusses or on two-dimensional beam lattices undergoing small deformations. Here, we extend the truss QC methodology to nonlinear deformations, general periodic beam lattices, and three dimensions. We introduce geometric nonlinearity into the model by using a corotational beam description at the level of individual truss members. Coarse-graining is achieved by the introduction of representative unit cells and a polynomial interpolation analogous to traditional QC. General periodic lattices defined by the periodic assembly of a single unit cell are modeled by retaining all unique degrees of freedom of the unit cell (identified by a lattice decomposition into simple Bravais lattices) at each macroscopic point in the simulation, and interpolating each degree of freedom individually. We show that this interpolation scheme accurately captures the homogenized properties of periodic truss lattices for uniform deformations. In order to showcase the efficiency and accuracy of the method, we compare coarse-grained simulations to fully-resolved simulations for various test problems, including: brittle fracture toughness prediction, static and dynamic indentation with geometric and material nonlinearities, and uniaxial tension of a truss lattice plate with a cylindrical hole. We also discover the notion of stretch locking --- a phenomenon where certain lattice topologies are over-constrained, resulting in artificially stiff behavior similar to volumetric locking in finite elements --- and show that using higher-order interpolation instead of affine interpolation significantly reduces the error in the presence of stretch locking in 2D and 3D. Overall, the new technique shows convincing agreement with exact, discrete results for a wide variety of lattice architectures, and offers opportunities to reduce computational expenses in structural lattice simulations and thus to efficiently extract the effective mechanical performance of discrete networks
Long Term Implantable Pressure Sensors
Get PDFThe benefits of implantable pressure sensors for continuous monitoring of diseases like glaucoma or hydrocephalus has been well established, but it has been difficult to achieve accurate pressure sensing in the body for more than one month. In this thesis, a general MEMS pressure sensor packaging method called parylene-oil-encapsulation is developed and analyzed in order to make commercial barometers for use in air suitable for implantation inside the body long term. Accelerated aging bench top data is presented and a wireless implantable intraocular pressure sensor has been built towards proving the viability of the packaging method in vivo.</p
Biological Responses to Therapeutic Treatments of Human Vascular Diseases
Get PDFDiseases of the retina affect hundreds of millions of patients worldwide, with limited treatment options available. ALG-1001 is an investigational drug that showed success in mitigating disease symptoms in animal models and improved patient vision in multiple clinical trials. To gain a better understanding of the drug’s mechanism of action, RNA sequencing (RNA-seq) and shotgun proteomics were employed to study the drug-induced transcriptome change in retinal tissue and cell culture models. Chapter 2 focuses on application of this approach in an animal model of the disease that showed the drug can reversely modulate hypoxia-activated angiogenesis and inflammation gene expression changes. Chapter 3 discusses the study of drug-induced transcriptome response in two cell culture models relevant to pathophysiology of the retinal diseases. Chapter 4 explores retinal cell transcriptome after short and long-term exposure to disease-relevant hypoxia condition and after hypoxia recovery. Appendix A documents our shotgun proteomics protocol and includes results from the application of this method in the study of drug mechanism.
Typical RNA-seq studies use few biological replicates for differential expression analysis, mainly due to the high cost of generating sequencing data. As a result, not all comparisons have the proper statistical power, which result in false positives and false negatives that can lead the researcher to the wrong conclusion. Chapter 5 discusses a novel algorithm and software that help users perform quality control of their dataset to identify whether the appropriate sample size was used for differential gene discovery. The chapter covers demonstration of the software with four publicly available RNA-seq datasets to illustrate its utility.
Bioresorbable vascular scaffolds (BVSs) are the application of biocompatible polymer in the treatment of coronary heart disease, one of the leading causes of death worldwide. BVSs are designed to replace metal stents, which stay permanently in the body after surgery and can lead to various complications, such as lethal thrombosis. In contrast, BVSs provide the necessary support and are resorbed by the body to leave behind a healthy artery after 2-3 years. Improving on the existing BVS material, chapter 6 explores a new polymer nanocomposite that increases the structure’s radial strength in a thinner profile and provides radio-opacity to enhance surgery success.</p
Neural Correlates of Sensorimotor Control in Human Cortex: State Estimates and Reference Frames
Get PDFInteracting with our environment involves multiple sensory-motor circuits throughout the human brain. How do these circuits transform sensory inputs into discernable motor actions? Our understanding of this question is critical to behavioral neuroscience and implementation of brain-machine interfaces (BMIs). In this thesis, we present experiments that explore the contributions of human cerebral cortex (parietal, premotor, and primary somatosensory cortices) to sensory-motor transformations. First, we provide evidence in support of primary somatosensory cortex (S1) encoding cognitive motor signals. Next, we describe a series of experiments that explore contributions of posterior parietal cortex (PPC) to the internal state estimate. Neural correlates for the state estimate are found in PPC; furthermore, it is found to be encoded with respect to gaze position. Finally, we investigate reference frame encoding in regions throughout human cortex (AIP, SMG, PMv, and S1) during an imagined reaching task. We find the greatest heterogeneity among brain regions during movement planning, which collapses to a largely single reference frame representation (hand-centered) during execution of the imagined reach. However, this result is dependent upon brain region. These findings yield new perspectives and evidence on the organization of sensory-motor transformations and the location the human brain’s internal estimate of the body’s state.</p
Optimization of CCD Charge Transfer for Ground and Space-Based Astronomy
Get PDFThis thesis will be of particular interest to anyone integrating Charge-Coupled Devices (CCDs) into any precision scientific imaging instrument, especially so in space. The first part of the thesis concerns optimization of a CCD camera as a whole. CCDs for the WaSP imager at the Hale telescope are characterized using a minimal amount of data using just a flat-field illumination source. By measuring performance over the entire parameter space of (clock and bias) inputs and analyzing the multidimensional output (linearity, dynamic range, read noise etc), optimal operating conditions can be selected quickly (and possibly automatically). With ever growing sizes of detector arrays such as the recently launched Gaia mission, the upcoming Euclid mission and ground-based cameras such as the LSST (189 CCDs), the task of streamlining detector optimization will be increasingly important. In the second (larger) part, the optimization of Charge Transfer Efficiency (CTE) is explored in particular. In modern CCDs, CTE is caused by lattice defects in the bulk silicon and is significantly worsened by radiation exposure, which is unavoidable in space. As shown in the literature, just a year of exposure to high energy solar proton radiation at low earth orbit can result in CTE reducing to 0.9999 for a signal level of 10,000e- — problematic for most precision astronomical measurements. Here, CTE degrading traps are fully explored in an undamaged CCD to new levels of accuracy. Several unique species are identified, and their population statistics are analyzed by both wafer and sub-pixel location. Subsequently, easily applied CTE measurement techniques are presented, yielding results with new levels of accuracy, concluding in the presentation of a new trap mitigating readout clocking scheme. This scheme can be readily applied to any CCD employing a parallel transfer gate without readout speed penalty. It is proposed that the results herein may be used to construct a simple model to predict CTE given a temperature, readout timing and signal level. This model could then be used to automatically optimize CTE for any CCD, given only its trap parameter statistics.</p
Representations of Action Monitoring and Cognitive Control by Single Neurons in the Human Brain
Get PDFCognitive control arises whenever a prepotent and often automatic response needs to be overcome by another response. Control is usually effortful and relies on monitoring processes that detect when control is needed and/or when it failed. Control is one of the most important aspects of human behavior in everyday life and is a critical component of executive function. In a series of three empirical chapters, I present results from invasive single-neuron recordings from the frontal cortex of neurosurgical human patients while they perform tasks requiring cognitive control. I show that a substantial proportion of neurons in the pre-supplementary motor area (pre-SMA), and in the dorsal anterior cingulate cortex (dACC), signal response errors shortly after they occurred, but well before onset of feedback. Here I demonstrate that these error neurons signal self-detected errors and that they were separate from neurons signaling conflict. The response of error neurons correlated trial-by-trial with the simultaneously recorded intracranial error-related negativity (iERN), thereby establishing a single-neuron correlate of this important scalp potential. iERN-error neuron synchrony in dACC, but not pre-SMA, predicted whether post-error slowing, which is a measure of control, occurred or not. Spike-field coherence between action potentials and local field potentials in specific frequency bands, and latency differences between the different brain regions, suggest a mechanistic model whereby information relevant to control is passed between sectors of the medial frontal cortex. Multiplexing of different ex-post monitoring signals by individual neurons further documents that control relies on multiple sources of information, which can be dynamically routed in the brain depending on task demands. These findings provide the most complete set of single-neuron data on how errors and conflict signals at the single neuron level contribute to cognitive controls in humans. They provide a first-single neuron correlate of an extensively utilized scalp EEG potential. Together, this work provides a strong complement to investigations of this topic using fMRI in humans, and using electrophysiology in monkeys, and suggests specific future directions
Resonant Thermoelectric Nanophotonics: Applications in Spectral and Thermal Sensing
Get PDFPlasmon excitation enables extreme light confinement at the nanoscale, localizing energy in subwavelength volumes and thus can enable increased absorption in photovoltaic or photoconductive detectors. Nonetheless, plasmon decay also results in energy transfer to the lattice as heat which is detrimental to photovoltaic detector performance. However, heat generation in resonant subwavelength nanostructures also represents an energy source for voltage generation, as we demonstrate in the first part of this thesis via design of resonant thermoelectric (TE) plasmonic absorbers for optical detection. Though TEs have been used to observe resonantly coupled surface plasmon polaritons in noble-metal thin films and microelectrodes, they have not been employed previously as resonant absorbers in functional TE nanophotonic structures.
We demonstrate nanostructures composed of TE thermocouple junctions using established TE materials – chromel/alumel and bismuth telluride/antimony telluride – but patterned so as to support guided mode resonances with sharp absorption profiles, and which thus generate large thermal gradients upon optical excitation and localized heat generation in the TE material. Unlike previous TE absorbers, our structures feature tunable narrowband absorption and measured single junction responsivities 4 times higher than the most similar (albeit broadband) graphene structures, with potential for much higher responsivities in thermopile architectures. For bismuth telluride – antimony telluride single thermocouple structures, we measure a maximum responsivity of 38 V/W, referenced to incident illumination power. We also find that the small heat capacity of optically resonant TE nanowires enables a fast, 3 kHz temporal response, 10-100 times faster than conventional TE detectors. We show that TE nanophotonic structures are tunable from the visible to the MIR, with small structure sizes of 50 microns x 100 micons. Our nanophotonic TE structures are suspended on thin membranes to reduce substrate heat losses and improve thermal isolation between TE structures arranged in arrays suitable for imaging or spectroscopy. Whereas photoconductive and photovoltaic detectors are typically insensitive to sub-bandgap radiation, nanophotonic TEs can be designed to be sensitive to any specific wavelength dictated by nanoscale geometry, without bandgap wavelength cutoff limitations. From the point of view of imaging and spectroscopy, they enable integration of filter and photodetector functions into a single structure. Other thermoelectric nanophotonic motifs are also explored.
Generating localized, high electric field intensity in nanophotonic and plasmonic devices has many applications, from enhancing chemical reaction rates, to thermal radiation steering, to chemical sensing, and to photovoltaics. Along with a strongly localized electric field comes a temperature rise in non-lossless photonic materials, which can affect reaction rate, photovoltaic efficiency, or other properties of the system. Measuring temperature rises in nanophotonic structures is difficult, and methods commonly employed suffer from various limitations, such as low spatial resolution (Fourier transform infrared microscopy), bulky and expensive setups (scanning thermal microscopy), intrusive methods that interfere with nanophotonic structures (Pt resistive thermometry), or the need for specialized materials (temperature dependent photoluminescence).
In the second part of this thesis, we overcome these limitations with the first-ever demonstration of temperature measurements of nanophotonic structures by employing both room temperature noise thermometry and the thermoelectric effect under ambient conditions without external probes by utilizing the properties of the materials that make up the nanophotonic structure itself. We have previously estimated the Δ T in a nanophotonic device using the thermoelectric effect, but could not determine the absolute temperature of the system. In the application we will discuss, the absolute electron temperature of the nanophotonic material itself is measured. Because Johnson-Nyquist noise is material independent and is a fundamental measure of absolute temperature, there is theoretically no need for calibration as in the case of resistive thermometry. To measure the temperature rise of a nanophotonic resonant region remotely, the Seebeck coefficient of the material is first carefully measured using noise thermometry, then the thermoelectric voltage generated in the nanophotonic materials themselves is measured from electrical leads spanning the resonantly excited region. To accomplish this, we have developed a metrology technique capable of simultaneously measuring electrical noise at two locations on the nanophotonic structure as well as the electrical potential between the two points, under chopped laser illumination that heats the structure via nanophotonic absorption, thus providing drift-corrected light on/off temperature information.</p