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Mechanics of Viscoelastic Thin-Walled Structures
Get PDFThin-walled structures made of polymers and reinforced polymer composites are prominent candidates for constructing large lightweight structures. A major challenge in designing polymer-based thin-walled structures is their time and temperature dependent behavior originating from material viscoelasticity and its interaction with the highly geometrically nonlinear response due to thinness of the walls. Although polymer viscoelasticity and geometric nonlinearity have been extensively studied, the mechanics of structures exhibiting both phenomena are not well understood.
This thesis presents a combination of experimental, numerical, and analytical investigations of the behavior of viscoelastic thin-walled structures. The first goal of this research is to establish general methods of analysis for two types of structural components, namely composite shells and polymer membranes, that will serve as the basis for full-scale structural analysis. The second goal is to demonstrate the capability of the developed methods by analyzing time and temperature dependent behavior of deployable structures and balloon structures.
In the study of deployable structures, the deployment and shape recovery processes after stowage are investigated. Fundamental features of viscoelastic deployable structures are studied first with homogeneous polymer beams and shells. A simple closed-form solution describing the shape evolution of a beam after stowage is proposed. The effects of rate and temperature on the bending instability of shells are revealed. Building on the understanding gained from the analysis of homogeneous structures, modeling techniques are developed for polymer composite structures. A micromechanical viscoelastic model for carbon fiber reinforced polymer thin shells is established through finite element homogenization and applied to evaluate the effects of long-term stowage in a representative composite deployable structure.
In the study of balloon structures, a membrane model is developed to study polymer balloon films with stress concentrations due to thickness variation. A nonlinear viscoelastic constitutive model is first formulated for the film material. The wrinkling instability behavior is incorporated into the model through correction of stress and strain states in the presence of wrinkling. Stress concentration factors in balloon films are predicted and measured with the membrane model and full-field displacement measurement techniques, respectively.</p
Applications of Computational Protein Design to Red Fluorescent Proteins
Get PDFThe research comprising this thesis is presented in three chapters divided into two parts. Part One, Chapters 2 and 3, of the thesis focuses on the application of rational design and CPD to the core residues of FPs. Chapter 2 applies CPD to the well known red fluorescent protein mCherry. Design hypotheses in this work were driven by a desire to red-shift the fluorescence emission of the parent protein. Chapter 3 takes the most successful results from the mCherry system and attempts to applies these results to the far-red FP mPlum. These two proteins, mCherry and mPlum, share a directed evolution parent, mRFP1. Part Two, consisting of Chapter 4, presents the beginnings of a comprehensive study into the applications CPD for designing FP surfaces. The system used is based on DsRed, the oligomeric parent of monomer mCherry. Professional and personal acknowledgments conclude the thesis
Phase Stability and Defect Behavior in Complex Thermoelectric Zinc-Antimonides
Get PDFThe Zn-Sb binary phase system has been of interest for many years in the search for efficient and low-cost thermoelectric materials. Of primary interest has been the Zn4Sb3 phase which exhibits a thermoelectric figure of merit, zT, in excess of 1 in an intermediate temperature range. In this study, Zn4Sb3 is shown to be entropically stabilized with respect to decomposition to Zn and ZnSb through the effects of configurational disorder and phonon free energy. Single-phase stability is predicted for a range of compositions and temperatures. Retrograde solubility of Zn is predicted on the two-phase boundary region between Zn4Sb3 and Zn. The complex temperature-dependent solubility can be used to explain the variety of nanoparticle formation observed in the system: formation of ZnSb on the Sb-rich side, Zn on the far Zn-rich side, and nano-void formation due to Zn precipitates being reabsorbed at lower temperatures.
A new binary compound, Zn8Sb7, known only in nanoparticulate form, is also studied using density functional calculations. The free energies of formation, including effects from vibrations and configurational disorder, are calculated to compare with the relevant phases ZnSb, Zn, and Zn4Sb3, yielding insight into the phase stability of Zn8Sb7. Band structure calculations predict Zn8Sb7, much like ZnSb and Zn4Sb3, to be an intermetallic semiconductor with similar thermoelectric properties. If sufficient entropy or surface energy exists to stabilize the bulk material, it would be stable in a limited temperature window at high temperature.
In the AZn2Sb2 series of materials—A = Ca, Sr, Yb, and Eu—I show that a large concentration of thermodynamically stable cation vacancies leads to high extrinsic carrier concentrations. The stable defect level depends on the choice of A, and is consistent with experimentally observed carrier concentrations in these materials. These results demonstrate that point defects are the primary mechanism by which the covalency of the cation bond can influence carrier concentration in nominally valence-precise AZn2Sb2compounds. This mechanism may be generally applicable to other Zintl phases, perhaps explaining similar trends seen in A14MSb11, A2MSb2 (A=2+ cation, M = 2+ or 3+ metal),and similar materials. </p
Isotopic Proxies for Microbial and Environmental Change: Insights from Hydrogen Isotopes and the Ediacaran Khufai Formation
Get PDFMicrobes have profoundly influenced the Earth’s environments through time. Records of these interactions come primarily from the development and implementation of proxies that relate known modern processes to chemical signatures in the sedimentary record. This thesis is presented in two parts, focusing first on novel proxy development in the modern and second on interpretation of past environments using well-established methods. Part 1, presented in two chapters, builds on previous observations that different microbial metabolisms produce vastly different lipid hydrogen isotopic compositions. Chapter 1 evaluates the potential environmental expression of metabolism-based fractionation differences by exploiting the natural microbial community gradients in hydrothermal springs. We find a very large range in isotopic composition that can be demonstrably linked to the microbial source(s) of the fatty acids at each sample site. In Chapter 2, anaerobic culturing techniques are used to evaluate the hydrogen isotopic fractionations produced by anaerobic microbial metabolisms. Although the observed fractionation patterns are similar to those reported for aerobic cultures for some organisms, others show large differences. Part 2 changes focus from the modern to the ancient and uses classical stratigraphic methods combined with isotope stratigraphy to interpret microbial and environmental changes during the latest Precambrian Era. Chapter 3 presents a detailed characterization of the facies, parasequence development, and stratigraphic architecture of the Ediacaran Khufai Formation. Chapter 4 presents measurements of carbon, oxygen, and sulfur isotopic ratios in stratigraphic context. Large oscillations in the isotopic composition of sulfate constrain the size of the marine sulfate reservoir and suggest incorporation of an enriched isotopic source. Because this data was measured in stratigraphic context, we can assert with confidence that these isotopic shifts are not related to stratigraphic surfaces or facies type but instead reflect the evolution of the ocean through time. This data integrates into the chemostratigraphic global record and contributes to the emerging picture of changing marine chemistry during the latest Precambrian Era
Liquid Silicate Equation of State: Using Shock Waves to Understand the Properties of the Deep Earth
Get PDFThe equations of state (EOS) of several geologically important silicate liquids have been constrained via preheated shock wave techniques. Results on molten Fe2SiO4 (fayalite), Mg2SiO4 (forsterite), CaFeSi2O6 (hedenbergite), an equimolar mixture of CaAl2Si2O8-CaFeSi2O6 (anorthite-hedenbergite), and an equimolar mixture of CaAl2Si2O8-CaFeSi2O6-CaMgSi2O6(anorthite-hedenbergite-diopside) are presented. This work represents the first ever direct EOS measurements of an iron-bearing liquid or of a forsterite liquid at pressures relevant to the deep Earth (> 135 GPa). Additionally, revised EOS for molten CaMgSi2O6 (diopside), CaAl2Si2O8 (anorthite), and MgSiO3 (enstatite), which were previously determined by shock wave methods, are also presented.
The liquid EOS are incorporated into a model, which employs linear mixing of volumes to determine the density of compositionally intermediate liquids in the CaO-MgO-Al2O3-SiO2-FeO major element space. Liquid volumes are calculated for temperature and pressure conditions that are currently present at the core-mantle boundary or that may have occurred during differentiation of a fully molten mantle magma ocean.
The most significant implications of our results include: (1) a magma ocean of either chondrite or peridotite composition is less dense than its first crystallizing solid, which is not conducive to the formation of a basal mantle magma ocean, (2) the ambient mantle cannot produce a partial melt and an equilibrium residue sufficiently dense to form an ultralow velocity zone mush, and (3) due to the compositional dependence of Fe2+ coordination, there is a threshold of Fe concentration (molar XFe ≤ 0.06) permitted in a liquid for which its density can still be approximated by linear mixing of end-member volumes.</p
Terahertz Time Domain Spectroscopy of Amino Acids and Sugars
Get PDFA time-domain spectrometer for use in the terahertz (THz) spectral range was designed and constructed. Due to there being few existing methods of generating and detecting THz radiation, the spectrometer is expected to have vast applications to solid, liquid, and gas phase samples. In particular, knowledge of complex organic chemistry and chemical abundances in the interstellar medium (ISM) can be obtained when compared to astronomical data. The THz spectral region is of particular interest due to reduced line density when compared to the millimeter wave spectrum, the existence of high resolution observatories, and potentially strong transitions resulting from the lowest-lying vibrational modes of large molecules.
The heart of the THz time-domain spectrometer (THz-TDS) is the ultrafast laser. Due to the femtosecond duration of ultrafast laser pulses and an energy-time uncertainty relationship, the pulses typically have a several-THz bandwidth. By various means of optical rectification, the optical pulse carrier envelope shape, i.e. intensity-time profile, can be transferred to the phase of the resulting THz pulse. As a consequence, optical pump-THz probe spectroscopy
is readily achieved, as was demonstrated in studies of dye-sensitized TiO2, as discussed in chapter 4. Detection of the terahertz radiation is commonly based on electro-optic sampling and provides full phase information. This allows for accurate determination of both the real and imaginary index of refraction, the so-called optical constants, without additional analysis. A suite of amino acids and sugars, all of which have been found in meteorites, were studied in crystalline form embedded in a polyethylene matrix. As the temperature was varied between 10 and 310 K, various strong vibrational modes were found to shift in spectral intensity and frequency. Such modes can be attributed to intramolecular, intermolecular, or phonon modes, or to some combination of the three.</p
Determinantal Hypersurface from a Geometric Perspective
Get PDFIn this paper, we give a geometric interpretation of determinantal forms, both in the case of general matrices and symmetric matrices. We will prove irreducibility of the determinantal singular loci and state its dimension. We also provide detailed description of the singular locus for small dimensions
Parylene-C as a New Piezoelectric Material
Get PDFThe goal of this thesis is to develop a proper microelectromechanical systems (MEMS) process to manufacture piezoelectric Parylene-C (PA-C), which is famous for its chemical inertness, mechanical and thermal properties and electrical insulation. Furthermore, piezoelectric PA-C is used to build miniature, inexpensive, non-biased piezoelectric microphones.
These piezoelectric PA-C MEMS microphones are to be used in any application where a conventional piezoelectric and electret microphone can be used, such as in cell phones and hearing aids. However, they have the advantage of a simplified fabrication process compared with existing technology. In addition, as a piezoelectric polymer, PA-C has varieties of applications due to its low dielectric constant, low elastic stiffness, low density, high voltage sensitivity, high temperature stability and low acoustic and mechanical impedance. Furthermore, PA-C is an FDA approved biocompatible material and is able to maintain operate at a high temperature.
To accomplish piezoelectric PA-C, a MEMS-compatible poling technology has been developed. The PA-C film is poled by applying electrical field during heating. The piezoelectric coefficient, -3.75pC/N, is obtained without film stretching.
The millimeter-scale piezoelectric PA-C microphone is fabricated with an in-plane spiral arrangement of two electrodes. The dynamic range is from less than 30 dB to above 110 dB SPL (referenced 20 µPa) and the open-circuit sensitivities are from 0.001 – 0.11 mV/Pa over a frequency range of 1 - 10 kHz. The total harmonic distortion of the device is less than 20% at 110 dB SPL and 1 kHz.</p
Relative Mirror Symmetry and Ramifications of a Formula for Gromov-Witten Invariants
Get PDFFor a toric Del Pezzo surface S, a new instance of mirror symmetry, said relative, is introduced and developed. On the A-model, this relative mirror symmetry conjecture concerns genus 0 relative Gromov-Witten of maximal tangency of S. These correspond, on the B-model, to relative periods of the mirror to S. Furthermore, for S not necessarily toric, two conjectures for BPS state counts are related. It is proven that the integrality of BPS state counts of the total space of the canonical bundle on S implies the integrality for the relative BPS state counts of S. Finally, a prediction of homological mirror symmetry for the open complement is explored. The B-model prediction is calculated in all cases and matches the known A-model computation for the projective plane
Topics in Randomized Numerical Linear Algebra
Get PDFThis thesis studies three classes of randomized numerical linear algebra algorithms, namely: (i) randomized matrix sparsification algorithms, (ii) low-rank approximation algorithms that use randomized unitary transformations, and (iii) low-rank approximation algorithms for positive-semidefinite (PSD) matrices.
Randomized matrix sparsification algorithms set randomly chosen entries of the input matrix to zero. When the approximant is substituted for the original matrix in computations, its sparsity allows one to employ faster sparsity-exploiting algorithms. This thesis contributes bounds on the approximation error of nonuniform randomized sparsification schemes, measured in the spectral norm and two NP-hard norms that are of interest in computational graph theory and subset selection applications.
Low-rank approximations based on randomized unitary transformations have several desirable properties: they have low communication costs, are amenable to parallel implementation, and exploit the existence of fast transform algorithms. This thesis investigates the tradeoff between the accuracy and cost of generating such approximations. State-of-the-art spectral and Frobenius-norm error bounds are provided.
The last class of algorithms considered are SPSD "sketching" algorithms. Such sketches can be computed faster than approximations based on projecting onto mixtures of the columns of the matrix. The performance of several such sketching schemes is empirically evaluated using a suite of canonical matrices drawn from machine learning and data analysis applications, and a framework is developed for establishing theoretical error bounds.
In addition to studying these algorithms, this thesis extends the Matrix Laplace Transform framework to derive Chernoff and Bernstein inequalities that apply to all the eigenvalues of certain classes of random matrices. These inequalities are used to investigate the behavior of the singular values of a matrix under random sampling, and to derive convergence rates for each individual eigenvalue of a sample covariance matrix.</p