Between Dec 19, 2024 and Jan 2, 2025, datasets can be submitted to DRUM but will not be processed until after the break. Staff will not be available to answer email during this period, and will not be able to provide DOIs until after Jan 2. If you are in need of a DOI during this period, consider Dryad or OpenICPSR. Submission responses to the UDC may also be delayed during this time.

Browsing by Subject "Elasticity"

Now showing 1 - 8 of 8
  • Thumbnail Image
    Item
    Consequences of nematoelasticity in structurally disordered quantum materials
    (2024-05) Meese, William
    Electronic nematicity – a state of broken rotational symmetry but preserved translational symmetry – appears to be a general feature of quantum materials, and it often develops in the vicinity of unconventional superconductivity. Strains are conjugate fields for the electronic nematic order parameter – a relationship known as nematoelasticity. While external, homogeneous strains are useful tools in studying electronic nematicity, crystals simultaneously contain inhomogeneous strains because of structural disorder generated by crystalline defects. In this thesis, I demonstrate that these unavoidable, internal, random strains lead to a host of new electronic and relaxational behavior in electronic nematics. Electronic nematicity manifests as either an isolated instability or a vestigial one. The latter is a partially melted phase of some underlying primary order, meaning it is borne out of the fluctuations of the primary order parameter. In the former case, the impact of random strains has been studied before using the random-field Ising model (RFIM). In the case of vestigial nematicity, the RFIM description is incomplete, as random strain plays the simultaneous role of both a random field for the nematic order parameter and a random mass for the primary order parameter. I generalized the RFIM to a new model that is then applied to systems such as the iron pnictide superconductors. This disorder-free limit is built upon the Ashkin-Teller model, whose composite “Baxter” order parameter plays the role of the vestigial nematic comprised of two primary magnetic degrees of freedom. These magnetic degrees of freedom are mapped onto the interpenetrating Néel vectors in the pnictides. The Baxter variable is then subject to a random field, making this random “Baxter field” act as both a random field and a random mass. In analogy with the RFIM, the model is dubbed the random-Baxter-field model (RBFM), and massively-parallel Monte Carlo simulations were used to characterize its impact on nematicity. It was found that the random strains break the vestigial nematic order into domains while creating new correlations in the primary order parameters, enhancing their fluctuations. In a following experimental collaboration, electronic nematic domain formation was then used to explain optical dichroism measurements on the compound FePSe3 which showed evidence of vestigial 3-state Potts nematic domains. In the limit of nearly perfect crystals, however, neither the RFIM nor the RBFM account for the nature of long-ranged strains from crystalline defects. Recent heat capacity measurements on the nematic insulator, Tm1–xYxVO4, show that, even in the purest samples, random strains are ubiquitous and correlated. To this end, I reexamined nematoelastic interactions in structurally disordered elastic media. I developed a realistic description of elastically generated random strains from a veritable zoo of different crystalline defects, and used numerical simulations of dislocations to qualitatively account for the experimental results. It was found that even simple ensembles of defects – in this case, dislocations – can generate strain distributions that can fit the data just as well as conventional, uncorrelated random strains can without needing to overfit. These elastically generated random strains contain not only long-ranged and anisotropic correlations, but also higher-order statistics that are frequently omitted in random field models. This way of viewing random strains constitutes a new type of random field disorder and will lead to exciting new phenomena in future work.
  • Thumbnail Image
    Item
    Cross-Elasticities in Frequencies and Ridership for Urban Local Routes
    (2016-08-01) Totten, Joseph C; Levinson, David M
    Observational data from the Minneapolis-Saint Paul region’s Metro Transit, are analyzed to determine the effects of service levels on ridership levels at different intervals. This research is innovative because it compares changes in service levels and ridership in several service intervals, and includes the elasticities and cross elasticities, or the influence that these service levels have on different service intervals’ ridership. These cross-elasticities are not known to have been researched previously, and are found to have little effect during the week; however, weekend ridership was found to be influenced by rush hour and overnight frequencies. Future research should replicate this study in other cities, and should use express and suburban routes.
  • Thumbnail Image
    Item
    Essays in health care economics: structural approaches to measuring moral hazard and adverse selection.
    (2010-07) Marsh, Christina L.
    The classic issues of moral hazard and adverse selection as they appear in health care are addressed in this dissertation using new tools of analysis. In the first essay, I construct a new estimator and estimates to measure the price response of patients in health insurance. These estimates allow us to measure the magnitude of moral hazard. Recent health care initiatives attempt to stem rising costs by increasing patients' cost sharing. These initiatives include high deductible plans, the Medicare Drug Plan \doughnut hole," and Health Savings Accounts (HSAs). The success of such initiatives depends on how health expenditures change as patients' reimbursement decreases. Estimating this elasticity is complicated by selection bias, as high expenditure patients can self-select into high reimbursement plans. Additionally, nonlinear reimbursement is prevalent in U.S. insurance contracts and the aforementioned initiatives. Nonlinearities introduce bias when using previous estimation methods by simultaneously determining expenditure and reimbursement rate. This paper develops an elasticity estimation method that controls for selection bias by taking advantage of nonlinear reimbursement rates. Discontinuous reimbursement rates induced by a nonlinearity are used to isolate patients' expenditure choices. Using detailed claims-level data of employer-sponsored health insurance, I nd a tight range of elasticities between -0.25 and -0.33 in the range of average U.S. spending. I then use these estimates in a policy experiment measuring moral hazard and calculate the resulting welfare eects. This paper's estimation method may be used on many policies with nonlinear reimbursement which previous tools could not address. In the second essay, I present joint work with Patrick Bajari, Han Hong, and Ahmed Khwaja wherein we construct an estimator that can address both moral hazard and adverse selection simultaneously. Theoretical models predict asymmetric information in health insurance markets may generate inefficient outcomes due to adverse selection and moral hazard. However, previous empirical research has found it dicult to disentangle adverse selection from moral hazard in health care. We empirically study this question by a using unique data set with condential information from a large self-insured employer to estimate a structural model of the demand for health insurance and medical care. We propose a two-step semiparametric estimation strategy that builds on the work on identification and estimation of auction models. We find significant evidence of moral hazard and adverse selection.
  • Thumbnail Image
    Item
    HOT or Not: driver elasticity to price and alternative pricing strategies on the MnPASS HOT Lanes
    (2013-12) Janson, Michael Risch
    The Minnesota Department of Transportation (MnDOT) has added MnPASS High Occupancy Toll (HOT) lanes on two freeway corridors in the Twin Cities. While not the first HOT lanes in the country, the MnPASS lanes are the first implementation of road pricing in Minnesota and possess a dynamic pricing schedule. Tolls charged to single occupancy vehicles (SOVs) are adjusted every three minutes according to HOT lane vehicle density. Given the infancy of systems like MnPASS, questions remain about drivers' responses to toll prices. Three field experiments were conducted on the corridors during which prices were changed. Data from the field experiments as well as two years of toll and traffic data were analyzed to measure driver responses to pricing changes. Driver elasticity to price was positive with magnitudes less than 1.0. This positive relationship between price and demand is in contrast with the previously held belief that raising the price would discourage demand. In addition, drivers consistently paid between approximately \$60-120 per hour of travel time savings, much higher than the average value of time. Four alternative pricing strategies are then proposed and calibrated. These pricing strategies are tested using a HOT lane choice model based on previous research. Adjusting parameters of the pricing strategies altered the resulting HOT lane share. Measuring the changes in HOT demand against the changes in price led to similar positive elasticity results.
  • Thumbnail Image
    Item
    In-Die Techniques to Characterize Powder Compression
    (2023-06) Vreeman, Gerrit
    Powder compaction plays a large role in many industries, including pharmaceutical tablet, metal part, detergent, cosmetics, and food manufacturing. Assessing the mechanical properties of a powdered material is an important step in developing processes that can effectively transform a powdered material into a product via densification. In-die analyses performed during compaction are fast and materials sparing compared to traditional out-of-die approaches. The goal of this work includes: (1) evaluate the effectiveness of fast, materials- sparing in-die methods for characterizing powder compaction compared to traditional out- of-die methods; (2) explore the benefits of using in-die elastic recovery measures to predict compact lamination via air entrapment; and (3) develop a universal compressibility model framework that can fully describe in-die compaction data, including all low- and high-pressure mechanisms. These goals aim to enable a fast and materials-sparing assessment of powder mechanical properties and lays a foundation for optimal formulation composition, processing strategy, and quality control assessment from such mechanical property assessments.
  • Thumbnail Image
    Item
    Interplay between electronic nematicity and elasticity in finite-size samples and surfaces
    (2021-05) Lahiri, Aritra
    In the phase diagram of iron-based superconductors, the proximity of superconductivityto electronic nematicity, the spontaneous breaking of the discrete rotational symmetry, has prompted numerous studies of a detailed understanding of nematicity and its interplay with superconductivity. Several studies have suggested the onset of nematic order above the bulk nematic critical temperature, along with indications of it being associated with the surface of the sample. In this work, motivated by the strong nemato-elastic interaction, we consider aspects of the interplay of elasticity and nematicity in realistic finite-size samples, considering both bulk and surface effects. First, we demonstrate non-trivial boundary effects in a finite-size sample, which significantly alter the order parameter profiles and the critical temperature. Elaborate finite-element simulations are carried out to solve the full nemato-elastic problem, demonstrating a strong inhomogeneity, dependent on the sample aspect ratio and geometric constraints. We find that the nematic critical temperature is bounded by the corresponding bulk value and, in fact, decreases rapidly with decreasing sample thickness, thereby necessitating the presence of other mechanisms to generate supercritical nematicity. We propose surface elastic disorder, such as domains of anisotropic defects, as possible avenues to realize supercritical nematicity. We show that these, in fact, lead to an incommensurate supercritical smectic state, localized at the sample surface, eventually transitioning into the standard uniform bulk nematic state. The smectic modulation wavevector is dependent only on the elastic parameters, and the coefficients entering the nematic free energy.
  • Thumbnail Image
    Item
    Mixed methods with weak symmetry for time dependent problems of elasticity and viscoelasticity.
    (2012-07) Lee, Jeonghun
    In this dissertation, we study numerical algorithms for time dependent problems in continuum mechanics using mixed finite element methods. We are particularly interested in linear elastodynamics and the Kelvin--Voigt, Maxwell, and generalized Zener models in linear viscoelasticity. We use mixed finite elements for elasticity with weak symmetry of stress, and show the a priori error analysis. A main contribution of our analysis is proving existence of a new elliptic projection map, called a weakly symmetric elliptic projection. In our analysis we prove that a priori error estimates for elastodynamics and viscoelasticity problems are as good as that of stationary elasticity problems. We present numerical results supporting our error analysis. We also present some basic numerical simulations which are more involved in physical situations.
  • Thumbnail Image
    Item
    Theoretical and Computational Methods for Mesoscopic Textures in Nematic Liquid Crystals with Anisotropic Elasticity
    (2022-07) Schimming, Cody
    Nematic liquid crystals are materials in which the underlying constituents are anisotropic which, in turn, leads to anisotropic properties and response at the meso and macro scales. As has been shown in recent experiments on nematic systems composed of complex aggregates, anisotropic polymers, and biologically inspired active materials, as the constituents become more complicated, the material properties become more anisotropic. Thus, nematic liquid crystals represent an interesting opportunity to probe the interplay between elasticity, anisotropy, geometry, and topology. This dissertation focuses on these interplays in an effort to expand the understanding of the structure and dynamics of mesoscopic textures in nematics, particularly two phase domains and topological defects. To accomplish this, we review the shortcomings of the classical Landau-de Gennes theory when posed with the problem of anisotropic elasticity. We then develop a computational, self-consistent field theory to advance the state of computational mesoscale modelling of anisotropic nematics. We show that, despite the increased computational complexity, this theory can resolve three dimensional nematic configurations well. We apply it directly to the case of two phase domains and disclinations in systems of lyotropic chromonic liquid crystals, of which many recent experiments have demonstrated anisotropic properties and structures. We find good qualitative and quantitative agreement with the experiments, while positing new directions for further experimental research. We also review existing theoretical gaps in the study of three dimensional nematic disclination lines and loops. These are much more complicated objects, both geometrically and topologically, than their two dimensional counterparts. We develop a mathematical construction of the disclination loop charge, which leads to the definition of a novel tensor which we call the “disclination density tensor.” This tensor is locally defined in terms of the nematic tensor order parameter and can be used to identify both the location and geometric structure of line disclinations. We further show that the disclination density tensor is related to the conservation of topological charge, and this connection is used to derive a kinematic law of motion for nematic disclinations. We show with analytical calculation and numerical computation that the disclination density tensor and the derived line velocity are important tools that give insight into the structure and dynamics that reflect the complex interplay between elasticity, anisotropy, geometry, and topology of disclination lines in three dimensional nematics. The results of this dissertation represent not only a new set of tools for future research and engineering endeavors, but also fundamental insights into the nature of complex structures in nematic liquid crystals.