Tb6FeSb2 and Tb6FeBi2 are novel rare earth compounds with little prior research. These compounds show high and variable curie temperatures for rare-earth compounds. This has lead to a literature review which includes the discussion of: elasticity, resonance, and magnetism. This review is used to discuss the theory and methodology which can relate these various properties to each other. Furthermore, synthesis, x-ray analysis, and RUS sample preparation of Tb6FeSb2 and Tb6FeBi2 were completed. Resonant Ultrasound Spectroscopy (RUS) elastic studies were taken for Tb6FeSb2 and Tb6FeBi2 as a function temperature from 5-300K, in various magnetic fields ranging from 0-9T. Tb6FeSb2’s and Tb6FeBi2’s elastic moduli are related to their magnetic properties. Magnetization data, primarily M v. H, provides another measure the magnetic properties are used to help correlate the data to elasticity. Tb6FeSb2 and Tb6FeBi2 Curie temperatures are 253(3)K and 246(5)K respectively. The low temperature magnetic transition of Tb6FeSb2 is 65-90K and Tb6FeBi2 is 55-75K. RUS suggests that this low temperature transition is somehow related to a structural transition but this transition does not occur in these two compounds. Co-substitution of Tb6FeSb2 and Tb6FeBi2 seem to greatly affect this lower temperature transition in RUS. It does not greatly effect the curie temperature. Low temperature XRD shows that Co-substitution also creates a structural transition in this family of compounds.

The aerospace industry is utilizing low cost miniature inertial measurement units (IMUs) that employ Micro Electro-Mechanical Systems (MEMS) technology in an effort to reduce size, weight, and cost of systems. A drawback of these MEMS devices is they are sensitive to vibration, shock and acoustic environments, which limits the usefulness of such devices in the severe environments imposed by many aerospace applications. In an effort to reduce the vibration, shock and acoustic environments experienced by these MEMS devices, the desire to develop passive damping treatments to structural components used to mount these devices. The damping treatments can be applied at the printed circuit board (PCB) level, the component level, the component interface, or at the airframe level. The purpose is to reduce the overall environment and improve the usefulness and performance of the MEMS based sensors. The primary technique to introduce damping into metallic parts and PCBs is to provide a viscoelastic coating or layer. The ability to analyze structures with this configuration requires a thorough understanding of the dynamic properties. Hooke’s law of elasticity is one of the most fundamental relationships governing dynamic properties. Metals typically have a low damping coefficient, and Hooke’s law of elasticity represents a linear relationship between the ratio of stress and strain, known as the modulus of elasticity. But for viscous materials the modulus of elasticity becomes a complex value since the stress and strain are not in phase. The complex modulus of elasticity is a complex function of frequency. The complex modulus can be established via frequency response function measurements of compliance, mobility, and accelerance, and the dimensions of the block of material under test. At low frequencies (less than resonance of the block) the results are relatively straight forward, but at higher frequencies where resonances of the block occur the inertial forces begin to influence the FRF results. This thesis effort establishes techniques for measuring the complex moduli associated with viscoelastic materials, and presents methods and results from modulus tests conducted for this thesis.

In this dissertation, we study the mixed finite element method for the linear plane elasticity problem and iterative solvers for the resulting discrete system. We use the Arnold-Winther Element in the mixed finite element discretization. An overlapping Schwarz preconditioner and a multigrid preconditioner for the discrete system are developed and analyzed. We start by introducing the mixed formulation (stress-displacement formulation) for the linear plane elasticity problem and its discretization. A detailed analysis of the Arnold-Winther Element is given. The finite element discretization of the mixed formulation leads to a symmetric indefinite linear system. Next, we study efficient iterative solvers for the symmetric indefinite linear system which arises from the mixed finite element discretization of the linear plane elasticity problem. The preconditioned Minimum Residual Method is considered. It is shown that the problem of constructing a preconditioner for the indefinite linear system can be reduced to the problem of constructing a preconditioner for the H(div) problem in the Arnold-Winther finite element space. Our main work involves developing an overlapping Schwarz preconditioner and a multigrid preconditioner for the H(div) problem. We give condition number estimates for the preconditioned systems together with supporting numerical results.

Chapter 1 discusses the econometric pitfalls associated with the use of patent production functions to study the invention process. It then goes on to argue that a sound understanding of the invention process necessarily requires an understanding of the propensity to patent. The empirical analysis carried out in Chapter 1 seeks to explain the proportion of inventions patented – a potential metric for the propensity to patent – from an international sample of manufacturing firms. Chapter 2 proposes a methodology to filter out the noise induced by varying patent practices in the R&D-patent relationship. The methodology explicitly decomposes the patent-to-R&D ratio into its components of productivity and propensity. It is then applied to a novel data set of priority patent applications in four countries and six industries. Chapter 3 takes stock of the literature on the role of fees in patent systems while Chapter 4 presents estimates of the price elasticity of demand for patents at the trilateral offices (that is, in the U.S., Japan and Europe). The estimation of dynamic panel data models of patent applications suggests that the long-term price elasticity is about -0.30.

In dieser Arbeit werden Knickinstabilitäten von Filamenten in biologischen Systemen untersucht. Das Zytoskelett von Zellen ist aus solchen Filamenten aufgebaut. Sie sind für die mechanische Stabilität der Zelle verantwortlich und spielen eine große Rolle bei intrazellulären Transportprozessen durch molekulare Motoren, die verschiedene Lasten wie beispielsweise Organellen entlang der Filamente des Zytoskeletts transportieren. Filamente sind semiflexible Polymere, deren Biegeenergie ähnlich groß ist wie die thermische Energie, so dass sie auch als elastische Balken auf der Nanoskala gesehen werden können, die signifikante thermische Fluktuationen zeigen. Wie ein makroskopischer elastischer Balken können auch Filamente eine mechanische Knickinstabilität unter Kompression zeigen. Im ersten Teil dieser Arbeit wird untersucht, wie diese Instabilität durch thermische Fluktuationen der Filamente beeinflusst wird. In Zellen können Kompressionskräfte durch molekulare Motoren erzeugt werden. Das geschieht zum Beispiel während der Zellteilung in der mitotischen Spindel. Im zweiten Teil der Arbeit untersuchen wir, wie die stochastische Natur einer von Motoren generierten Kraft die Knickinstabilität von Filamenten beeinflusst. Zunächst stellen wir kurz das Problem von Knickinstabilitäten auf der makroskopischen Skala dar und führen ein Modell für das Knicken von Filamenten oder elastischen Stäben in zwei Raumdimensionen und in Anwesenheit thermischer Fluktuationen ein. Wir präsentieren eine analytische Lösung für Knickinstabilitäten in Anwesenheit thermischer Fluktuationen, die auf einer Renormierungsgruppenrechnung im Rahmen des nichtlinearen Sigma-Models basiert. Wir integrieren die kurzwelligen Fluktuationen aus, um eine effektive Theorie für die langwelligen Moden zu erhalten, die die Knickinstabilität bestimmen. Wir berechnen die Änderung der kritischen Kraft für die Knickinstabilität und zeigen, dass die thermischen Fluktuationen in zwei Raumdimensionen zu einer Zunahme der kritischen Kraft führen. Außerdem zeigen wir, dass thermische Fluktuationen im geknickten Zustand zu einer Zunahme der mittleren projizierten Länge des Filaments in Richtung der wirkenden Kraft führen. Als Funktion der Konturlänge des Filaments besitzt die mittlere projizierte Länge eine Spitze an der Knickinstabilität, die durch thermische Fluktuationen abgerundet wird. Unser Hauptresultat ist die Beobachtung, dass ein geknicktes Filament unter dem Einfluss thermischer Fluktuationen gestreckt wird, d.h. dass seine mittlere projizierte Länge in Richtung der Kompressionskraft auf Grund der thermischen Fluktuationen zunimmt. Unsere analytischen Resultate werden durch Monte-Carlo Simulationen der Knickinstabilität semiflexibler Filamente in zwei Raumdimensionen bestätigt. Wir führen auch Monte-Carlo Simulationen in höheren Raumdimensionen durch und zeigen, dass die Zunahme der projizierten Länge unter dem Einfluss thermischer Fluktuationen weniger ausgeprägt ist und stark von der Wahl der Randbedingungen abhängt. Im zweiten Teil der Arbeit formulieren wir ein Modell für die Knickinstabilität semiflexibler Filamente unter dem Einfluss molekularer Motoren. Wir untersuchen ein System, in dem sich eine Gruppe von Motoren entlang eines fixierten Filaments bewegt, und dabei ein zweites Filament als Last trägt. Das Last-Filament wird gegen eine Wand gedrückt und knickt. Während des Knickvorgangs können die Motoren, die die Kraft auf das Filament generieren, stochastisch von dem Filament ab- und an das Filament anbinden. Wir formulieren ein stochastisches Model für dieses System und berechnen die “mean first passage time“, d.h. die mittlere Zeit für den Übergang von einem Zustand, in dem alle Motoren gebundenen sind zu einem Zustand, in dem alle Motoren abgebunden sind. Dieser Übergang entspricht auch einem Übergang aus dem gebogenen zurück in einen ungebogenen Zustand des Last-Filaments. Unser Resultat zeigt, dass für genügend kurze Mikrotubuli die Bewegung der Motoren von der durch das Last-Filament generierten Kraft beeinflusst wird. Diese Ergebnisse können in zukünftigen Experimenten überprüft werden. / We study buckling instabilities of filaments in biological systems. Filaments in a cell are the building blocks of the cytoskeleton. They are responsible for the mechanical stability of cells and play an important role in intracellular transport by molecular motors, which transport cargo such as organelles along cytoskeletal filaments. Filaments of the cytoskeleton are semiflexible polymers, i.e., their bending energy is comparable to the thermal energy such that they can be viewed as elastic rods on the nanometer scale, which exhibit pronounced thermal fluctuations. Like macroscopic elastic rods, filaments can undergo a mechanical buckling instability under a compressive load. In the first part of the thesis, we study how this buckling instability is affected by the pronounced thermal fluctuations of the filaments. In cells, compressive loads on filaments can be generated by molecular motors. This happens, for example, during cell division in the mitotic spindle. In the second part of the thesis, we investigate how the stochastic nature of such motor-generated forces influences the buckling behavior of filaments. In chapter 2 we review briefly the buckling instability problem of rods on the macroscopic scale and introduce an analytical model for buckling of filaments or elastic rods in two spatial dimensions in the presence of thermal fluctuations. We present an analytical treatment of the buckling instability in the presence of thermal fluctuations based on a renormalization-like procedure in terms of the non-linear sigma model where we integrate out short-wavelength fluctuations in order to obtain an effective theory for the mode of the longest wavelength governing the buckling instability. We calculate the resulting shift of the critical force by fluctuation effects and find that, in two spatial dimensions, thermal fluctuations increase this force. Furthermore, in the buckled state, thermal fluctuations lead to an increase in the mean projected length of the filament in the force direction. As a function of the contour length, the mean projected length exhibits a cusp at the buckling instability, which becomes rounded by thermal fluctuations. Our main result is the observation that a buckled filament is stretched by thermal fluctuations, i.e., its mean projected length in the direction of the applied force increases by thermal fluctuations. Our analytical results are confirmed by Monte Carlo simulations for buckling of semiflexible filaments in two spatial dimensions. We also perform Monte Carlo simulations in higher spatial dimensions and show that the increase in projected length by thermal fluctuations is less pronounced than in two dimensions and strongly depends on the choice of the boundary conditions. In the second part of this work, we present a model for buckling of semiflexible filaments under the action of molecular motors. We investigate a system in which a group of motors moves along a clamped filament carrying a second filament as a cargo. The cargo-filament is pushed against the wall and eventually buckles. The force-generating motors can stochastically unbind and rebind to the filament during the buckling process. We formulate a stochastic model of this system and calculate the mean first passage time for the unbinding of all linking motors which corresponds to the transition back to the unbuckled state of the cargo filament in a mean-field model. Our results show that for sufficiently short microtubules the movement of kinesin-I-motors is affected by the load force generated by the cargo filament. Our predictions could be tested in future experiments.

Boundary-contact problems (BCPs) are studied within the frames of classical mathematical theory of elasticity and plasticity elaborated by Landau, Kupradze, Timoshenko, Goodier, Fichera and many others on the basis of analysis of two- and three-dimensional boundary value problems for linear partial differential equations. A great attention is traditionally paid both to theoretical investigations using variational methods and boundary singular integral equations (Muskhelishvili) and construction of solutions in the form that admit efficient numerical evaluation (Kupradze). A special family of BCPs considered by Shtaerman, Vorovich, Alblas, Nowell, and others arises within the frames of the models of squeezing thin multilayer elastic sheets. We show that mathematical models based on the analysis of BCPs can be also applied to modeling of the clich\'-surface printing contacts and paper surface compressibility in flexographic printing. The main result of this work is formulation and complete investigation of BCPs in layered structures, which includes both the theoretical (statement of the problems, solvability and uniqueness) and applied parts (approximate and numerical solutions, codes, simulation). We elaborate a mathematical model of squeezing a thin elastic sheet placed on a stiff base without friction by weak loads through several openings on one of its boundary surfaces. We formulate and consider the corresponding BCPs in two- and three-dimensional bands, prove the existence and uniqueness of solutions, and investigate their smoothness including the behavior at infinity and in the vicinity of critical points. The BCP in a two-dimensional band is reduced to a Fredholm integral equation (IE) with a logarithmic singularity of the kernel. The theory of logarithmic IEs developed in the study includes the analysis of solvability and development of solution techniques when the set of integration consists of several intervals. The IE associated with the BCP is solved by three methods based on the use of Fourier-Chebyshev series, matrix-algebraic determination of the entries in the resulting infinite system matrix, and semi-inversion. An asymptotic theory for the BCP is developed and the solutions are obtained as asymptotic series in powers of the characteristic small parameter. We propose and justify a technique for the solution of BCPs and boundary value problems with boundary conditions of mixed type called the approximate decomposition method (ADM). The main idea of ADM is simplifying general BCPs and reducing them to a chain of auxiliary problems for 'shifted' Laplacian in long rectangles or parallelepipeds and then to a sequence of iterative problems such that each of them can be solved (explicitly) by the Fourier method. The solution to the initial BCP is then obtained as a limit using a contraction operator, which constitutes in particular an independent proof of the BCP unique solvability. We elaborate a numerical method and algorithms based on the approximate decomposition and the computer codes and perform comprehensive numerical analysis of the BCPs including the simulation for problems of practical interest. A variety of computational results are presented and discussed which form the basis for further applications for the modeling and simulation of printing-plate contact systems and other structures of flexographic printing. A comparison with finite-element solution is performed.

In this thesis, material properties have been examined under extreme conditions in computer-based calculations. The research on iron (Fe), nickel (Ni), and ferropericlase (Mg1-xFexO) are not only important for our understanding of the Earth, but also for an improved knowledge of these materials per se. An embedded-atom model for Fe demonstrated to reproduce properties such as structure factors, densities and diffusion constants, and was employed to evaluate temperature gradients at Earth core conditions. A similar interaction together with a two-temperature method was applied for the analysis of shock-induced melting of Ni. For Mg1-xFexO, the magnetic transition pressure was shown to increase with iron content. Furthermore, the C44 softening with pressure and iron composition supports the experimentally observed phase transition for Mg0.8Fe0.2O at 35 GPa. The properties of high density helium (He) is of great interest as the gas is one of the most abundant elements in the solar system. Furthermore, He and neon (Ne) are often used as pressure media in diamond anvil cells. The melting of He showed a possible fcc-bcc-liquid transition starting at T=340 K, P=22 GPa with a Buckingham potential, whereas the bcc phase was not seen with the Aziz form. For Ne, Monte Carlo calculations at ambient pressure showed very accurate results when extrapolating the melting temperatures to an infinite cluster limit. At high pressure, a one-phase ab initio melting curve showed a match with one-phase L-J potential results, which could imply a correspondence between ab initio/classical one-phase/two-phase calculations. In the search for hard materials, ab initio calculations for four TiO2 phases were compared. Just as imposed by experiment, the cotunnite phase was found to be very hard. The anomalous elastic behavior of the superconducting group-V metals V, Nb, Ta was found to be related to shrinking nesting vectors and the electronic topological transition (ETT).

Organic consumption is currently experiencing a boom of sales on the Swedish and international market. Whether this occurrence is a contemporary trend or if it will prove to be sustainable in the future, the demographics of the so-called ‘green consumer’ are of great interest for economic agents on markets such as foods and textiles. Therefore, the writers have chosen to highlight this topic by focusing on the relation between income and purchase of organic products.. Economic data for the Swedish market has been gathered and analyzed through various statistical and macroeconomic perspectives, where the basis has been Kelvin Lancaster’s models of consumer choice theory. The results showed that income does not generally have a direct effect on the choice of purchasing an organic good in Sweden, although it cannot be fully dismissed when discussing the demographics of the green consumer. Other factors are of importance as well, including education, marital status and geographical location. The study of the green consumer is a rather new area and this study, along with its previous counterparts, has proved it difficult to draw any firm conclusions regarding the characteristics of the organic consumer. Therefore, future studies within this area will have plenty to discover about a subject of increasing interest and importance on the market. / Ekologisk konsumtion upplever för närvarande en försäljningsboom på den svenska och internationella marknaden. Oavsett om detta är en tillfällig trend eller om det kommer bestå såväl i framtiden, är demografierna av de såkallade ’gröna konsumenterna’ av stort intresse för ekonomiska agenter inom marknader såsom textil och dagligvaror. Därför har författarna valt att framhäva detta ämne genom att fokusera på relationen mellan inkomst och inköp av ekologiska produkter. Ekonomisk data för den svenska marknaden har samlats in och analyserats genom olika statistiska och makroekonomiska perspektiv, där basen har varit Kelvin Lancasters modeller av konsumentteori. Resultaten har visat på att inkomst generellt inte har en direkt effekt på valet att köpa en ekologisk vara i Sverige, även om denna faktor inte helt kan uteslutas när demografier av den gröna konsumenten diskuteras. Andra faktorer har också betydelse, däribland utbildning, civilstånd och geografisk lokalisering. Studier om den gröna konsumenten är ett relativt nytt område, och denna kandidatuppsatsen har, tillsammans med föregående rapporter inom ämnet, funnit det svårt att dra några fasta slutsatser om den ekologiska konsumentens karaktärer. Därför kommer framtida studier inom detta område ha mycket att upptäcka om ett ämne av ökande intresse och angelägenhet på marknaden.

<p>This dissertation investigates the feasibility of a real-time transthoracic Acoustic Radiation Force Impulse (ARFI) imaging system to measure myocardial function non-invasively in clinical setting. Heart failure is an important cardiovascular disease and contributes to the leading cause of death for developed countries. Patients exhibiting heart failure with a low left ventricular ejection fraction (LVEF) can often be identified by clinicians, but patients with preserved LVEF might be undetected if they do not exhibit other signs and symptoms of heart failure. These cases motivate development of transthoracic ARFI imaging to aid the early diagnosis of the structural and functional heart abnormalities leading to heart failure.</p><p>M-Mode ARFI imaging utilizes ultrasonic radiation force to displace tissue several micrometers in the direction of wave propagation. Conventional ultrasound tracks the response of the tissue to the force. This measurement is repeated rapidly at a location through the cardiac cycle, measuring timing and relative changes in myocardial stiffness. ARFI imaging was previously shown capable of measuring myocardial properties and function via invasive open-chest and intracardiac approaches.</p><p>The prototype imaging system described in this dissertation is capable of rapid acquisition, processing, and display of ARFI images and shear wave elasticity imaging (SWEI) movies. Also presented is a rigorous safety analysis, including finite element method (FEM) simulations of tissue heating, hydrophone intensity and mechanical index (MI) measurements, and thermocouple transducer face heating measurements. For the pulse sequences used in later animal and clinical studies, results from the safety analysis indicates that transthoracic ARFI imaging can be safely applied at rates and levels realizable on the prototype ARFI imaging system. </p><p>Preliminary data are presented from <italic>in vivo</italic> trials studying changes in myocardial stiffness occurring under normal and abnormal heart function. Presented is the first use of transthoracic ARFI imaging in a serial study of heart failure in a <italic>porcine</italic> model. Results demonstrate the ability of transthoracic ARFI to image cyclically-varying stiffness changes in healthy and infarcted myocardium under good B-mode imaging conditions at depths in the range of 3-5 cm. Challenging imaging scenarios such as deep regions of interest, vigorous lateral motion and stable, reverberant clutter are analyzed and discussed.</p><p>Results are then presented from the first study of clinical feasibility of transthoracic cardiac ARFI imaging. At the Duke University Medical Center, healthy volunteers and patients having magnetic resonance imaging-confirmed apical infarcts were enrolled for the study. The number of patients who met the inclusion criteria in this preliminary clinical trial was low, but results showed that the limitations seen in animal studies were not overcome by allowing transmit power levels to exceed the FDA mechanical index (MI) limit. The results suggested the primary source of image degradation was clutter rather than lack of radiation force. Additionally, the transthoracic method applied in its present form was not shown capable of tracking propagating ARFI-induced shear waves in the myocardium.</p><p>Under current instrumentation and processing methods, results of these studies support feasibility for transthoracic ARFI in high-quality B-Mode imaging conditions. Transthoracic ARFI was not shown sensitive to infarct or to tracking heart failure in the presence of clutter and signal decorrelation. This work does provide evidence that transthoracic ARFI imaging is a safe non-invasive tool, but clinical efficacy as a diagnostic tool will need to be addressed by further development to overcome current challenges and increase robustness to sources of image degradation.</p> / Dissertation

This dissertation investigates whether higher levels of “governmental fragmentation” in metropolitan statistical areas (MSA) leads to worse environmental outcomes. Fragmentation refers to the number of local governments in a given region or MSA as defined by the census. This research contributes to two bodies of literature, that of environmental federalism and that of urban growth and local government form. In the area of environmental federalism this dissertation extends the collective action model to include local governments. An empirical framework is developed that includes cross-sectional and panel data. In the urban growth and local government form literature, this dissertation comprehensively tests many existing measures of local government fragmentation within an environmental policy framework. It also modifies and extends some of the fragmentation variables. The results suggest that local government fragmentation does hinder MSAs from attaining the ozone standard. This dissertation extends the literature by examining the effect that local government fragmentation has on regional environmental quality. Six local government structure variables, jurisdiction count, special district dominance, central city dominance, county primacy, central city growth, and metropolitan power diffusion index are comprehensively tested to determine which might affect regional environmental quality. In addition, this research extends the use of the computationally complex measure of metropolitan power diffusion index to include additional local government expenditures as well as additional years of panel data. Two empirical estimation strategies were implemented, a cross-sectional approach and a panel data approach. The cross-sectional approach estimates the effects that long-term changes in local government structure have on attaining the ozone standard by measuring differences across MSAs. The panel data model’s primary purpose was that of a robustness check on the cross-sectional results. Three of the six tested fragmentation variables were found to have statistically significant effects on MSA attainment of the ozone standard in the cross-sectional model. Higher levels of metropolitan power diffusion index and jurisdiction count were found to hinder attainment of the ozone standard, while greater values of central city growth aided in reaching the attainment standard. Generally, the panel data results’ supported the results from the cross-sectional models. In addition, the panel model resolved some important estimation issues. Metropolitan power diffusion index was found to be correlated with unobservables in the random effects model, indicating that the cross-sectional results for metropolitan power diffusion index may be biased as well. This was not an issue for the variable jurisdiction count. Metropolitan power diffusion index and jurisdiction count are highly correlated with each other and this relationship was used to estimate a reasonable range for the effect metropolitan power diffusion index might have on the attainment of the ozone standard.