Showing papers on "Elasticity (economics) published in 1998"

Measuring the Elastic Properties of Thin Polymer Films with the Atomic Force Microscope

Abstract: The elastic properties of thin gelatin films were investigated with the atomic force microscope (AFM). The degree of swelling and thus the softness of the gelatin can be tuned by immersing it in mixtures of propanol and water. Therefore, we have chosen gelatin films as a model system to characterize the measurement of elasticity of thin and soft samples. The major aim of this study was to investigate the influence of the film thickness on the apparent elastic (Young's) modulus. Thus, we prepared wedge-shaped samples with a well-defined thickness of up to 1 μm. The Young's modulus of our samples was between 1 MPa and 20 kPa depending on the degree of swelling. The elasticity was calculated by analyzing the recorded force curves with the help of the Hertz model. We show that the calculated Young's modulus is dependent on the local film thickness and the applied loading force of the AFM tip. Thus, the influence of the hard substrate on the calculated softness of the film can be characterized as a function of...

Polymerization shrinkage and elasticity of flowable composites and filled adhesives

Abstract: OBJECTIVES The magnitude and kinetics of polymerization shrinkage, together with elastic modulus, may be potential predictors of bond failure of adhesive restorations. This study examined these properties in visible-light-cured resins, in particular new flowable composites and filled adhesives. METHODS Polymerization shrinkage values were obtained by digital video imaging before and after light-curing; shrinkage kinetics were obtained by the "deflecting disk" method and the elastic modulus by analysis of the fundamental period of vibration. RESULTS Flowable composites generally showed higher shrinkage than traditional non-flowable composites, while more densely filled adhesives presented lower shrinkage than lightly filled or unfilled resins. The elastic moduli of flowable composites were in the low-medium range, whilst the hybrid composites showed the highest values and the microfilled the lowest. More densely filled adhesives were more rigid than lightly filled and unfilled adhesives. The kinetics behavior was material dependent, mainly characterized by the coefficient of near-linear contraction between 10 and 40% of the final shrinkage and the time to reach 75% of the final shrinkage. SIGNIFICANCE The higher shrinkage of flowable composites over that of hybrids may indicate a potential for higher interfacial stresses. However, their lower rigidity may be a counteracting factor. The microfilled composite showed low shrinkage and low rigidity, a combination that may prove less damaging to the interface. As the kinetics parameters tended to be material specific, no specific class of materials should be seen as more stress inducing until studies determine the relative importance of each examined parameter. The performance of adhesive resins as stress buffers also remains unpredictable.

Comparison of two methods for describing the strain profiles in quantum dots

Abstract: The electronic structure of interfaces between lattice-mismatched semiconductors is sensitive to the strain. We compare two approaches for calculating such inhomogeneous strain—continuum elasticity [(CE), treated as a finite difference problem] and atomistic elasticity. While for small strain the two methods must agree, for the large strains that exist between lattice-mismatched III-V semiconductors (e.g., 7% for InAs/GaAs outside the linearity regime of CE) there are discrepancies. We compare the strain profile obtained by both approaches (including the approximation of the correct C2 symmetry by the C4 symmetry in the CE method) when applied to C2-symmetric InAs pyramidal dots capped by GaAs.

Force-mediated kinetics of single P-selectin/ligand complexes observed by atomic force microscopy

Abstract: Leukocytes roll along the endothelium of postcapillary venules in response to inflammatory signals. Rolling under the hydrodynamic drag forces of blood flow is mediated by the interaction between selectins and their ligands across the leukocyte and endothelial cell surfaces. Here we present force-spectroscopy experiments on single complexes of P-selectin and P-selectin glycoprotein ligand-1 by atomic force microscopy to determine the intrinsic molecular properties of this dynamic adhesion process. By modeling intermolecular and intramolecular forces as well as the adhesion probability in atomic force microscopy experiments we gain information on rupture forces, elasticity, and kinetics of the P-selectin/P-selectin glycoprotein ligand-1 interaction. The complexes are able to withstand forces up to 165 pN and show a chain-like elasticity with a molecular spring constant of 5.3 pN nm−1 and a persistence length of 0.35 nm. The dissociation constant (off-rate) varies over three orders of magnitude from 0.02 s−1 under zero force up to 15 s−1 under external applied forces. Rupture force and lifetime of the complexes are not constant, but directly depend on the applied force per unit time, which is a product of the intrinsic molecular elasticity and the external pulling velocity. The high strength of binding combined with force-dependent rate constants and high molecular elasticity are tailored to support physiological leukocyte rolling.

An Analysis of the Impact of Sample Attrition on the Second Generation of Respondents in the Michigan Panel Study of Income Dynamics

Abstract: Only a few studies have tried to estimate the trend in the elasticity of children's economic status with respect to parents' economic status, and these studies produce conflicting results. In an attempt to reconcile these findings, we use the Panel Study ...

Elasticity and rheology of iron above 220 GPa and the nature of the Earth's inner core

Abstract: Recent numerical-modelling and seismological results have raised new questions about the dynamics1,2 and magnetism3,4 of the Earth's core. Knowledge of the elasticity and texture of iron5,6 at core pressures is crucial for understanding the seismological observations, such as the low attenuation of seismic waves, thelow shear-wave velocity7,8 and the anisotropy of compressional-wave velocity9,10,11. The density and bulk modulus of hexagonal-close-packed iron have been previously measured to core pressures by static12 and dynamic13,14 methods. Here we study,using radial X-ray diffraction15 and ultrasonic techniques16, the shear modulus, single-crystal elasticity tensor, aggregate compressional- and shear-wave velocities, and orientation dependence of these velocities in iron. The inner core shear-wave velocity is lower than the aggregate shear-wave velocity of iron, suggesting the presence of low-velocity components or anelastic effects in the core. Observation of a strong lattice strain anisotropy in iron samples indicates a large (∼24%) compressional-wave anisotropy under the isostress assumption, and therefore a perfect alignment of crystals6 would not be needed to explain the seismic observations. Alternatively the strain anisotropy may indicate stress variation due to preferred slip systems.

Estimation of single-crystal elastic moduli from polycrystalline x-ray diffraction at high pressure: application to FeO and Iron

Abstract: X-ray diffraction data obtained under nonhydrostatic compression of a polycrystalline sample yield an estimate of the single-crystal elasticity tensor of the material when analyzed using appropriate equations. The analysis requires as input the aggregate shear modulus from independent measurements. The high-pressure elastic moduli of face-centered-cubic FeO, body-centered-cubic iron (a-Fe), and the pressure-induced hexagonal close-packed iron (e-Fe) are obtained. This analysis currently provides the only method of determining single-crystal elasticity tensors in the megabar pressure range and of studying elasticity of very high-pressure phases. [S0031-9007(98)05436-2]

Elasticities of mode choice probabilities and market elasticities of demand: Evidence from a simultaneous mode choice/shipment-size freight transport model

Abstract: This paper presents empirical estimates of market elasticities of demand and elasticities of mode choice probabilities in the intercity freight transport market. Results are derived from a mixed discrete/continuous choice model of mode and shipment size. The mode choice component of the full model was specified as a binary probit function. The two modes considered were rail and regulated common carriers (full truck load). Data was drawn from the US Commodity Transportation Survey consisting of individual shipments of manufactured goods identified at the most disaggregate level. Results obtained in this study are compared with those obtained in previous studies, and areas of similarities and dissimilarities in the magnitude as well as interpretation of the results are highlighted. The own-price and cross-price elasticities of mode choice probabilities were found to vary from 1.44 to 1.88, and from 1.54 to 1.75, respectively. The market price elasticities of demand were found to vary significantly across commodity groups and geographic territories. Among the 40 market segments considered, the truck price elasticity of demand ranged between −0.749 and −2.525; the rail price elasticity of demand was slightly larger, ranging between −0.956 and −2.489; and the rail–truck cross-price elasticity of demand ranged between 0.904 and 2.532.

Elasticity reconstructive imaging by means of stimulated echo MRI

Abstract: A method is introduced to measure internal mechanical displacement and strain by means of MRI. Such measurements are needed to reconstruct an image of the elastic Young's modulus. A stimulated echo acquisition sequence with additional gradient pulses encodes internal displacements in response to an externally applied differential deformation. The sequence provides an accurate measure of static displacement by limiting the mechanical transitions to the mixing period of the simulated echo. Elasticity reconstruction involves definition of a region of interest having uniform Young's modulus along its boundary and subsequent solution of the discretized elasticity equilibrium equations. Data acquisition and reconstruction were performed on a urethane rubber phantom of known elastic properties and an ex vivo canine kidney phantom using <2% differential deformation. Regional elastic properties are well represented on Young's modulus images. The long-term objective of this work is to provide a means for remote palpation and elasticity quantitation in deep tissues otherwise inaccessible to manual palpation.

Mathematical and numerical aspects of wave propagation

Abstract: This volume contains the 178 papers presented at the Fourth International Conference on Mathematical and Numerical Aspects of Wave Propagation in Colorado in June 1998. The papers include theoretical and applied wave propagation in the areas of acoustics, electromagnetism and elasticity.

Atomistic Simulation of Polymer Melt Elasticity: Calculation of the Free Energy of an Oriented Polymer Melt

Abstract: A method is developed for predicting the elasticity of a polymer melt through detailed atomistic simulations. The Helmholtz energy of a melt oriented by flow is postulated to be of the form A(T,ρ,c...

Elasticity of an upper mantle clinopyroxene

Abstract: The ambient pressure elastic properties of a natural clinopyroxene (C2/c symmetry) from Kilbourne Hole, NM have been determined. In terms of end-members, diopside (CaMgSi2O6), hedenbergite (CaFeSi2O6), jadeite (NaAlSi2O6), cosmochlor (NaCrSi2O6), and Mg-Tschermak (MgAl(AlSi)O6), its composition is Di72He9Jd3Cr3Ts12. The analytic density, based on chemistry and cell parameters is 3.327 (0.003) g/cm3. The elastic constants [c11, c12, c13, c15, c22, c23, c25, c33, c35, c44, c46, c55, c66] are [273.8 (0.9), 83.5 (1.3), 80.0 (1.1), 9.0 (0.6), 183.6 (0.9), 59.9 (1.6), 9.5 (1.0), 229.5 (0.9), 48.1 (0.6), 76.5 (0.9), 8.4 (0.8), 73.0 (0.4), 81.6 (1.0)] GPa where uncertainties are reported at the 95% confidence level. The aggregate (mean of Hashin-Strikman bounds) adiabatic bulk modulus is 117.2 (0.7) GPa, and the shear modulus is 72.2 (0.2) GPa. Although measured moduli are broadly consistent with trends in elasticity versus atomic volume, deviations from the systematics would produce significant (percent level) changes in calculated velocities for candidate mantle mineral assemblages. The compositional dependence of elasticity for several clinopyroxenes is explored on the basis of just the Di+He and Jd+Ts mole fractions. The bulk modulus lies within experimental uncertainties of the linear mixture of end-member properties while the shear modulus deviates by 3%.

Elasticity of Single-Crystal MgO to 8 Gigapascals and 1600 Kelvin

Abstract: The cross pressure (P) and temperature (T) dependence of the elastic moduli (Cij) of single-crystal samples of periclase (MgO) from acoustic wave travel times was measured with ultrasonic interferometry: partial differential2C11/ partial differentialP partial differentialT = (-1.3 +/- 0.4) x 10(-3) per kelvin; partial differential2C110/ partial differentialP partial differentialT = (1. 7 +/- 0.7) x 10(-3) per kelvin; and partial differential2C44/ partial differentialP partial differentialT = (-0.2 +/- 0.3) x 10(-3) per kelvin. The elastic anisotropy of MgO decreases with increasing pressure at ambient temperature, but then increases as temperature is increased at high pressure. An assumption of zero cross pressure and temperature derivatives for the elastic moduli underestimates the elastic anisotropy and overestimates the acoustic velocities of MgO at the extrapolated high-pressure and high-temperature conditions of Earth's mantle.

Recent advances in theoretical liquid crystal rheology

Abstract: Recent significant advances in theoretical liquid crystalline rheology are presented. Dynamic simulations are performed using a complete theory which include the three major effects of liquid crystalline materials: (1) short range order elasticity, (2) long range order elasticity, and (3) viscous flow effects. The results and discussions include rectilinear simple shear flow, complex non-linear phenomena such as defect texture generation and coarsening processes under quiescent and shear conditions, and pattern formation such as banded texture during and after cessation of flow. The complete theory predicts four in-plane (1-D orientation) flow modes and five out-of-plane (2-D orientation) flow modes in one-dimensional shear flow, depending on the magnitudes of R (ratio of short to long range order elasticity) and Er (Ericksen number: ratio of viscous to elastic force). The multistability of these flow modes is clearly explained in terms of degrees of freedoms in the nematic orientation. The number of degrees of freedom increases with increasing the spatial dimension of the system, and thus more complex orientation patterns arise in the higher dimension. Well-known defect structures arise and coarsen during simulations of the isotropic to nematic phase transition. The effect of shear flow on the defect generation process is to suppress the defect nucleation, and the simulations suggest a method of how to create defect-free nematic samples. The banded textures during and after cessation of flow are also captured by the complete theory.

Bone Elasticity and Ultrasound Velocity Are Affected by Subtle Changes in the Organic Matrix

Abstract: The mechanical competence of bone can be studied through the measurement of the components of its material elasticity, a property which can vary both in magnitude and in dependence upon orientation (anisotropy). While it is known that the elasticity is largely determined by the mineral constituents of the bone matrix, it is nonetheless clear that it must be also dependent upon the remaining constituents of bone material. In this work, the influence of organic components on the elasticity is explored by altering specific constituents of the bone matrix to varying degrees. This study addresses two questions: first, are the resulting changes in elasticity strongly or weakly dependent upon direction, and second, are they substantially dependent upon the nature and magnitude of the induced matrix alteration? To answer these questions, we performed different chemical manipulations of the bone matrix and measured the changes in elasticity and velocity using the technique of ultrasound critical angle reflectometry. Altering the properties of the organic matrix resulted in substantial and complex changes in the elasticity of bone. The observed changes were strongly dependent upon direction, could not be explained by changes in density alone, and varied strongly with the specific chemical treatment of the matrix. Immersion in urea selectively affected protein components of the organic matrix and resulted in reversible changes in velocity and elasticity, while removal of collagen caused anisotropic decreases and removal of all organic matter caused a collapse of all components of the elasticity. In conclusion, this study confirms that the organic matrix exerts a profound influence on the elasticity and indicates that the measurement of elastic properties at multiple directions is necessary in the assessment of bone mechanical competence.

Alternative functional forms for production, cost and returns to scale functions

Abstract: We consider generalized production functions, introduced in Zellner and Revankar (1969), for output y=g(f) where g is a monotonic function and f is a homogeneous production function. For various choices of the scale elasticity or returns to scale as a function of output, differential equations are solved to determine the associated forms of the monotonic transformation, g(f). Then by choice of the form of f, the elasticity of substitution, constant or variable, is determined. In this way, we have produced and generalized a number of homothetic production functions, some already in the literature. Also, we have derived and studied their associated cost functions to determine how their shapes are affected by various choices of the scale elasticity and substitution elasticity functions. In general, we require that the returns to scale function be a monotonically decreasing function of output and that associated average cost functions be U- or L-shaped with a unique minimum. We also represent production functions in polar coordinates and show how this representation simplifies study of production functions' properties. Using data for the US transportation equipment industry, maximum likelihood and Bayesian methods are employed to estimate many different generalized production functions and their associated average cost functions. In accord with results in the literature, it is found that the scale elasticities decline with output and that average cost curves are U- or L-shaped with unique minima. © 1998 John Wiley & Sons, Ltd.

Model elastic liquids with water-soluble polymers

Abstract: Model liquids with nearly constant viscosity and adjustable elasticity are needed to resolve the role of elasticity in coating and other free-surface flows. Available Boger liquids are not well suited to free-surface flows, because they are solutions in organic solvents and their viscosities exceeding 1 Pa · s fall on the high side. Aqueous liquids are preferred in laboratory studies partly due to environmental hazards. Aqueous polymer solutions with constant shear viscosity and adjustable elasticity were prepared by adding small amounts of a high-molecular-weight polymer to a more concentrated aqueous solution of the same polymer but of a much lower molecular weight. Up to 0.2 wt. % of high-molecular weight poly(ethylene oxide) (PEO, Mw from 400,000 to 4 million g/mol) was added to almost inelastic solutions of low-MW polyethylene glycol (PEG, Mn = 8,000 g/mol). PEG concentrations in these solutions varied between 16.7 and 42.9 wt. %. Shear viscosities of these solutions ranged from about 0.02 to 0.3 Pa · s and were constant up to shear rates of 100 s−1. The stress ratio is one measure of the elasticity of the liquid. Stress ratios up to 0.2 were estimated from small-amplitude oscillatory measurements. Terminal behavior (elastic modulus rising with the square of the frequency) was not observed even at 10−2 rad/s. Viscosity and elasticity of the liquids can be manipulated over a wide range by varying the amounts and molecular weights of PEG and PEO within the unentangled and dilute regions of the concentration–molecular weight diagram, respectively. Fits of experimental data to candidate differential and integral constitutive equations are also discussed.

Structure−Properties Relation for Agarose Thermoreversible Gels in Binary Solvents

Abstract: The structure of agarose gels prepared in aqueous binary solvents has been studied by means of X-ray and neutron small-angle scattering. The scattering curves are interpreted by considering a random assembly of straight fibers displaying cross-section polydispersity. The cross-section polydispersity is well accounted for with a distribution function of the type w(r) ∼ r-λ bounded by two radii, rmin and rmax, and where λ depends upon both the nature of the binary solvent and the agarose concentration. Departure from the Porod regime at wide scattering angles suggests the existence of free and/or dangling chains that do not participate in the network elasticity (loose chains). The fraction of loose chains gradually vanishes upon increasing the agarose concentration. Experimental elastic modulus−concentration relations obtained on the same type of samples point to the occurrence of entropic elasticity once analyzed in light of the existence of loose chains. Entropic elasticity is rather consistent with disor...

New Method for Solving Elasticity Problems of Some Planar Quasicrystals and Solutions

Abstract: A new method for solving elasticity problems of some planar quasicrystals is presented. The set of partial differential equations for the phonon and phason displacement components is reduced to a single higher-order equation by introducing a displacement function. A general solution formulation is suggested. As an example, the elastic field caused by a dislocation in planar quasicrystals of point groups 5 m, 10, and 10 mm is calculated.