Showing papers on "Elasticity (economics) published in 2004"

Elastic Behavior of Cross-Linked and Bundled Actin Networks

Abstract: Networks of cross-linked and bundled actin filaments are ubiquitous in the cellular cytoskeleton, but their elasticity remains poorly understood. We show that these networks exhibit exceptional elastic behavior that reflects the mechanical properties of individual filaments. There are two distinct regimes of elasticity, one reflecting bending of single filaments and a second reflecting stretching of entropic fluctuations of filament length. The mechanical stiffness can vary by several decades with small changes in cross-link concentration, and can increase markedly upon application of external stress. We parameterize the full range of behavior in a state diagram and elucidate its origin with a robust model.

Finite crystal elasticity of carbon nanotubes based on the exponential Cauchy-Born rule

Abstract: A finite deformation continuum theory is derived from interatomic potentials for the analysis of the mechanics of carbon nanotubes. This nonlinear elastic theory is based on an extension of the Cauchy-Born rule called the exponential Cauchy-Born rule. The continuum object replacing the graphene sheet is a surface without thickness. The method systematically addresses both the characterization of the small strain elasticity of nanotubes and the simulation at large strains. Elastic moduli are explicitly expressed in terms of the functional form of the interatomic potential. The expression for the flexural stiffness of graphene sheets, which cannot be obtained from standard crystal elasticity, is derived. We also show that simulations with the continuum model combined with the finite element method agree very well with zero temperature atomistic calculations involving severe deformations.

Quantifying elasticity and viscosity from measurement of shear wave speed dispersion

Abstract: The propagation speed of shear waves is related to frequency and the complex stiffness (shear elasticity and viscosity) of the medium. A method is presented to solve for shear elasticity and viscosity of a homogeneous medium by measuring shear wave speed dispersion. Harmonic radiation force, introduced by modulating the energy density of incident ultrasound, is used to generate cylindrical shear waves of various frequencies in a homogeneous medium. The speed of shear waves is measured from phase shift detected over the distance propagated. Measurements of shear wave speed at multiple frequencies are fit with the theoretical model to solve for the complex stiffness of the medium. Experiments in gelatin phantoms show promising results validated by an independent method. Practical considerations and challenges in possible medical applications are discussed.

Elasticity of an interfacial particle raft

Abstract: We study the collective behaviour of a close-packed monolayer of non-Brownian particles at a fluid-liquid interface. Such a particle raft forms a two-dimensional elastic solid and can support anisotropic stresses and strains, e.g. it buckles in uniaxial compression and cracks in tension. We characterise this solid in terms of Young's modulus and Poisson ratio derived from simple theoretical considerations and show the validity of these estimates by using an experimental buckling assay to deduce Young's modulus.

Stability of Foam Films and Surface Rheology: An Oscillating Bubble Study at Low Frequencies

Abstract: The dilational surface elasticity e and the dilational surface viscosity η of the two nonionic surfactants n-dodecyl-β-d-maltoside (β-C12G2) and tetraethyleneglycol-monodecyl ether (C10E4) were studied using the oscillating drop method. The experiments were carried out at different concentrations and frequencies with an accessible frequency range of 0.005−0.2 Hz. The results are discussed in the light of previous disjoining pressure measurements that demonstrated that the stability of thin liquid films cannot be explained solely by the magnitude of the surface forces. Indeed, a comparison of the results obtained for β-C12G2 with those obtained for C10E4 reveals a correlation between the stability of the films and the surface dilational elasticity of the respective monolayers.

Effect of long branches on the rheology of polypropylene

Abstract: In order to study the rheology of long chain branched polymers, branches have been added on linear polypropylene precursors in varying amounts using reactive modification with peroxydicarbonates. The branched polypropylene samples show distinct strain hardening, something absent from the linear melt; this considerably improves the melt strength of the modified polymer. The zero shear viscosity and the elasticity measured by the relaxation spectrum also increase with the number of branches per molecule. Two models are applied to describe strain hardening of the viscosity during the course of elongation. The model parameters were found to vary systematically with the degree of branching and, therefore, their values can be used as a measure of this. Consequently, fluidity, elasticity, strain hardening, and melt strength are all related to the degree of long chain branching.

Measurement of membrane elasticity by micro-pipette aspiration.

Abstract: The classical micro-pipette aspiration technique, applied for measuring the membrane bending elasticity, is in the present work reviewed and extended to span the range of pipette aspiration pressures going through the flaccid (low pressures) to tense (high pressures) membrane regime. The quality of the conventional methods for analysing data is evaluated using numerically generated data and a new method for data analysis, based on thermodynamic analysis and detailed statistical mechanical modelling, is introduced. The analysis of the classical method, where the membrane bending modulus is obtained from micro-pipette aspiration data acquired in the low-pressure regime, reveals a significant correction from membrane stretching elasticity. The new description, which includes the full vesicle geometry and both the membrane bending and stretching elasticity, is used for the interpretation of micro-pipette aspiration experiments conducted on SOPC (stearoyl-oleoyl-phosphatidyl-choline) lipid vesicles in the fluid phase. The data analysis, which is extended by detailed image analysis and a fitting procedure based on Monte Carlo integration, gives an estimate of the bending modulus, that agrees with previously published results obtained by the use of shape fluctuation analysis of giant unilamellar vesicles. The obtained estimate of the area expansion modulus, is automatically corrected for contributions from residual thermal undulations and the equilibrium area of the vesicle is resolved.

Stress singularities in classical elasticity—II: Asymptotic identification

Abstract: This review article~Part II! is a sequel to an earlier one ~Part I! that dealt with means of removal and interpretation of stress singularities in elasticity, as well as their asymptotic and numerical analysis. It reviews contributions to the literature that have actually effected asymptotic identifications of possible stress singularities for specific configurations. For the most part, attention is focused on 2D elastostatic configurations with constituent materials being homogeneous and isotropic. For such configurations, the following types of stress singularity are identified: power singularities with both real and complex exponents, logarithmic intensification of power singularities with real exponents, pure logarithmic singularities, and log-squared singularities. These identifications are reviewed for the in-plane loading of angular elastic plates comprised of a single material in Section 2, and for such plates comprised of multiple materials in Section 3. In Section 4, singularity identifications are examined for the out-of-plane shear of elastic wedges comprised of single and multiple materials, and for the out-of-plane bending of elastic plates within the context of classical and higher-order theory. A review of stress singularities identified for other geometries is given in Section 5, axisymmetric and 3D configurations being considered. A limited examination of the stress singularities identified for other field equations is given as well in Section 5. The paper closes with an overview of the status of singularity identification within elasticity. This Part II of the review has 227 references. @DOI: 10.1115/1.1767846 #

That elusive elasticity : a long-panel approach to estimating the capital-labor substitution elasticity

Abstract: The elasticity of substitution between capital and labor features prominently in several areas of economic research. However, a consensus estimate remains elusive. We develop an estimation strategy that filters panel data in an original way and avoids several pitfalls - difficult-to-specify dynamics, transitory time-series variation, and positively sloped supply schedules - inherent in investment equations that can bias the estimated elasticity. Results are based on an extensive panel containing 1,860 manufacturing and non-manufacturing firms. Our model generates a precisely estimated elasticity of approximately 0.40. The method developed here may prove useful in estimating other structural parameters from panel datasets.

Does oilrig activity react to oil price changes? An empirical investigation

Abstract: In this paper we analyse how oilrig activity in different Non-OPEC regions is affected by the crude oil price. Oilrig activity outside OPEC is an important indicator for production in the near future, and is more sensitive to the oil price than production from existing fields. We estimate relationships between oilrig activity and crude oil prices using Equilibrium Correction Models (ECM) augmented with a stochastic time trend. The results generally show a positive relationship between oilrig activity and the crude oil price, but the strength of the relationship differs across regions. Rig activity in the US seems to react much faster and stronger to oil price changes compared to other regions. In the long-run the price elasticity in the US is above 1.5. Half the effect is observed after six months. In other regions the long-run elasticity is mainly between 0.5 and 1. Overall, it seems to be a clear relationship between the oil industry structure in the region and the reaction to price changes.

In vivo elasticity measurements of extremity skeletal muscle with MR elastography.

Abstract: MR elastography (MRE) has been shown to be capable of non-invasively measuring tissue elasticity even in deep-lying regions. Although limited studies have already been published examining in vivo muscle elasticity, it is still not clear over what range the in vivo elasticity values vary. The present study intends to produce further information by examining four different skeletal muscles in a group of 12 healthy volunteers in the age range of 27-38 years. The examinations were performed in the biceps brachii, the flexor digitorum profundus, the soleus and the gastrocnemius. The average shear modulus was determined to be 17.9 (+/- 5.5), 8.7 (+/- 2.8), 12.5 (+/- 7.3) and 9.9 (+/- 6.8) kPa for each muscle, respectively. To ascertain the reproducibility of the examination, the stiffness measurements in two volunteers were repeated seven times for the biceps brachii. These examinations yielded a mean shear modulus of 11.3 +/-.7 and 13.3 +/- 4.7 kPa for the two subjects. For elasticity reconstruction, an automated reconstruction algorithm is introduced which eliminates variation due to subjective manual image analysis. This study yields new information regarding the expected variation in muscle elasticity in a healthy population, and also reveals the expected variability of the MRE technique in skeletal muscle.

Polymeric Liquids & Networks : Structure and Properties

Abstract: 1. Introduction 2. Molecular Liquids 3. Molecular Mixtures 4. The Random Coil Model 5. Dilute Solution Characterization 6. Dilute Solution Properties 7. Polymer Solutions 8. Polymer Blends 9. Network Structure and Elasticity 10. Network Properties

Microscopic theory of gelation and elasticity in polymer-particle suspensions.

Abstract: A simplified mode-coupling theory (MCT) of ergodic-nonergodic transitions, in conjunction with an accurate two-component polymer reference interaction site model (PRISM) theory for equilibrium structural correlations, has been systematically applied to investigate gelation, localization, and elasticity of flexible polymer-hard particle suspensions. The particle volume fraction at the fluid-gel transition is predicted to depend exponentially on reduced polymer concentration and size asymmetry ratio at relatively high colloid concentrations. In contrast, at lower particle volume fractions, a power-law dependence on polymer concentration is found with effective exponents and prefactors that depend systematically on the polymer/particle size ratio. Remarkable power-law and near universal scaling behavior is found for the localization length and elastic shear modulus. Multiple experiments for gel boundaries and shear moduli are in good agreement with the no adjustable parameter theory. The one exception is the absolute magnitude of the shear modulus which is strongly overpredicted, apparently due to nonequilibrium dense cluster formation. The simplified MCT-PRISM theory also captures the qualitative aspects of the weak depletion-driven "glass melting" phenomenon at high particle volume fractions. Calculations based on an effective one-component model of structure within a low particle volume fraction framework yield qualitatively different features than the two-component approach and are apparently all in disagreement with experiments. This suggests that volume fraction and size asymmetry dependent many-body screening of polymer-mediated depletion attractions at finite particle concentrations are important.

Calculating scale elasticity in DEA models

Abstract: In the data envelopment analysis (DEA) efficiency literature, qualitative characterizations of returns to scale (increasing, constant, or decreasing) are most common. In economics it is standard to use the scale elasticity as a quantification of scale properties for a production function representing efficient operations. Our contributions are to review DEA practices, apply the concept of scale elasticity from economic multi-output production theory to DEA piecewise linear frontier production functions, and develop formulas for scale elasticity for radial projections of inefficient observations in the relative interior of fully dimensional facets. The formulas are applied to both constructed and real data and show the differences between scale elasticities for the two valid projections (input and output orientations). Instead of getting qualitative measures of returns to scale only as was done earlier in the DEA literature, we now get a quantitative range of scale elasticity values providing more information to policy-makers.

Swelling, Elasticity and Spatial Inhomogeneity of Poly(N,N-dimethylacrylamide) Hydrogels Formed at Various Polymer Concentrations

Abstract: Summary: The equilibrium swelling degree, modulus of elasticity and the spatial inhomogeneity of poly(N,N-dimethylacrylamide) (PDMAAm) hydrogels were investigated over the entire range of the initial monomer concentration. The degree of dilution of the networks after their preparation was denoted by ν, the volume fraction of crosslinked polymer after the gel preparation. The linear swelling ratio of the gels increased linearly with increasing ν. Depending on the value of ν, three different gel regimes were observed: (1) For ν 0.7, the modulus of elasticity increases sharply with increasing ν due to the increasing extent of chain entanglements in this high concentration regime. Static light scattering measurements on the gels show that the degree of spatial gel inhomogeneity in PDMAAm gels attains a maximum value at ν = 0.06. The appearance of a maximum as well as the ν-dependence of scattered light intensities from gels was successfully reproduced by the theory proposed by Panyukov and Rabin. Effective crosslink density νe of the hydrogels shown as a function of ν.

Elastic nonwoven fabrics made from blends of polyolefins and processes for making the same

Abstract: Articles and nonwoven fabrics having improved elasticity manufactured from compositions, for example, made from 5 wt % to 100 wt % of a first polymer component of polymers selected from homopolymers of propylene and random copolymers of propylene and from 95 wt % to 0 wt % of a second polymer component of polymers selected from propylene homopolymers and propylene copolymers.

Pressure-Dependent Elasticity and Energy Conservation in Elastoplastic Models for Soils

Abstract: This paper presents a study on the consequences of combining energy conservative or non-conservative elasticity within a plasticity framework. Toward this end, a versatile energy potential function is first presented and examined. It is shown to cover a wide range of existing empirical relations for pressure-dependent stiffness of soils. Utilization of these functions within hyperplastic constitutive framework allows for the resulting models to satisfy the Law of Energy Conservation for both elastic and plastic components of soil behavior. Apart from the theoretical rigor, a very important result of this approach is that it automatically implies stress-induced cross-anisotropy of the elastic component of soil behavior and dilatancy term occurs due to shear modulus dependency on pressure. Proper modeling of these phenomena, normally neglected by conventional hypoelastic-plastic models, has been shown to have a significant effect on the accuracy of the model predictions of undrained behavior of overconsolidated clays both in laboratory tests and in tunnel excavation problem.

Sum rules for the quasi-static and visco-elastic response of disordered solids at zero temperature

Abstract: We study exact results concerning the non-affine displacement fields observed by Tanguy et al [Europhys. Lett. {\bf 57}, 423 (2002), Phys. Rev. B {\bf 66}, 174205 (2002)] and their contributions to elasticity. A normal mode analysis permits us to estimate the dominant contributions to the non-affine corrections to elasticity, and relate these corrections to the correlator of a fluctuating force field. We extend this analysis to the visco-elastic dynamical response of the system.

Models of two-dimensional solution assuming the internal compressibility of adsorbed molecules: A comparative analysis

Abstract: The description of surface dilational rheology data by theoretical models has some general problems, essentially in the range of larger surface coverage. Typically, the dilational elasticity calculated from theoretical models increases with surfactant bulk concentration and reaches values so far not observed in any experiment. In contrast, the experimental elasticities in the high-frequency limit show an increase with concentration followed by a plateau or flat maximum. Various thermodynamic models for the state of interfacial layers are discussed with respect to the corresponding limiting dilational elasticity. With the reorientation model (Fainerman; et al. J. Phys. Chem. 1996, 100, 7669) and the additional assumption of an intrinsic compressibility of the assembled adsorption layer, the data for some oxyethylene surfactants and dodecyl dimethyl phosphine oxide are well described.

A Comparison of the Hart-Smith Model with Arruda-Boyce and Gent Formulations for Rubber Elasticity

Abstract: The present paper demonstrates that the Hart-Smith constitutive model and the more recent Arruda and Boyce eight chains and Gent constitutive models are closely related. The ability of these three models to predict both small and large strain responses of rubbers is highlighted and equations that relate their material parameters are established.