Showing papers on "Elasticity (economics) published in 2012"

Mathematical Problems in Elasticity and Homogenization

Abstract: Some Mathematical Problems of the Theory of Elasticity. Some Functional Spaces and Their Properties. Auxiliary Propositions. Korn's Inequalities. Boundary Value Problems of Linear Elasticity. Perforated Domains with a Periodic Structure. Extension Theorems. Estimates for Solutions of Boundary Value Problems of Elasticity in Perforated Domains. Periodic Solutions of Boundary Value Problems for the System of Elasticity. Saint-Venant's Principle for Periodic Solutions of the Elasticity System. Estimates and Existence Theorems for Solutions of the Elasticity System in Unbounded Domains. Strong G -Convergence of Elasticity Operators. Homogenization of the System of Linear Elasticity. Composites and Perforated Materials. The Mixed Problem in a Perforated Domain with the Dirichlet Boundary Conditions on the Outer Part of the Boundary and the Neumann Conditions on the Surface of the Cavities. The Boundary Value Problem with Neumann Conditions in a Perforated Domain. Asymptotic Expansions for Solutions of Boundary Value Problems of Elasticity in a Perforated Layer. Asymptotic Expansions for Solutions of the Dirichlet Problem for the Elasticity System in a Perforated Domain. Asymptotic Expansions for Solutions of the Dirichlet Problem for the Biharmonic Equation. Some Generalizations for the Case of Perforated Domains with a Non-Periodic Structure. Homogenization of the System of Elasticity with Almost-Periodic Coefficients. Homogenization of Stratified Structures. Estimates for the Rate of G -Convergence of Higher-Order Elliptic Operators. Spectral Problems . Some Theorems from Functional Analysis. Spectral Problems for Abstract Operators. Homogenization of Eigenvalues and Eigenfunctions of Boundary Value Problems for Strongly Non-Homogeneous Elastic Bodies. On the Behaviour of Eigenvalues and Eigenfunctions of the Dirichlet Problem for Second Order Elliptic Equations in Perforated Domains. Third Boundary Value Problem for Second Order Elliptic Equations in Domains with Rapidly Oscillating Boundary. Free Vibrations of Bodies with Concentrated Masses. On the Behaviour of Eigenvalues of the Dirchlet Problem in Domains with Cavities Whose Concentration is Small. Homogenization of Eigenvalues of Ordinary Differential Operators. Asymptotic Expansion of Eigenvalues and Eigenfunctions of the Sturm-Liouville Problem for Equations with Rapidly Oscillating Coefficients. On the Behaviour of the Eigenvalues and Eigenfunctions of a G -Convergent Sequence of Non-Self-Adjoint Operators. References.

Supersonic shear wave elastography of in vivo pig kidney: influence of blood pressure, urinary pressure and tissue anisotropy.

Abstract: The in vivo influence of renal anisotropy and of urinary and vascular pressure on elasticity values using ultrasonic supersonic shear wave elastography was studied in pigs. Experiments were conducted in agreement with the European Commission guidelines and directives of the French Research Ministry. Six kidneys in three pigs were studied in vivo . Elasticity of renal cortex and medulla was quantified through the shear modulus ( μ ) by using the supersonic shear imaging technique with an 8 MHz linear ultrasound probe. All measurements were done peroperatively both in the axis and perpendicular to the main axis of pyramids, in normal condition, after progressive increase of urinary pressure, and after renal artery and renal vein ligation. In normal conditions, cortical (C) and medullary (M) elasticity values were always higher when acquisitions were realized with the ultrasound main axis perpendicular to main pyramid axis (C // : 7.7 ± 2.3 kPa; M // : 8.7 ± 2.5 kPa) than parallel (C ⊥ : 6.9 ± 1.4 kPa; M ⊥ : 6.6 ± 2.3 kPa), demonstrating an effect of renal anisotropy. In renal cortex, two bands were separated, inner cortex showing higher elasticity values (IC ⊥ : 8.1 ± 1.9 kPa) than outer cortex (OC ⊥ : 6.9 ± 1.4 kPa). Renal artery and renal vein ligation induced a decrease and an increase of elasticity respectively. Parenchymal elasticity increased linearly with elevation of urinary pressure. Intrarenal elasticity values vary with tissue anisotropy and, with vascular and urinary pressure levels. These parameters have to be taken into account for interpretation of tissue changes. Separation of outer and inner cortex could be attributable to perfusion differences.

Comb-Push Ultrasound Shear Elastography (CUSE): A Novel Method for Two-Dimensional Shear Elasticity Imaging of Soft Tissues

Abstract: Fast and accurate tissue elasticity imaging is essential in studying dynamic tissue mechanical properties. Various ultrasound shear elasticity imaging techniques have been developed in the last two decades. However, to reconstruct a full field-of-view 2-D shear elasticity map, multiple data acquisitions are typically required. In this paper, a novel shear elasticity imaging technique, comb-push ultrasound shear elastography (CUSE), is introduced in which only one rapid data acquisition (less than 35 ms) is needed to reconstruct a full field-of-view 2-D shear wave speed map (40 × 38 mm). Multiple unfocused ultrasound beams arranged in a comb pattern (comb-push) are used to generate shear waves. A directional filter is then applied upon the shear wave field to extract the left-to-right (LR) and right-to-left (RL) propagating shear waves. Local shear wave speed is recovered using a time-of-flight method based on both LR and RL waves. Finally, a 2-D shear wave speed map is reconstructed by combining the LR and RL speed maps. Smooth and accurate shear wave speed maps are reconstructed using the proposed CUSE method in two calibrated homogeneous phantoms with different moduli. Inclusion phantom experiments demonstrate that CUSE is capable of providing good contrast (contrast-to-noise ratio ≥25 dB) between the inclusion and background without artifacts and is insensitive to inclusion positions. Safety measurements demonstrate that all regulated parameters of the ultrasound output level used in CUSE sequence are well below the FDA limits for diagnostic ultrasound.

Micro Data and Macro Technology

Abstract: We study the implications of microeconomic heterogeneity for aggregate technology, showing that the aggregate elasticity of substitution between capital and labor can be expressed as a simple function of plant level structural parameters and sufficient statistics for plant heterogeneity This allows for a new approach to estimating the aggregate elasticity using microeconomic data and allows us to examine how the aggregate elasticity varies over time or across countries We then use plant level data from the Census of Manufactures to construct an aggregate elasticity of substitution for the manufacturing sector, and estimate an aggregate elasticity of approximately 072 in 1987 We find that the aggregate elasticity has risen over time in the US and is higher in less developed countries These differences are quantitatively important; our estimates imply that a change in the interest rate has a 50 percent larger impact on India than the US Finally, we measure the bias of aggregate technical change using our estimates of the aggregate elasticity, and find that the bias of technical change has increased in recent years

Cell visco-elasticity measured with AFM and optical trapping at sub-micrometer deformations

Abstract: The measurement of the elastic properties of cells is widely used as an indicator for cellular changes during differentiation, upon drug treatment, or resulting from the interaction with the supporting matrix. Elasticity is routinely quantified by indenting the cell with a probe of an AFM while applying nano-Newton forces. Because the resulting deformations are in the micrometer range, the measurements will be affected by the finite thickness of the cell, viscous effects and even cell damage induced by the experiment itself. Here, we have analyzed the response of single 3T3 fibroblasts that were indented with a micrometer-sized bead attached to an AFM cantilever at forces from 30-600 pN, resulting in indentations ranging from 0.2 to 1.2 micrometer. To investigate the cellular response at lower forces up to 10 pN, we developed an optical trap to indent the cell in vertical direction, normal to the plane of the coverslip. Deformations of up to two hundred nanometers achieved at forces of up to 30 pN showed a reversible, thus truly elastic response that was independent on the rate of deformation. We found that at such small deformations, the elastic modulus of 100 Pa is largely determined by the presence of the actin cortex. At higher indentations, viscous effects led to an increase of the apparent elastic modulus. This viscous contribution that followed a weak power law, increased at larger cell indentations. Both AFM and optical trapping indentation experiments give consistent results for the cell elasticity. Optical trapping has the benefit of a lower force noise, which allows a more accurate determination of the absolute indentation. The combination of both techniques allows the investigation of single cells at small and large indentations and enables the separation of their viscous and elastic components.

Non-affine deformations in polymer hydrogels

Abstract: Most theories of soft matter elasticity assume that the local strain in a sample after deformation is identical everywhere and equal to the macroscopic strain, or equivalently that the deformation is affine. We discuss the elasticity of hydrogels of crosslinked polymers with special attention to affine and non-affine theories of elasticity. Experimental procedures to measure non-affine deformations are also described. Entropic theories, which account for gel elasticity based on stretching out individual polymer chains, predict affine deformations. In contrast, simulations of network deformation that result in bending of the stiff constituent filaments generally predict non-affine behavior. Results from experiments show significant non-affine deformation in hydrogels even when they are formed by flexible polymers for which bending would appear to be negligible compared to stretching. However, this finding is not necessarily an experimental proof of the non-affine model for elasticity. We emphasize the insights gained from experiments using confocal rheoscope and show that, in addition to filament bending, sample micro-inhomogeneity can be a significant alternative source of non-affine deformation.

Static analysis of nanobeams including surface effects by nonlocal finite element

Abstract: In reality, there are two phenomena should be considered to describe behaviors of nanostructures adequately and accurately. The first one is the surface properties, especially for a relatively high ratio of the surface area to the volume of structural. The second phenomenon is the information about bulk material, which contains the forces between atoms and the internal length scale. Therefore, the objective of the current work is to study the coupled effects of surface properties and nonlocal elasticity on the static deflection of nanobeams. Surface elasticity is employed to describe the behavior of the surface layer and the Euler-Bernoulli beam hypothesis is used to state the bulk deformation kinematics. Both, the surface layer and bulk volume of the beam are assumed elastically isotropic. Information about the forces between atoms, and the internal length scale are proposed by the nonlocal Eringen model. Galerkin finite element technique is employed for the discretization of the nonlocal mathematical model with surface properties. The present results are compared favorably with those published results. The effects of nonlocal parameter and surface elastic constants are figured out and presented.

Analysis of Sandwich Beams With a Compliant Core and With In-Plane Rigidity—Extended High-Order Sandwich Panel Theory Versus Elasticity

Abstract: A new one-dimensional high-order theory for orthotropic elastic sandwich beams is formulated. This new theory is an extension of the high-order sandwich panel theory (HSAPT) and includes the in-plane rigidity of the core. In this theory, in which the compressibility of the soft core in the transverse direction is also considered, the displacement field of the core has the same functional structure as in the high-order sandwich panel theory. Hence, the transverse displacement in the core is of second order in the transverse coordinate and the in-plane displacements are of third order in the transverse coordinate. The novelty of this theory is that it allows for three generalized coordinates in the core (the axial and transverse displacements at the centroid of the core and the rotation at the centroid of the core) instead of just one (midpoint transverse displacement) commonly adopted in other available theories. It is proven, by comparison to the elasticity solution, that this approach results in superior accuracy, especially for the cases of stiffer cores, for which cases the other available sandwich computational models cannot predict correctly the stress fields involved. Thus, this theory, referred to as the “extended high-order sandwich panel theory” (EHSAPT), can be used with any combinations of core and face sheets and not only the very “soft” cores that the other theories demand. The theory is derived so that all core=face sheet displacement continuity conditions are fulfilled. The governing equations as well as the boundary conditions are derived via a variational principle. The solution procedure is outlined and numerical results for the simply supported case of transverse distributed loading are produced for several typical sandwich configurations. These results are compared with the corresponding ones from the elasticity solution. Furthermore, the results using the classical sandwich model without shear, the first-order shear, and the earlier HSAPT are also presented for completeness. The comparison among these numerical results shows that the solution from the current theory is very close to that of the elasticity in terms of both the displacements and stress or strains, especially the shear stress distributions in the core for a wide range of cores. Finally, it should be noted that the theory is formulated for sandwich panels with a generally asymmetric geometric layout. [DOI: 10.1115/1.4005550]

Filament-Length-Controlled Elasticity in 3D Fiber Networks

Abstract: We present a model for disordered 3D fiber networks to study their linear and nonlinear elasticity. In contrast to previous 2D models, these 3D networks with binary crosslinks are underconstrained with respect to fiber stretching elasticity, suggesting that bending may dominate their response. We find that such networks exhibit a bending-dominated elastic regime controlled by fiber length, as well as a crossover to a stretch-dominated regime for long fibers. Finally, by extending the model to the nonlinear regime, we show that these networks become intrinsically nonlinear with a vanishing linear response regime in the limit of flexible or long filaments.

Reconciling micro and macro estimates of the frisch labor supply elasticity

Abstract: This paper explores the large gap between the microeconometric estimates of the Frisch labor supply elasticity (0–.5) and the values used by macroeconomists to calibrate general equilibrium models (2–4). These two ranges identify two fundamentally different notions, the micro and macro Frisch elasticity, respectively. Due to the different definitions, there are two restrictions in the micro Frisch elasticity that are relaxed in the macro Frisch elasticity. First, the micro Frisch elasticity focuses only on prime-aged married males who are the head of their household, while the macro Frisch elasticity represents the whole population. Second, the micro Frisch elasticity only incorporates intensive margin fluctuations in hours, while the macro Frisch elasticity includes both intensive and extensive margin fluctuations. This paper finds that relaxing these two restrictions causes estimates of the Frisch elasticity to increase from 0.2 to between 2.9 and 3.1, indicating that these two restrictions can explain the gap between the microeconometric estimates and the calibration values. However, this paper demonstrates that these estimates of the macro Frisch elasticity are sensitive to the estimation procedure and also the exclusion of older individuals, implying that calibration values used for macroeconomic models should be selected carefully. (JEL E24, J22)

An improved complex variable element-free Galerkin method for two-dimensional elasticity problems

Abstract: In this paper, the improved complex variable moving least-squares (ICVMLS) approximation is presented. The ICVMLS approximation has an explicit physics meaning. Compared with the complex variable moving least-squares (CVMLS) approximations presented by Cheng and Ren, the ICVMLS approximation has a great computational precision and efficiency. Based on the element-free Galerkin (EFG) method and the ICVMLS approximation, the improved complex variable element-free Galerkin (ICVEFG) method is presented for two-dimensional elasticity problems, and the corresponding formulae are obtained. Compared with the conventional EFG method, the ICVEFG method has a great computational accuracy and efficiency. For the purpose of demonstration, three selected numerical examples are solved using the ICVEFG method.

Three-dimensional cellular structures with negative Poisson's ratio and negative compressibility properties

Abstract: A three-dimensional cellular system that may be made to exhibit some very unusual but highly useful mechanical properties, including negative Poisson’s ratio (auxetic), zero Poisson’s ratio, negative linear and negative area compressibility, is proposed and discussed. It is shown that such behaviour is scale-independent and may be obtained from particular conformations of this highly versatile system. This model may be used to explain the auxetic behaviour in auxetic foams and in other related cellular systems; such materials are widely known for their superior performance in various practical applications. It may also be used as a blueprint for the design and manufacture of new man-made multifunctional systems, including auxetic and negative compressibility systems, which can be made to have tailor-made mechanical properties.

Third-Degree Price Discrimination and Consumer Surplus

Abstract: This paper considers the effects of monopoly third-degree price discrimination on aggregate consumer surplus. Discrimination is likely to reduce surplus (relative to that obtained with a uniform price), but surplus can rise under reasonable conditions. If the ratio of the pass-through coefficient to the price elasticity at the uniform price is higher in the market with the higher price elasticity then surplus is larger with discrimination (for a large set of demand functions). The relatively high pass-through coefficient implies a large price reduction in this market. With logit demand functions surplus is higher with discrimination if pass-through is above 0.5.

Communication: Correlation of the instantaneous and the intermediate-time elasticity with the structural relaxation in glassforming systems

Abstract: The elastic models of the glass transition relate the increasing solidity of the glassforming systems with the huge slowing down of the structural relaxation and the viscous flow. The solidity is quantified in terms of the instantaneous shear modulus G(∞), i.e., the immediate response to a step change in the strain. By molecular-dynamics simulations of a model polymer system, one shows the virtual absence of correlations between the instantaneous elasticity and the structural relaxation. Instead, a well-defined scaling is evidenced by considering the elastic response observed at intermediate times after the initial fast stress relaxation. The scaling regime ranges from sluggish states with virtually pure elastic response on the picosecond time scale up to high-mobility states where fast restructuring events are more apparent.

The Costs of Agglomeration: Land Prices in French Cities

Abstract: We develop a new methodology to estimate the elasticity of urban costs with respect to city population using French land price data. Our preferred estimate, which handles a number of estimation concerns, stands at 0.041. Our approach also yields a number of intermediate outputs of independent interest such as a distance gradient for land prices and the elasticity of unit land prices with respect to city population. For the latter, our preferred estimate is 0.72.

Temporal analysis of vascular smooth muscle cell elasticity and adhesion reveals oscillation waveforms that differ with aging.

Abstract: Summary A spectral analysis approach was developed for detailed study of time-resolved, dynamic changes in vascular smooth muscle cell (VSMC) elasticity and adhesion to identify differences in VSMC from young and aged monkeys. Atomic force microscopy (AFM) was used to measure Young’s modulus of elasticity and adhesion as assessed by fibronectin (FN) or anti-beta 1 integrin interaction with the VSMC surface. Measurements demonstrated that VSMC cells from old vs. young monkeys had increased elasticity (21.6 kPa vs. 3.5 kPa or a 612% increase in elastic modulus) and adhesion (86 pN vs. 43 pN or a 200% increase in unbinding force). Spectral analysis identified three major frequency components in the temporal oscillation patterns for elasticity (ranging from 1.7 × 10−3 to 1.9 × 10−2 Hz in old and 8.4 × 10−4 to 1.5 × 10−2 Hz in young) and showed that the amplitude of oscillation was larger (P < 0.05) in old than in young at all frequencies. It was also observed that patterns of oscillation in the adhesion data were similar to the elasticity waveforms. Cell stiffness was reduced and the oscillations were inhibited by treatment with cytochalasin D, ML7 or blebbistatin indicating the involvement of actin–myosin-driven processes. In conclusion, these data demonstrate the efficacy of time-resolved analysis of AFM cell elasticity and adhesion measurements and that it provides a uniquely sensitive method to detect real-time functional differences in biomechanical and adhesive properties of cells. The oscillatory behavior suggests that mechanisms governing elasticity and adhesion are coupled and affected differentially during aging, which may link these events to changes in vascular stiffness.

Nonlocal elasticity based vibration of initially pre-stressed coupled nanobeam systems

Abstract: Vibration analyses of coupled nanobeam system under initial compressive pre-stressed condition are presented. An elastically connected double-nanobeam-system is considered. Expressions for bending-vibration of pre-stressed double-nanobeam-system are formulated using Eringen's nonlocal elasticity model. An analytical method is proposed to obtain natural frequencies of the nonlocal double-nanobeam-system (NDNBS). Nano-scale effects and coupling spring effects in (i) in-phase type, (ii) out-of-phase type vibration; and (ii) vibration with one nanobeam fixed are examined. Scale effects in higher natural frequencies of NDNBS are also highlighted in this manuscript. Results reveal the difference (quantitatively) by which the pre-load affects the nonlocal frequency in the in-phase type and out-of-phase type vibrations mode of NDNBS.

Atomic force microscopy: A tip for diagnosing cancer.

Abstract: Stiffness measurements of tumour biopsies and single cells show unique fingerprints that identify the different stages of cancer.