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A Transforming Metal Nanocomposite with Large Elastic Strain, Low Modulus, and High Strength
Freestanding nanowires have ultrahigh elastic strain limits (4 to 7%) and yield strengths, but exploiting their intrinsic mechanical properties in bulk composites has proven to be difficult. We exploited the intrinsic mechanical properties of nanowires in a phase-transforming matrix based on the concept of elastic and transformation strain matching. By engineering the microstructure and residual stress to couple the true elasticity of Nb nanowires with the pseudoelasticity of a NiTi shape-memory alloy, we developed an in situ composite that possesses a large quasi-linear elastic strain of over 6%, a low Young's modulus of ∼28 gigapascals, and a high yield strength of ∼1.65 gigapascals. Our elastic strain-matching approach allows the exceptional mechanical properties of nanowires to be exploited in bulk materials.
Journal Article
Is it flexible or rigid?
Discusses the properties of matter, focusing on whether an object is flexible or not with definitions and examples to illustrate.
Book
Optimal Regularity and the Free Boundary in the Parabolic Signorini Problem
We give a comprehensive treatment of the parabolic Signorini problem based on a generalization of Almgren’s monotonicity of the
frequency. This includes the proof of the optimal regularity of solutions, classification of free boundary points, the regularity of the
regular set and the structure of the singular set.
eBook
Reverberant 3D optical coherence elastography maps the elasticity of individual corneal layers
The elasticity mapping of individual layers in the cornea using non-destructive elastography techniques advances diagnosis and monitoring of ocular diseases and treatments in ophthalmology. However, transient Lamb waves, currently used in most dynamic optical coherence and ultrasound elastography techniques, diminish the translation of wave speed into shear/Young’s modulus. Here, we present reverberant 3D optical coherence elastography (Rev3D-OCE), a novel approach leveraging the physical properties of diffuse fields in detecting elasticity gradients not only in the lateral direction, but also along the depth axis of the cornea. A Monte Carlo analysis, finite element simulations, and experiments in layered phantoms are conducted to validate the technique and to characterize the axial elastography resolution. Experiments in ex vivo porcine cornea at different intraocular pressures reveal that Rev3D-OCE enables the elastic characterization of single layers that matches the anatomical description of corneal layers with unprecedented contrast in the dynamic OCE field.
Elastic mapping of individual layers of the cornea with elastography uses Lamb waves, which are dependent on the thickness of each layer and the direction of propagation. Here the authors present Reverberant 3D Optical Coherence Elastography to measure elasticity of single layers using waves propagating in all directions.
Journal Article
Liver elasticity in healthy individuals by two novel shear-wave elastography systems—Comparison by age, gender, BMI and number of measurements
Establishing normal liver stiffness (LS) values in healthy livers is a prerequisite to differentiate normal from pathological LS values. Our aim was to define normal LS using two novel elastography methods head-to-head and to assess the number of measurements, variability and reproducibility.
We evaluated shear wave elastography (SWE) methods integrated in Samsung RS80A and GE S8 by obtaining LS measurements (LSM) in 100 healthy subjects (20-70 years). Transient Elastography (TE) was used as reference method. Data were analyzed according to age, sex, BMI and 5 vs. 10 measurements. All subjects underwent B-mode ultrasound examination and lab tests to exclude liver pathology. Interobserver variation was evaluated in a subset (n = 24).
Both methods showed excellent feasibility, measuring LS in all subjects. LSM-mean for GE S8 2D-SWE was higher compared to TE (4.5±0.8 kPa vs. 4.2±1.1, p<0.001) and Samsung RS80A (4.1±0.8 kPa, p<0.001). Both methods showed low intra- and interobserver variation. LSM-mean was significantly higher in males than females using 2D-SWE, while a similar trend for Samsung SWE did not reach significance. No method demonstrated statistical significant difference in LSM across age and BMI groups nor between LSM-mean based on 5 vs. 10 measurements.
LSM was performed with high reproducibility in healthy adult livers. LSM-mean was significantly higher for GE S8 2D-SWE compared to Samsung RS80A and TE in healthy livers. Males had higher LSM than females. No method demonstrated statistical significant difference in LSM-mean across age- and non-obese BMI groups. Our results indicate that five LSM may be sufficient for reliable results.
Journal Article
Establishing an Elastography calibration standard: Validation of a shear wave TOF device for measuring Elasticity and Viscosity in tissue-mimicking phantoms using rheometry
This study designed a novel shear wave Time of Flight (TOF) device to measure frequency-dependent shear wave velocity in tissue-mimicking materials, from which viscoelastic parameters were estimated through Kelvin-Voigt fractional derivative modeling to establish a reliable calibration standard. Tissue-mimicking phantoms were fabricated using 10 wt% polyvinyl alcohol (PVA) and 2 wt% α-alumina powder, with mechanical properties modulated through freeze-thaw cycling. Bimorph transducers operating in the 40–180 Hz range induced and captured shear waves. A single-cycle sine wave excitation ensures narrowband propagation, and a custom algorithm based on the cumulative energy technique robustly detects the shear wave arrival time to estimate TOF. Frequency-dependent shear velocity data were fitted to the Kelvin Voigt fractional derivative (KVFD) model to derive the relaxed elastic modulus ( E o ), viscosity (η), and fractional order (α), with Poisson’s ratio and damping effects accounted for in the model assumptions. The fitting demonstrated high accuracy, with an R ² value of 98.8% (RMSE = 0.013 m/s) for the hard phantom and 99.1% (RMSE = 0.002 m/s) for the soft phantom. Validation with standard rheometer data showed reasonable agreement in elasticity, with percent differences of 2.1% for the hard and 13.3% for the soft phantoms. The latter reflects greater sensitivity to damping effects and assumptions on Poisson’s ratio, as reported in previous studies. However, η and α showed larger deviations because they are strongly dependent on the measurement band; therefore, a direct comparison of these parameters across techniques with nonoverlapping frequency ranges is inappropriate. To enable a fair cross-method assessment, we performed band-matched velocity domain projections in both directions using the KVFD forward model and a constrained TOF refit with E o fixed to the rheometer value. This analysis revealed that the discrepancies in η and α primarily stem from frequency band sensitivity rather than methodological bias. These findings support the shear wave TOF device as a robust, frequency-tunable alternative to rheometry for ex vivo tissue characterization and for calibrating clinical elastography. Its immediate clinical relevance is to provide a rapid and low-cost approach for phantom standardization and to inform elastography parameter settings. Key limitations of the present study are the restriction to ex vivo validation, operation within 40–180 Hz, and use of a dispersion-only inversion model; consequently, the viscous parameters (η, α) are frequency sensitive and not directly comparable to low-frequency rheometry. Future evaluation of in vivo performance and spatial heterogeneity is therefore essential.
Journal Article
Evidence of a Shift in the Short-Run Price Elasticity of Gasoline Demand
Understanding the sensitivity of gasoline demand to changes in prices and income has important implications for policies related to climate change, optimal taxation and national security. The short-run price and income elasticities of gasoline demand in the United States during the 1970s and 1980s have been studied extensively. However, transportation analysts have hypothesized that behavioral and structural factors over the past several decades have changed the responsiveness of U.S. consumers to changes in gasoline prices. We compare the price and income elasticities of gasoline demand in two periods of similarly high prices from 1975 to 1980 and 2001 to 2006. The short-run price elasticities differ considerably: and range from -0.034 to -0.077 during 2001 to 2006, versus -0.21 to -0.34 for 1975 to 1980. The estimated short-run income elasticities range from 0.21 to 0.75 and when estimated with the same models are not significantly different between the two periods.
Journal Article
Geometric Optics for Surface Waves in Nonlinear Elasticity
This work is devoted to the analysis of high frequency solutions to the equations of nonlinear elasticity in a half-space. The authors consider surface waves (or more precisely, Rayleigh waves) arising in the general class of isotropic hyperelastic models, which includes in particular the Saint Venant-Kirchhoff system. Work has been done by a number of authors since the 1980s on the formulation and well-posedness of a nonlinear evolution equation whose (exact) solution gives the leading term of an approximate Rayleigh wave solution to the underlying elasticity equations. This evolution equation, which is referred to as \"the amplitude equation\", is an integrodifferential equation of nonlocal Burgers type. The authors begin by reviewing and providing some extensions of the theory of the amplitude equation. The remainder of the paper is devoted to a rigorous proof in 2D that exact, highly oscillatory, Rayleigh wave solutions $u^{\\varepsilon} $ to the nonlinear elasticity equations exist on a fixed time interval independent of the wavelength $\\varepsilon $, and that the approximate Rayleigh wave solution provided by the analysis of the amplitude equation is indeed close in a precise sense to $u^{\\varepsilon}$ on a time interval independent of $\\varepsilon $. This paper focuses mainly on the case of Rayleigh waves that are pulses, which have profiles with continuous Fourier spectrum, but the authors' method applies equally well to the case of wavetrains, whose Fourier spectrum is discrete.
eBook
Are Micro and Macro Labor Supply Elasticities Consistent? A Review of Evidence on the Intensive and Extensive Margins
We evaluate whether state-of-the-art macro models featuring indivisible labor are consistent with modern quasi-experimental micro evidence by synthesizing evidence on both the intensive and extensive margins. We find that micro estimates are consistent with macro estimates of the steady-state (Hicksian) elasticities relevant for cross-country comparisons on both the extensive and intensive margins. However, micro estimates of intertemporal substitution (Frisch) elasticities are an order of magnitude smaller than the values needed to explain business cycle fluctuations in aggregate hours by preferences. The key puzzle to be resolved is why micro and macro estimates of the Frisch extensive margin elasticity are so different.
Journal Article