Statistical characterization of the anisotropic strain energy in soft materials with distributed fibers

We discuss analytical and numerical tools for the statistical characterization of the anisotropic strain energy density of soft hyperelastic materials embedded with fibers. We consider spatially distributed orientations of fibers following a tridimensional or a planar architecture. We restrict our analysis to material models dependent on the fourth pseudo-invariant I4 of the Cauchy-Green tensor, and to exponential forms of the fiber strain energy function Ψaniso. Under different loading conditions, we derive the closed-form expression of the probability density function for I4 and Ψaniso. In view of bypassing the cumbersome extension-contraction switch, commonly adopted for shutting down the contribution of contracted fibers in models based on generalized structure tensors, for significant loading conditions we identify analytically the support of the fibers in pure extension. For uniaxial loadings, the availability of the probability distribution function and the knowledge of the support of the fibers in extension yield to the analytical expression of average and variance of I4 and Ψaniso, and to the direct definition of the average second Piola-Kirchhoff stress tensor. For generalized loadings, the dependence of I4 on the spatial orientation of the fibers can be analyzed through angle plane diagrams. Angle plane diagrams facilitate the assessment of the influence of the pure extension condition on the definition of the stable support of fibers for the statistics related to the anisotropic strain energy density. © 2015 Elsevier Ltd. All rights reserved

Inequality in Pre-Industrial Europe (1260–1850): New Evidence From the Labor Share

The dynamics of economic inequality and its relationship with economic growth in the preindustrial world is increasingly attracting the attention of both economists and economic historians. In this paper, we tackle this theme by introducing new estimates of the labor share in five major European countries (England, France, Holland, Spain, and Portugal) for the period 1250–1850. Our estimates are constructed using an innovative method based on the conversion of real wages in 2011 PPP $. Overall, we find a complex pattern of evolution of the labor share with major fluctuations. Furthermore, using the inequality possibility frontier (IPF) framework, our results suggest that preindustrial Europe was characterized by a negative relationship between the extraction ratio and GDP

The origins of the Italian regional divide: Evidence from real wages, 1861-1913

The origins of the Italian North-South divide have always been controversial. We fill this gap by estimating a new dataset of real wages (Allen 2001; Allen et al. 2011) from Unification (1861) to WWI. Italy was very poor throughout the period, with a modest improvement since the late nineteenth century. This improvement started in the Northwest industrializing regions, while real wages in other macro-areas remained stagnant. The gap Northwest/South widened until the end of the period. Focusing on the drivers of regional trends, we find that human capital formation exerted strong positive effect on the growth of real wages

Classification of Sensory Neural Signals through Deep Learning Methods

The recording and analysis of peripheral neural signals can be beneficial to provide feedback to prosthetic limbs and recover the sensory functionality in people with nerve injuries. Nevertheless, the interpretation of sensory recordings extracted from the nerve is not trivial, and only few studies have applied classifiers on sequences of neural signals without previous feature extraction. This paper evaluates the classification performance of two deep learning (DL) models (CNN and ConvLSTM) applied to the electroneurographic (ENG) activity recorded from the sciatic nerve of rats. The ENG signals, available from two public datasets, were recorded using multi-channel cuff electrodes in response to four sensory inputs (plantarflexion, dorsiflexion, nociception, and touch) elicited in response to mechanical stimulation applied to the hind paw of the rats. Different temporal lengths of the signals were considered (2.5 s, 1 s, 500 ms, 200 ms, and 100 ms), Both the two DL models proved to correctly discriminate sensory stimuli without the need of hand-engineering feature extraction. Moreover, ConvLSTM outperformed state-of-the-art results in classifying sensory ENG activity (more than 90% F1-score for sequences greater than 500 ms), and it showed promising results for real-time application scenarios

A numerical model of the human cornea accounting for the fiber-distributed collagen microstructure

We present a fiber-distributed model of the reinforcing collagen of the human cornea. The model describes the basic connections between the components of the tissue by defining an elementary block (cell) and upscaling it to the physical size of the cornea. The cell is defined by two sets of collagen fibrils running in approximately orthogonal directions, characterized by a random distribution of the spatial orientation and connected by chemical bonds of two kinds. The bonds of the first kind describe the lamellar crosslinks, forming the ribbon-like lamellae; while the bonds of the second kind describe the stacking crosslinks, piling up the lamellae to form the structure of the stroma. The spatial replication of the cell produces a truss structure with a considerable number of degrees of freedom. The statistical characterization of the collagen fibrils leads to a mechanical model that reacts to the action of the deterministic intraocular pressure with a stochastic distribution of the displacements, here characterized by their mean value and variance. The strategy to address the solution of the heavy resulting numerical problem is to use the so-called stochastic finite element improved perturbation method combined with a fully explicit solver. Results demonstrate that the variability of the mechanical properties affects in a non-negligible manner the expected response of the structure to the physiological action

Testing PDR models against ISO fine structure line data for extragalactic sources

Far-infrared [C ii] 158-μm, [O i] 145-μm and [O i] 63-μm fine structure emission-line fluxes were measured from archival Infrared Space Observatory Long Wavelength Spectrometer spectra of 46 extragalactic sources, with 28 sources providing detections in all three lines. For 12 of the sources, the contribution to the [C ii] 158-μm line flux from H ii regions could be estimated from their detected [N ii] 122-μm line fluxes. The measured [C ii]/[O i] and [O i] 63/145-μm line flux ratios were compared with those from a grid of photodissociation region (PDR) models previously computed using the ucl_pdr code. Persistent offsets between the observed and modelled line ratios could be partly attributed to the effects of [O i] 63-μm self-absorption. Using the Spherical Multi-Mol (smmol) code, we calculated model [O i] line profiles and found that the strength of the [O i] 63-μm line was reduced by 20–80 per cent, depending on the PDR parameters. We conclude that high PDR densities and radiation field strengths, coupled with the effects of [O i] 63-μm self-absorption, are likely to provide the best match to the observed line flux ratios