A recursive-faulting model of distributed damage in confined brittle materials

We develop a model of distributed damage in brittle materials deforming in triaxial compression based on the explicit construction of special microstructures obtained by recursive faulting. The model aims to predict the effective or macroscopic behavior of the material from its elastic and fracture properties; and to predict the microstructures underlying the microscopic behavior. The model accounts for the elasticity of the matrix, fault nucleation and the cohesive and frictional behavior of the faults. We analyze the resulting quasistatic boundary value problem and determine the relaxation of the potential energy, which describes the macroscopic material behavior averaged over all possible fine-scale structures. Finally, we present numerical calculations of the dynamic multi-axial compression experiments on sintered aluminum nitride of Chen and Ravichandran [1994. Dynamic compressive behavior of ceramics under lateral confinement. J. Phys. IV 4, 177–182; 1996a. Static and dynamic compressive behavior of aluminum nitride under moderate confinement. J. Am. Soc. Ceramics 79(3), 579–584; 1996b. An experimental technique for imposing dynamic multiaxial compression with mechanical confinement. Exp. Mech. 36(2), 155–158; 2000. Failure mode transition in ceramics under dynamic multiaxial compression. Int. J. Fracture 101, 141–159]. The model correctly predicts the general trends regarding the observed damage patterns; and the brittle-to-ductile transition resulting under increasing confinement

Frictional Collisions Off Sharp Objects

This work develops robust contact algorithms capable of dealing with multibody nonsmooth contact geometries for which neither normals nor gap functions can be defined. Such situations arise in the early stage of fragmentation when a number of angular fragments undergo complex collision sequences before eventually scattering. Such situations precludes the application of most contact algorithms proposed to date

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

Modelling and solutions to the linear stability of a detonation wave in the kinetic frame

Artigo publicado num número especial da revista.The analysis of linear stability of a steady detonation wave is formulated for the first time at the kinetic level in the frame of the Boltzmann equation extended to reacting gases. Within this context and for a reversible reaction, the stability problem is carried out, in agreement with most classical papers on gas detonation, through a normal mode approach for the one-dimensional disturbances of the steady wave solution, and an acoustic radiation condition at the final equilibrium as closure condition. The proposed modelling leads to an initial value problem, constituted by the linearized reactive Euler equations in the perturbed shock frame with related Rankine-Hugoniot conditions, which can be solved by means of a proper numerical technique. An application is provided for an elementary bimolecular reaction.Centro de Matemática da Universidade do MinhoFundação para a Ciência e a Tecnologia (FCT)Italian INDAM-GNF

Evolution of the fine-structure constant in runaway dilaton models

We study the detailed evolution of the fine-structure constant $\alpha$ in the string-inspired runaway dilaton class of models of Damour, Piazza and Veneziano. We provide constraints on this scenario using the most recent $\alpha$ measurements and discuss ways to distinguish it from alternative models for varying $\alpha$. For model parameters which saturate bounds from current observations, the redshift drift signal can differ considerably from that of the canonical $\Lambda$CDM paradigm at high redshifts. Measurements of this signal by the forthcoming European Extremely Large Telescope (E-ELT), together with more sensitive $\alpha$ measurements, will thus dramatically constrain these scenarios.Comment: 11 pages, 4 figure

Kinetic approach to transport properties of a reacting gas

A multicomponent reacting gas with reversible reactions is studied at a kinetic level with the main objective of deriving the reactive Navier-Stokes equations in dependence on the macroscopic variables, and characterizing the dissipative terms related to shear viscosity, heat conduction and thermal diffusion. A step-by-step procedure, which can be applied to a quite large variety of reactive flows, is proposed in order to identify the transport coefficients, basically resorting to a first-order density approximation of Chapman-Enskog type.Fundação para a Ciência e Tecnologia (FCT) - Programa Operacional "Ciência, Tecnologia, Inovação" (POCTI).National Research Project PRIN 2003

Progressive high-fluence epithelium-on accelerated corneal crosslinking: a novel corneal photodynamic therapy for early progressive keratoconus

Purpose: To assess the preliminary clinical results of a new, progressively higher fluence-pulsed light Epi-On accelerated crosslinking nomogram (PFPL M Epi-On ACXL) in the treatment of progressive keratoconus (KC). Setting: Siena Crosslinking Center, Siena, Italy. Methods: A prospective pilot open, non-randomized interventional study, including 32 eyes of 32 young-adult patients over 26 years old with Stages I- III progressive KC undergoing PFPL M Epi-On ACXL, was conducted. Riboflavin loading was performed by using Paracel I 0.25% for 4min and Paracel II 0.22% for 6min. The Avedro KXL System (Glaukos-Avedro, Burlington, USA) was used for pulsed-light accelerated crosslinking (ACXL) at air room 21% oxygenation and 13min of UV-A irradiation. The treatment fluence was set at 7.2 J/cm2, 8.6 J/cm2, and 10.0 J/cm2 in corneas with baseline pachymetry <420μm(group 1: 8 eyes), 420μm<460μm(group 2, 11 eyes), and 460μm(group 3, 13 eyes), respectively. Uncorrected distance visual acuity (UDVA), best-spectacle corrected visual acuity (BSCVA), Scheimpflug corneal tomography, and anterior segment OCT (AS-OCT) data were collected at baseline and postoperatively at 1, 3, and 6 months. Results:UDVA and BSCVA improved in all groups (P 0.05).Maximumkeratometry values (K max) showed a significant decrease in the 10.0 J/cm2 group (1 −1.68 D). The coma (HOAs) value improved significantly by the sixthmonth in all groups. OCT average demarcation lines were 211 ± 19μm in group 1, 245 ± 23μm in group 2, and 267 ± 21μm in group 3. Conclusions: The preliminary results show that pachymetry-based PFPL M Epi-On ACXL nomogram stabilizes ectasia progression. Higher fluence Epi-On ACXL increases CXL penetration, with better functional outcomes in the absence of complications

An optimal-transport finite-particle method for mass diffusion

We formulate a class of velocity-free finite-particle methods for mass transport problems based on a time-discrete incremental variational principle that combines entropy and the cost of particle transport, as measured by the Wasserstein metric. The incremental functional is further spatially discretized into finite particles, i.~e., particles characterized by a fixed spatial profile of finite width, each carrying a fixed amount of mass. The motion of the particles is then governed by a competition between the cost of transport, that aims to keep the particles fixed, and entropy maximization, that aims to spread the particles so as to increase the entropy of the system. We show how the optimal width of the particles can be determined variationally by minimization of the governing incremental functional. Using this variational principle, we derive optimal scaling relations between the width of the particles, their number and the size of the domain. We also address matters of implementation, including the acceleration of the computation of diffusive forces by exploiting the Gaussian decay of the particle profiles and by instituting fast nearest-neighbor searches. {\red Sources, advection, boundary flux and diffusion are accounted for by fractional steps.} We demonstrate the robustness and versatility of the finite-particle method by means of a test problem concerned with the injection of mass into a sphere. There test results demonstrate the meshless character of the method in any spatial dimension, its ability to redistribute mass particles and follow their evolution in time, its ability to satisfy flux boundary conditions for general domains based solely on a distance function, and its robust convergence characteristics

Variability of aerosol optical properties in the Western Mediterranean Basin

Aerosol light scattering, absorption and particulate matter (PM) concentrations were measured at Montseny, a regional background site in the Western Mediterranean Basin (WMB) which is part of the European Supersite for Atmospheric Aerosol Research (EUSAAR). Off line analyses of 24 h PM filters collected with Hi-Vol instruments were performed for the determination of the main chemical components of PM. Mean scattering and hemispheric backscattering coefficients (@ 635 nm) were 26.6±23.2 Mm<sup>−1</sup> and 4.3±2.7 Mm<sup>−1</sup>, respectively and the mean aerosol absorption coefficient (@ 637 nm) was 2.8±2.2 Mm<sup>−1</sup>. Mean values of Single Scattering Albedo (SSA) and Ångström exponent (<i>å</i>) (calculated from 450 nm to 635 nm) at MSY were 0.90±0.05 and 1.3±0.5 respectively. A clear relationship was observed between the PM<sub>1</sub>/PM<sub>10</sub> and PM<sub>2.5</sub>/PM<sub>10</sub> ratios as a function of the calculated Ångström exponents. Mass scattering cross sections (MSC) for fine mass and sulfate at 635 nm were 2.8±0.5 m<sup>2</sup> g<sup>−1</sup> and 11.8±2.2 m<sup>2</sup> g<sup>−1</sup>, respectively, while the mean aerosol absorption cross section (MAC) was 10.4±2.0 m<sup>2</sup> g<sup>−1</sup>. The variability in aerosol optical properties in the WMB were largely explained by the origin and ageing of air masses over the measurement site. The MAC values appear dependent of particles aging: similar to the expected absorption cross-section for fresh emissions under Atlantic Advection episodes and higher under aerosol pollution episodes. The analysis of the Ångström exponent as a function of the origin the air masses revealed that polluted winter anticyclonic conditions and summer recirculation scenarios typical of the WMB led to an increase of fine particles in the atmosphere (<i>å</i> = 1.5±0.1) while the aerosol optical properties under Atlantic Advection episodes and Saharan dust outbreaks were clearly dominated by coarser particles (<i>å</i> = 1.0±0.4). The sea breeze played an important role in transporting pollutants from the developed WMB coastlines towards inland rural areas, changing the optical properties of aerosols. Aerosol scattering and backscattering coefficients increased by around 40 % in the afternoon when the sea breeze was fully developed while the absorption coefficient increased by more than 100 % as a consequence of the increase in the equivalent black carbon concentration (EBC) observed at MSY under sea breeze circulation