Wave reflection at a free interface in an anisotropic pyroelectric medium with nonclassical thermoelasticity

In this paper, the well-established two-dimensional mathematical model for linear pyroelectric materials is employed to investigate the reflection of waves at the boundary between a vacuum and an elastic, transversely isotropic, pyroelectric material. A comparative study between the solutions of (a) classical thermoelasticity, (b) Cattaneo–Lord–Shulman theory and (c) Green–Lindsay theory equations, characterised by none, one and two relaxation times, respectively, is presented. Suitable boundary conditions are considered in order to determine the reflection coefficients when incident elasto–electro–thermal waves impinge the free interface. It is established that, in the quasi-electrostatic approximation, three different classes of waves: (1) two principally elastic waves, namely a quasi-longitudinal Primary (qP) wave and a quasi-transverse Secondary (qS) wave; and (2) a mainly thermal (qT) wave. The observed electrical effects are, on the other hand, a direct consequence of mechanical and thermal phenomena due to pyroelectric coupling. The computed reflection coefficients of plane qP waves are found to depend upon the angle of incidence, the elastic, electric and thermal parameters of the medium, as well as the thermal relaxation times. The special cases of normal and grazing incidence are also derived and discussed. Finally, the reflection coefficients are computed for cadmium selenide observing the influence of (1) the anisotropy of the material, (2) the electrical potential and (3) temperature variations and (4) the thermal relaxation times on the reflection coefficients.     

Dislocation Patterns and Work-Hardening in Crystalline Plasticity

We propose a continuum model for the evolution of the total dislocation densities in fcc crystals, in the framework of rate-independent plasticity. The basic physical features which are taken into account are: (i) the role of dislocations in hardening; (ii) the relations between the slip velocity and dislocation mobility; (iii) the energetics of self and mutual interactions between dislocations; (iv) nonlocal effects in the interaction between dislocations. A set of reaction–diffusion equations is obtained, with mobilities depending on the slip velocities, which is able to describe the formation of dislocation walls and cells. To this effect, the results of numerical simulations in two special cases are presented. Mathematics Subject Classifications (2000) 74C15, 74C20.     

Identification of Material Damage Model Parameters: an Inverse Approach Using Digital Image Processing

A reliable prediction of ductile failure in metals is still a wide-open matter of research. Several models are available in the literature, ranging from empirical criteria, porosity-based models and continuum damage mechanics (CDM). One major issue is the accurate identification of parameters which describe material behavior. For some damage models, parameter identification is more or less straightforward, being possible to perform experiments for their evaluation. For the others, direct calibration from laboratory tests is not possible, so that the approach of inverse methods is required for a proper identification. In material model calibration, the inverse approach consists in a non-linear iterative fitting of a parameter-dependent load–displacement curve (coming from a FEM simulation) on the experimental specimen response. The test is usually a tensile test on a round-notched cylindrical bar. The present paper shows a novel inverse procedure aimed to estimate the material parameters of the Gurson–Tvergaard–Needleman (GTN) porosity-based plastic damage model by means of experimental data collected using image analysis. The use of digital image processing allows to substitute the load–displacement curve with other global quantities resulting from the measuring of specimen profile during loading. The advantage of this analysis is that more data are available for calibration thus allowing a greater level of confidence and accuracy in model parameter evaluation.     

Well-Posedness of Stochastic Continuity Equations on Riemannian Manifolds

The authors analyze continuity equations with Stratonovich stochasticity,■defined on a smooth closed Riemannian manifold M with metric h.The velocity field u is perturbed by Gaussian noise terms ■₁（t）,…,■_N（t） driven by smooth spatially dependent vector fields a₁（x）,…,a_N（x） on M.The velocity u belongs to L_t¹W_x^1,2 with div_hu bounded in L_t,x^p for p> d+2,where d is the dimension of M(they do not assume div_h u∈L_t,x^∞).For carefully chosen noise vector fields a_i（and the number N of them）,they show that the initial-value problem is well-posed in the class of weak L² solutions,although the problem can be ill-posed in the deterministic case because of concentration effects.The proof of this \"regularization by noise\" result is based on a L² estimate,which is obtained by a duality method,and a weak compactness argument.     

Rational Design of Fe2(μ-PR2)2(L)6 Coordination Compounds Featuring Tailored Potential Inversion

It was recently discovered that some redox proteins can thermodynamically and spatially split two incoming electrons towards different pathways, resulting in the one-electron reduction of two different substrates, featuring reduction potential respectively higher and lower than the parent reductant. This energy conversion process, referred to as electron bifurcation, is relevant not only from a biochemical perspective, but also for the ground-breaking applications that electron-bifurcating molecular devices could have in the field of energy conversion. Natural electron-bifurcating systems contain a two-electron redox centre featuring potential inversion (PI), i. e. with second reduction easier than the first. With the aim of revealing key factors to tailor the span between first and second redox potentials, we performed a systematic density functional study of a 26-molecule set of models with the general formula Fe₂(μ-PR₂)₂(L)₆. It turned out that specific features such as i) a Fe−Fe antibonding character of the LUMO, ii) presence of electron-donor groups and iii) low steric congestion in the Fe's coordination sphere, are key ingredients for PI. In particular, the synergic effects of i)-iii) can lead to a span between first and second redox potentials larger than 700 mV. More generally, the “molecular recipes” herein described are expected to inspire the synthesis of Fe₂P₂ systems with tailored PI, of primary relevance to the design of electron-bifurcating molecular devices.