On the variational limits of lattice energies on prestrained elastic bodies

We study the asymptotic behaviour of the discrete elastic energies in presence of the prestrain metric $G$, assigned on the continuum reference configuration $\Omega$. When the mesh size of the discrete lattice in $\Omega$ goes to zero, we obtain the variational bounds on the limiting (in the sense of $\Gamma$-limit) energy. In case of the nearest-neighbour and next-to-nearest-neibghour interactions, we derive a precise asymptotic formula, and compare it with the non-Euclidean model energy relative to $G$

Domain formation in magnetic polymer composites: an approach via stochastic homogenization

We study the magnetic energy of magnetic polymer composite materials as the average distance between magnetic particles vanishes. We model the position of these particles in the polymeric matrix as a stochastic lattice scaled by a small parameter $\varepsilon$ and the magnets as classical $\pm 1$ spin variables interacting via an Ising type energy. Under surface scaling of the energy we prove, in terms of $\Gamma$-convergence that, up to subsequences, the (continuum) $\Gamma$-limit of these energies is finite on the set of Caccioppoli partitions representing the magnetic Weiss domains where it has a local integral structure. Assuming stationarity of the stochastic lattice, we can make use of ergodic theory to further show that the $\Gamma$-limit exists and that the integrand is given by an asymptotic homogenization formula which becomes deterministic if the lattice is ergodic.Comment: 31 page

Derivation of linear elasticity for a general class of atomistic energies

The purpose of this paper is the derivation, in the framework of Gamma-convergence, of linear elastic continuum theories from a general class of atomistic models, in the regime of small deformations. Existing results are available only in the special case of one-well potentials accounting for very short interactions. We consider here the general case of multi-well potentials accounting for interactions of finite but arbitrarily long range. The extension to this setting requires a novel idea for the proof of the Gamma-convergence which is interesting in its own right and potentially relevant in other applications

Random parking, Euclidean functionals, and rubber elasticity

We study subadditive functions of the random parking model previously analyzed by the second author. In particular, we consider local functions $S$ of subsets of $\mathbb{R}^d$ and of point sets that are (almost) subadditive in their first variable. Denoting by $\xi$ the random parking measure in $\mathbb{R}^d$, and by $\xi^R$ the random parking measure in the cube $Q_R=(-R,R)^d$, we show, under some natural assumptions on $S$, that there exists a constant $\bar{S}\in \mathbb{R}$ such that % $$\lim_{R\to +\infty} \frac{S(Q_R,\xi)}{|Q_R|}\,=\,\lim_{R\to +\infty}\frac{S(Q_R,\xi^R)}{|Q_R|}\,=\,\bar{S}$$ % almost surely. If $\zeta \mapsto S(Q_R,\zeta)$ is the counting measure of $\zeta$ in $Q_R$, then we retrieve the result by the second author on the existence of the jamming limit. The present work generalizes this result to a wide class of (almost) subadditive functions. In particular, classical Euclidean optimization problems as well as the discrete model for rubber previously studied by Alicandro, Cicalese, and the first author enter this class of functions. In the case of rubber elasticity, this yields an approximation result for the continuous energy density associated with the discrete model at the thermodynamic limit, as well as a generalization to stochastic networks generated on bounded sets.Comment: 28 page

Derivation of a linearised elasticity model from singularly perturbed multiwell energy functionals

Linear elasticity can be rigorously derived from finite elasticity under the assumption of small loadings in terms of Gamma-convergence. This was first done in the case of one-well energies with super-quadratic growth and later generalised to different settings, in particular to the case of multi-well energies where the distance between the wells is very small (comparable to the size of the load). In this paper we study the case when the distance between the wells is independent of the size of the load. In this context linear elasticity can be derived by adding to the multi-well energy a singular higher order term which penalises jumps from one well to another. The size of the singular term has to satisfy certain scaling assumptions whose optimality is shown in most of the cases. Finally, the derivation of linear elasticty from a two-well discrete model is provided, showing that the role of the singular perturbation term is played in this setting by interactions beyond nearest neighbours

ALBA FUCENS ARCHAEOLOGICAL SITE: MULTISCALE AND MULTIDISCIPLINARY APPROACH FOR RISK ASSESSMENT AND CONSERVATION

Abstract. The Latin Colony (303 BC) of Alba Fucens (L'Aquila, Italy) is the largest archaeological area of the whole Apennines. Due to its extension, location and environmental context, the conservation of the site is particularly complex.For these reasons, in the paper a multiscale and multidisciplinary geoarchaeological study (remote sensing and UAV photogrammetry) of the site, to extract and measure morphostructural information to be associated to the environmental context, risk assessment and conservation, is reported.The study area is located on a higher geostructure with a subangular shape, which suggests a tectonic origin, with respect to the surrounding plain and bounded to the East by a large fan that takes place towards the Piana del Fucino.First, the geo-structural analysis, using the Landsat-8 and GeoEye multispectral sensors, was performed. The GeoEye satellite image allowed carrying out the morphological analysis of the archaeological area, its physical characteristics, the drainage pattern and the land use. Subsequently, after image processing of satellite data, a UAV survey was carried out in some relevant zones. Considering the UAV photogrammetry accuracy information, it was possible to extract data as map producing with several advantages (economic and time saving, minimum field work). With a multiscale and metric approach, the geomatics techniques allowed to deeply investigate some areas, creating detailed 3D models for evaluate risks and the decay. Finally, a general discussion about risk mitigation and conservation is reported.</p

On the effect of interactions beyond nearest neighbours on non-convex lattice systems

We analyse the rigidity of non-convex discrete energies where at least nearest and next-to-nearest neighbour interactions are taken into account. Our purpose is to show that interactions beyond nearest neighbours have the role of penalising changes of orientation and, to some extent, they may replace the positive-determinant constraint that is usually required when only nearest neighbours are accounted for. In a discrete to continuum setting, we prove a compactness result for a family of surface-scaled energies and we give bounds on its possible Gamma-limit in terms of interfacial energies that penalise changes of orientation

Cost of cystic fibrosis: Analysis of treatment costs in a specialized center in Northern Italy

Introduction: Advances in cystic fibrosis (CF) therapy have resulted in improved survival and increasing treatment burden and costs. The economic impact of current treatment strategies for CF is poorly defined. Methods: The authors prospectively assessed direct medical costs (including hospitalizations, outpatient interventions, drugs, devices, dietetic products) in 165 consecutive CF patients (aged 5-39 years) seen between March and July 2009. Results: The mean annual cost/patient increased with age and lung disease severity from \u20ac4,164 in children aged 5 years to \u20ac30,123 in patients aged >5 years with severe lung disease (forced expiratory volume in 1 second [FEV1] <40% of predicted). The increase in costs involved all items, with a progressive increase in cost attributed to hospitalizations. Conclusion: Treatment of CF is associated with relevant cost for the Italian National Healthcare Service. Costs of illness tend to increase progressively with age, suggesting that increasing economic resources should be allocated to the treatment of CF, given the increasing number of patients surviving into adulthood. \ua9 The Author(s) 2013

Outcomes of Elderly Patients with ST-Elevation or Non-ST-Elevation Acute Coronary Syndrome Undergoing Percutaneous Coronary Intervention

Introduction: Acute coronary syndromes (ACS) have been classified according to the finding of ST-segment elevation on the presenting electrocardiogram, with different treatment strategies and practice guidelines. However, a comparative description of the clinical characteristics and outcomes of acute coronary syndrome elderly patients undergoing percutaneous coronary intervention during index admission has not been published so far. Methods: Retrospective cohort study of patients enrolled in the Elderly ACS-2 multicenter randomized trial. Main outcome measures were crude cumulative incidence and cause-specific hazard ratio (cHR) of cardiovascular death, noncardiovascular death, reinfarction, and stroke. Results: Of 1443 ACS patients aged >75 years (median age 80 years, interquartile range 77-84), 41% were classified as ST-elevation myocardial infarction (STEMI), and 59% had non-ST-elevation ACS (NSTEACS) (48% NSTEMI and 11% unstable angina). As compared with those with NSTEACS, STEMI patients had more favorable baseline risk factors, fewer prior cardiovascular events, and less severe coronary disease, but lower ejection fraction (45% vs 50%, P <.001). At a median follow-up of 12 months, 51 (8.6%) STEMI patients had died, vs 39 (4.6%) NSTEACS patients. After adjusting for sex, age, and previous myocardial infarction, the hazard among the STEMI group was significantly higher for cardiovascular death (cHR 1.85; 95% confidence interval [CI], 1.02-3.36), noncardiovascular death (cHR 2.10; 95% CI, 1.01-4.38), and stroke (cHR 4.8; 95% CI, 1.7-13.7). Conclusions: Despite more favorable baseline characteristics, elderly STEMI patients have worse survival and a higher risk of stroke compared with NSTEACS patients after percutaneous coronary intervention