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

Derivation of a rod theory for biphase materials with dislocations at the interface

Starting from three-dimensional elasticity we derive a rod theory for biphase materials with a prescribed dislocation at the interface. The stored energy density is assumed to be non-negative and to vanish on a set consisting of two copies of SO(3). First, we rigorously justify the assumption of dislocations at the interface. Then, we consider the typical scaling of multiphase materials and we perform an asymptotic study of the rescaled energy, as the diameter of the rod goes to zero, in the framework of $\Gamma$-convergence

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

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

Enzyme variability and neonatal jaundice. The role of adenosine deaminase and acid phosphatase

Peer Reviewe

Local invertibility in Sobolev spaces with applications to nematic elastomers and magnetoelasticity

We define a class of deformations in W^1,p(\u3a9,R^n), p>n 121, with positive Jacobian that do not exhibit cavitation. We characterize that class in terms of the non-negativity of the topological degree and the equality between the distributional determinant and the pointwise determinant of the gradient. Maps in this class are shown to satisfy a property of weak monotonicity, and, as a consequence, they enjoy an extra degree of regularity. We also prove that these deformations are locally invertible; moreover, the neighbourhood of invertibility is stable along a weak convergent sequence in W^1,p, and the sequence of local inverses converges to the local inverse. We use those features to show weak lower semicontinuity of functionals defined in the deformed configuration and functionals involving composition of maps. We apply those results to prove existence of minimizers in some models for nematic elastomers and magnetoelasticity

Enzyme variability and neonatal jaundice. The role of adenosine deaminase and acid phosphatase

A sample of children treated by phototherapy during the neonatal period has been studied in the population of Penne (South Eastern Italy) in order to confirm the association previously reported in newborns from the population of Rome between neonatal jaundice and phenotypes of adenosine deaminase (ADA) and acid phosphatase (ACP1). The present data confirm that the incidence of clinically relevant jaundice is much greater in newborns of phenotype ACP1 BA carrying ADA2 allele than in other infants. Since ACP1 probably acts as flavin mononucleotide phosphatase and is modulated by purine nucleotides, it is likely that enzymes of purine nucleotide metabolism (including ADA), ACP1 and flavoenzymes (including gluthatione reductase and enzymes of Krebs cycle), may represent a polygenic complex influencing bilirubin levels in the first few days of life

Nutritional interventions targeting gut microbiota during cancer therapies

The gut microbiome is increasingly being recognized for its influence on intestinal and extra-intestinal disorders such as cancer. Today, diet is the most studied environmental modulator of gut microbiota, capable of altering or improving it in terms of richness and diversity. Recent evidence from several preclinical and clinical trials suggested that gut microbiota composition could modulate cancer therapies (toxicities, treatment responses) and vice versa. This review highlights the latest research on the bidirectional associations between gut microbiota and cancer. We also dissect the role of gut microbiota during cancer therapies in terms of toxicity and treatment response and, in turn, how cancer therapies could impact gut microbiota composition and functions. In this context, we summarize the state-of-the-art research regarding the role of various nutritional interventions—prebiotics, dietary strategies, and dietary restrictions—as cutting-edge possibilities to modulate gut microbiota during cancer therapies