Fracture and debonding of a thin film on a stiff substrate: analytical and numerical solutions of a one-dimensional variational model

We study multi-fissuration and debonding phenomena of a thin film bonded to a stiff substrate using the variational approach to fracture mechanics. We consider a reduced one-dimensional membrane model where the loading is introduced through uniform inelastic (e.g., thermal) strains in the film or imposed displacements of the substrate. Fracture phenomena are accounted for by adopting a Griffith model for debonding and transverse fracture. On the basis of energy minimization arguments, we recover the key qualitative properties of the experimental evidences, like the periodicity of transverse cracks and the peripheral debonding of each regular segment. Phase diagrams relate the maximum number of transverse cracks that may be created before debonding takes place, as a function of the material properties and the sample’s geometry. The theoretical results are illustrated with numerical simulations obtained through a finite element discretization and a regularized variational formulation of the Ambrosio–Tortorelli type, which is suited to further extensions in two-dimensional settings.     

Pigment Production by Filamentous Fungi on Agro-Industrial Byproducts: an Eco-Friendly Alternative

The search for new sources of natural pigments has increased, mainly because of the toxic effects caused by synthetic dyes used in food, pharmaceutical, textile, and cosmetic industries. Fungi provide a readily available alternative source of natural pigments. In this context, the fungi Penicillium chrysogenum IFL1 and IFL2, Fusarium graminearum IFL3, Monascus purpureus NRRL 1992, and Penicillium vasconiae IFL4 were selected as pigments producers. The fungal identification was performed using ITS and part of the β-tubulin gene sequencing. Almost all fungi were able to grow and produce water-soluble pigments on agro-industrial residues, with the exception of P. vasconiae that produced pigments only on potato dextrose broth. The production of yellow pigments was predominant and the two strains of P. chrysogenum were the largest producers. In addition, the production of pigments and mycotoxins were evaluated in potato dextrose agar using TOF-MS and TOF-MS/MS. Metabolites as roquefortine C, chrysogine were found in both extracts of P. chrysogenum, as well fusarenone X, diacetoxyscirpenol, and neosolaniol in F. graminearum extract. In the M. purpureus extract, the pigments monascorubrin, rubropunctatin, and the mycotoxin citrinin were found. The crude filtrates have potential to be used in the textile industry; nevertheless, additional pigment purification is required for food and pharmaceutical applications.     

A simple,efficient, regioselective and one-pot preparation of N-hydroxy- and N–O-protected hydroxyindoles via cycloaddition of nitrosoarenes with alkynes. Synthetic scope,applications and novel by-products

The thermal reaction between nitrosoarenes and alkynes under alkylating conditions produces N-alkoxyindoles as the major products in moderate to good yields and excellent regioselectivity. Various electrophiles are used affording different N–O-protected hydroxyindoles in a multi-component fashion. Privileged acetylenic substrates used in reactions with substituted nitrosoarenes are arylalkynes or propiolates. Potentially bioactive compounds and other classes of highly functionalizable indole products were prepared. Reactions between o-carbomethoxy-nitrosoarenes and arylacetylenes provided tricyclic compounds containing an acylaziridine indoline skeleton.     

Trajectory Planning in Robotics

Trajectory planning is a fundamental issue for robotic applications and automation in general. The ability to generate trajectories with given features is a key point to ensure significant results in terms of quality and ease of performing the required motion, especially at the high operating speeds necessary in many applications. The general problem of trajectory planning in Robotics is addressed in the paper, with an overview of the most significant methods, that have been proposed in the robotic literature to generate collision-free paths. The problem of finding an optimal trajectory for a given path is then discussed and some significant solutions are described.     

Computation of Smooth Manifolds Via Rigorous Multi-parameter Continuation in Infinite Dimensions

In this paper, we introduce a constructive rigorous numerical method to compute smooth manifolds implicitly defined by infinite-dimensional nonlinear operators. We compute a simplicial triangulation of the manifold using a multi-parameter continuation method on a finite-dimensional projection. The triangulation is then used to construct local charts and an atlas of the manifold in the infinite-dimensional domain of the operator. The idea behind the construction of the smooth charts is to use the radii polynomial approach to verify the hypotheses of the uniform contraction principle over a simplex. The construction of the manifold is globalized by proving smoothness along the edge of adjacent simplices. We apply the method to compute portions of a two-dimensional manifold of equilibria of the Cahn–Hilliard equation.