Deployment and surface accuracy of regularly creased membranes

Creases are highly localized regions ubiquitous across different length scales in low-dimensional natural and engineering systems. Their presence strongly influences the mechanical response and surface accuracy of creased membrane materials and structures. In this paper, we study the deployment of folded sheets composed of an arbitrary number of non-interacting and parallel creases. We develop a mathematical formulation that describes the nonlinear mechanics of systematically creased membranes composed of a single or multiple folds, and predicts their surface accuracy during unfolding. The proposed solution shows the contribution of membrane bending and crease energies during deployment, and reveals the presence of two dimensionless parameters that govern the unfolding behaviour. Sensitivity analyses are also performed to assess the influence of the crease geometry and constitutive behaviour. The analytical predictions are validated through finite element analyses and deployment tests performed on thin films with one, two and three fold lines, where imaging techniques are employed to quantify deformation. The excellent agreement between theoretical and experimental results testifies that the developed formulation represents a precise tool to assess the tensioning of creased membranes, with applications ranging from origami metamaterials to lightweight space structures where precise shape control is paramount

Experimental investigation of the elastoplastic response of aluminum silicate spray dried powder during cold compaction

Mechanical experiments have been designed and performed to investigate the elasto-plastic behaviour of green bodies formed from an aluminum silicate spray dried powder used for tiles production. Experiments have been executed on samples obtained from cold compaction into a cylindrical mould and include: uniaxial strain, equi-biaxial flexure and high-pressure triaxial compression/extension tests. Two types of powders have been used to realize the green body samples, differing in the values of water content, which have been taken equal to those usually employed in the industrial forming of traditional ceramics. Yielding of the green body during compaction has been characterized in terms of yield surface shape, failure envelope, and evolution of cohesion and void ratio with the forming pressure, confirming the validity of previously proposed constitutive models for dense materials obtained through cold compaction of granulates.Comment: 17 pages; Journal of the European Ceramic Society, 201

The relationship between Mathematical Utility Theory and the Integrability Problem: some arguments in favour

The resort to utility-theoretical issues will permit us to propose a constructive procedure for deriving a homogeneous of degree one, continuous function that gives raise to a primitive demand function under suitably mild conditions. This constitutes the first elementary proof of a necessary and sufficient condition for an integrability problem to have a solution by continuous (subjective utility) functions. Such achievement reinforces the relevance of a technique that was succesfully formalized in Alcantud and Rodríguez-Palmero (2001). The analysis of these two works exposes deep relationships between two apparently separate fields: mathematical utility theory and the revealed preference approach to the integrability problem.Strong Axiom of Homothetic Revelation; revealed preference; continuous homogeneous of degree one utility; integrability of demand.

Reconstruction and stability in Gel'fand's inverse interior spectral problem

Assume that $M$ is a compact Riemannian manifold of bounded geometry given by restrictions on its diameter, Ricci curvature and injectivity radius. Assume we are given, with some error, the first eigenvalues of the Laplacian $\Delta$ on $M$ as well as the corresponding eigenfunctions restricted on an open set in $M$. We then construct a stable approximation to the manifold $(M,g)$. Namely, we construct a metric space and a Riemannian manifold which differ, in a proper sense, just a little from $M$ when the above data are given with a small error. We give an explicit logarithmic stability estimate on how the constructed manifold and the metric on it depend on the errors in the given data. Moreover a similar stability estimate is derived for the Gel'fand's inverse problem. The proof is based on methods from geometric convergence, a quantitative stability estimate for the unique continuation and a new version of the geometric Boundary Control metho

Dietary Nitrate: Effects on the health of weaning pigs and Antimicrobial activity on seven probiotic Bifidobacterium spp. strains

The potential role of nitrite as an antimicrobial substance in the stomach may be of some importance in the ecology of the gastrointestinal tract and in host physiology. It has been shown that nitrite, under the acidic conditions of the stomach, may kill gut pathogens like Salmonella enteritidis, Escherichia coli, Salmonella typhimurium, and Yersinia enterocolitica, whereas acid alone has only a bacteriostatic effect. An in vivo study was conducted in order to assess the effects of dietary nitrate on microbiota and on the health of the gut (particularly in the stomach and small intestine). 96 weaning pigs were fed a diet containing high nitrate levels (15 mg and 150 mg) and then challenged with Salmonella enterica serovar typhimurium. Differences in composition of the gut microbiota were assessed by analysing samples from the pigs: To date analysis of 48 pigs has been completed.. Preliminary results demonstrated no effect on the population densities of microbial groups either from the challenge or from nitrate intake. However, increasing the time from challenge decreased either the counts of LAB in the stomach and jejunum or of clostridia in the stomach. Bifidobacteria also decreased in the stomach contents as nitrate supplementation increased. Supplementing the feedstuff with high dietary nitrate intake and then challenging with Salmonella did not affect the gastric pH or the degree of ulceration in the pigs. The synergistic bactericidal effects of pH, nitrite and thiocyanate on seven probiotic Bifidobacterium spp. strains were also investigated in an in vitro study. The results of the in vitro study demonstrated that an inhibitory effect exists on the seven probiotic bifidobacteria investigated with an exposure longer than 2 hours and pH values < 5.0. Addition of thiocyanate also increased the susceptibility of the tested strains. In this in vitro study, the most resistant strains at all conditions were B. animalis subsp. lactis Ra 18 and P32 and B. choerinum Su 877, Su 837 and Su 891