Branching Structures in Elastic Shape Optimization

Fine scale elastic structures are widespread in nature, for instances in plants or bones, whenever stiffness and low weight are required. These patterns frequently refine towards a Dirichlet boundary to ensure an effective load transfer. The paper discusses the optimization of such supporting structures in a specific class of domain patterns in 2D, which composes of periodic and branching period transitions on subdomain facets. These investigations can be considered as a case study to display examples of optimal branching domain patterns. In explicit, a rectangular domain is decomposed into rectangular subdomains, which share facets with neighbouring subdomains or with facets which split on one side into equally sized facets of two different subdomains. On each subdomain one considers an elastic material phase with stiff elasticity coefficients and an approximate void phase with orders of magnitude softer material. For given load on the outer domain boundary, which is distributed on a prescribed fine scale pattern representing the contact area of the shape, the interior elastic phase is optimized with respect to the compliance cost. The elastic stress is supposed to be continuous on the domain and a stress based finite volume discretization is used for the optimization. If in one direction equally sized subdomains with equal adjacent subdomain topology line up, these subdomains are consider as equal copies including the enforced boundary conditions for the stress and form a locally periodic substructure. An alternating descent algorithm is employed for a discrete characteristic function describing the stiff elastic subset on the subdomains and the solution of the elastic state equation. Numerical experiments are shown for compression and shear load on the boundary of a quadratic domain.Comment: 13 pages, 6 figure

Singular kernels, multiscale decomposition of microstructure, and dislocation models

We consider a model for dislocations in crystals introduced by Koslowski, Cuiti\~no and Ortiz, which includes elastic interactions via a singular kernel behaving as the $H^{1/2}$ norm of the slip. We obtain a sharp-interface limit of the model within the framework of $\Gamma$-convergence. From an analytical point of view, our functional is a vector-valued generalization of the one studied by Alberti, Bouchitt\'e and Seppecher to which their rearrangement argument no longer applies. Instead we show that the microstructure must be approximately one-dimensional on most length scales and exploit this property to derive a sharp lower bound

Frontal brain asymmetries as effective parameters to assess the quality of audiovisual stimuli perception in adult and young cochlear implant users

How is music perceived by cochlear implant (CI) users? This question arises as "the next step" given the impressive performance obtained by these patients in language perception. Furthermore, how can music perception be evaluated beyond self-report rating, in order to obtain measurable data? To address this question, estimation of the frontal electroencephalographic (EEG) alpha activity imbalance, acquired through a 19-channel EEG cap, appears to be a suitable instrument to measure the approach/withdrawal (AW index) reaction to external stimuli. Specifically, a greater value of AW indicates an increased propensity to stimulus approach, and vice versa a lower one a tendency to withdraw from the stimulus. Additionally, due to prelingually and postlingually deafened pathology acquisition, children and adults, respectively, would probably differ in music perception. The aim of the present study was to investigate children and adult CI users, in unilateral (UCI) and bilateral (BCI) implantation conditions, during three experimental situations of music exposure (normal, distorted and mute). Additionally, a study of functional connectivity patterns within cerebral networks was performed to investigate functioning patterns in different experimental populations. As a general result, congruency among patterns between BCI patients and control (CTRL) subjects was seen, characterised by lowest values for the distorted condition (vs. normal and mute conditions) in the AW index and in the connectivity analysis. Additionally, the normal and distorted conditions were significantly different in CI and CTRL adults, and in CTRL children, but not in CI children. These results suggest a higher capacity of discrimination and approach motivation towards normal music in CTRL and BCI subjects, but not for UCI patients. Therefore, for perception of music CTRL and BCI participants appear more similar than UCI subjects, as estimated by measurable and not self-reported parameters

A study of methyl formate in astrochemical environments

Several complex organic molecules are routinely detected in high abundances towards hot cores and hot corinos. For many of them, their paths of formation in space are uncertain, as gas phase reactions alone seem to be insufficient. In this paper, we investigate a possible solid-phase route of formation for methyl formate (HCOOCH3). We use a chemical model updated with recent results from an experiment where simulated grain surfaces were irradiated with 200 keV protons at 16 K, to simulate the effects of cosmic ray irradiation on grain surfaces. We find that this model may be sufficient to reproduce the observed methyl formate in dark clouds, but not that found in hot cores and corinos.Comment: 6 pages, 2 figures, 2 tables Accepted by MNRA

Tightness for a stochastic Allen--Cahn equation

We study an Allen-Cahn equation perturbed by a multiplicative stochastic noise which is white in time and correlated in space. Formally this equation approximates a stochastically forced mean curvature flow. We derive uniform energy bounds and prove tightness of of solutions in the sharp interface limit, and show convergence to phase-indicator functions.Comment: 27 pages, final Version to appear in "Stochastic Partial Differential Equations: Analysis and Computations". In Version 4, Proposition 6.3 is new. It replaces and simplifies the old propositions 6.4-6.

Motion of a droplet for the Stochastic mass conserving Allen-Cahn equation

We study the stochastic mass-conserving Allen-Cahn equation posed on a smoothly bounded domain of R2 with additive, spatially smooth, space-time noise. This equation describes the stochastic motion of a small almost semicircular droplet attached to domain's boundary and moving towards a point of locally maximum curvature. We apply It^o calculus to derive the stochastic dynamics of the center of the droplet by utilizing the approximately invariant manifold introduced by Alikakos, Chen and Fusco [2] for the deterministic problem. In the stochastic case depending on the scaling, the motion is driven by the change in the curvature of the boundary and the stochastic forcing. Moreover, under the assumption of a su ciently small noise strength, we establish stochastic stability of a neighborhood of the manifold of boundary droplet states in the L2- and H1-norms, which means that with overwhelming probability the solution stays close to the manifold for very long time-scales

Therapeutic sequences in patients with grade 1−2 neuroendocrine tumors (NET): an observational multicenter study from the ELIOS group

Purpose: Many different treatments are suggested by guidelines to treat grade 1−2 (G1−G2) neuroendocrine tumors (NET). However, a precise therapeutic algorithm has not yet been established. This study aims at identifying and comparing the main therapeutic sequences in G1−G2 NET. Methods: A retrospective observational Italian multicenter study was designed to collect data on therapeutic sequences in NET. Median progression-free survival (PFS) was compared between therapeutic sequences, as well as the number and grade of side effects and the rate of dose reduction/treatment discontinuation. Results: Among 1182 patients with neuroendocrine neoplasia included in the ELIOS database, 131 G1–G2 gastroenteropancreatic, lung and unknown primary NET, unresectable or persistent/relapsing after surgery, treated with ≥2 systemic treatments, were included. Four main therapeutic sequences were identified in 99 patients: (A) somatostatin analogs (SSA) standard dose to SSA high dose (n = 36), (B) SSA to everolimus (n = 31), (C) SSA to chemotherapy (n = 17), (D) SSA to peptide receptor radionuclide therapy (PRRT) (n = 15). Median PFS of the second-line treatment was not reached in sequence A, 33 months in sequence B, 20 months in sequence C, 30 months in sequence D (p = 0.16). Both total number and severity of side effects were significantly higher in sequences B and C than A and D (p = 0.04), as well as the rate of dose reduction/discontinuation (p = 0.03). Conclusions: SSA followed by SSA high dose, everolimus, chemotherapy or PRRT represent the main therapeutic sequences in G1−G2 NET. Median PFS was not significantly different between sequences. However, the sequences with SSA high dose or PRRT seem to be better tolerated than sequences with everolimus or chemotherapy

The Mediterranean island states : Malta and Cyprus

The 2004 European Union enlargement also included the Mediterranean island-states of Cyprus and Malta, two former British colonies and members of the British Commonwealth. The islands share a number of similarities but they are also dissimilar in uniquely distinct ways. The membership applications of both states initially presented the EU with a number of political difficulties. With respect to Cyprus, many member states would have preferred to see the island join the Union after the ‘Cyprus Problem’ had been settled. As for Malta, the island showed a very high degree of Euroskepticism. It froze its application in 1996 but reactivated it in 1998. Apart from this skepticism the island’s neutral status, enshrined in the Constitution could present insurmountable problems.peer-reviewe

Reverse Electrodialysis with saline waters and concentrated brines: a laboratory investigation towards technology scale-up

The use of concentrated brines and brackish water as feed solutions in reverse electrodialysis represents a valuable alternative to the use of river/sea water, allowing the enhancement of power output through the increase of driving force and reduction of internal stack resistance. Apart from a number of theoretical works, very few experimental investigations have been performed so far to explore this possibility. In the present work, two RED units of different size were tested using artificial saline solutions. The effects of feed concentration, temperature and flowrate on process performance parameters were analysed, adopting two different sets of membranes. These experiments allowed to identify the most favourable conditions for maximising the power output within the presently investigated range, i.e. 0.1 M NaCl as diluate and 5 M NaCl as concentrate at 40°C. Under these conditions a power density equal to 12 W/m2cell_pair was reached, among the highest so far reported in the literature. Increasing the unit size a slight reduction in power density was observed. These results indicate new directions for a successful scale-up and development of the Reverse Eletrodialysis technology

Factors influencing hindgut fermentation characteristics of the leopard tortoise (Stigmochelys pardalis): Survey of the microbiome

Novel fecal microbiome identification of mature female leopard tortoises (Stigmochelys pardalis, n = 16) fed exclusively one of three, nutritionally complete, pelleted diets was evaluated in a blind, complete randomized design study. Two diets included insoluble fiber (powdered cellulose) consisting of either 2.0 mm or 0.2 mm length. There were no differences in diversity indices (J’ and H’) of total OTUs by diet, with and without unidentified sequences. Analysis of phyla similarity by diet revealed three distinct groups with \u3e 92% similarity. Analysis of genera similarity revealed two distinct groups with \u3e 80% similarity. At both phyla and genera levels, fecal microbiomes were more similar between tortoises fed the cellulose-added diets versus the control diet, suggesting that the hindgut microbial communities adjusted in the hindgut of tortoises fed the cellulose-added diets by shifting proportions of microbes, based on their role in the hindgut (i.e., cellulose digestion), to accommodate for the addition of cellulose in the two treatment diets. This suggests that adaptability of the hindgut microbial communities should be considered when choosing dietary fiber lengths for hindgut-fermenting vertebrates