Asymptotic expansions for high-contrast elliptic equations

In this paper, we present a high-order expansion for elliptic equations in high-contrast media. The background conductivity is taken to be one and we assume the medium contains high (or low) conductivity inclusions. We derive an asymptotic expansion with respect to the contrast and provide a procedure to compute the terms in the expansion. The computation of the expansion does not depend on the contrast which is important for simulations. The latter allows avoiding increased mesh resolution around high conductivity features. This work is partly motivated by our earlier work in \cite{ge09_1} where we design efficient numerical procedures for solving high-contrast problems. These multiscale approaches require local solutions and our proposed high-order expansion can be used to approximate these local solutions inexpensively. In the case of a large-number of inclusions, the proposed analysis can help to design localization techniques for computing the terms in the expansion. In the paper, we present a rigorous analysis of the proposed high-order expansion and estimate the remainder of it. We consider both high and low conductivity inclusions

Randomized oversampling for generalized multiscale finite element methods

In this paper, we develop efficient multiscale methods for ows in heterogeneous media. We use the generalized multiscale finite element (GMsFEM) framework. GMsFEM approxi- mates the solution space locally using a few multiscale basis functions. This approximation selects an appropriate snapshot space and a local spectral decomposition, e.g., the use of oversampled regions, in order to achieve an efficient model reduction. However, the successful construction of snapshot spaces may be costly if too many local problems need to be solved in order to obtain these spaces. We use a moderate quantity of local solutions (or snapshot vectors) with random boundary conditions on oversampled regions with zero forcing to deliver an efficient methodology. Motivated by the random- ized algorithm presented in [P. G. Martinsson, V. Rokhlin, and M. Tygert, A Randomized Algorithm for the approximation of Matrices, YALEU/DCS/TR-1361, Yale University, 2006], we consider a snapshot space which consists of harmonic extensions of random boundary conditions defined in a domain larger than the target region. Furthermore, we perform an eigenvalue decomposition in this small space. We study the application of randomized sampling for GMsFEM in conjunction with adaptivity, where local multiscale spaces are adaptively enriched. Convergence analysis is provided. We present representative numerical results to validate the method proposed

Pulmonary Aspergillosis: A Review on Diagnosis and Management

Aspergillosis is acquired by inhalation of spores of Aspergillus, a ubiquitous species in the environment. In normal hosts, spore inhalation rarely causes lung disease. Pulmonary aspergillosis covers a wide spectrum of clinical syndromes depending on the interaction between Aspergillus and the host (immune-status, prior bronchopulmonary disease). It runs the gamut from invasive aspergillosis to Aspergillus bronchitis and colonization. Invasive aspergillosis occurs in severely immunocompromised patients, typically with neutropenia. Chronic pulmonary aspergillosis affects patients with chronic structural lung disease such as chronic obstructive pulmonary disease, mycobacterial lung disease, but without significant immunocompromise. Aspergillus bronchitis affects patients with bronchial disease such as bronchiectasis. Allergic bronchopulmonary aspergillosis affects patients with bronchial asthma or cystic fibrosis, and is due to an allergic response to Aspergillus. In this review of literature, we discuss the pulmonary manifestations of Aspergillus infection, its diagnosis and treatments

Anodic oxidation of titanium for implants and prothesis: processing characterization and potential improvement of osteointegration

Among all biomaterials used for bone replacement, it is recognized that both commercially pure titanium (Ti c.p.) and Ti6Al4V alloy are the materials that show the best in vivo performance due to their excellent balance between mechanical, physical-chemical and biofunctional properties. However, one of its main drawbacks, which compromise the service reliability of the implants and its osteointegration capacity, is the thin film of fibrous tissue around the implant due to the bioinert behaviour of titanium. One of the alternatives more studied to improve the titanium osteointegration is the surface modification through the control of the roughness parameters within a specific range which is recognized that improve the osteoblasts adhesion. In this work is investigated the influence of different electrochemical processing conditions for surface modification of c.p. Ti, in their microstructural, morphological, topographical and mechanical properties, as well as in their biological behaviour. The electrochemical anodizing treatment was performed by using different electrolytes based on phosphoric acid (H3PO4), sulphuric acid (H2SO4) with a fluoride salt; and the Focused Ion Beam (FIB) technique, normally named as Nanolab, was used for the microstructural, chemical and morphological characterization, as well as the confocal laser microscopy technique which also served for roughness measurements. The mechanical response of the anodic layers was evaluated through the using of a scratch tester which showed the critical loads for the coating damages. The characterization results showed that both, concentrations and electrolyte species, clearly influenced the morphological and topographical features, as well as the chemical composition of the anodic layer. By using the FIB was possible to detect nanopores within both the surface and the bulk of the coating. Some of the conditions generated a very special coating morphology which promoted a better osteoblasts adhesion. Contrary to what it was a priory expected, all anodic coatings showed high critical loads for damages during scratch test, despite their high porosity, which could be related with some defects coalescence mechanism that allows dissipating the high stress concentration applied during the test.Postprint (published version

A phylogenetic analysis of macroevolutionary patterns in fermentative yeasts

� 2016 The Authors. Ecology and Evolution published by John Wiley & Sons Ltd. When novel sources of ecological opportunity are available, physiological innovations can trigger adaptive radiations. This could be the case of yeasts (Saccharomycotina), in which an evolutionary novelty is represented by the capacity to exploit simple sugars from fruits (fermentation). During adaptive radiations, diversification and morphological evolution are predicted to slow-down after early bursts of diversification. Here, we performed the first comparative phylogenetic analysis in yeasts, testing the “early burst” prediction on species diversification and also on traits of putative ecological relevance (cell-size and fermentation versatility). We found that speciation rates are constant during the time-range we considered (ca., 150�millions of years). Phylogenetic signal of both traits was significant (but lower for cell-size), suggesting that lineages resemble each other in trait-values. Disparity analysis suggested accelerated evolution (diversification in trait values above Brownian Motion expectations) in cell-size. We also found a significant phylogenetic regression between cell-size and fermentation versatility (R 2 �=�0.10), which suggests correlated evolution between both traits. Overall, our results do not support the early burst prediction both in species and traits, but suggest a number of interesting evolutionary patterns, that warrant further exploration. For instance, we show that the Whole Genomic Duplication that affected a whole clade of yeasts, does not seems to have a statistically detectable phenotypic effect at our level of analysis. In this regard, further studies of fermentation under common-garden conditions combined with comparative analyses are warranted.Link_to_subscribed_fulltex

Inverse Problems in a Bayesian Setting

In a Bayesian setting, inverse problems and uncertainty quantification (UQ) --- the propagation of uncertainty through a computational (forward) model --- are strongly connected. In the form of conditional expectation the Bayesian update becomes computationally attractive. We give a detailed account of this approach via conditional approximation, various approximations, and the construction of filters. Together with a functional or spectral approach for the forward UQ there is no need for time-consuming and slowly convergent Monte Carlo sampling. The developed sampling-free non-linear Bayesian update in form of a filter is derived from the variational problem associated with conditional expectation. This formulation in general calls for further discretisation to make the computation possible, and we choose a polynomial approximation. After giving details on the actual computation in the framework of functional or spectral approximations, we demonstrate the workings of the algorithm on a number of examples of increasing complexity. At last, we compare the linear and nonlinear Bayesian update in form of a filter on some examples.Comment: arXiv admin note: substantial text overlap with arXiv:1312.504

Asymptotic expansions for high-contrast linear elasticity

We study linear elasticity problems with high contrast in the coefficients using asymptotic limits recently introduced. We derive an asymptotic expansion to solve heterogeneous elasticity problems in terms of the contrast in the coefficients. We study the convergence of the expansion in the H1 norm