Nonlinear Statistical Filtering and Applications to Segregation in Steels from Microprobe Images

Microprobe images of solidification studies are well known to be subject to a Poisson noise. That is, the radiation count at a pixel x for a certain element may be considered to be an observation of a Poisson random variable whose parameter is equal to the true chemical concentration of the element at x. By modeling the image as a random function, we are able to use geostatistical techniques to perform various filtering operations. This filtering of the image itself may be done using linear kriging. For explicitely nonlinear problems such as the estimation of the underlying histogram of the noisy image, or the estimation of the probability that locally the concentration passes a certain value (this probability is needed for segregation studies), it is usually not possible to use linear techniques as they give biased results. For this reason, we applied the nonlinear technique of Disjunctive Kriging to these nonlinear problems. Linear kriging needs only second order statistical models ( covariance functions or variograms) while disjunctive kriging needs bivariate distribution models. This approach 1s illustrated by examples of filtering of various X-ray mappings in steel samples

Multi-Scale Statistical Approach of the Elastic and Thermal Behavior of a Thermoplastic Polyamid-Glass Fiber Composite

The strong heterogeneity and the anisotropy of composite materials require a rigorous and precise analysis as a result of their impact on local properties. First, mechanical tests are performed to determine the macroscopical behavior of a polyamid glass  fiber composite. Then we focus on the influence of the heterogeneities of the microstructure on thermal and mechanical properties from finite element calculations on the real microstructure, after plane strain assumptions. 100 images in 10 different sizes (50, 100, 150, 200, 250, 300, 350, 400, 450, 600 pixels) are analysed. The influence of the area fraction and the spatial arrangement of fibers is then established. For the thermal conductivity and the bulk modulus the fiber area fraction is the most important factor. These properties are improved by increasing the area fraction. On the other hand, for the shear modulus, the fibers spatial arrangement plays the paramount role if the size of the microstructure is smaller than the RVE. Therefore, to make a good prediction from a multi-scale approach the knowledge of the RVE is fundamental. By a statistical approach and a numerical homogenization method, we determine the RVE of the composite for the elastic behavior (shear and bulk moduli), the thermal behavior (thermal conductivity), and for the area fraction. There is a relatively good agreement between the effective properties of this RVE and the experimental macroscopical behavior. These effective properties are estimated by the Hashin-Shtrikman lower bound

Modelling the Microstructure and the Viscoelastic Behaviour of Carbon Black Filled Rubber Materials from 3D Simulations

Volume fraction and spatial repartition of fillers impact the physical properties of rubber. Extended percolating networks of nano-sized fillers significantly modify the macroscopic mechanical properties of rubbers. Random models that describe the multiscale microstructure of rubber and efficient Fourier-based numerical algorithms are combined to predict the material’s mechanical properties. From TEM image analysis, various types of multiscale models were proposed and validated, accounting for the non-homogeneous distribution of fillers: in the present work, aggregates are located outside of an exclusion polymer simulated by two families of random models. The first model generates the exclusion polymer by a Boolean model of spheres. In the second model, the exclusion polymer is a mosaic model built from a Johnson-Mehl tessellation. Here the exclusion polymer and the polymer containing the filler show a similar morphology, contrary to the Boolean model. Aggregates are then described as the intersection of a Boolean model of spheres and of the complementary of the exclusion polymer. Carbon black particles are simulated by a Cox model of spheres in the aggregates. The models rely on a limited number of parameters fitted from experimental covariance and cumulative granulometry. The influence of the model parameters on percolation properties of the models is studied numerically from 3D simulations. Finally, a novel Fourier-based algorithm is proposed to estimate the viscoelastic properties of linear heterogeneous media, in the harmonic regime. The method is compared to analytical results and to a different, time-discretized FFT scheme. As shown in this work, the proposed numerical method is efficient for computing the viscoelastic response of microstructures containing rubbers and fillers

Influence de la morphologie tridimensionnelle sur le comportement mécanique de réfractaires électrofondus

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Material-independent crack arrest statistics: Application to indentation experiments

An extensive experimental study of indentation and crack arrest statistics is presented for four different brittle materials (alumina, silicon carbide, silicon nitride, glass). Evidence is given that the crack length statistics can be described by a universal (i.e. material independent) distribution. The latter directly derives from results obtained when modeling crack propagation as a depinning phenomenon. Crack arrest (or effective toughness) statistics appears to be fully characterized by two parameters, namely, an asymptotic crack length (or macroscopic toughness) value and a power law size dependent width. The experimental knowledge of the crack arrest statistics at one given scale thus gives access to its knowledge at all scales

Modélisation de la nanostructure d'un élastomère chargé

Les matériaux élastomères chargés présentent une microstructure hétérogène que l'on cherche à modéliser et à simuler afin de mieux comprendre leur comportement mécanique macroscopique. Leur comportement macroscopique dépend fortement de la microstucture et plus particulièrement de la fraction volumique et de l'agencement des phases. L'idée est, à partir d'observations de la microstructure (MET), de définir un modèle et de mettre en place une méthode d'identification de ses paramètres

Effective toughness of heterogeneous brittle materials

A heterogeneous brittle material characterized by a random field of local toughness Kc(x) can be represented by an equivalent homogeneous medium of toughness, Keff. Homogenization refers to a process of estimating Keff from the local field Kc(x). An approach based on a perturbative expansion of the stress intensity factor along a rough crack front shows the occurrence of different regimes depending on the correlation length of the local toughness field in the direction of crack propagation. A `"weak pinning" regime takes place for long correlation lengths, where the effective toughness is the average of the local toughness. For shorter correlation lengths, a transition to "strong pinning" occurs leading to a much higher effective toughness, and characterized by a propagation regime consisting in jumps between pinning configurations

On arbitrages arising from honest times

In the context of a general continuous financial market model, we study whether the additional information associated with an honest time gives rise to arbitrage profits. By relying on the theory of progressive enlargement of filtrations, we explicitly show that no kind of arbitrage profit can ever be realised strictly before an honest time, while classical arbitrage opportunities can be realised exactly at an honest time as well as after an honest time. Moreover, stronger arbitrages of the first kind can only be obtained by trading as soon as an honest time occurs. We carefully study the behavior of local martingale deflators and consider no-arbitrage-type conditions weaker than NFLVR.Comment: 25 pages, revised versio

Cross-resistance to elvitegravir and dolutegravir in 502 patients failing on raltegravir: a French national study of raltegravir-experienced HIV-1-infected patients

OBJECTIVES: The objectives of this study were to determine the prevalence and patterns of resistance to integrase strand transfer inhibitors (INSTIs) in patients experiencing virological failure on raltegravir-based ART and the impact on susceptibility to INSTIs (raltegravir, elvitegravir and dolutegravir). PATIENTS AND METHODS: Data were collected from 502 treatment-experienced patients failing a raltegravir-containing regimen in a multicentre study. Reverse transcriptase, protease and integrase were sequenced at failure for each patient. INSTI resistance-associated mutations investigated were those included in the last ANRS genotypic algorithm (v23). RESULTS: Among the 502 patients, at failure, median baseline HIV-1 RNA (viral load) was 2.9 log10 copies/mL. Patients had been previously exposed to a median of five NRTIs, one NNRTI and three PIs. Seventy-one percent harboured HIV-1 subtype B and the most frequent non-B subtype was CRF02_AG (13.3%). The most frequent mutations observed were N155H/S (19.1%), Q148G/H/K/R (15.4%) and Y143C/G/H/R/S (6.7%). At failure, viruses were considered as fully susceptible to all INSTIs in 61.0% of cases, whilst 38.6% were considered as resistant to raltegravir, 34.9% to elvitegravir and 13.9% to dolutegravir. In the case of resistance to raltegravir, viruses were considered as susceptible to elvitegravir in 11% and to dolutegravir in 64% of cases. High HIV-1 viral load at failure (P < 0.001) and low genotypic sensitivity score of the associated treatment with raltegravir (P < 0.001) were associated with the presence of raltegravir-associated mutations at failure. Q148 mutations were selected more frequently in B subtypes versus non-B subtypes (P = 0.004). CONCLUSIONS: This study shows that a high proportion of viruses remain susceptible to dolutegravir in the case of failure on a raltegravir-containing regimen