An optimal mass transport approach for limits of eigenvalue problems for the fractional pp-Laplacian

We find interpretation using optimal mass transport theory for eigenvalue problems obtained as limits of the eigenvalue problems for the fractional $p-$Laplacian operators as $p\to +\infty$. We deal both with Dirichlet and Neumann boundary conditions.Comment: 20 page

Estimates for the Sobolev trace constant with critical exponent and applications

In this paper we find estimates for the optimal constant in the critical Sobolev trace inequality S\|u\|^p_{L^{p_*}(\partial\Omega) \hookrightarrow \|u\|^p_{W^{1,p}(\Omega)} that are independent of $\Omega$. This estimates generalized those of [3] for general $p$. Here $p_* := p(N-1)/(N-p)$ is the critical exponent for the immersion and $N$ is the space dimension. Then we apply our results first to prove existence of positive solutions to a nonlinear elliptic problem with a nonlinear boundary condition with critical growth on the boundary, generalizing the results of [16]. Finally, we study an optimal design problem with critical exponent.Comment: 22 pages, submitte

Investigation of damage evolution in short glass fibers reinforced polyamide 6,6 under tensile loading using infrared thermography

AbstractMechanical properties of polymers are very sensitive to environmental conditions in particular temperature. In the case of mechanical testing, thermomechanical coupling induce heat sources to be activated during the deformation and damage processes so that the temperature of the specimen may vary during testing. Depending on the characteristic temporal and spacial scales of the deformation and damage processes involved by the loading this temperature increase might be uniform or highly localized. The aim of the study is to investigate the temperature field evolution of glass fibers reinforced polyamide 6,6 with 0% (PA66GF00), 10% (PA66GF10), 20% (PA66GF20) and 30% (PA66GF30) glass fiber. In addition to infrared thermography, digital image correlation (DIC) was used to quantify deformation localization zones and correlate them to identified heat dissipation sources. Until necking, the heat distribution was found to be nearly homogeneous on PA66GF00 with a well marked thermoelastic region, succeeded by an homogeneous heat increase due to viscoplastic dissipation. Necking is associated to strong heat increase that is localized on the the necking area. The thermal response of short fiber reinforced materials was found to differ markedly from the uncharged one. Strong heterogeneity of the thermal was observed and was associated to localisation processes at different scales (investigated by DIC). The effect of the applied strain rate on the observed thermal heterogenities was investigated. In addition to DIC, the volume damage evolution was monitored using X-ray computed microtomography in particular region

Estrogen regulation of apoptosis: how can one hormone stimulate and inhibit?

The link between estrogen and the development and proliferation of breast cancer is well documented. Estrogen stimulates growth and inhibits apoptosis through estrogen receptor-mediated mechanisms in many cell types. Interestingly, there is strong evidence that estrogen induces apoptosis in breast cancer and other cell types. Forty years ago, before the development of tamoxifen, high-dose estrogen was used to induce tumor regression of hormone-dependent breast cancer in post-menopausal women. While the mechanisms by which estrogen induces apoptosis were not completely known, recent evidence from our laboratory and others demonstrates the involvement of the extrinsic (Fas/FasL) and the intrinsic (mitochondria) pathways in this process. We discuss the different apoptotic signaling pathways involved in E2 (17β-estradiol)-induced apoptosis, including the intrinsic and extrinsic apoptosis pathways, the NF-κB (nuclear factor-kappa-B)-mediated survival pathway as well as the PI3K (phosphoinositide 3-kinase)/Akt signaling pathway. Breast cancer cells can also be sensitized to estrogen-induced apoptosis through suppression of glutathione by BSO (L-buthionine sulfoximine). This finding has implications for the control of breast cancer with low-dose estrogen and other targeted therapeutic drugs

A general stochastic target problem with jump diffusion and an application to a hedging problem for large investors

Let Zv t, z be a ℝd-valued jump diffusion controlled by v with initial condition Zv t, z(t) = z. The aim of this paper is to characterize the set V (t) of initial conditions z such that Zv t, z can be driven into a given target at a given time by proving that the function u(, z) = 1 − 1V(t) satisfies, in the viscosity sense, the equation (2) below. As an application, we study the problem of hedging in a financial market with a large investor. © 2007 Applied Probability Trust

Asymptotics of best Sobolev constants on thin manifolds

We study the asymptotic behaviour of best Sobolev constants on a compact manifold with boundary that we contract in k directions or to a point. We find in the limit best Sobolev constants for weighted Sobolev spaces of the limit manifold. © 2008 Elsevier Inc. All rights reserved

Nocivité des défauts sous revêtement et vieillissement dans les cuves de réacteur à eau sous pression

Les viroles des cuves du circuit primaire des réacteurs nucléaires à eau sous pression sont forgées, creusées, bigornées et étirées à partir de lingots en acier 16MND5 de plusieurs dizaines de tonnes. De ce fait, il est difficile de s'affranchir du problème des veines sombres qui sont plus riches en carbone et impuretés que la matrice. Ces veines sombres sont des zones plus dures et plus fragiles qui peuvent modifier les conditions d'amorçage d'une fissure. La protection contre la corrosion de ces viroles nécessite le soudage de deux épaisseurs de feuillard d'acier inoxydable austénitique sur toute la surface interne. Après fabrication des cuves, l'opération de détensionnement peut favoriser la formation de Décohésions Intergranulaires Dues au Réchauffage (DIDR) dans la zone à gros grains proche de la ligne de fusion. La nocivité de ces deux types de défauts doit être évaluée et pour garantir la sécurité des cuves sur la durée, l'étude de l'influence du vieillissement sur les conditions de fissuration s'avère essentielle. Un traitement thermique de fragilisation par refroidissement étagé a été appliqué en laboratoire pour exacerber les ségrégations d'impuretés qui abaissent les valeurs de ténacité du matériau. Un modèle statistique de type Beremin généralisé à quatre paramètres prend correctement en compte la bimodalité des ruptures observées. La probabilité de rupture associée au mode le plus fragile est quasi nulle pour les éprouvettes de ténacité

Ni Based Powder Reconditioning and Reuse for LMD Process

AbstractLMD is an additive manufacturing process based on the injection of metallic powder into a melt-pool created by a heat laser source on a substrate. One of the benefits of this technology is the reduction of the wasted material since it is a near-shape process. Moreover one of the main drawbacks is the relatively low efficiency of the trapped powder, which can be loss than 5% in some cases. The non-trapped powder represents a significant cost in the LMD process, since powder metal material is very expensive and usually is not reused.This article proposes a methodology of the reconditioning and posterior reuse of a nickel base powder commonly used in the aerospace industry, with the main objectives of cost saving, higher environmental cleanup and increase of the overall efficiency in the LMD process. The results are checked by the development of a prototype part built up from reused powder