Linear relaxation to planar Travelling Waves in Inertial Confinement Fusion

We study linear stability of planar travelling waves for a scalar reaction-diffusion equation with non-linear anisotropic diffusion. The mathematical model is derived from the full thermo-hydrodynamical model describing the process of Inertial Confinement Fusion. We show that solutions of the Cauchy problem with physically relevant initial data become planar exponentially fast with rate s(\eps',k)>0, where \eps'=\frac{T_{min}}{T_{max}}\ll 1 is a small temperature ratio and $k\gg 1$ the transversal wrinkling wavenumber of perturbations. We rigorously recover in some particular limit (\eps',k)\rightarrow (0,+\infty) a dispersion relation s(\eps',k)\sim \gamma_0 k^{\alpha} previously computed heuristically and numerically in some physical models of Inertial Confinement Fusion

A JKO splitting scheme for Kantorovich-Fisher-Rao gradient flows

In this article we set up a splitting variant of the JKO scheme in order to handle gradient flows with respect to the Kantorovich-Fisher-Rao metric, recently introduced and defined on the space of positive Radon measure with varying masses. We perform successively a time step for the quadratic Wasserstein/Monge-Kantorovich distance, and then for the Hellinger/Fisher-Rao distance. Exploiting some inf-convolution structure of the metric we show convergence of the whole process for the standard class of energy functionals under suitable compactness assumptions, and investigate in details the case of internal energies. The interest is double: On the one hand we prove existence of weak solutions for a certain class of reaction-advection-diffusion equations, and on the other hand this process is constructive and well adapted to available numerical solvers.Comment: Final version, to appear in SIAM SIM

Traveling Wave Solutions of Advection-Diffusion Equations with Nonlinear Diffusion

We study the existence of particular traveling wave solutions of a nonlinear parabolic degenerate diffusion equation with a shear flow. Under some assumptions we prove that such solutions exist at least for propagation speeds c {\in}]c*, +{\infty}, where c* > 0 is explicitly computed but may not be optimal. We also prove that a free boundary hy- persurface separates a region where u = 0 and a region where u > 0, and that this free boundary can be globally parametrized as a Lipschitz continuous graph under some additional non-degeneracy hypothesis; we investigate solutions which are, in the region u > 0, planar and linear at infinity in the propagation direction, with slope equal to the propagation speed.Comment: 40 pages, 1 figur

Des décharges à ciel ouvert aux agglomérations de débris plastique dans le milieu océanique : les déchets ménagers sont-ils devenus un problème environnemental

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Adrenal involvement in MEN1. Analysis of 715 cases from the Groupe d'etude des Tumeurs Endocrines database.

Objective Limited data regarding adrenal involvement in multiple endocrine neoplasia type 1 (MEN1) is available. We describe the characteristics of MEN1-associated adrenal lesions in a large cohort to provide a rationale for their management. Methods Analysis of records from 715 MEN1 patients from a multicentre database between 1956 and 2008. Adrenal lesions were compared with those from a multicentre cohort of 144 patients with adrenal sporadic incidentalomas. Results Adrenal enlargement was reported in 20.4% (146/715) of patients. Adrenal tumours (>10 mm in size) accounted for 58.1% of these cases (10.1% of the whole patient cohort). Tumours were bilateral and >40 mm in size in 12.5 and 19.4% of cases respectively. Hormonal hypersecretion was restricted to patients with tumours and occurred in 15.3% of them. Compared with incidentalomas, MEN1-related tumours exhibited more cases of primary hyperaldosteronism, fewer pheochromocytomas and more adrenocortical carcinomas (ACCs; 13.8 vs 1.3%). Ten ACCs occurred in eight patients. Interestingly, ACCs occurred after several years of follow-up of small adrenal tumours in two of the eight affected patients. Nine of the ten ACCs were classified as stage I or II according to the European Network for the Study of Adrenal Tumors. No evident genotype/phenotype correlation was found for the occurrence of adrenal lesions, endocrine hypersecretion or ACC. Conclusions Adrenal pathology in MEN1 differs from that observed in sporadic incidentalomas. In the absence of relevant symptoms, endocrine biology can be restricted to patients with adrenal tumours and should focus on steroid secretion including the aldosterone-renin system. MEN1 is a high-risk condition for the occurrence of ACCs. It should be considered regardless of the size of the tumour