Convergence to the Reynolds approximation with a double effect of roughness

We prove that the lubrication approximation is perturbed by a non-regular roughness of the boundary. We show how the flow may be accelerated using adequate rugosity profiles on the bottom. We explicit the possible effects of some abrupt changes in the profile. The limit system is mathematically justified through a variant of the notion of two-scale convergence. Finally, we present some numerical results, illustrating the limit system in the three-dimensional case

Existence, uniqueness and asymptotic analysis of optimal control problems for a model of groundwater pollution

International audienceOn considère un problème de contrôle optimal de contamination des eaux souterraines. L'objectiféconomique prend en compte le nécessaire compromis entre l'utilisation du polluant-par exemple de l'engrais-et les coûts de dépollution. Il est soumisà la contrainte d'un modèle hy-drogéologique pour la propagation de la pollution dans l'aquifère. On considère une large gamme de réactions cinétiques. L'objectif de cet article est double. D'une part, nous construisons rigoureusement, par analyse asymptotique, le problème de contrôle optimal e↵ectif pour des contaminants présents en faible concentration dans l'aquifère. D'autre part, nous analysons le problème de contrôle optimal et nous montrons en particulier que le problème e↵ectif est bien posé. De plus, nous démontrons une pro-priété de stabilité du processus de contrôle optimal : toute solution optimale du problème adimensionné converge vers la solution optimale du problème e↵ectif lorsque l'ordre de grandeur de la concentration du polluant décroît.An optimal control problem of contaminated underground water is considered. The spatio-temporal objective takes into account the economic trade o↵ between the pollutant use-for instance fertilizer-and the cleaning costs. It is constrained by a hydrogeological model for the spread of the pollution in the aquifer. We consider a broad range of reaction kinetics. The aim of the paper is twofold. On the one hand, we rigorously derive, by asymptotic analysis, the e↵ective optimal control problem for contaminant species that are slightly concentrated in the aquifer. On the other hand, the mathematical analysis of the optimal control problems is performed and we prove in particular that the latter e↵ective problem is well-posed. Furthermore, a stability property of the optimal control process is provided: any optimal solution of the properly scaled problem tends to the optimal solution of the e↵ective problem as the characteristic pollutant concentration decreases

Nonlinear double porosity models with non-standard growth

Abstract We study the solutions to quasilinear elliptic equations with high contrast coefficients. The energy formulation leads to work with variable exponent Lebesgue spaces L p ε (·) in domains with a complex microstructure scaled by a small parameter ε. We derive rigorously the corresponding homogenized problem. It is completely described in terms of local energy characteristics of the original domain. Version française abrégée Nous considérons le problème variationnel (2), où K ε est une fonction qui dégénère sur une partie asymptotiquement dense du domaine (voir (K.1)-(K.2)). Le domaine est un milieu dispersé vérifiant (C.1)-(C.2). En contrôlant les caractéristiques locales (7)-(8) du domaine, nous obtenons rigoureusement le problème homogénéisé correspondant à (2). Il est décrit dans le théorème 2.1 : la solution u ε de (2) converge dans [m3SC+; v 1.113; Prn:18/09/2009; 9:34] plus, dans la partie matricielle du domaine, ( (Ω)) ; 3. on prouve le résultat de convergence dans la partie matricielle. Finalement, nous illustrons notre résultat dans le cadre d'un exemple périodique, retrouvant ainsi une formulation plus usuelle du problème homogénéisé

A large multi-ethnic genome-wide association study identifies novel genetic loci for intraocular pressure.

Elevated intraocular pressure (IOP) is a major risk factor for glaucoma, a leading cause of blindness. IOP heritability has been estimated to up to 67%, and to date only 11 IOP loci have been reported, accounting for 1.5% of IOP variability. Here, we conduct a genome-wide association study of IOP in 69,756 untreated individuals of European, Latino, Asian, and African ancestry. Multiple longitudinal IOP measurements were collected through electronic health records and, in total, 356,987 measurements were included. We identify 47 genome-wide significant IOP-associated loci (P < 5 × 10-8); of the 40 novel loci, 14 replicate at Bonferroni significance in an external genome-wide association study analysis of 37,930 individuals of European and Asian descent. We further examine their effect on the risk of glaucoma within our discovery sample. Using longitudinal IOP measurements from electronic health records improves our power to identify new variants, which together explain 3.7% of IOP variation

A Game Theory Approach for the Groundwater Pollution Control

A differential game modeling the noncooperative outcome of pollution in groundwater is studied. Spatio-temporal objectives are constrained by a convection-diffusion-reaction equation ruling the spread of the pollution in the aquifer, and the velocity of the flow solves an elliptic partial differential equation. The existence of a Nash equilibrium is proved using a fixed point strategy. A uniqueness result for the Nash equilibrium is also proved under some additional assumptions. Some numerical illustrations are provided

Deletion of Nkx2-5 in trabecular myocardium reveals the developmental origins of pathological heterogeneity associated with ventricular non-compaction cardiomyopathy.

Left ventricular non-compaction (LVNC) is a rare cardiomyopathy associated with a hypertrabeculated phenotype and a large spectrum of symptoms. It is still unclear whether LVNC results from a defect of ventricular trabeculae development and the mechanistic basis that underlies the varying severity of this pathology is unknown. To investigate these issues, we inactivated the cardiac transcription factor Nkx2-5 in trabecular myocardium at different stages of trabecular morphogenesis using an inducible Cx40-creERT2 allele. Conditional deletion of Nkx2-5 at embryonic stages, during trabecular formation, provokes a severe hypertrabeculated phenotype associated with subendocardial fibrosis and Purkinje fiber hypoplasia. A milder phenotype was observed after Nkx2-5 deletion at fetal stages, during trabecular compaction. A longitudinal study of cardiac function in adult Nkx2-5 conditional mutant mice demonstrates that excessive trabeculation is associated with complex ventricular conduction defects, progressively leading to strain defects, and, in 50% of mutant mice, to heart failure. Progressive impaired cardiac function correlates with conduction and strain defects independently of the degree of hypertrabeculation. Transcriptomic analysis of molecular pathways reflects myocardial remodeling with a larger number of differentially expressed genes in the severe versus mild phenotype and identifies Six1 as being upregulated in hypertrabeculated hearts. Our results provide insights into the etiology of LVNC and link its pathogenicity with compromised trabecular development including compaction defects and ventricular conduction system hypoplasia