A priori convergence estimates for a rough Poisson-Dirichlet problem with natural vertical boundary conditions

Stents are medical devices designed to modify blood flow in aneurysm sacs, in order to prevent their rupture. Some of them can be considered as a locally periodic rough boundary. In order to approximate blood flow in arteries and vessels of the cardio-vascular system containing stents, we use multi-scale techniques to construct boundary layers and wall laws. Simplifying the flow we turn to consider a 2-dimensional Poisson problem that conserves essential features related to the rough boundary. Then, we investigate convergence of boundary layer approximations and the corresponding wall laws in the case of Neumann type boundary conditions at the inlet and outlet parts of the domain. The difficulty comes from the fact that correctors, for the boundary layers near the rough surface, may introduce error terms on the other portions of the boundary. In order to correct these spurious oscillations, we introduce a vertical boundary layer. Trough a careful study of its behavior, we prove rigorously decay estimates. We then construct complete boundary layers that respect the macroscopic boundary conditions. We also derive error estimates in terms of the roughness size epsilon either for the full boundary layer approximation and for the corresponding averaged wall law.Comment: Dedicated to Professor Giovanni Paolo Galdi 60' Birthda

Asymptotic description of solutions of the exterior Navier Stokes problem in a half space

We consider the problem of a body moving within an incompressible fluid at constant speed parallel to a wall, in an otherwise unbounded domain. This situation is modeled by the incompressible Navier-Stokes equations in an exterior domain in a half space, with appropriate boundary conditions on the wall, the body, and at infinity. We focus on the case where the size of the body is small. We prove in a very general setup that the solution of this problem is unique and we compute a sharp decay rate of the solution far from the moving body and the wall

Integral potential method for a transmission problem with Lipschitz interface in R^3 for the Stokes and Darcy–Forchheimer–Brinkman PDE systems

The purpose of this paper is to obtain existence and uniqueness results in weighted Sobolev spaces for transmission problems for the non-linear Darcy-Forchheimer-Brinkman system and the linear Stokes system in two complementary Lipschitz domains in R3, one of them is a bounded Lipschitz domain with connected boundary, and the other one is the exterior Lipschitz domain R3 n. We exploit a layer potential method for the Stokes and Brinkman systems combined with a fixed point theorem in order to show the desired existence and uniqueness results, whenever the given data are suitably small in some weighted Sobolev spaces and boundary Sobolev spaces

Penalty finite element approximations of the stationary power- law Stokes problem

Finite element approximations of the stationary power-law Stokes problem using penalty formulation are considered. A priori error estimates under appropriate smoothness assumptions on the solutions are established without assuming a discrete version of the BB condition. Numerical solutions are presented by implementing a nonlinear conjugate gradient metho

Syntheses, Structures, and Photophysical Properties of Mono- and Dinuclear Sulfur-Rich Gold(I) Complexes

Sulfur-rich 1,2 dithiolene and neutral thione ligands were used for the synthesis of gold complexes, some of them exhibiting aurophilic interactions. Surprisingly, the closest Au···Au contact is observed in an unsupported dinuclear complex, which makes part of a supramolecular network. Photophysical studies, combined with DFT calculations, indicate that the participations of the Au···Au interactions have some relevance to the rich luminescence properties of these compounds

Z boson production in Pb+Pb collisions at √Snn = 5.02 TeV measured by the ATLAS experiment

The production yield of Z bosons is measured in the electron and muon decay channels in Pb+Pb collisions at √S = 5.02 TeV with the ATLAS detector. Data from the 2015 LHC run corresponding to an integrated luminosity of 0.49 nb are used for the analysis. The Z boson yield, normalised by the total number of minimum-bias events and the mean nuclear thickness function, is measured as a function of dilepton rapidity and event centrality. The measurements in Pb+Pb collisions are compared with similar measurements made in proton-proton collisions at the same centre-of-mass energy. The nuclear modification factor is found to be consistent with unity for all centrality intervals. The results are compared with theoretical predictions obtained at next-to-leading order using nucleon and nuclear parton distribution functions. The normalised Z boson yields in Pb+Pb collisions lie 1-3σ above the predictions. The nuclear modification factor measured as a function of rapidity agrees with unity and is consistent with a next-to-leading-order QCD calculation including the isospin effect. nn -

Measurement of J/ψ production in association with a W ± boson with pp data at 8 TeV

A measurement of the production of a prompt J/ψ meson in association with a W± boson with W± → μν and J/ψ → μ+μ− is presented for J/ψ transverse momenta in the range 8.5–150 GeV and rapidity |yJ/ψ| < 2.1 using ATLAS data recorded in 2012 at the LHC. The data were taken at a proton-proton centre-of-mass energy of s = 8 TeV and correspond to an integrated luminosity of 20.3 fb−1. The ratio of the prompt J/ψ plus W± cross-section to the inclusive W± cross-section is presented as a differential measurement as a function of J/ψ transverse momenta and compared with theoretical predictions using different double-parton-scattering cross-sections. [Figure not available: see fulltext.]