This paper is devoted to the study of the Navier~Stok.es équations descnbing the flow of an incompressible fluid in a shallow domain and to the hydrostatic approximation of these équations Wefirst study the behaviour of solutions of the Navier-Stokes équations when the depth of the domain tends to zero We then dérive the existence of solutions for the hydrostatic approximation Résumé — Ce papie...

Consider the random intervals In = ωn+ (0, n) (modulo 1) with their left points ωn independently and uniformly distributed over the interval [0,1)=R/Z and with their lengths decreasing to zero. We prove that the Hausdorff dimension of the set limnIn of points covered infinitely often is almost surely equal to 1/α when n = a/nα for some a > 0 and α > 1.  2003 Elsevier SAS. All rights reserved. ...

We are interested in the life span and the asymptotic behaviour of the solutions to a system governing the motion of a pressureless gas, submitted to a strong, inhomogeneous magnetic field εB(x), of variable amplitude but fixed direction — this is a first step in the direction of the study of rotating Euler equations. This leads to the study of a multi–dimensional Burgers type system on the vel...

A chromatic root is a zero of the chromatic polynomial of a graph. At a Newton Institute workshop on Combinatorics and Statistical Mechanics in 2008, two conjectures were proposed on the subject of which algebraic integers can be chromatic roots, known as the “α + n conjecture” and the “nα conjecture”. These say, respectively, that given any algebraic integer α there is a natural number n such ...

Growth dominance is a relatively new, simple, quantitative metric of within-stand individual tree growth patterns, and is defined as positive when larger trees in the stand display proportionally greater growth than smaller trees, and negative when smaller trees display proportionally greater growth than larger trees. We examined long-term silvicultural experiments in red pine (Pinus resinosa A...

In this work, we present a HLLC scheme modification for application to nonhomogeneous shallow-water equations with pollutant transport. This new version is related to the definition of a consistent approximation of the intermediate wave speed. Numerical results are presented to illustrate the importance of such approximation to get appropriate pollutant concentration profiles. Une vitesse inter...