2014 We derive a model of convection appropriate for containers with large width to height ratios. It couples a real rapidly varying convective variable to a slowly varying « drift » velocity field given by its stream-function. The derivation assumes stress-free boundary conditions at the top and the bottom. We discuss its extension to the more realistic no-slip case and the analogies/differenc...

Using a weak convergence approach, we prove a LPD for the solution of 2D stochastic Navier Stokes equations when the viscosity converges to 0 and the noise intensity is multiplied by the square root of the viscosity. Unlike previous results on LDP for hydrodynamical models, the weak convergence is proven by tightness properties of the distribution of the solution in appropriate functional spaces.

where T ≥ 2 is a positive integer andΔu k u k 1 −u k is the forward difference operator. Throughout this paper, we denote by Z a, b the discrete interval {a, a 1, . . . , b}, where a and b are integers and a < b. We consider in 1.1 two different boundary conditions: a Dirichlet boundary condition u 0 0 and a Neumann boundary condition Δu T 0 . In the literature, the boundary condition considere...

The aim of this paper is to derive spectral and condition number estimates of the singlelayer operator for low-frequency multiple scattering problems. This work extends the analysis initiated in [6] to dense media. Estimates are obtained first in the case of circular cylinders by Fourier analysis and are next formally adapted to disks, ellipses and rectangles in the framework of boundary elemen...

In this work we deduce an explicit Sommerfeld-type radiation condition able to prove uniqueness for the problem of outgoing wave propagation in isotropic elastic half-spaces with free boundary condition. The expression is obtained by a rigorous asymptotic analysis of the Green’s function associated with this problem. Observe that this is an exterior problem with unbounded frontier. The main dif...

This note concerns a nonlinear differential equation problem in which both the nonlinearity in the equation and its solution are determined by prescribed data. The question under consideration arises from a study of two-dimensional steady parallel-flows of a perfect fluid governed by Euler’s equations and a free-boundary condition, when the distribution of vorticity is arbitrary but prescribed.

The aim of this paper is to derive spectral and condition number estimates of the single-layer operator for low-frequency multiple scattering problems. This work extends to dense media the analysis initiated in [7]. Estimates are obtained first in the case of circular cylinders by Fourier analysis and are next formally adapted to disks, ellipses and rectangles in the framework of boundary eleme...

Distributed sensing of structural states is essential to vibration control, health monitoring and shape control of precision structronic systems. Paraboloidal shells of revolution are widely used in aerospace, telecommunication, etc. structures. However, distributed sensing of paraboloidal shell structures is rarely investigated over the years. Micro-sensing characteristics, sensor segmentation...

Thin-walled structures like crash boxes may be used as energy absorption members in automotive chassis. There have been many studies addressing the behaviors of energy absorption members on frontal crash. These researches have attempted to predict the energy absorption and maximum impact load in shell structures. The energy absorption and maximum impact load depend on many parameters including ...

We consider stability properties of discrete-time bilinear lters. Simple su cient conditions are given for bounded-input bounded-output stability (with not necessarily zero initial conditions), lp stability, and three other important types of stability. In particular, conditions are given under which asymptotically periodic inputs produce asymptotically periodic outputs with the same period. Re...