A Conservative Space-time Mesh Refinement Method for the 1-D Wave Equation. Part I: Construction

Summary. We propose a new method for space-time refinement for the 1-D wave equation. This method is based on the conservation of a discrete energy through two different discretization grids which guarantees the stability of the scheme. Our approach results in a non-interpolatory scheme whose stability condition is not affected by the transition between the two grids. Mathematics Subject Classification (1991):65M12     

Thin films of functionalized amorphous silica for immunosensors application

Within the framework of the development of an optical immunosensor, the sol-gel process has been used to prepare a thin film of amorphous silica, deposited by spin coating on a gold-coated glass slide, and possessing chemically active functional groups (SH, NH₂...). After activation of the sol-gel film in aqueous buffers by a bifunctional coupling agent, biological molecules such as antibodies could be covalently bonded on or inside the sol-gel film. Therefore, the behavior in aqueous solutions of the functionalized silica thin films has been analysed by Surface Plasmon Resonance (SPR) and guided wave propagation. Results show a modification of the thickness and of the refractive index of the silica film. Pore size range has been deduced by the infiltration of different molecular weight dextran molecules diluted in water into the sol-gel material. Immunosassays have demonstrated biological activity of antibodies which are covalently linked to or entraped in the sol-gel film.     

Augmented Galerkin schemes for the numerical solution of scattering by small obstacles

We are interested in the problem of a bidimensional acoustic wave propagation in a medium including a small obstacle with homogeneous Dirichlet boundary condition. We present and analyse a numerical scheme suitable for finite elements that does not suffer from numerical locking, and takes the presence of the small obstacle into account. It is based on the fictitious domain method combined with matched asymptotic expansions.     

Indecomposable higher Chow cycles on Jacobians

We construct some natural indecomposable elements of with trivial regulator, and in particular, prove that is uncountable for C a generic curve or a generic hyperelliptic curve of genus . Received: 10 October 2000 / in final form: 12 June 2001 / Published online: 1 February 2002