Development of a Community of Science Teachers: Participation in a Collaborative Action Research Project

This article presents a study exploring the beliefs, knowledge, and practices of four middle and secondary science teachers participating in a collaborative curriculum action research project. Using a case study methodology, the views and practices of these teachers were described and analyzed as they investigated novel ideas about scientific inquiry and nature of science, critically examined their practice, and implemented and reflected upon modified curricular practices. Findings indicated that by the end of the study, all participants had enhanced their views of scientific inquiry and nature of science, and the collaborative group evolved as a community of teachers. Wenger's (1998a) community of practice theory provided a useful framework to describe and analyze the experiences of these science teachers. Implications for the professional development of science teachers and the compatibility between a community of practice and collaborative action research projects are presented.     

Sharp Global Well-Posedness for a Higher Order Schrodinger Equation

Using the theory of almost conserved energies and the "I-method" developed by Colliander, Keel, Staffilani, Takaoka and Tao, we prove that the initial value problem for a higher order Schrodinger equation is globally well-posed in Sobolev spaces of order s > 1/4. This result is sharp.     

Necessary and Sufficient Conditions to be an Eigenvalue for Linearly Recurrent Dynamical Cantor Systems

Necessary and sufficient conditions are given for linearly recurrentCantor dynamical systems to have measurable and continuous eigenfunctions.Also an example of a linearly recurrent system with a nontrivialKronecker factor and a trivial maximal equicontinuous factoris constructed explicitly.     

A dynamic gradient approach to Pareto optimization with nonsmooth convex objective functions

In a general Hilbert framework, we consider continuous gradient-like dynamical systems for constrained multiobjective optimization involving nonsmooth convex objective functions. Based on the Yosida regularization of the subdifferential operators involved in the system, we obtain the existence of strong global trajectories. We prove a descent property for each objective function, and the convergence of trajectories to weak Pareto minima. This approach provides a dynamical endogenous weighting of the objective functions, a key property for applications in cooperative games, inverse problems, and numerical multiobjective optimization.     

Multigrid preconditioned Krylov subspace methods for three-dimensional numerical solutions of the incompressible Navier–Stokes equations

We consider numerical methods for the incompressible Reynolds averaged Navier–Stokes equations discretized by finite difference techniques on non-staggered grids in body-fitted coordinates. A segregated approach is used to solve the pressure–velocity coupling problem. Several iterative pressure linear solvers including Krylov subspace and multigrid methods and their combination have been developed to compare the efficiency of each method and to design a robust solver. Three-dimensional numerical experiments carried out on scalar and vector machines and performed on different fluid flow problems show that a combination of multigrid and Krylov subspace methods is a robust and efficient pressure solver. This revised version was published online in June 2006 with corrections to the Cover Date.     

Trapped instability and vortex formation by an unstable coastal current

This paper addresses the instability of a two-layer coastal current in a quasigeostrophic model; the potential vorticity (PV) structure of this current consists in two uniform cores, located at different depths, with finite width and horizontally shifted. This shift allows both barotropic and baroclinic instability for this current. The PV cores can be like-signed or opposite-signed, leading to their vertical alignment or to their hetonic coupling. These two aspects are novel compared to previous studies. For narrow vorticity cores, short waves dominate, associated with barotropic instability; for wider cores, longer waves are more unstable and are associated with baroclinic processes. Numerical experiments were performed on the f-plane with a finite-difference model. When both cores have like-signed PV, trapped instability develops during the nonlinear evolution: vertical alignment of the structures is observed. For narrow cores, short wave breaking occurs close to the coast; for wider cores, substantial turbulence results from the entrainment of ambient fluid into the coastal jet. When the two cores have opposite-signed PV, the nonlinear regimes range from short wave breaking to the ejection of dipoles or tripoles, via a regime of dipole oscillation near the wall. The Fourier analysis of the perturbed flow is appropriate to distinguish the regimes of short wave breaking, of dipole formation, and of turbulence, but not the differences between regimes involving only vortex pairs. To explain more precisely the regimes where two vortices (and their wall images) interact, a point vortex model is appropriate.     

Évaluation de l'influence des changements de géométrie sur les déformations de séchage d'un milieu poreux fissuréInfluence of geometry changes on drying-induced strains in a cracked solid

The macroscopic response of a cracked solid subjected to drying is investigated within the framework of micromechanics. The originality of this contribution lies in the fact that the variations of the aspect ratios of cracks induced by the capillary pressure increase are accounted for. When the initial aspect ratio is small enough, it is shown that neglecting the geometrical changes yields an erroneous prediction of the sign of the macroscopic volume strain rate. To cite this article: X. Chateau et al., C. R. Mecanique 331 (2003).