École normale supérieure de Cachan

About: École normale supérieure de Cachan is a education organization based out in Cachan, Île-de-France, France. It is known for research contribution in the topics: Decidability & Nonlinear system. The organization has 2717 authors who have published 5585 publications receiving 175925 citations.

Plasmonic coupling between metallic nanocavities

Abstract: We demonstrate strong coupling of nanocavities in metal films, sparked by propagating surface plasmons. Unlike the coupling of metallic nanoparticles which decays over distances of tens of nanometers, the metallic nanocavities display long range coupling at distances of hundreds of nanometers for the properly selected metal/wavelength combinations. Such strong coupling drastically changes the symmetry of the charge distribution around the nanocavities as is evidenced by the nonlinear optical response of the medium. We show that when strongly coupled, equilateral triangular nanocavities lose their individual symmetry to adopt the lower symmetry of the coupled system and respond like a single dipolar entity. A quantitative model is suggested for the transition from individual to strongly coupled nanocavities.

Contrôle et stabilisation d'ondes électromagnétiques

Abstract: We consider the exact controllability and stabilization of Maxwell equation by using results on the propagation of singularities of the electromagnetic field. We will assume geometrical control condition and use techniques of the work of Bardos et al. on the wave equation. The problem of internal stabilization will be treated with more attention because the condition divE=0 is not preserved by the system of Maxwell with Ohm's law.

Incremental model for fatigue crack growth based on a displacement partitioning hypothesis of mode I elastic–plastic displacement fields

Abstract: The mode I displacement field in the near crack tip region is assumed to be depicted by its partition into an elastic field and a plastic field. Then, each part of the displacement field is also assumed to be the product of a reference field, a function of space coordinates only, and of an intensity factor, function of the loading conditions. This assumption, classical in fracture mechanics, enables one to work at the global scale since fracture criteria can be formulated as a function of the stress intensity factors only. In the present case, the intensity factor of the plastic part of the displacement field measures crack tip plastic flow rate at the global scale. On the basis of these hypotheses, the energy balance equation and the second law of thermodynamics are written at the global scale, i.e. the scale of the K-dominance area. This enables one to establish a yield criterion and a plastic flow rule for the crack tip region. Then, assuming a relation between plastic flow in the crack tip region and fatigue crack growth allows an incremental model for fatigue crack growth to be built. A few examples are given to show the versatility of the model and its ability to reproduce memory effects associated with crack tip plasticity.

Stability of some stationary solutions to the forced KdV equation with one or two bumps

Abstract: Free-surface flows past submerged obstacles in a channel are considered. The fluid is assumed to be inviscid and incompressible and the flow to be irrotational. The first-order approximation of long nonlinear surface waves over one or two bumps results in a forced Korteweg–de Vries (fKdV) equation. Solutions of the stationary fKdV equation are constructed and their stability is studied, either analytically or numerically. These various solutions include solitary waves over a single bump, solitary waves with two humps over a double bump, table-top solutions over a double bump and fronts.