In the articleMatrices de Stokes-Ramis et constantes de connexion pour les systèmes différentiels linéaires de niveau unique (P. Remy), we considered linear differential systems with a unique but arbitrary level and we stated formulae to express all the Stokes multipliers in terms of connection constants in the Borel plane generalizing thus the calculations made in the article Resurgence, Stoke...

A coupled Legendre-Laguerre spectral element method is proposed for the Stokes and Navier-Stokes equations in unbounded domains. The method combines advantages of the high accuracy of the Laguerre-spectral method for unbounded domains and the geometric flexibility of the spectral-element method. Rigorous stability and error analysis for the Stokes problem is carried out. Numerical results indic...

The first observation of parametric down-conversion in silicon is reported. Conversion from 1542.3nm to 1328.8nm is achieved using a CW pump laser at 1427 nm. The conversion occurs via Coherent Anti-Stokes Raman Scattering (CARS) in which two pump photons and one Stokes photon couple through a zone-center optical phonon to an anti-Stokes photon. The maximum measured Stokes/anti-Stokes power con...

We study the relations between the long-time dynamics of the Navier–Stokes-α model and the exact 3D Navier–Stokes system. We prove that bounded sets of solutions of the Navier–Stokes-α model converge to the trajectory attractor A0 of the 3D Navier–Stokes system as time tends to infinity and α approaches zero. In particular, we show that the trajectory attractor Aα of the Navier–Stokes-α model c...

We study how coherent Stokes and anti-Stokes Raman scattering influence coherent population trapping. In an experiment using an atomic sodium vapor cell we observe induced transparency, induced absorption, and gain features, all of subnatural linewidth. The electromagnetically induced resonance is a peak or a dip depending on which side of the optical transition the fields are tuned to, and thu...