In an earlier paper preconditioning of stationary Stokes-constrained optimal control problems has been considered. In this article we construct an efficient preconditioner for solving the algebraic systems arising from discretized optimal control problems with time-periodic Stokes equations. A simplified analysis of the derivation of the preconditioner and its properties is presented. The preco...

CDNS [1], Compressible Direct Navier-Stokes Simulation code, is an explicit finitedifference code developed by Gordon Erlebacher (Institute for Computer Applications in Science and Engineering) to study 3-D compressible turbulence. This code solves the full Navier-Stokes equations using constant viscosity and Prandtl number. Spatial derivatives are calculated using a sixth-order compact scheme,...

We report a parametric anti-Stokes Raman laser using potassium gadolinium tungstate, generating output chiefly at the first anti-Stokes at 508 nm. The compact 4.5 cm long device is pumped by a Q-switched 532 nm laser and uses an off-axis Stokes resonator to provide non-collinear phase matching between the pump and the generated Stokes and anti-Stokes fields. Anti-Stokes output energies up 0.27 ...

To achieve high-spectral-resolution multiplex coherent anti-Stokes Raman scattering (CARS), one typically uses a narrowband pump pulse and a broadband Stokes pulse. This is to ensure a correspondence between anti-Stokes and vibrational frequencies. We obtain high-resolution CARS spectra of isopropanol, using a broadband chirped pump pulse and a broadband Stokes pulse, by detecting the anti-Stok...

We present a simple filtering procedure for stabilizing the spectral element method (SEM) for the unsteady advection-diffusion and Navier-Stokes equations. A number of example applications are presented, along with basic analysis for the advection-diffusion case. Stabilisation par filtrage pour la méthode des éléments spectraux Résumé. Nous présentons une procédure simple de filtrage pour la st...

Fluid turbulence is commonly modeled by the Navier-Stokes equations with a large Reynolds number. However, direct numerical simulations are not possible in practice, so that turbulence modeling is introduced. We study artificial spectral viscosity models that render the simulation of turbulence tractable. We show that the models are well posed and have solutions that converge, in certain parame...

We introduce a method of estimating the space analyticity radius of solutions for the Navier Stokes and related equations in terms of L p and L norms of the initial data. The method enables us to express the space analyticity radius for 3D Navier Stokes equations in terms of the Reynolds number of the flow. Also, for the Kuramoto Sivashinsky equation, we give a partial answer to a conjecture th...

A method of fundamental solutions has been used to study adiabatic transition amplitudes in two energy level systems for a class of Hamiltonians allowing some simplifications of Stokes graphs corresponding to such transitions. It has been shown that for simplest such cases the amplitudes take the Nikitin Umanski form but for more complicated ones they are formed by a sum of terms strictly relat...

We examine whether the Stokes parameters of a two-mode electromagnetic field results from the superposition of the spins of the photons it contains. To this end we express any n-photon state as the result of the action on the vacuum of n creation operators generating photons which can have may different polarization states in general. We find that the macroscopic polarization holds as sum of th...

The nonlinearity of the Navier-Stokes equations makes predicting the flow of fluid around rapidly moving small bodies highly resistant to all approaches save careful experiments or brute force computation. Here, we show how a linearization of the Navier-Stokes equations captures the drag-determining features of the flow and allows simplified or analytical computation of the drag on bodies up to...