Historically, the “lowest-order” JWKB “parabolic” connection formula between the left and right classically allowed regions for tunneling through a parabolic barrier involved a rather non-JWKB-like square-root √ 1 + e−2π(−E)/~ and a non-JWKB phase factor that had been extracted from the asymptotic expansion of the parabolic cylinder function. Generalization to higher order was not obvious. We s...

A quantity of considerable interest in studies of polarized light is the degree of polarization of a beam of radiation. Every transformation of Stokes parameters described by a Mueller matrix may change the degree of polarization. The nature of this change, however, is not so obvious (see, e.g., Ref. 1). The main purpose of this Letter is to present simple upper and lower bounds for the change ...

We study the local exponential stabilization, near a given steady-state flow, of solutions of the Navier-Stokes equations in a bounded domain. The control is performed through a Dirichlet boundary condition. We apply a linear feedback controller, provided by a well-posed infinite dimensional Riccati equation. We give a characterization of the domain of the closed-loop operator which is obtained...

LLE Review, Volume 72 177 In stimulated Brillouin scattering1 (SBS) an incident (pump) light wave is scattered by the electron-density fluctuations associated with an ion-acoustic (sound) wave. This process generates a frequency-upshifted (anti-Stokes) light wave and a frequency-downshifted (Stokes) light wave. For most scattering angles the anti-Stokes wave is driven nonresonantly and can be n...

The aim of this dissertation is to study stochastic Navier-Stokes equations with a fractional Brownian motion noise. The second chapter will introduce the background results on fractional Brownian motions and some of their properties. The third chapter will focus on the Stokes operator and the semigroup generated by this operator. The Navier-Stokes equations and the evolution equation setup wil...

The Stokes problem describes flow of an incompressible constant-viscosity fluid when the Reynolds number is small so that inertial and transient-time effects are negligible. The numerical solution of the Stokes problem requires special care, since classical finite element discretization schemes, such as piecewise linear interpolation for both the velocity and the pressure, fail to perform. Even...