A case-study of the Stokes geometry in the large is given for some concrete examples of WKB type operators that admit infinitely many phases. In all the examples discussed in this article virtual turning points and new Stokes curves emanating from them neatly resolve the trouble we encounter. Some computerassisted study of the configuration of the steepest descent paths is employed to show that...

The Stokes problem plays an important role in computational fluid dynamics since it is encountered in the time discretization of (incompressible) Navier-Stokes equations by operator-splitting methods [2, 3]. Space discretization of the Stokes problem leads to large scale ill-conditioned systems. The Uzawa (preconditioned) conjugate gradient method is an efficient method for solving the Stokes p...

The paper shows an inf-sup stability property for several well-known 2D and 3D Stokes elements on triangulations which are not fitted to a given smooth or polygonal domain. The property implies stability and optimal error estimates for a class of unfitted finite element methods for the Stokes and Stokes interface problems, such as Nitsche-XFEM or cutFEM. The error analysis is presented for the ...

Organic dyes generally suffer from small Stokes shift that usually leads to self-quenching and -gaining errors during the fluorescent imaging process. Here, a through-bond energy transfer (TBET) cassette is developed with large Stokes shift to pursue precise cell imaging. The TBET is constructed by covalently conjugated tetraphenylethene (acts as donor) and rhodamine (acceptor) through an acety...

In this work we study the correlated Stokes and anti-Stokes Raman scattering process, called here SaS. The SaS, proposed by Klyshko in 1977 [1], is an effect where the same phonon participates in the Stokes and anti-Stokes scattering processes. The Feynman diagrams of Figure 1 show the Stokes (S), the anti-Stokes (as) and the SaS processes. The SaS process has not been considered in current tre...

Cascaded Raman Stokes lasing in an ultrahigh-Q silica microsphere resonator coupled to a tapered fiber is demonstrated and analyzed. With less than 900 microW of pump power near 980 nm, five cascaded Stokes lasing lines are generated. In addition, a threshold power of 56.4 microW for the first-order Stokes lasing is achieved. The Stokes lasing lines exhibit distinct characteristics depending on...

We provide a conclusive demonstration of vibrational pumping under Surface Enhanced Raman Scattering (SERS) conditions by performing anti-Stokes/Stokes ratio measurements over a large spatial area and low power density, down to 10 K with dried silver colloids, the dye rhodamine 6G, and 676 nm laser excitation. The method we propose allows for the measurement of the cross sections for different ...

On regularity of stationary Stokes and Navier-Stokes equations near boundary KYUNGKEUN KANG Received: date / Revised version: date – c Springer-Verlag 2001 Abstract. We obtain local estimates of the steady-state Stokes system “without pressure” near boundary. As an application of the local estimates, we prove the partial regularity up to the boundary for the stationary Navier-Stokes equations i...

We present finite volume schemes for Stokes and Navier-Stokes equations. These schemes are based on the mixed finite volume introduced in [6], and can be applied to any type of grid (without “orthogonality” assumptions as for classical finite volume methods) and in any space dimension. We present numerical results on some irregular grids, and we prove, for both Stokes and Navier-Stokes equation...

Coherent anti-Stokes Raman scattering (CARS) is a well-known Raman scattering process that occurs when Stokes, anti-Stokes and pump waves are properly phase-matched. Using a quantum-field approach with Langevin noise sources, we calculate the noise figure for wavelength conversion between the Stokes and anti-Stokes waves in CARS and show its dependence on phase mismatch. Under phase matched con...