We have developed a new technique for efficient suppression of the nonresonant background in coherent anti-Stokes Raman scattering (CARS). The advantage of this technique, which is based upon phase-controlled superposition of an appropriately selected reference signal, is presented in theory and demonstrated experimentally by the example of the S(3) (pure rotational) transition of molecular hyd...

Abstract. This paper is concerned with the dynamics of vesicle membranes in incompressible viscous fluids. Some rigorous theory are presented for the phase field Navier-Stokes model proposed in [7], which is based on an energetic variation approach and incorporates the effect of bending elasticity energy for the vesicle membranes. The existence and uniqueness results of the global weak solution...

This paper is concerned with the implementation of efficient solution algorithms for elliptic problems with constraints. We establish theory which shows that including a simple scaling within well-established block diagonal preconditioners for Stokes problems can result in significantly faster convergence when applying the preconditioned MINRES method. The codes used in the numerical studies ar...

We present a polarimetric technique that provides a complete description of a mixture of uncorrelated optical fields with different spectral and polarization properties. The second-order coherence theory is used to describe the superposition of two random optical fields, and an imaging experiment is reported that illustrates the capability to separate radiations with different spectral composit...

The gauge theory approach to the geometric Langlands program is extended to the case of wild ramification. The new ingredients that are required, relative to the tamely ramified case, are differential operators with irregular singularities, Stokes phenomena, isomonodromic deformation, and, from a physical point of view, new surface operators associated with higher order singularities.

The activation energy of a reasonable order of magnitude was estimated for the coalescence of oil droplets in an O/W emulsion by formulating the balance of forces acting on a droplet that crosses over the potential barrier to coalesce with another droplet by the DLVO theory and Stokes' law. An emulsion with smaller oil droplets was shown to be more stable.

In the present paper, we prove a sufficient condition of local regularity for suitable weak solutions to the Navier-Stokes equations having axial symmetry. Our condition is an axially symmetric analog of the so-called L3,∞-case in the general local regularity theory. 1991 Mathematical subject classification (Amer. Math. Soc.): 35K, 76D.

We present a general theory for regularization models of the Navier-Stokes equations based on the Leray deconvolution model with a general deconvolution operator designed to fit a few important key properties. We provide examples of this type of operator, such as the modified TikhonovLavrentiev and modified Iterated Tikhonov-Lavrentiev operators, and study their mathematical properties. An exis...

We inquire into the scaling properties of the 2D Navier-Stokes equation sustained by a force field with Gaussian statistics, white noise in time, and with a power-law correlation in momentum space of degree 2 - 2 epsilon. This is at variance with the setting usually assumed to derive Kraichnan's classical theory. We contrast accurate numerical experiments with the different predictions provided...

Fundamental aspects of inverse kinetic theories for the incompressible Navier-Stokes equations [Ellero and Tessarotto, 2004, 2005] include the possibility of defining uniquely the kinetic equation underlying such models and furthermore, the construction of a kinetic theory implying also the energy equation. The latter condition is consistent with the requirement that fluid fields result classic...