In the coherent anti-Stokes Raman scattering process, the spectrum of the generated optical phonon depends on the degree of temporal correlation between the pump laser field and the Stokes field. When the two fields are strongly correlated, such as when the Stokes field is generated with stimulated Raman scattering (SRS), the spectral shape of the optical phonon is found experimentally and theo...

In this paper, by including Raman scattering in the coupled-mode equations, the scalar modulation instability in photonic crystal fibers is investigated. The evolution of the pump, Stokes and anti-Stokes waves along the fiber as well as the conversion efficiency for two cases, with and without Raman effect, are studied. The effect of anti-Stokes seed and the pump depletion on the evolution of S...

By applying the fluctuation dissipation theorem [1] to the Navier Stokes equation, Landau and Lifshitz developed long ago the standard theory of fluctuating hydrodynamics [2] [3] [4]. This theory is both appealing and successful, and it is consistent with the fluctuating hydrodynamics which is derived if fluctuation dissipation theory is first applied to the Boltzmann equation [5], and then the...

Dispersion and deposition of aerosol particles over two square cylinders confined in a channel in laminar unsteady vortical flow were investigated numerically. Lattice Boltzmann method was used to calculate fluid characteristics and modify Euler method was employed as Lagrangian particle tracing procedure to obtain particle trajectories. Drag, Saffman lift, gravity, buoyancy and Brownian motion...

We study the partial regularity of a 3D model of the incompressible Navier-Stokes equations which was recently introduced by the authors in [11]. This model is derived for axisymmetric flows with swirl using a set of new variables. It preserves almost all the properties of the full 3D Euler or Navier-Stokes equations except for the convection term which is neglected in the model. If we add the ...

Abstract. We study the initial-boundary value problem of the Navier-Stokes equations for incompressible fluids in a domain in R with compact and smooth boundary, subject to the kinematic and Navier boundary conditions. We first reformulate the Navier boundary condition in terms of the vorticity, which is motivated by the Hodge theory on manifolds with boundary from the viewpoint of differential...

We introduce an approach to expand gauge-invariant Wilson operators on lattice. This approach is based on non-abelian Stokes theorem and overcomes some shortage of some former methods. It is also suitable for expanding any Wilson operator on lattice.

Abstract We discuss models for flow in a class of generalized Navier–Stokes equations. The work concentrates on producing thermal convection, analysing these detail, and deriving critical Rayleigh wave numbers the onset convective fluid motion. In addition to linear instability theory we present careful analysis fully nonlinear stability theory. theories analysed all possess bi-Laplacian term n...

‎In this paper‎, ‎we have dealt with the distribution theory of concomitants of order statistics arising from Farlie-Gumbel-Morgenstern bivariate Lomax distribution‎. ‎We have discussed the estimation of the parameters associated with the distribution of the variable Y of primary interest‎, ‎based on the ranked set sample defined by ordering the marginal observations...

A complete mathematical description of oscillatory Couette flows within the framework of kinetic theory is not available in the literature. Motivated by this and their vast engineering applications, we present a parametric study of time-periodic oscillatory Couette flows using the unsteady direct simulation Monte Carlo ~DSMC! method. Computations are performed as a function of the Knudsen ~Kn! ...