The Stokes-Einstein relation for the self-diffusion coefficient of a spherical particle suspended in an incompressible fluid is an asymptotic result in the limit of large Schmidt number, that is, when momentum diffuses much faster than the particle. When the Schmidt number is moderate, which happens in most particle methods for hydrodynamics, deviations from the Stokes-Einstein prediction are e...

Recent advances in the theory of turbulent solutions of the Navier-Stokes equations are discussed and the existence of their associated invariant measures. The statistical theory given by the invariant measures is described and associated with historically-known scaling laws. These are Hack’s law in one dimension, the Bachelor-Kraichnan law in two dimensions and the Kolmogorov’s scaling law in ...

We construct the Navier-Stokes equation from first principle using relativistic bosonic lagrangian which is invariant under local gauge transformations. We show that by defining the bosonic field to represent the dynamic of fluid in a particular form, a general Navier-Stokes equation with conservative forces can be reproduced exactly. It also induces two new forces, one is relevant for rotation...

Two methods are developed to average V and I Stokes parameters over a circular sensor aperture collecting light scattered from an optically active sphere. One method uses a two-dimensional numerical integration of Bohren’s theory in scalar form, which explicitly shows the connection with Mueller matrix elements. The second method uses expansions of vector spherical harmonics in Bohren’s theory ...

* Present address: Applied Mathematics Department, Brookhaven National Laboratory, Upton, New York. • See, for instance, L. Landau and E. Lifshitz, Fluid Mechanics (Addison-Wesley Publishing Co., Inc., Reading, Mass., 1959). scribed by the classical theory of Stokes and Kirchoff. • This theory is, of course, based on the Navier-Stokes equations. However, for high-frequency sound propagation in ...

In this paper, we derive a posteriori error estimates for space-discrete approximations of the timedependent Stokes equations. By using an appropriate Stokes reconstruction operator, we are able to write an auxiliary error equation, in pointwise form, that satisfies the exact divergence-free condition. Thus, standard energy estimates from partial differential equation theory can be applied dire...

A consistent quantum theory of polarization squeezed light formation in a inertial nonlinear medium is developed taking into account the response time of electronic Kerr nonlinearity. Stokes parameters are considered and their fluctuations spectra are investigated. It is established that the frequency at which the suppression of quantum fluctuations of Stokes parameters is the greatest can be c...