The Stokes-Einstein Relation at Moderate Schmidt Number

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 expected. We study these corrections computationally using a recently-developed minimally-resolved method for coupling particles to an incompressible fluctuating fluid in both two and three dimensions. We find that for moderate Schmidt numbers the diffusion coefficient is reduced relative to the Stokes-Einstein prediction by an amount inversely proportional to the Schmidt number in both two and three dimensions. We find, however, that the Einstein formula is obeyed at all Schmidt numbers, consistent with linear response theory. The numerical data is in good agreement with an approximate self-consistent theory, which can be used to estimate finite-Schmidt number corrections in a variety of methods. Our results indicate that the corrections to the Stokes-Einstein formula come primarily from the fact that the particle itself diffuses together with the momentum. Our study separates effects coming from corrections to no-slip hydrodynamics from those of finite separation of time scales, allowing for a better understanding of widely observed deviations from the Stokes-Einstein prediction in particle methods such as molecular dynamics.Comment: Submitte

Sub-Plate Overlap Code Documentation

An expansion of the plate overlap method of astrometric data reduction to a single plate has been proposed and successfully tested. Each plate is (artificially) divided into sub-plates which can then be overlapped. This reduces the area of a 'plate' over which a plate model needs to accurately represent the relationship between measured coordinates and standard coordinates. Application is made to non-astrographic plates such as Schmidt plates and to wide-field astrographic plates. Indeed, the method is completely general and can be applied to any type of recording media

Children’s Vulnerability Related to Chlorine Exposure, Container Confusion, and Mixing Household Cleaners – Florida, 2006-2008

Acute and chronic effects of exposure to chlorine and chloramines can result in the irritation of the skin and mucous mem- branes, often leading to airway edema resulting in respiratory difficulties, burning in the throat, eyes and nose. Ingestion of bleach or bleach-containing products often results in adverse gastrointestinal effects. Data captured by the three centers com- prising the Florida Poison Information Center Network (FPICN) between 2006 and 2008 was examined to characterize the extent oftoxic effects from chlorine gas exposures related to misuse ofhousehold cleaners. A known outcome was determined in 48.4% of the 5315 cases. Of those with a known outcome, 0.2% (6) had a major effect. Children two and younger were the most frequently exposed population (22.7%). Children 19 and under accounted for 39.1% (2079), whereas children 2 and under accounted for 22.7% (1204) of the chlorine exposure population. Container confusion accounted for 12%, and mixing cleaning products accounted for 17% of the cases reviewed in 2006. The most common route of exposure in cases reviewed in 2006 was by-mouth and the most common symptom was gastrointestinal (GI). Fact sheets and educational outreach related to reducing the mixing of household cleaners, reading manufacturers safety instructions carefully, and storing the chemical clean- ers safely away from children and in original containers is warranted to reduce chlorine exposures in children

A diffusive system driven by a battery or by a smoothly varying field

We consider the steady state of a one dimensional diffusive system, such as the symmetric simple exclusion process (SSEP) on a ring, driven by a battery at the origin or by a smoothly varying field along the ring. The battery appears as the limiting case of a smoothly varying field, when the field becomes a delta function at the origin. We find that in the scaling limit, the long range pair correlation functions of the system driven by a battery turn out to be very different from the ones known in the steady state of the SSEP maintained out of equilibrium by contact with two reservoirs, even when the steady state density profiles are identical in both models

Lattice Boltzmann - Langevin simulations of binary mixtures

We report a hybrid numerical method for the solution of the model H fluctuating hydrodynamic equations for binary mixtures. The momentum conservation equations with Landau-Lifshitz stresses are solved using the fluctuating lattice Boltzmann equation while the order parameter conservation equation with Langevin fluxes are solved using the stochastic method of lines. Two methods, based on finite difference and finite volume, are proposed for spatial discretisation of the order parameter equation. Special care is taken to ensure that the fluctuation-dissipation theorem is maintained at the lattice level in both cases. The methods are benchmarked by comparing static and dynamic correlations and excellent agreement is found between analytical and numerical results. The Galilean invariance of the model is tested and found to be satisfactory. Thermally induced capillary fluctuations of the interface are captured accurately, indicating that the model can be used to study nonlinear fluctuations

Numerical Methods for the Stochastic Landau-Lifshitz Navier-Stokes Equations

The Landau-Lifshitz Navier-Stokes (LLNS) equations incorporate thermal fluctuations into macroscopic hydrodynamics by using stochastic fluxes. This paper examines explicit Eulerian discretizations of the full LLNS equations. Several CFD approaches are considered (including MacCormack's two-step Lax-Wendroff scheme and the Piecewise Parabolic Method) and are found to give good results (about 10% error) for the variances of momentum and energy fluctuations. However, neither of these schemes accurately reproduces the density fluctuations. We introduce a conservative centered scheme with a third-order Runge-Kutta temporal integrator that does accurately produce density fluctuations. A variety of numerical tests, including the random walk of a standing shock wave, are considered and results from the stochastic LLNS PDE solver are compared with theory, when available, and with molecular simulations using a Direct Simulation Monte Carlo (DSMC) algorithm

Spatial correlations of hydrodynamic fluctuations in simple fluids under shear flow: a mesoscale simulation study

Hydrodynamic fluctuations in simple fluids under shear flow are demonstrated to be spatially correlated, in contrast to the fluctuations at equilibrium, using mesoscopic hydrodynamic simulations. The simulation results for the equal-time hydrodynamic correlations in a multiparticle collision dynamics (MPC) fluid in shear flow are compared with the explicit expressions obtained from fluctuating hydrodynamics calculations. For large wave vectors k , the nonequilibrium contributions to transverse and longitudinal velocity correlations decay as k − 4 for wave vectors along the flow direction and as k − 2 for the off-flow directions. For small wave vectors, a crossover to a slower decay occurs, indicating long-range correlations in real space. The coupling between the transverse velocity components, which vanishes at equilibrium, also exhibits a k − 2 dependence on the wave vector. In addition, we observe a quadratic dependency on the shear rate of the nonequilibrium contribution to pressure