A Study of the Brownian Transport in Straining Flows

2006 ◽  
Author(s):  
David Swailes ◽  
Yasmine Ammar ◽  
Michael Reeks
Keyword(s):  
Particle Dynamics ◽  
Combined Effects ◽  
Third Order ◽  
Equilibrium Distributions ◽  
Closure Modelling ◽  
Pdf Model ◽  
Velocity Moments ◽  
True Equilibrium ◽  
Fokker Planck

The combined effects of Brownian forcing and straining flow on the statistical description of particle dynamics are considered. Using a Fokker-Planck (pdf) model results are obtained for both instantaneous and continuous releases of particles into the flow. The approach shows that continuous sources generate true equilibrium distributions, and highlights important features of these distributions that have implications for the closure modelling of third-order velocity moments.

scholarly journals Collisional Evolution of Galaxy Clusters: Fokker–Planck and N-body models

2003 ◽  
Vol 208 ◽  
pp. 449-450
Author(s):  
Koji Takahashi ◽  
Tomohiro Sensui ◽  
Yoko Funato ◽  
Junichiro Makino
Keyword(s):  
Power Law ◽  
Dynamical Evolution ◽  
Cluster Center ◽  
Combined Effects ◽  
Clusters Of Galaxies ◽  
Relative Importance ◽  
Self Consistent ◽  
The Common ◽  
Good Agreement ◽  
Fokker Planck

We investigate the dynamical evolution of clusters of galaxies in virial equilibrium by using Fokker–Planck models and self-consistent N-body models. In particular we focus on the growth of the common halos and the development of the central density cusps in the clusters. We find good agreement between the Fokker–Planck and N-body models. At the cluster center the cusp approximated by a power law, ρ(r) ∝ r-α (α ∼ 1), develops. We conclude that this shallow cusp results from the combined effects of two-body relaxation and tidal stripping. The cusp steepness α weakly depends on the relative importance of tidal stripping.

Comparison Between Theoretical Values and Simulation Results of Transport Coefficients for the Dissipative Particle Dynamics Method

2004 ◽  
Author(s):  
Akira Satoh
Keyword(s):  
Transport Coefficients ◽  
Dissipative Particle Dynamics ◽  
Planck Equation ◽  
Equation Of Motion ◽  
Particle Dynamics ◽  
Momentum Conservation ◽  
Distribution Functions ◽  
Fokker Planck Equation ◽  
Dynamics Method ◽  
Fokker Planck

In the present study, we have derived an expression for transport coefficients such as viscosity, from the equation of motion of dissipative particles. In the concrete, we have shown the Fokker-Planck equation in phase space, and macroscopic conservation equations such as the equation of continuity and the equation of momentum conservation. The basic equations of the single-particle and pair distribution functions have been derived using the Fokker-Planck equation. The solutions of these distribution functions have approximately been solved by the perturbation method under the assumption of molecular chaos. The expression of the viscosity due to dissipative forces has been obtained using the approximate solutions of the distribution functions. Also, we have conducted non-equilibrium dynamics simulations to investigate the influence of the parameters, which have appeared in defining the equation of motion in the dissipative particle dynamics method.

Velocity measurements in a high-Reynolds-number, momentum-conserving, axisymmetric, turbulent jet

1994 ◽  
Vol 258 ◽  
pp. 31-75 ◽  
Author(s):  
Hussein J. Hussein ◽  
Steven P. Capp ◽  
William K. George
Keyword(s):  
Reynolds Number ◽  
Laser Doppler Anemometry ◽  
Cross Flow ◽  
Hot Wire ◽  
Velocity Measurements ◽  
Third Order ◽  
Burst Mode ◽  
High Turbulence ◽  
High Reynolds ◽  
Velocity Moments

The turbulent flow resulting from a top-hat jet exhausting into a large room was investigated. The Reynolds number based on exit conditions was approximately 105. Velocity moments to third order were obtained using flying and stationary hot-wire and burst-mode laser-Doppler anemometry (LDA) techniques. The entire room was fully seeded for the LDA measurements. The measurements are shown to satisfy the differential and integral momentum equations for a round jet in an infinite environment.The results differ substantially from those reported by some earlier investigators, both in the level and shape of the profiles. These differences are attributed to the smaller enclosures used in the earlier works and the recirculation within them. Also, the flying hot-wire and burst-mode LDA measurements made here differ from the stationary wire measurements, especially the higher moments and away from the flow centreline. These differences are attributed to the cross-flow and rectification errors on the latter at the high turbulence intensities present in this flow (30% minimum at centreline). The measurements are used, together with recent dissipation measurements, to compute the energy balance for the jet, and an attempt is made to estimate the pressure-velocity and pressure-strain rate correlations.

Some properties of the Fokker-Planck equation

1985 ◽  
Vol 33 (2) ◽  
pp. 183-189
Author(s):  
G. J. Lewak ◽  
L. A. Soto
Keyword(s):  
Distribution Function ◽  
Plasma Heating ◽  
Electron Distribution Function ◽  
Planck Equation ◽  
Small Mass ◽  
Mass Ratio ◽  
Physical Conditions ◽  
Fokker Planck Equation ◽  
Velocity Moments ◽  
Fokker Planck

The solution of the Fokker-Planck equation for the distribution function of heavy ions in a background of electrons is studied. It is found that quite broad physical conditions on the distribution function (such as the positive requirement and the existence of all velocity moments) are sufficient to eliminate any ambiguity in the time-independent steady-state solutions and to determine a discrete spectrum of the time-dependent Fokker–Planck operator. The more physical case of a Maxwell-Boltzman electron distribution function is treated using the small mass ratio expansion. First-order mass ratio corrections are calculated. A plasma heating application-is suggested.

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