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Stokes-Einstein relation

2007-12-17T12:27:47Z

77.99.43.51: Changed r in equation to R

{{Stub-general}}
The '''Stokes-Einstein relation''', originally derived by William Sutherland (Ref. 1) but almost simultaneously published by [[Albert Einstein |Einstein]] (Ref. 2), states that, for a sphere of radius <math>R</math> immersed in a fluid,

:<math> D=\frac{k_B T}{6\pi\eta R} </math>

where ''D'' is the diffusion constant, <math>k_B</math> is the [[Boltzmann constant]], ''T'' is the [[temperature]] and <math>\eta</math> is the [[viscosity]].
==References==
#William Sutherland "A dynamical theory of diffusion for non-electrolytes and the molecular mass of albumin", Philosophical Magazine '''9''' pp. 781-785 (1905)
#[http://dx.doi.org/10.1002/andp.19053220806 A. Einstein "Über die von der molekularkinetischen Theorie der Wärme geforderte Bewegung von in ruhenden Flüssigkeiten suspendierten Teilchen", Annalen der Physik '''17''' pp. 549-560 (1905)]
#[http://dx.doi.org/10.1063/1.449616 Robert Zwanzig and Alan K. Harrison "Modifications of the Stokes–Einstein formula", Journal of Chemical Physics '''83''' pp. 5861-5862 (1985)]
#[http://dx.doi.org/10.1063/1.2738063 M. Cappelezzo, C. A. Capellari, S. H. Pezzin, and L. A. F. Coelho "Stokes-Einstein relation for pure simple fluids", Journal of Chemical Physics '''126''' 224516 (2007)]
[[category: Non-equilibrium thermodynamics]]

Smoluchowski equation

2007-12-12T17:47:40Z

77.99.43.51:

{{stub-general}}
The '''Smoluchowski equation''' was
introduced by [[Smoluchowski | Marian Smoluchowski ]]. It is a generalisation of the [[diffusion | diffusion equation]].
It provides the [[Boltzmann distribution]] as an [[equilibrium]] solution.
[[Category: Non-equilibrium thermodynamics]]

RESPA

2007-12-12T17:43:23Z

77.99.43.51:

This means the ''reversible reference system propagator algorithm'', a well known multiple
[[time step]] method.

== References ==
*[http://dx.doi.org/10.1063/1.460004 Mark E. Tuckerman, Bruce J. Berne, and Angelo Rossi "Molecular dynamics algorithm for multiple time scales: Systems with disparate masses" J. Chem. Phys. '''94''' 1465 (1990)]
*[http://dx.doi.org/10.1063/1.463137 M. Tuckerman, B. J. Berne and G. J. Martyna "Reversible multiple time scale molecular dynamics", Journal of Chemical Physics '''97''' pp. 1990-2001 (1992)]
*[http://dx.doi.org/10.1063/1.472005 Steven J. Stuart, Ruhong Zhou, and B. J. Berne "Molecular dynamics with multiple time scales: The selection of efficient reference system propagators" Stuart, S., Zhou, R., and Berne, B., J. Chem. Phys. '''105''' 1426 (1996)]
*[http://dx.doi.org/10.1063/1.471067 Piero Procacci and Massimo Marchi "Taming the Ewald sum in molecular dynamics simulations of solvated proteins via a multiple time step algorithm" Procacci, P., and Marchi, M., J. Chem. Phys. '''104''' 3003 (1996)]
[[category:molecular dynamics]]

Time step

2007-12-12T17:41:44Z

77.99.43.51: /* Multiple time steps */

{{Stub-general}}
The time-step is an important variable in molecular dynamics simulations. It is usually of the order of femto (<math>10^{-15}</math>) seconds for molecular simulations.
==Multiple time steps==
A well known multiple time step method is the reversible reference system propagator algorithm ([[RESPA]]):
*[http://dx.doi.org/10.1063/1.463137 M. Tuckerman, B. J. Berne and G. J. Martyna "Reversible multiple time scale molecular dynamics", Journal of Chemical Physics '''97''' pp. 1990-2001 (1992)]

==See also==
*[[Dissipative particle dynamics]]
[[category:molecular dynamics]]