http://www.sklogwiki.org/SklogWiki/api.php?action=feedcontributions&user=77.99.43.51&feedformat=atomSklogWiki - User contributions [en]2024-03-29T06:28:33ZUser contributionsMediaWiki 1.41.0http://www.sklogwiki.org/SklogWiki/index.php?title=Stokes-Einstein_relation&diff=5208Stokes-Einstein relation2007-12-17T12:27:47Z<p>77.99.43.51: Changed r in equation to R</p>
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<div>{{Stub-general}}<br />
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,<br />
<br />
:<math> D=\frac{k_B T}{6\pi\eta R} </math><br />
<br />
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]].<br />
==References==<br />
#William Sutherland "A dynamical theory of diffusion for non-electrolytes and the molecular mass of albumin", Philosophical Magazine '''9''' pp. 781-785 (1905)<br />
#[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)]<br />
#[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)]<br />
#[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)]<br />
[[category: Non-equilibrium thermodynamics]]</div>77.99.43.51http://www.sklogwiki.org/SklogWiki/index.php?title=Smoluchowski_equation&diff=5203Smoluchowski equation2007-12-12T17:47:40Z<p>77.99.43.51: </p>
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<div>{{stub-general}}<br />
The '''Smoluchowski equation''' was <br />
introduced by [[Smoluchowski | Marian Smoluchowski ]]. It is a generalisation of the [[diffusion | diffusion equation]].<br />
It provides the [[Boltzmann distribution]] as an [[equilibrium]] solution.<br />
[[Category: Non-equilibrium thermodynamics]]</div>77.99.43.51http://www.sklogwiki.org/SklogWiki/index.php?title=RESPA&diff=5202RESPA2007-12-12T17:43:23Z<p>77.99.43.51: </p>
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<div>This means the ''reversible reference system propagator algorithm'', a well known multiple <br />
[[time step]] method.<br />
<br />
== References ==<br />
*[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)]<br />
*[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)]<br />
*[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)]<br />
*[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)]<br />
[[category:molecular dynamics]]</div>77.99.43.51http://www.sklogwiki.org/SklogWiki/index.php?title=Time_step&diff=5201Time step2007-12-12T17:41:44Z<p>77.99.43.51: /* Multiple time steps */</p>
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<div>{{Stub-general}}<br />
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.<br />
==Multiple time steps==<br />
A well known multiple time step method is the reversible reference system propagator algorithm ([[RESPA]]):<br />
*[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)]<br />
<br />
==See also==<br />
*[[Dissipative particle dynamics]]<br />
[[category:molecular dynamics]]</div>77.99.43.51