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<div>'''Stokesian dynamics'''<ref><br />
{{cite journal<br />
| last =Brady<br />
| first =John<br />
| coauthors = Bossis, Georges<br />
| title = Stokesian Dynamics<br />
| journal = Ann. Rev. Fluid Mech.<br />
| volume = 20<br />
| pages = 111–157<br />
| date = 1988<br />
| doi = 10.1146/annurev.fl.20.010188.000551<br />
|bibcode = 1988AnRFM..20..111B }}</ref><br />
is a solution technique for the [[Langevin equation]], which is the relevant form of [[Newton's laws of motion|Newton's 2nd law]] for a [[Brownian motion|Brownian particle]]<br />
:<math>m\frac{du}{dt} = F^{H} + F^{B} + F^{P}. </math><br />
In the above equation <math>F^{H}</math> is the hydrodynamic force, i.e., force exerted by the fluid on the particle due to relative motion between them. <math>F^{B}</math> is the [[stochastic]] [[Brownian motion|Brownian]] force due to thermal motion of fluid particles. <math> F^{P}</math> is the inter particle force,e.g. electrostatic repulsion between like charged particles. [[Brownian dynamics]] is one of the popular techniques of solving the [[Langevin equation]], but the hydrodynamic interaction in [[Brownian dynamics]] is highly simplified and normally includes only the isolated body resistance. On the other hand, Stokesian dynamics includes the many body hydrodynamic interactions. Hydrodynamic interaction is very important for non-equilibrium suspensions, like a sheared [[Suspension (chemistry)|suspension]], where it plays a vital role in its microstructure and hence its properties. Stokesian dynamics is used primarily for non-equilibrium suspensions where it has been shown to provide results which agree with experiments.{{Citation needed|date=June 2009}}<br />
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==Hydrodynamic interaction==<br />
One of the key features of Stokesian dynamics is its handing of the hydrodynamic interactions, which is fairly accurate without being computationally inhibitive (like [[boundary element method|boundary integral methods]]) for a large number of particles. Classical Stokesian dynamics requires <math>O(N^{3})</math> operations where ''N'' is the number of particles in the system (usually a periodic box). Recent advances have reduced the computational cost to <math> O(N^{1.25} \, \log N). </math><ref><br />
{{cite journal<br />
| last =Brady<br />
| first =John<br />
| coauthors = Sierou, Asimina<br />
| title = Accelerated Stokesian Dynamics simulations<br />
| journal = Journal of Fluid Mechanics<br />
| volume = 448<br />
| pages = 115–146<br />
| year = 2001<br />
| doi = 10.1017/S0022112001005912<br />
}}</ref><br />
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== See also ==<br />
* [[Immersed boundary method]]<br />
* [[Stochastic Eulerian Lagrangian method]]<br />
<br />
==References==<br />
{{reflist}}<br />
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[[Category:Statistical mechanics]]<br />
[[Category:Equations]]<br />
[[Category:Fluid mechanics]]</div>75.131.113.53