Constant-pressure Monte Carlo: Difference between revisions
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In '''constant-pressure Monte Carlo''' a trial change in the volume becomes one of the [[Monte Carlo]] moves. | In '''constant-pressure Monte Carlo''' a trial change in the volume becomes one of the [[Monte Carlo]] moves. | ||
The [[weighting function]], ''w'', is given by ( | The [[weighting function]], ''w'', is given by (Eq. 2 in <ref>[http://dx.doi.org/10.1080/00268978400101951 R. Eppenga and D. Frenkel "Monte Carlo study of the isotropic and nematic phases of infinitely thin hard platelets", Molecular Physics '''52''' pp. 1303-1334 (1984)]</ref>) | ||
:<math>w \simeq c \frac{V^N}{N!} \exp \left | :<math>w \simeq c \frac{V^N}{N!} \exp \left\{ -\beta [ U(q^N) +pV ] \right\} </math> | ||
for a change in volume, <math>\Delta V</math>, one has | for a change in volume, <math>\Delta V</math>, one has | ||
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==References== | ==References== | ||
<references/> | |||
;Related reading | |||
*[http://molsim.chem.uva.nl/frenkel_smit Daan Frenkel and Berend Smit "Understanding Molecular Simulation: From Algorithms to Applications", Second Edition (2002)] § 5.4 | |||
[[category: Monte Carlo]] | [[category: Monte Carlo]] | ||
Latest revision as of 11:55, 17 May 2013
In constant-pressure Monte Carlo a trial change in the volume becomes one of the Monte Carlo moves. The weighting function, w, is given by (Eq. 2 in [1])
![{\displaystyle w\simeq c{\frac {V^{N}}{N!}}\exp \left\{-\beta [U(q^{N})+pV]\right\}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/e273fa3bb7762d9238306b389bd1d7b4b4815215)
for a change in volume, , one has
![{\displaystyle r={\frac {w_{\rm {new}}}{w_{\rm {old}}}}=\exp \left[-\beta \left(\Delta U+p\Delta V-Nk_{B}T\ln {\frac {V+\Delta V}{V}}\right)\right]}](https://wikimedia.org/api/rest_v1/media/math/render/svg/ee39f2e32f0d105ac442a447e3b0f59b762c73f3)
If then the move is accepted, and if then r is compared with a random number . If then the move is accepted.
References[edit]
- Related reading