Constant-pressure Monte Carlo: Difference between revisions
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Carl McBride (talk | contribs) (New page: 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 (Ref 1 Eq. 2) :<math>w \simeq ...) |
m (correction of first eq.) |
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The [[weighting function]], ''w'', is given by (Ref 1 Eq. 2) | The [[weighting function]], ''w'', is given by (Ref 1 Eq. 2) | ||
:<math>w \simeq c \frac{V^N}{N!} \exp \left[ -\beta ( U(q^N | :<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 | ||
Revision as of 14:39, 20 February 2009
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 (Ref 1 Eq. 2)
![{\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/b0a54c12502b0d2435c02c77c14129d90e92cd88)
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.
