Constant-pressure Monte Carlo - Revision history

Carl McBride: Added a reference

2013-05-17T09:55:48Z

Added a reference

← Older revision		Revision as of 11:55, 17 May 2013
Line 1:		Line 1:
	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 (~~Ref 1~~ Eq. 2)		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\{ -\beta [ U(q^N) +pV ] \right\} </math>		:<math>w \simeq c \frac{V^N}{N!} \exp \left\{ -\beta [ U(q^N) +pV ] \right\} </math>
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	==References==		==References==
	#[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~~)]		<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]]

Noe: cosmetic changes

2009-02-24T09:37:54Z

cosmetic changes

← Older revision		Revision as of 11:37, 24 February 2009
Line 2:		Line 2:
	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) +pV )\right]</math>		:<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

Noe: correction of first eq.

2009-02-20T13:39:31Z

correction of first eq.

← Older revision		Revision as of 15:39, 20 February 2009
Line 2:		Line 2:
	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)) +pV \right]</math>		:<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

Carl McBride: 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) : $w \simeq ...$

2007-07-04T16:23:44Z

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 ...

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 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

:<math>r = \frac{w_{\rm new}}{w_{\rm old}} = \exp \left[ -\beta \left( \Delta U + p\Delta V - Nk_BT \ln \frac{V+\Delta V}{V}\right)\right]</math>

If <math>r \ge 1</math> then the move is accepted, and if <math>0 < r < 1</math> then ''r'' is compared with a random number
<math>0 < x < 1</math>. If <math>x \le r</math> then the move is accepted.

==References==
#[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)]
[[category: Monte Carlo]]

Constant-pressure Monte Carlo - Revision history

Carl McBride: Added a reference

Noe: cosmetic changes

Noe: correction of first eq.

Carl McBride: 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) :w \simeq ...

Carl McBride: 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) : $w \simeq ...$