Metropolis Monte Carlo - Revision history

134.109.16.22: /* Main features */ grammar

2012-06-13T08:37:45Z

Main features: grammar

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	In the case of mixtures, it is useful to consider the so-called [[Semi-grand ensembles]].		In the case of mixtures, it is useful to consider the so-called [[Semi-grand ensembles]].
	The purpose of these techniques is to sample representative configurations of the system at the corresponding		The purpose of these techniques is to sample representative configurations of the system at the corresponding
	thermodynamic conditions. The sampling techniques make use the so-called pseudo-[[Random numbers \|random number]] generators.		thermodynamic conditions. The sampling techniques make use of the so-called pseudo-[[Random numbers \|random number]] generators.

	== Configuration ==		== Configuration ==

Nice and Tidy: /* Boundary Conditions */ Changed an internal link

2010-02-11T13:57:18Z

Boundary Conditions: Changed an internal link

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	== Boundary Conditions ==		== Boundary Conditions ==
			The simulation of homogeneous systems is usually carried out using [[periodic boundary conditions]].
	The simulation of homogeneous systems is usually carried out using [[~~boundary conditions \|~~periodic boundary conditions]].

	== Initial configuration ==		== Initial configuration ==

Nice and Tidy: /* Advanced techniques */ Removed partial list.

2009-10-08T15:12:51Z

Advanced techniques: Removed partial list.

← Older revision		Revision as of 17:12, 8 October 2009
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	== Advanced techniques ==		== Advanced techniques ==
	:''Main article: [[Monte Carlo]]''		:''Main article: [[Monte Carlo]]''
	* [[Configurational bias Monte Carlo]]
	* [[Gibbs-Duhem integration]]
	* [[Cluster algorithms]]
	*[[Computing the Helmholtz energy function of solids]]
	*[[Wang-Landau method]]
	== References ==		== References ==
	<references/>		<references/>

Nice and Tidy: Added Cite type references.

2009-03-24T17:16:49Z

Added Cite type references.

← Older revision		Revision as of 19:16, 24 March 2009
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	The '''Metropolis Monte Carlo''' technique (~~Ref. 2~~) is a variant of the original [[Monte Carlo]] method proposed by [[Nicholas Metropolis]] and [[Stanislaw Ulam]] in 1949 (~~Ref. 1~~).		The '''Metropolis Monte Carlo''' technique
			<ref>[http://dx.doi.org/10.1063/1.1699114 Nicholas Metropolis, Arianna W. Rosenbluth, Marshall N. Rosenbluth, Augusta H. Teller and Edward Teller, "Equation of State Calculations by Fast Computing Machines", Journal of Chemical Physics '''21''' pp.1087-1092 (1953)]</ref>
			is a variant of the original [[Monte Carlo]] method proposed by [[Nicholas Metropolis]] and [[Stanislaw Ulam]] in 1949 <ref>[http://links.jstor.org/sici?sici=0162-1459%28194909%2944%3A247%3C335%3ATMCM%3E2.0.CO%3B2-3 Nicholas Metropolis and S. Ulam "The Monte Carlo Method", Journal of the American Statistical Association '''44''' pp. 335-341 (1949)]</ref>
	== Main features ==		== Main features ==
	Metropolis Monte Carlo simulations can be carried out in different ensembles. For the case of one-component systems the usual ensembles are:		Metropolis Monte Carlo simulations can be carried out in different ensembles. For the case of one-component systems the usual ensembles are:
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	The usual choices for the initial configuration in fluid simulations are:		The usual choices for the initial configuration in fluid simulations are:

	* an equilibrated configuration under similar conditions (for example see ~~Ref~~. 3)		* an equilibrated configuration under similar conditions (for example see <ref>[http://dx.doi.org/10.1016/j.cpc.2005.02.006 Carl McBride, Carlos Vega and Eduardo Sanz "Non-Markovian melting: a novel procedure to generate initial liquid like phases for small molecules for use in computer simulation studies", Computer Physics Communications '''170''' pp. 137-143 (2005)]</ref>)

	* an ordered lattice structure. For details concerning the construction of such structures see: [[Lattice Structures \| lattice structures]].		* an ordered lattice structure. For details concerning the construction of such structures see: [[Lattice Structures \| lattice structures]].
	==~~Interesting reading~~==		== Advanced techniques ==
			:''Main article: [[Monte Carlo]]''
			* [[Configurational bias Monte Carlo]]
			* [[Gibbs-Duhem integration]]
			* [[Cluster algorithms]]
			*[[Computing the Helmholtz energy function of solids]]
			*[[Wang-Landau method]]
			== References ==
			<references/>
			'''Related reading'''
	*[http://links.jstor.org/sici?sici=0162-1459%28194909%2944%3A247%3C335%3ATMCM%3E2.0.CO%3B2-3 Nicholas Metropolis and S. Ulam "The Monte Carlo Method", Journal of the American Statistical Association '''44''' pp. 335-341 (1949)]		*[http://links.jstor.org/sici?sici=0162-1459%28194909%2944%3A247%3C335%3ATMCM%3E2.0.CO%3B2-3 Nicholas Metropolis and S. Ulam "The Monte Carlo Method", Journal of the American Statistical Association '''44''' pp. 335-341 (1949)]
	*[http://library.lanl.gov/cgi-bin/getfile?00326886.pdf Herbert L. Anderson "Metropolis, Monte Carlo, and the MANIAC", Los Alamos Science '''14''' pp. 96-107 (1986)]		*[http://library.lanl.gov/cgi-bin/getfile?00326886.pdf Herbert L. Anderson "Metropolis, Monte Carlo, and the MANIAC", Los Alamos Science '''14''' pp. 96-107 (1986)]
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	*[http://dx.doi.org/10.1063/1.1632124 David P. Landau "The Metropolis Monte Carlo Method in Statistical Physics", AIP Conference Proceedings '''690''' pp. 134-146 (2003)]		*[http://dx.doi.org/10.1063/1.1632124 David P. Landau "The Metropolis Monte Carlo Method in Statistical Physics", AIP Conference Proceedings '''690''' pp. 134-146 (2003)]

	~~== Advanced techniques ==~~
	* [[Configurational bias Monte Carlo]]
	* [[Gibbs-Duhem integration]]
	* [[Cluster algorithms]]
	*[[Computing the Helmholtz energy function of solids]]
	*[[Wang-Landau method]]
	~~== References ==~~
	#[http://links.jstor.org/sici?sici=0162-1459%28194909%2944%3A247%3C335%3ATMCM%3E2.0.CO%3B2-3 Nicholas Metropolis and S. Ulam "The Monte Carlo Method", Journal of the American Statistical Association '''44''' pp. 335-341 (1949)]
	#[http://dx.doi.org/10.1063/1.1699114 Nicholas Metropolis, Arianna W. Rosenbluth, Marshall N. Rosenbluth, Augusta H. Teller and Edward Teller, "Equation of State Calculations by Fast Computing Machines", Journal of Chemical Physics '''21''' pp.1087-1092 (1953)]
	#[http://dx.doi.org/10.1016/j.cpc.2005.02.006 Carl McBride, Carlos Vega and Eduardo Sanz "Non-Markovian melting: a novel procedure to generate initial liquid like phases for small molecules for use in computer simulation studies", Computer Physics Communications '''170''' pp. 137-143 (2005)]
	[[Category: Monte Carlo]]		[[Category: Monte Carlo]]

Nice and Tidy: Added an internal link.

2009-03-17T16:17:15Z

Added an internal link.

← Older revision		Revision as of 18:17, 17 March 2009
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	The '''Metropolis Monte Carlo''' technique (Ref. 2) is a variant of the original Monte Carlo method proposed by [[Nicholas Metropolis]] and [[Stanislaw Ulam]] in 1949 (Ref. 1).		The '''Metropolis Monte Carlo''' technique (Ref. 2) is a variant of the original [[Monte Carlo]] method proposed by [[Nicholas Metropolis]] and [[Stanislaw Ulam]] in 1949 (Ref. 1).
	== Main features ==		== Main features ==
	Metropolis Monte Carlo simulations can be carried out in different ensembles. For the case of one-component systems the usual ensembles are:		Metropolis Monte Carlo simulations can be carried out in different ensembles. For the case of one-component systems the usual ensembles are:

Carl McBride: /* Interesting reading */ Changed numbering for bullet points.

2008-06-27T09:28:29Z

Interesting reading: Changed numbering for bullet points.

← Older revision		Revision as of 11:28, 27 June 2008
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	* an ordered lattice structure. For details concerning the construction of such structures see: [[Lattice Structures \| lattice structures]].		* an ordered lattice structure. For details concerning the construction of such structures see: [[Lattice Structures \| lattice structures]].
	==Interesting reading==		==Interesting reading==
	#[http://links.jstor.org/sici?sici=0162-1459%28194909%2944%3A247%3C335%3ATMCM%3E2.0.CO%3B2-3 Nicholas Metropolis and S. Ulam "The Monte Carlo Method", Journal of the American Statistical Association '''44''' pp. 335-341 (1949)]		*[http://links.jstor.org/sici?sici=0162-1459%28194909%2944%3A247%3C335%3ATMCM%3E2.0.CO%3B2-3 Nicholas Metropolis and S. Ulam "The Monte Carlo Method", Journal of the American Statistical Association '''44''' pp. 335-341 (1949)]
	#[http://library.lanl.gov/cgi-bin/getfile?00326886.pdf Herbert L. Anderson "Metropolis, Monte Carlo, and the MANIAC", Los Alamos Science '''14''' pp. 96-107 (1986)]		*[http://library.lanl.gov/cgi-bin/getfile?00326886.pdf Herbert L. Anderson "Metropolis, Monte Carlo, and the MANIAC", Los Alamos Science '''14''' pp. 96-107 (1986)]
	#[http://library.lanl.gov/cgi-bin/getfile?00326866.pdf N. Metropolis "The Beginnning of the Monte Carlo Method" Los Alamos Science '''15''' pp. 125-130 (1987)]		*[http://library.lanl.gov/cgi-bin/getfile?00326866.pdf N. Metropolis "The Beginnning of the Monte Carlo Method" Los Alamos Science '''15''' pp. 125-130 (1987)]
	#[http://dx.doi.org/10.1063/1.1632112 Marshall N. Rosenbluth "Genesis of the Monte Carlo Algorithm for Statistical Mechanics", AIP Conference Proceedings '''690''' pp. 22-30 (2003)]		*[http://cise.aip.org/getpdf/servlet/GetPDFServlet?filetype=pdf&id=CSENFA000002000001000065000001&idtype=cvips&prog=normal Isabel Beichl and Francis Sullivan "The Metropolis Algorithm", Computing in Science & Engineering '''2''' Issue 1 pp. 65-69 (2000)]
	#[http://dx.doi.org/10.1063/1.1632114 Marshall N. Rosenbluth "Proof of Validity of Monte Carlo Method for Canonical Averaging", AIP Conference Proceedings '''690''' pp. 32-38 (2003)]		*[http://dx.doi.org/10.1063/1.1632112 Marshall N. Rosenbluth "Genesis of the Monte Carlo Algorithm for Statistical Mechanics", AIP Conference Proceedings '''690''' pp. 22-30 (2003)]
	#[http://dx.doi.org/10.1063/1.1632115 William W. Wood "A Brief History of the Use of the Metropolis Method at LANL in the 1950s", AIP Conference Proceedings '''690''' pp. 39-44 (2003)]		*[http://dx.doi.org/10.1063/1.1632114 Marshall N. Rosenbluth "Proof of Validity of Monte Carlo Method for Canonical Averaging", AIP Conference Proceedings '''690''' pp. 32-38 (2003)]
	#[http://dx.doi.org/10.1063/1.1632124 David P. Landau "The Metropolis Monte Carlo Method in Statistical Physics", AIP Conference Proceedings '''690''' pp. 134-146 (2003)]		*[http://dx.doi.org/10.1063/1.1632115 William W. Wood "A Brief History of the Use of the Metropolis Method at LANL in the 1950s", AIP Conference Proceedings '''690''' pp. 39-44 (2003)]
	#[http://cise.aip.org/getpdf/servlet/GetPDFServlet?filetype=pdf&id=CSENFA000002000001000065000001&idtype=cvips&prog=normal Isabel Beichl and Francis Sullivan "The Metropolis Algorithm", Computing in Science & Engineering '''2''' Issue 1 pp. 65-69 (2000)]		*[http://dx.doi.org/10.1063/1.1632124 David P. Landau "The Metropolis Monte Carlo Method in Statistical Physics", AIP Conference Proceedings '''690''' pp. 134-146 (2003)]

	== Advanced techniques ==		== Advanced techniques ==
	* [[Configurational bias Monte Carlo]]		* [[Configurational bias Monte Carlo]]

Carl McBride: Added internal links to Metropolis and Ulam

2008-06-25T12:40:24Z

Added internal links to Metropolis and Ulam

← Older revision		Revision as of 14:40, 25 June 2008
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	The '''Metropolis Monte Carlo''' technique (Ref. 2) is a variant of the original Monte Carlo method proposed by Metropolis and Ulam in 1949 (Ref. 1).		The '''Metropolis Monte Carlo''' technique (Ref. 2) is a variant of the original Monte Carlo method proposed by [[Nicholas Metropolis]] and [[Stanislaw Ulam]] in 1949 (Ref. 1).
	== Main features ==		== Main features ==
	Metropolis Monte Carlo simulations can be carried out in different ensembles. For the case of one-component systems the usual ensembles are:		Metropolis Monte Carlo simulations can be carried out in different ensembles. For the case of one-component systems the usual ensembles are:

Carl McBride: Added a very short introduction.

2008-06-25T12:38:33Z

Added a very short introduction.

← Older revision		Revision as of 14:38, 25 June 2008
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			The '''Metropolis Monte Carlo''' technique (Ref. 2) is a variant of the original Monte Carlo method proposed by Metropolis and Ulam in 1949 (Ref. 1).
	== Main features ==		== Main features ==
	Metropolis Monte Carlo simulations can be carried out in different ensembles. For the case of one-component systems the usual ensembles are:		Metropolis Monte Carlo simulations can be carried out in different ensembles. For the case of one-component systems the usual ensembles are:
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	*[[Wang-Landau method]]		*[[Wang-Landau method]]
	== References ==		== References ==
	#M.P. ~~Allen~~ and ~~D.J~~. ~~Tildesley~~ "~~Computer simulation of liquids~~", ~~Oxford University Press~~		#[http://links.jstor.org/sici?sici=0162-1459%28194909%2944%3A247%3C335%3ATMCM%3E2.0.CO%3B2-3 Nicholas Metropolis and S. Ulam "The Monte Carlo Method", Journal of the American Statistical Association '''44''' pp. 335-341 (1949)]
	#[http://dx.doi.org/10.1063/1.1699114 Nicholas Metropolis, Arianna W. Rosenbluth, Marshall N. Rosenbluth, Augusta H. Teller and Edward Teller, "Equation of State Calculations by Fast Computing Machines", Journal of Chemical Physics '''21''' pp.1087-1092 (1953)]		#[http://dx.doi.org/10.1063/1.1699114 Nicholas Metropolis, Arianna W. Rosenbluth, Marshall N. Rosenbluth, Augusta H. Teller and Edward Teller, "Equation of State Calculations by Fast Computing Machines", Journal of Chemical Physics '''21''' pp.1087-1092 (1953)]
	#[http://dx.doi.org/10.1016/j.cpc.2005.02.006 Carl McBride, Carlos Vega and Eduardo Sanz "Non-Markovian melting: a novel procedure to generate initial liquid like phases for small molecules for use in computer simulation studies", Computer Physics Communications '''170''' pp. 137-143 (2005)]		#[http://dx.doi.org/10.1016/j.cpc.2005.02.006 Carl McBride, Carlos Vega and Eduardo Sanz "Non-Markovian melting: a novel procedure to generate initial liquid like phases for small molecules for use in computer simulation studies", Computer Physics Communications '''170''' pp. 137-143 (2005)]
	[[Category: Monte Carlo]]		[[Category: Monte Carlo]]

Carl McBride: /* Boundary Conditions */ Changed internal link to boundary conditions

2008-04-09T09:10:37Z

Boundary Conditions: Changed internal link to boundary conditions

← Older revision		Revision as of 11:10, 9 April 2008
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	== Boundary Conditions ==		== Boundary Conditions ==

	The simulation of homogeneous systems is usually carried out using [[periodic boundary conditions]].		The simulation of homogeneous systems is usually carried out using [[boundary conditions \|periodic boundary conditions]].

	== Initial configuration ==		== Initial configuration ==

Carl McBride: /* Temperature */

2008-01-30T14:33:35Z

Temperature

← Older revision		Revision as of 16:33, 30 January 2008
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	== Temperature ==		== Temperature ==

	The temperature is usually fixed in Metropolis Monte Carlo simulations, since in classical statistics the kinetic degrees of freedom (momenta) can be generally, integrated out. However, it is possible to design procedures to perform Metropolis Monte Carlo simulations in the [[Microcanonical ensemble\| microcanonical ensemble]] (NVE).		The [[temperature]] is usually fixed in Metropolis Monte Carlo simulations, since in classical statistics the kinetic degrees of freedom (momenta) can be generally, integrated out. However, it is possible to design procedures to perform Metropolis Monte Carlo simulations in the [[Microcanonical ensemble\| microcanonical ensemble]] (NVE).

	See [[Monte Carlo in the microcanonical ensemble]]		See [[Monte Carlo in the microcanonical ensemble]]