Periodic boundary conditions - Revision history

Carl McBride: Corrected typo in Cite

2017-12-18T12:27:04Z

Corrected typo in Cite

← Older revision		Revision as of 14:27, 18 December 2017
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	<ref name="multiple1">[http://dx.doi.org/10.1080/08927029308022499 W. Smith; D. Fincham "The Ewald Sum in Truncated Octahedral and Rhombic Dodecahedral Boundary Conditions", Molecular Simulation '''10''' pp. 67-71 (1993)]</ref>		<ref name="multiple1">[http://dx.doi.org/10.1080/08927029308022499 W. Smith; D. Fincham "The Ewald Sum in Truncated Octahedral and Rhombic Dodecahedral Boundary Conditions", Molecular Simulation '''10''' pp. 67-71 (1993)]</ref>
	====Rhombic dodecahedral====		====Rhombic dodecahedral====
	<ref name="multiple1"> </ref>		<ref name="multiple1"></ref>
	====Slab====		====Slab====
	====Hexagonal prism====		====Hexagonal prism====

Carl McBride: /* References */ Added a recent publication

2015-04-16T11:21:25Z

References: Added a recent publication

← Older revision		Revision as of 13:21, 16 April 2015
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	* Daan Frenkel and Berend Smit "Understanding Molecular Simulation: From Algorithms to Applications", Second Edition pp. 32-35 (2002) ISBN 0-12-267351-4		* Daan Frenkel and Berend Smit "Understanding Molecular Simulation: From Algorithms to Applications", Second Edition pp. 32-35 (2002) ISBN 0-12-267351-4
	*[http://dx.doi.org/10.1080/00268970600744768 Phil Attard "Non-periodic boundary conditions for molecular simulations of condensed matter", Molecular Physics '''104''' pp. 1951-1960 (2006)]		*[http://dx.doi.org/10.1080/00268970600744768 Phil Attard "Non-periodic boundary conditions for molecular simulations of condensed matter", Molecular Physics '''104''' pp. 1951-1960 (2006)]
			*[http://dx.doi.org/10.1063/1.4916294 Dhairyashil Ghatage, Gaurav Tomar and Ratnesh K. Shukla "Soft-spring wall based non-periodic boundary conditions for non-equilibrium molecular dynamics of dense fluids", Journal of Chemical Physics '''142''' 124108 (2015)]

	==External resources==		==External resources==
	*[ftp://ftp.dl.ac.uk/ccp5/ALLEN_TILDESLEY/F.01 Periodic boundary conditions in various geometries] sample FORTRAN computer code from the book [http://www.oup.com/uk/catalogue/?ci=9780198556459 M. P. Allen and D. J. Tildesley "Computer Simulation of Liquids", Oxford University Press (1989)].		*[ftp://ftp.dl.ac.uk/ccp5/ALLEN_TILDESLEY/F.01 Periodic boundary conditions in various geometries] sample FORTRAN computer code from the book [http://www.oup.com/uk/catalogue/?ci=9780198556459 M. P. Allen and D. J. Tildesley "Computer Simulation of Liquids", Oxford University Press (1989)].
	[[category: Computer simulation techniques]]		[[category: Computer simulation techniques]]

Carl McBride: Updated external link

2014-04-02T12:11:10Z

Updated external link

← Older revision		Revision as of 14:11, 2 April 2014
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	A liquid, in the [[thermodynamic limit]], would occupy an infinite volume. It is common experience that one can perfectly well obtain the thermodynamic properties of a material from a more modest sample. However, even a droplet has more atoms or molecules than one can possibly hope to introduce into ones [[Computer simulation techniques \| computer simulation]]. Thus to simulate a bulk sample of liquid it is common practice to use a 'trick' known as '''periodic boundary conditions'''. If one has a cube of atoms/molecules, the molecule leaving one side enters on the diametrically opposite side. This is analogous to the arcade video game Asteriods <ref>[http://www.atari.com/arcade/asteroids play the official on-line version from Atari]</ref>, where one can imagine the action takes place on the surface of a torus.		A liquid, in the [[thermodynamic limit]], would occupy an infinite volume. It is common experience that one can perfectly well obtain the thermodynamic properties of a material from a more modest sample. However, even a droplet has more atoms or molecules than one can possibly hope to introduce into ones [[Computer simulation techniques \| computer simulation]]. Thus to simulate a bulk sample of liquid it is common practice to use a 'trick' known as '''periodic boundary conditions'''. If one has a cube of atoms/molecules, the molecule leaving one side enters on the diametrically opposite side. This is analogous to the arcade video game Asteriods <ref>[http://www.atari.com/arcade/asteroids#!/arcade/asteroids/play play the official on-line version from Atari]</ref>, where one can imagine the action takes place on the surface of a torus.
	In general, a simulation box whose dimensions are several times the range of the interaction potential works well for equilibrium properties, although in the region of a [[phase transitions \|phase transition]], where long-range fluctuations play an important role, problems may arise. In [[confined systems]] periodicity is only required in some spacial dimensions.		In general, a simulation box whose dimensions are several times the range of the interaction potential works well for equilibrium properties, although in the region of a [[phase transitions \|phase transition]], where long-range fluctuations play an important role, problems may arise. In [[confined systems]] periodicity is only required in some spacial dimensions.
	==List of periodic boundary conditions==		==List of periodic boundary conditions==

Carl McBride: Added an internal link

2010-04-14T11:11:53Z

Added an internal link

← Older revision		Revision as of 13:11, 14 April 2010
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	*[[Binder cumulant]]		*[[Binder cumulant]]
	*[[Finite size scaling]]		*[[Finite size scaling]]
			*[[Lees-Edwards boundary conditions]]
	*[[System-size dependence]]		*[[System-size dependence]]

	==References==		==References==
	<references/>		<references/>

Carl McBride: /* See also */ Added an internal link

2010-02-11T14:56:28Z

Nice and Tidy: /* References */ Added a book

2010-02-11T14:08:38Z

References: Added a book

← Older revision		Revision as of 16:08, 11 February 2010
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	*[http://dx.doi.org/10.1063/1.441276 Lawrence R. Pratt and Steven W. Haan "Effects of periodic boundary conditions on equilibrium properties of computer simulated fluids. I. Theory", Journal of Chemical Physics '''74''' pp. 1864- (1981)]		*[http://dx.doi.org/10.1063/1.441276 Lawrence R. Pratt and Steven W. Haan "Effects of periodic boundary conditions on equilibrium properties of computer simulated fluids. I. Theory", Journal of Chemical Physics '''74''' pp. 1864- (1981)]
	*[http://www.oup.com/uk/catalogue/?ci=9780198556459 M. P. Allen and D. J. Tildesley "Computer Simulation of Liquids", Oxford University Press (1989)] Section 1.5.2		*[http://www.oup.com/uk/catalogue/?ci=9780198556459 M. P. Allen and D. J. Tildesley "Computer Simulation of Liquids", Oxford University Press (1989)] Section 1.5.2
			* Daan Frenkel and Berend Smit "Understanding Molecular Simulation: From Algorithms to Applications", Second Edition pp. 32-35 (2002) ISBN 0-12-267351-4
	*[http://dx.doi.org/10.1080/00268970600744768 Phil Attard "Non-periodic boundary conditions for molecular simulations of condensed matter", Molecular Physics '''104''' pp. 1951-1960 (2006)]		*[http://dx.doi.org/10.1080/00268970600744768 Phil Attard "Non-periodic boundary conditions for molecular simulations of condensed matter", Molecular Physics '''104''' pp. 1951-1960 (2006)]

	==External resources==		==External resources==
	*[ftp://ftp.dl.ac.uk/ccp5/ALLEN_TILDESLEY/F.01 Periodic boundary conditions in various geometries] sample FORTRAN computer code from the book [http://www.oup.com/uk/catalogue/?ci=9780198556459 M. P. Allen and D. J. Tildesley "Computer Simulation of Liquids", Oxford University Press (1989)].		*[ftp://ftp.dl.ac.uk/ccp5/ALLEN_TILDESLEY/F.01 Periodic boundary conditions in various geometries] sample FORTRAN computer code from the book [http://www.oup.com/uk/catalogue/?ci=9780198556459 M. P. Allen and D. J. Tildesley "Computer Simulation of Liquids", Oxford University Press (1989)].
	[[category: Computer simulation techniques]]		[[category: Computer simulation techniques]]

Carl McBride: Merged content form Boundary conditions page.

2010-02-11T13:54:27Z

Merged content form Boundary conditions page.

← Older revision		Revision as of 15:54, 11 February 2010
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	A liquid, in the [[thermodynamic limit]], would occupy an infinite volume. It is common experience that one can perfectly well obtain the thermodynamic properties of a material from a more modest sample. However, even a droplet has more atoms or molecules than one can possibly hope to introduce into ones [[Computer simulation techniques \| computer simulation]]. Thus to simulate a bulk sample of liquid it is common practice to use a 'trick' known as '''periodic boundary conditions'''. If one has a cube of atoms/molecules, the molecule leaving one side enters on the diametrically opposite side. This is analogous to the arcade video game Asteriods <ref>[http://www.atari.com/arcade/asteroids play the official on-line version from Atari]</ref>, where one can imagine the action takes place on the surface of a torus.		A liquid, in the [[thermodynamic limit]], would occupy an infinite volume. It is common experience that one can perfectly well obtain the thermodynamic properties of a material from a more modest sample. However, even a droplet has more atoms or molecules than one can possibly hope to introduce into ones [[Computer simulation techniques \| computer simulation]]. Thus to simulate a bulk sample of liquid it is common practice to use a 'trick' known as '''periodic boundary conditions'''. If one has a cube of atoms/molecules, the molecule leaving one side enters on the diametrically opposite side. This is analogous to the arcade video game Asteriods <ref>[http://www.atari.com/arcade/asteroids play the official on-line version from Atari]</ref>, where one can imagine the action takes place on the surface of a torus.
	In general, a simulation box whose dimensions are several times the range of the interaction potential works well for equilibrium properties, although in the region of a [[phase transitions \|phase transition]], where long-range fluctuations play an important role, problems may arise.		In general, a simulation box whose dimensions are several times the range of the interaction potential works well for equilibrium properties, although in the region of a [[phase transitions \|phase transition]], where long-range fluctuations play an important role, problems may arise. In [[confined systems]] periodicity is only required in some spacial dimensions.
	*[[~~Cubic periodic boundary conditions \| Cubic~~]]		==List of periodic boundary conditions==
	*[[Orthorhombic periodic boundary conditions \| Orthorhombic]]		====Cubic====
	*[[Parallelepiped periodic boundary conditions \| Parallelepiped]]		====Orthorhombic====
	*[[Truncated octahedral ~~periodic boundary conditions \|~~ Truncated ~~octahedral]~~]		====Parallelepiped====
	*[[Rhombic dodecahedral ~~periodic boundary conditions \| Rhombic dodecahedral]]~~		====Truncated octahedral====
	*[[Slab ~~periodic boundary conditions \| Slab]]~~		<ref name="multiple1">[http://dx.doi.org/10.1080/08927029308022499 W. Smith; D. Fincham "The Ewald Sum in Truncated Octahedral and Rhombic Dodecahedral Boundary Conditions", Molecular Simulation '''10''' pp. 67-71 (1993)]</ref>
	*[[Hexagonal prism ~~periodic boundary conditions \| Hexagonal prism]]~~		====Rhombic dodecahedral====
			<ref name="multiple1"> </ref>
			====Slab====
			====Hexagonal prism====
	==See also==		==See also==
	*[[Finite size scaling]]		*[[Finite size scaling]]
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	*[http://dx.doi.org/10.1007/BF01023055 M. J. Mandell "On the properties of a periodic fluid", Journal of Statistical Physics '''15''' pp. 299-305 (1976)]		*[http://dx.doi.org/10.1007/BF01023055 M. J. Mandell "On the properties of a periodic fluid", Journal of Statistical Physics '''15''' pp. 299-305 (1976)]
	*[http://dx.doi.org/10.1063/1.441276 Lawrence R. Pratt and Steven W. Haan "Effects of periodic boundary conditions on equilibrium properties of computer simulated fluids. I. Theory", Journal of Chemical Physics '''74''' pp. 1864- (1981)]		*[http://dx.doi.org/10.1063/1.441276 Lawrence R. Pratt and Steven W. Haan "Effects of periodic boundary conditions on equilibrium properties of computer simulated fluids. I. Theory", Journal of Chemical Physics '''74''' pp. 1864- (1981)]
			*[http://www.oup.com/uk/catalogue/?ci=9780198556459 M. P. Allen and D. J. Tildesley "Computer Simulation of Liquids", Oxford University Press (1989)] Section 1.5.2
			*[http://dx.doi.org/10.1080/00268970600744768 Phil Attard "Non-periodic boundary conditions for molecular simulations of condensed matter", Molecular Physics '''104''' pp. 1951-1960 (2006)]
	==External resources==		==External resources==
	*[ftp://ftp.dl.ac.uk/ccp5/ALLEN_TILDESLEY/F.01 Periodic boundary conditions in various geometries] sample FORTRAN computer code from the book [http://www.oup.com/uk/catalogue/?ci=9780198556459 M. P. Allen and D. J. Tildesley "Computer Simulation of Liquids", Oxford University Press (1989)].		*[ftp://ftp.dl.ac.uk/ccp5/ALLEN_TILDESLEY/F.01 Periodic boundary conditions in various geometries] sample FORTRAN computer code from the book [http://www.oup.com/uk/catalogue/?ci=9780198556459 M. P. Allen and D. J. Tildesley "Computer Simulation of Liquids", Oxford University Press (1989)].
	[[category: Computer simulation techniques]]		[[category: Computer simulation techniques]]

Carl McBride: Added a See also section

2010-02-11T13:40:00Z

Added a See also section

← Older revision		Revision as of 15:40, 11 February 2010
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	*[[Slab periodic boundary conditions \| Slab]]		*[[Slab periodic boundary conditions \| Slab]]
	*[[Hexagonal prism periodic boundary conditions \| Hexagonal prism]]		*[[Hexagonal prism periodic boundary conditions \| Hexagonal prism]]
			==See also==
			*[[Finite size scaling]]
			*[[System-size dependence]]
	==References==		==References==
	<references/>		<references/>

Carl McBride at 13:35, 11 February 2010

2010-02-11T13:35:25Z

← Older revision		Revision as of 15:35, 11 February 2010
Line 1:		Line 1:
	A liquid, in the [[thermodynamic limit]], would occupy an infinite volume. It is common experience that one can perfectly well obtain the thermodynamic properties of a material from a more modest sample. However, even a droplet has more atoms or molecules than one can possibly hope to introduce into ones [[Computer simulation techniques \| computer simulation]]. Thus to simulate a bulk sample of liquid it is common practice to use a 'trick' known as '''periodic boundary conditions'''. If one has a cube of atoms/molecules, the molecule leaving one side enters on the diametrically opposite side. This is analogous to the arcade video game Asteriods <ref>[http://www.atari.com/arcade/asteroids play the official on-line version from Atari]</ref>, where one can imagine the action takes place on the surface of a torus.		A liquid, in the [[thermodynamic limit]], would occupy an infinite volume. It is common experience that one can perfectly well obtain the thermodynamic properties of a material from a more modest sample. However, even a droplet has more atoms or molecules than one can possibly hope to introduce into ones [[Computer simulation techniques \| computer simulation]]. Thus to simulate a bulk sample of liquid it is common practice to use a 'trick' known as '''periodic boundary conditions'''. If one has a cube of atoms/molecules, the molecule leaving one side enters on the diametrically opposite side. This is analogous to the arcade video game Asteriods <ref>[http://www.atari.com/arcade/asteroids play the official on-line version from Atari]</ref>, where one can imagine the action takes place on the surface of a torus.
	In general, a simulation box whose dimensions are several times the range of the interaction potential works well for equilibrium properties, although in the region of a [[phase transitions \|phase transition]] problems may arise.		In general, a simulation box whose dimensions are several times the range of the interaction potential works well for equilibrium properties, although in the region of a [[phase transitions \|phase transition]], where long-range fluctuations play an important role, problems may arise.
	*[[Cubic periodic boundary conditions \| Cubic]]		*[[Cubic periodic boundary conditions \| Cubic]]
	*[[Orthorhombic periodic boundary conditions \| Orthorhombic]]		*[[Orthorhombic periodic boundary conditions \| Orthorhombic]]

Carl McBride: Added a couple of papers.

2010-02-11T13:28:47Z

Added a couple of papers.

← Older revision		Revision as of 15:28, 11 February 2010
Line 1:		Line 1:
	A liquid, in the [[thermodynamic limit]], would occupy an infinite volume. It is common experience that one can perfectly well obtain the thermodynamic properties of a material from a more modest sample. However, even a droplet has more atoms or molecules than one can possibly hope to introduce into ones [[Computer simulation techniques \| computer simulation]]. Thus to simulate a bulk sample of liquid it is common practice to use a 'trick' known as '''periodic boundary conditions'''. If one has a cube of atoms/molecules, the molecule leaving one side enters on the diametrically opposite side. This is analogous to the arcade video game Asteriods <ref>[http://www.atari.com/arcade/asteroids play the official on-line version from Atari]</ref>, where one can imagine the action takes place on the surface of a torus.		A liquid, in the [[thermodynamic limit]], would occupy an infinite volume. It is common experience that one can perfectly well obtain the thermodynamic properties of a material from a more modest sample. However, even a droplet has more atoms or molecules than one can possibly hope to introduce into ones [[Computer simulation techniques \| computer simulation]]. Thus to simulate a bulk sample of liquid it is common practice to use a 'trick' known as '''periodic boundary conditions'''. If one has a cube of atoms/molecules, the molecule leaving one side enters on the diametrically opposite side. This is analogous to the arcade video game Asteriods <ref>[http://www.atari.com/arcade/asteroids play the official on-line version from Atari]</ref>, where one can imagine the action takes place on the surface of a torus.
			In general, a simulation box whose dimensions are several times the range of the interaction potential works well for equilibrium properties, although in the region of a [[phase transitions \|phase transition]] problems may arise.
	*[[Cubic periodic boundary conditions \| Cubic]]		*[[Cubic periodic boundary conditions \| Cubic]]
	*[[Orthorhombic periodic boundary conditions \| Orthorhombic]]		*[[Orthorhombic periodic boundary conditions \| Orthorhombic]]
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	==References==		==References==
	<references/>		<references/>
			'''Related reading'''
			*[http://dx.doi.org/10.1007/BF01023055 M. J. Mandell "On the properties of a periodic fluid", Journal of Statistical Physics '''15''' pp. 299-305 (1976)]
			*[http://dx.doi.org/10.1063/1.441276 Lawrence R. Pratt and Steven W. Haan "Effects of periodic boundary conditions on equilibrium properties of computer simulated fluids. I. Theory", Journal of Chemical Physics '''74''' pp. 1864- (1981)]
	==External resources==		==External resources==
	*[ftp://ftp.dl.ac.uk/ccp5/ALLEN_TILDESLEY/F.01 Periodic boundary conditions in various geometries] sample FORTRAN computer code from the book [http://www.oup.com/uk/catalogue/?ci=9780198556459 M. P. Allen and D. J. Tildesley "Computer Simulation of Liquids", Oxford University Press (1989)].		*[ftp://ftp.dl.ac.uk/ccp5/ALLEN_TILDESLEY/F.01 Periodic boundary conditions in various geometries] sample FORTRAN computer code from the book [http://www.oup.com/uk/catalogue/?ci=9780198556459 M. P. Allen and D. J. Tildesley "Computer Simulation of Liquids", Oxford University Press (1989)].
	[[category: Computer simulation techniques]]		[[category: Computer simulation techniques]]

← Older revision		Revision as of 15:35, 11 February 2010
Line 1:		Line 1:
	A liquid, in the [[thermodynamic limit]], would occupy an infinite volume. It is common experience that one can perfectly well obtain the thermodynamic properties of a material from a more modest sample. However, even a droplet has more atoms or molecules than one can possibly hope to introduce into ones [[Computer simulation techniques \| computer simulation]]. Thus to simulate a bulk sample of liquid it is common practice to use a 'trick' known as '''periodic boundary conditions'''. If one has a cube of atoms/molecules, the molecule leaving one side enters on the diametrically opposite side. This is analogous to the arcade video game Asteriods <ref>[http://www.atari.com/arcade/asteroids play the official on-line version from Atari]</ref>, where one can imagine the action takes place on the surface of a torus.		A liquid, in the [[thermodynamic limit]], would occupy an infinite volume. It is common experience that one can perfectly well obtain the thermodynamic properties of a material from a more modest sample. However, even a droplet has more atoms or molecules than one can possibly hope to introduce into ones [[Computer simulation techniques \| computer simulation]]. Thus to simulate a bulk sample of liquid it is common practice to use a 'trick' known as '''periodic boundary conditions'''. If one has a cube of atoms/molecules, the molecule leaving one side enters on the diametrically opposite side. This is analogous to the arcade video game Asteriods <ref>[http://www.atari.com/arcade/asteroids play the official on-line version from Atari]</ref>, where one can imagine the action takes place on the surface of a torus.
	In general, a simulation box whose dimensions are several times the range of the interaction potential works well for equilibrium properties, although in the region of a [[phase transitions \|phase transition]] problems may arise.		In general, a simulation box whose dimensions are several times the range of the interaction potential works well for equilibrium properties, although in the region of a [[phase transitions \|phase transition]], where long-range fluctuations play an important role, problems may arise.
	*[[Cubic periodic boundary conditions \| Cubic]]		*[[Cubic periodic boundary conditions \| Cubic]]
	*[[Orthorhombic periodic boundary conditions \| Orthorhombic]]		*[[Orthorhombic periodic boundary conditions \| Orthorhombic]]

← Older revision		Revision as of 16:56, 11 February 2010
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	====Hexagonal prism====		====Hexagonal prism====
	==See also==		==See also==
			*[[Binder cumulant]]
	*[[Finite size scaling]]		*[[Finite size scaling]]
	*[[System-size dependence]]		*[[System-size dependence]]

	==References==		==References==
	<references/>		<references/>