Difference between revisions of "Periodic boundary conditions"

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*[[Cubic periodic boundary conditions | Cubic]]
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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#!/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.
*[[Orthorhombic periodic boundary conditions | Orthorhombic]]
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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.
*[[Parallelepiped periodic boundary conditions | Parallelepiped]]
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==List of periodic boundary conditions==
*[[Truncated octahedral periodic boundary conditions | Truncated octahedral]]
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====Cubic====
*[[Rhombic dodecahedral periodic boundary conditions | Rhombic dodecahedral]]
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====Orthorhombic====
*[[Slab periodic boundary conditions | Slab]]
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====Parallelepiped====
*[[Hexagonal prism periodic boundary conditions | Hexagonal prism]]
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====Truncated octahedral====
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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>
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====Rhombic dodecahedral====
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<ref name="multiple1"></ref>
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====Slab====
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====Hexagonal prism====
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==See also==
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*[[Binder cumulant]]
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*[[Finite size scaling]]
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*[[Lees-Edwards boundary conditions]]
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*[[System-size dependence]]
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==References==
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<references/>
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'''Related reading'''
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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)]
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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)]
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*[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
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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
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*[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)]
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*[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)]
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==External resources==
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*[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]]

Latest revision as of 13:27, 18 December 2017

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. 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 [1], 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 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[edit]

Cubic[edit]

Orthorhombic[edit]

Parallelepiped[edit]

Truncated octahedral[edit]

[2]

Rhombic dodecahedral[edit]

[2]

Slab[edit]

Hexagonal prism[edit]

See also[edit]

References[edit]

Related reading

External resources[edit]