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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.
| | *[[Cubic periodic boundary conditions | Cubic]] |
| 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.
| | *[[Orthorhombic periodic boundary conditions | Orthorhombic]] |
| ==List of periodic boundary conditions==
| | *[[Parallelepiped periodic boundary conditions | Parallelepiped]] |
| ====Cubic====
| | *[[Truncated octahedral periodic boundary conditions | Truncated octahedral]] |
| ====Orthorhombic====
| | *[[Rhombic dodecahedral periodic boundary conditions | Rhombic dodecahedral]] |
| ====Parallelepiped====
| | *[[Slab periodic boundary conditions | Slab]] |
| ====Truncated octahedral====
| | *[[Hexagonal prism periodic boundary conditions | Hexagonal prism]] |
| <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]] | |
| *[[Lees-Edwards boundary conditions]] | |
| *[[System-size dependence]] | |
| ==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)] | |
| *[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)] | |
| *[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)].
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| [[category: Computer simulation techniques]]
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