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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]] |

− | ~~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]] |

− | ~~==List of ~~periodic boundary conditions~~==~~
| + | *[[Parallelepiped periodic boundary conditions]] |

− | ~~====Cubic====~~
| + | *[[Truncated octahedral periodic boundary conditions]] |

− | ~~====Orthorhombic====~~
| + | *[[Rhombic dodecahedral periodic boundary conditions]] |

− | ~~====Parallelepiped====~~
| + | *[[Slab periodic boundary conditions]] |

− | ~~====Truncated octahedral====~~
| + | *[[Hexagonal prism periodic boundary conditions]] |

− | ~~<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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