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Efficient methods for handling long-range forces in particle-particle simulations

Efficient methods for handling long-range forces in particle-particle simulations
Efficient methods for handling long-range forces in particle-particle simulations
A number of problems arise when long-range forces, such as those governed by Bessel functions, are used in particle–particle simulations. If a simple cutoff for the interaction is used, the system may find an equilibrium configuration at zero temperature that is not a regular lattice yet has an energy lower than the theoretically predicted minimum for the physical system. We demonstrate two methods to overcome these problems in Monte Carlo and molecular dynamics simulations. The first uses a smoothed potential to truncate the interaction in a single unit cell: this is appropriate for phenomenological characterisations, but may be applied to any potential. The second is a new method for summing the unmodified potential in an infinitely tiled periodic system, which is in excess of 20,000 times faster than previous naive methods which add periodic images in shells of increasing radius: this is suitable for quantitative studies. Finally, we show that numerical experiments which do not handle the long-range force carefully may give misleading results: both of our proposed methods overcome these problems.
Infinite lattice summation, Cut-off, Long-range forces, Molecular Dynamics, Monte Carlo, Periodic boundaryconditions.
0021-9991
372-384
Fangohr, Hans
9b7cfab9-d5dc-45dc-947c-2eba5c81a160
Price, Andrew R.
b020e5b3-c608-4377-af0b-f97cd7ff64dd
Cox, Simon J.
0e62aaed-24ad-4a74-b996-f606e40e5c55
de Groot, Peter A.J.
98c21141-cf90-4e5c-8f2b-d2aae8efb84d
Daniell, Geoffrey J.
82c59eea-5002-4889-8823-2c6e5b3288d3
Thomas, Ken S.
b107015f-c7d9-42cc-b87b-207c49e5369a
Fangohr, Hans
9b7cfab9-d5dc-45dc-947c-2eba5c81a160
Price, Andrew R.
b020e5b3-c608-4377-af0b-f97cd7ff64dd
Cox, Simon J.
0e62aaed-24ad-4a74-b996-f606e40e5c55
de Groot, Peter A.J.
98c21141-cf90-4e5c-8f2b-d2aae8efb84d
Daniell, Geoffrey J.
82c59eea-5002-4889-8823-2c6e5b3288d3
Thomas, Ken S.
b107015f-c7d9-42cc-b87b-207c49e5369a

Fangohr, Hans, Price, Andrew R., Cox, Simon J., de Groot, Peter A.J., Daniell, Geoffrey J. and Thomas, Ken S. (2000) Efficient methods for handling long-range forces in particle-particle simulations. Journal of Computational Physics, 162 (2), 372-384. (doi:10.1006/jcph.2000.6541).

Record type: Article

Abstract

A number of problems arise when long-range forces, such as those governed by Bessel functions, are used in particle–particle simulations. If a simple cutoff for the interaction is used, the system may find an equilibrium configuration at zero temperature that is not a regular lattice yet has an energy lower than the theoretically predicted minimum for the physical system. We demonstrate two methods to overcome these problems in Monte Carlo and molecular dynamics simulations. The first uses a smoothed potential to truncate the interaction in a single unit cell: this is appropriate for phenomenological characterisations, but may be applied to any potential. The second is a new method for summing the unmodified potential in an infinitely tiled periodic system, which is in excess of 20,000 times faster than previous naive methods which add periodic images in shells of increasing radius: this is suitable for quantitative studies. Finally, we show that numerical experiments which do not handle the long-range force carefully may give misleading results: both of our proposed methods overcome these problems.

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More information

Published date: August 2000
Additional Information: Text and figures also available at http://arXiv.org/abs/physics/0004013
Keywords: Infinite lattice summation, Cut-off, Long-range forces, Molecular Dynamics, Monte Carlo, Periodic boundaryconditions.
Organisations: Electronic & Software Systems

Identifiers

Local EPrints ID: 252954
URI: https://eprints.soton.ac.uk/id/eprint/252954
ISSN: 0021-9991
PURE UUID: 2daa7305-ff35-4744-9f69-9320c3bc99bb

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Date deposited: 05 Oct 2000
Last modified: 13 Dec 2018 10:58

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Contributors

Author: Hans Fangohr
Author: Andrew R. Price
Author: Simon J. Cox
Author: Peter A.J. de Groot
Author: Geoffrey J. Daniell
Author: Ken S. Thomas

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