### Abstract

The Lennard-Jones potential energy function arises in the study of low-energy states of proteins and in the study of cluster statics. This paper presents a mathematical treatment of the potential function, deriving lower bounds as a function of the cluster size, in both two and three dimensional configurations. These results are applied to the minimization of a linear chain, or polymer, in two-dimensional space to illustrate the relationship between energy and cluster size. An algorithm is presented for finding the minimum-energy lattice structure in two dimensions. Computational results obtained on the CM-5, a massively parallel processor, support a mathematical proof showing an essentially linear relationship between minimum potential energy and the number of atoms in a cluster. Computational results for as many as 50000 atoms are presented. This largest case was solved on the CM-5 in approximately 40 minutes at an approximate rate of 1.1 32-bit gigaflops.

Original language | English (US) |
---|---|

Title of host publication | Proceedings of the 6th International Conference on Supercomputing, ICS 1992 |

Publisher | Association for Computing Machinery |

Pages | 409-416 |

Number of pages | 8 |

Volume | Part F129617 |

ISBN (Electronic) | 0897914856 |

DOIs | |

State | Published - Aug 1 1992 |

Externally published | Yes |

Event | 6th International Conference on Supercomputing, ICS 1992 - Washington, United States Duration: Jul 19 1992 → Jul 24 1992 |

### Other

Other | 6th International Conference on Supercomputing, ICS 1992 |
---|---|

Country | United States |

City | Washington |

Period | 7/19/92 → 7/24/92 |

### Fingerprint

### ASJC Scopus subject areas

- Computer Science(all)

### Cite this

*Proceedings of the 6th International Conference on Supercomputing, ICS 1992*(Vol. Part F129617, pp. 409-416). Association for Computing Machinery. https://doi.org/10.1145/143369.143443

**Minimizing the Lennard-Jones potential function on a massively parallel computer.** / Xue, Guoliang; Maier, R. S.; Rosen, J. B.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

*Proceedings of the 6th International Conference on Supercomputing, ICS 1992.*vol. Part F129617, Association for Computing Machinery, pp. 409-416, 6th International Conference on Supercomputing, ICS 1992, Washington, United States, 7/19/92. https://doi.org/10.1145/143369.143443

}

TY - GEN

T1 - Minimizing the Lennard-Jones potential function on a massively parallel computer

AU - Xue, Guoliang

AU - Maier, R. S.

AU - Rosen, J. B.

PY - 1992/8/1

Y1 - 1992/8/1

N2 - The Lennard-Jones potential energy function arises in the study of low-energy states of proteins and in the study of cluster statics. This paper presents a mathematical treatment of the potential function, deriving lower bounds as a function of the cluster size, in both two and three dimensional configurations. These results are applied to the minimization of a linear chain, or polymer, in two-dimensional space to illustrate the relationship between energy and cluster size. An algorithm is presented for finding the minimum-energy lattice structure in two dimensions. Computational results obtained on the CM-5, a massively parallel processor, support a mathematical proof showing an essentially linear relationship between minimum potential energy and the number of atoms in a cluster. Computational results for as many as 50000 atoms are presented. This largest case was solved on the CM-5 in approximately 40 minutes at an approximate rate of 1.1 32-bit gigaflops.

AB - The Lennard-Jones potential energy function arises in the study of low-energy states of proteins and in the study of cluster statics. This paper presents a mathematical treatment of the potential function, deriving lower bounds as a function of the cluster size, in both two and three dimensional configurations. These results are applied to the minimization of a linear chain, or polymer, in two-dimensional space to illustrate the relationship between energy and cluster size. An algorithm is presented for finding the minimum-energy lattice structure in two dimensions. Computational results obtained on the CM-5, a massively parallel processor, support a mathematical proof showing an essentially linear relationship between minimum potential energy and the number of atoms in a cluster. Computational results for as many as 50000 atoms are presented. This largest case was solved on the CM-5 in approximately 40 minutes at an approximate rate of 1.1 32-bit gigaflops.

UR - http://www.scopus.com/inward/record.url?scp=84955392660&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84955392660&partnerID=8YFLogxK

U2 - 10.1145/143369.143443

DO - 10.1145/143369.143443

M3 - Conference contribution

AN - SCOPUS:84955392660

VL - Part F129617

SP - 409

EP - 416

BT - Proceedings of the 6th International Conference on Supercomputing, ICS 1992

PB - Association for Computing Machinery

ER -