TY - GEN

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

AU - Xue, G. L.

AU - Maier, R. S.

AU - Rosen, J. B.

N1 - Funding Information:
This research was supported in part by the United States Army Contract Number DAAL03-89-C-O038, the Air Force Office of Scientific Research grant AFOSR91-0147, and the Minnesota Supercomputer Institute. Thanks are due to Don Aust& for his support and encouragement, to Jorge Mor4 and Panes Pardalos
Publisher Copyright:
© 1992 ACM.

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.

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U2 - 10.1145/143369.143443

DO - 10.1145/143369.143443

M3 - Conference contribution

AN - SCOPUS:84955392660

T3 - Proceedings of the International Conference on Supercomputing

SP - 409

EP - 416

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

PB - Association for Computing Machinery

T2 - 6th International Conference on Supercomputing, ICS 1992

Y2 - 19 July 1992 through 24 July 1992

ER -