论文信息 - Minimizing the Lennard-Jones potential function on a massively parallel computer

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

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.

[1] David Shalloway,et al. Packet annealing: a deterministic method for global minimization , 1992 .

[2] H. Scheraga,et al. Monte Carlo-minimization approach to the multiple-minima problem in protein folding. , 1987, Proceedings of the National Academy of Sciences of the United States of America.

[3] M. Prueitt. Computer Simulation of Molecular Dynamics. , 1971 .

[4] H. Scheraga,et al. On the multiple-minima problem in the conformational analysis of molecules: deformation of the potential energy hypersurface by the diffusion equation method , 1989 .

[5] M. Karplus,et al. CHARMM: A program for macromolecular energy, minimization, and dynamics calculations , 1983 .

[6] Jorge Nocedal,et al. On the limited memory BFGS method for large scale optimization , 1989, Math. Program..

[7] Roger Fletcher,et al. Practical methods of optimization; (2nd ed.) , 1987 .

[8] C. DeLisi,et al. Determining minimum energy conformations of polypeptides by dynamic programming , 1990, Biopolymers.

[9] L. Wille. Minimum-energy configurations of atomic clusters: new results obtained by simulated annealing , 1987 .

[10] W. Fischer,et al. Sphere Packings, Lattices and Groups , 1990 .

[11] J. Farges,et al. Cluster models made of double icosahedron units , 1985 .

[12] H. C. Andersen,et al. Molecular dynamics study of melting and freezing of small Lennard-Jones clusters , 1987 .

[13] R. Fletcher. Practical Methods of Optimization , 1988 .