A cost optimal parallel algorithm for computing force field in N-body simulations on a CREW PRAM
Theoretical Computer Science
Average Case Analysis of Algorithms on Sequences
Average Case Analysis of Algorithms on Sequences
Minimum Inter-Particle Distance at Global Minimizers of Lennard-Jones Clusters
Journal of Global Optimization
Minimal interatomic distance in Morse clusters
Journal of Global Optimization
Efficient Algorithms for Large Scale Global Optimization: Lennard-Jones Clusters
Computational Optimization and Applications
Lower Bound for the Interatomic Distance in Lennard-Jones Clusters
Computational Optimization and Applications
Minimal inter-particle distance in atom clusters
Acta Cybernetica
Global Optimization of Morse Clusters by Potential Energy Transformations
INFORMS Journal on Computing
Dissimilarity measures for population-based global optimization algorithms
Computational Optimization and Applications
Morse potential energy minimization: Improved bounds for optimal configurations
Computational Optimization and Applications
Improved bounds for interatomic distance in Morse clusters
Operations Research Letters
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We establish new lower bounds on the distance between two points of a minimum energy configuration of N points in 驴3 interacting according to a pairwise potential function. For the Lennard-Jones case, this bound is 0.67985 (and 0.7633 in the planar case). A similar argument yields an estimate for the minimal distance in Morse clusters, which improves previously known lower bounds. Moreover, we prove that the optimal configuration cannot be two-dimensional, and establish an upper bound for the distance to the nearest neighbour of every particle, which depends on the position of this particle. On the boundary of the optimal configuration polytope, this is unity while in the interior, this bound depends on the potential function. In the Lennard-Jones case, we get the value $\sqrt[6]{\frac {11}{5}}\approx1.1404$ . Also, denoting by V N the global minimum in an N point minimum energy configuration, we prove in Lennard-Jones clusters $\frac{V_{N}}{N}\ge-41.66$ for all N驴2, while asymptotically $\lim_{N\to\infty}\frac{V_{N}}{N}\le-8.611$ holds (as opposed to $\frac{V_{N}}{N}\ge-8.22$ in the planar case, confirming non-planarity for large N).