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- W1586326972 abstract "A novel unification for the problem of the search of optimal clusters under a well pair potential function is presented. My formulation introduces appropriate sets and lattices from where ecient methods can address this problem. First, as results of my propositions a discrete set is depicted such that the solution of a continuous and discrete searching of an optimal cluster is the same. Then, this discrete set is approximated by a special lattice IF. IF stands for a lattice that combines lattices IC and FC together. In fact, two lattices IF with 9483 and 1739 particles are obtained with the property that they include all putative optimal clusters from 2 trough 1000 particles, even the dicult optimal Lennard-Jones clusters, C ⁄, C ⁄, and the Ino’s decahedrons. C ⁄ 98 is the only cluster where its initial configuration has a dierent geometry than the putative optimal cluster in term of the adjacency matrix stated by Hoare. My paper is not a benchmark, I develop a theory and a numerical experiment for the state of the art of the optimal Lennard-Jones clusters and even I found new optimal Lennard-Jones clusters with a greedy search method called Modified Peeling Method. The paper includes all the necessary data to allow the researchers reproduce the state of the art of the optimal Lennard-Jones clusters at April 8, 2005. This novel formulation unifies the geometrical motifs of the optimal Lennard-Jones clusters and gives new insight towards the understanding of the complexity of the NP problems." @default.
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- W1586326972 date "2005-04-08" @default.
- W1586326972 modified "2023-10-01" @default.
- W1586326972 title "Minimum search space and ecient methods for structural cluster optimization" @default.
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