info:eu-repo/semantics/report
MINIMUM SEARCH SPACE AND EFFICIENT METHODS FOR STRUCTURAL CLUSTER OPTIMIZATION
Autor
CARLOS BARRON ROMERO
Institución
Resumen
A novel unification for the problem of search of optimal clusters under a well pair potential function is
presented. My formulation introduces appropriate sets and lattices from where efficient 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 search 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 difficult optimal Lennard-Jones clusters,
C
§
38
,
C
§
98
, and the Ino’s decahedrons.
C
§
98
is the only
cluster where its initial configuration has a different 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.
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