Nonlinear Sciences – Adaptation and Self-Organizing Systems
Scientific paper
2009-05-12
Nonlinear Sciences
Adaptation and Self-Organizing Systems
43 pages, 15 figures
Scientific paper
We address the inverse problem of designing isotropic pairwise particle interaction potentials that lead to the formation of a desired lattice when a system of particles is cooled. The design problem is motivated by the desire to produce materials with pre-specified structure and properties. We present a heuristic computation-free geometric method, as well as a fast and robust trend optimization method that lead to the formation of high quality honeycomb lattices. The trend optimization method is particularly successful since it is well-suited to efficient optimization of the noisy and expensive objective functions encountered in the self-assembly design problem. We also present anisotropic potentials that robustly lead to the formation of the kagome lattice, a lattice that has not previously been obtained with isotropic potentials.
Costiner Sorin
Grubits Katalin
Marsden Jerrold
Toit Philip du
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