2009/05/12 by Toit, Philip du, Grubits, Katalin, Marsden, Jerrold +1
#Adaptation and Self-Organizing Systems (nlin.AO) #FOS: Physical sciences #Pattern Formation and Solitons (nlin.PS)
paper · doi:10.48550/arxiv.0905.1926
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.