Controlled formation of self-assembled nanostructures with desired geometries: Robust dynamic paths to robust desired structures

This paper discusses the design principles underlying the controlled formation of nanostructures with desired geometries through a hybrid top-down and bottom-up approach: top-down formation of the physical domains with externally-imposed controls and bottom-up self-assembly of the nanoscale particles to form the desired structure. We propose a two-phase approach for this design problem. The first phase guarantees a robust desired structure, and the second allows the desired structure to be reachable from any initial particle distribution in the physical domain. Both phases require the solution of combinatorially-constrained quadratic optimization problems. The dynamics of the self-assembly process is described through a multiresolution view of the system. Crucial to the achievement of the design goals is the need to break the ergodicity of the system.