ABSTRACT
ABST R AC T This paper provides an overview of design principles and methods associated with the controlled formation of nanostructures with desired geometries. The approach is based on a hybrid top-down and bottomup approach: top-down formation of physical domains with externallyimposed controls and bottom-up generation of the desired structure through the self-assembly of the nanoscale particles, driven by interparticle interactions (short-and long-range) and interactions with external controls. The desired nanoscale structure must be locally stable and robust to the desired level of robustness, and it should be reachable from any random initial distribution of the nanoparticles in the physical domain. These two requirements frame the two elements of the design problem: The rst denes a static optimization problem with integer (position of controls) and continuous variables (intensities of controls). The second leads to a mixed-integer, time-dependent optimization problem, akin to those encountered in optimal control. Crucial to the achievement of the design goals is the necessity to break the ergodicity of the overall system and dene ergodic subsets of phase space that map the desired geometric features of the nanostructure to the features of the energy landscape within the system volume. The static and dynamic problems are solved through the formulation and solution of combinatorially-constrained mixed-integer quadratic optimization problems (QIP). The dynamics of the self-assembly process are described through multi-resolution models.
