1210.3510 (Erik Edlund et al.)

Using the uncertainty principle to simplify interactions designed for
targeted self-assembly    [PDF]

Erik Edlund, Oskar Lindgren, Martin Nilsson Jacobi

Advances in fabrication techniques allow for experimentation with custom designed meso- and nano-scale building blocks with complex interactions. The next step is to move beyond exploration and develop schemes for designing components that, in a predictable way, self-assemble into complex target structures and functional materials. There already exist theoretical design principles that solve this problem in silico. However, the theoretically derived interactions are typically too complicated to be of experimental use. We present a method that systematically simplifies isotropic interactions designed for targeted self-assembly. The uncertainty principle is used to show that an optimal simplification of the interaction is achieved with a combination of heat kernel smoothing and Gaussian screening. We use this method to design simple isotropic interactions for self-assembly of complex lattices and of materials with photonic band gaps. The interactions we derive are significantly simpler than those previously published, which narrows the gap between theory and experimental implementation of designed self-assembling materials.

View original: http://arxiv.org/abs/1210.3510