Multiscale Simulation for Scale-up of Nanotechnological Processes: Symbiosis of Traditional and Modern Tools

Self-organization of matter is under certain conditions an instability whose mathematical underpinnings go back to the old days of the Minnesotian school but new modeling challenges arise due to thermal fluctuations (disorder) and large disparity of scales. In this talk, recent developments from our work on coarse-grained Monte Carlo simulations and hierarchical multiscale simulation will be discussed. These tools enable simulation of realistic systems while retaining the correct level of fluctuations. In conjunction with nonlinear dynamics and optimal control theory, multiscale modeling becomes in invaluable toolbox for scale-up of materials' self-organization. An example of pattern formation leading to quantum dots (e.g., Pb on Cu) will be presented.