Nanoscience is a rapidly developing field at the nexus of all physical sciences which holds the potential for mankind to gain a new level of control of matter over matter and energy altogether. Directed-assembly is an emerging field within nanoscience in which non-equilibrium system dynamics are controlled to produce scalable, arbitrarily complex and interconnected multi-layered structures with custom chemical, biologically or environmentally-responsive, electronic, or optical properties. We construct mathematical models and interpret data from direct-assembly experiments via application and augmentation of classical and contemporary physics, biology, and chemistry methods. Crystal growth, protein pathway mapping, LASER tweezers optical trapping, and colloid processing are areas of directed-assembly with established experimental techniques. We apply a custom set of characterization, modeling, and simulation techniques to experiments to each of these four areas. Many of these techniques can be applied across several experimental areas within directed-assembly and to systems featuring multiscale system dynamics in general. We pay special attention to mathematical methods for bridging models of system dynamics across scale regimes, as they are particularly applicable and relevant to directed-assembly. We employ massively parallel simulations, enabled by custom software, to establish underlying system dynamics and develop new device production methods
