(4cc) Novel Material Design through Multiscale Numerical and Analytic Approaches

I discuss multiple approaches to multiscale modeling of novel materials that may be used in wide-ranging applications from biomaterial scaffolding to catalysis formation. The first uses a coarse-grained molecular approach to model the self-assembly of polymeric systems that have domains on the micron scale with interfaces of only a few nanometers. I have developed an extension to the typical mean-field theory approach to these models. Instead of relying on average polymer configurations, I allow for fluctuations around a minimal energy state. While previously intractable for large systems, I have developed a methodology for numerically resolving these systems. The progress has come primarily from a novel technique for finding the free energy of fluctuating complex systems as well as increasingly efficient computational algorithms. The second uses a primarily analytic approach to resolve the transport and reaction processes in stationary reacting waves. In such systems, the characteristic length scale of a typical reaction zone is asymptotically small relative to the characteristic length scale of conduction through the reacting media. Nonetheless, both scales must be considered to determine the behavior of coupled propagating reactions, including propagation velocity, extinction limits and conversion effectiveness. I have developed and applied approximation strategies to analyze the disparate length scales and develop relationships between reactant and material properties and the propagation of coupled reactions.