Mesoscale phenomena in physical and biological systems assume prominence when an intermediate length or time scale is required to assess gross system behavior or when the finer active scales cannot be directly interrogated. These systems are frequently metastable. Two broad areas for investigation have been identified directly from potential application: texture development dependent on interfacial properties of polycrystals and diffusion mediated transport with application to ensembles of molecular motors. A central materials science problem is to engineer a microstructure to attain a desired set of characteristics. The group of the investigator has discovered a new characterization of material texture, the description of a polycrystal in terms of its geometry and crystallography, called the grain boundary character distribution, which is found to be correlated to interfacial energy. A main objective of this project is to explain this characterization employing large scale simulation and analysis and stochastic analysis. Geometric coarsening is also studied. The goal of the second part of the project is to develop appropriate modeling and analytical methods to understand how molecular motors function in various circumstances, and in particular, to examine various transformation pathways and transduction scenarios. This involves mass transport theory among other new directions in nonlinear analysis. Understanding the predictive character of large scale simulations of metastable systems used to interrogate and model physical and biological systems is an emerging fundamental challenge for mathematical/computational science. It is a coarse graining or upscaling question at the informational level. The goal of this project is to address this challenge.
This project has two related parts. Most engineered materials arise as polycrystalline microstructures, composed of a myriad of small crystallites, called grains, separated by interfaces, called grain boundaries. The energetics and connectivity of this network of boundaries are implicated in many properties across all scales of use, from nanoscale medicine and electronics to aircraft structures. A new characterization of material texture is now available, the grain boundary character distribution, discovered very recently in the group of the investigator. It is as if each material leaves a unique footprint in the microscope. A project objective is to explain this distribution by simulation and innovative mathematical analysis in order to provide materials engineers with a predictive tool. Eukaryotic intracellular traffic owes to a network of molecular motors moving on cytoskeletal or actin filaments. This is the second part. The ability to successfully transduce chemical energy to motion owes to functional elements and relations in the system. These are modeled and analyzed. The opportunity to discover the interplay between chemistry and mechanics and to elaborate the implications of metastability could not offer a more exciting venue.
