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Carnegie Mellon Center for Nonlinear Analysis


Energy Methods for Energy Science

Keith Promislow
Michigan State University
Department of Mathematics

Abstract: The efficient conversion of energy from chemical and photonic forms to useful electric voltage requires the development of nanostructured materials with interpercolating structure. In practical applications this is achieved by functionalizing polymers, attaching acid groups to short side chains which extend from long, hydrophobic polymer backbones. When placed in solvent, these functionalized polymers form nanoscale solvent-filled pores lined with the tips of the acid groups, and ideal environment for the selective conduction of properly charged ions.

We present a family of models, which we call functionalized Lagrangians, which mimic the energy landscape of the functionalized polymer/solvent mixtures. The functionalized energies are higher order, and strongly nonlinear, but with special structure which renders them amenable to analysis. We outline the properties of the functionalized Lagrangians, and the multi-stage structure of the associated gradient flows.