This award supports research in theoretical modeling of patterns and disorder in nonequilibrium condensed matter materials. The PI proposes to concentrate the project in the areas of polytypism, polyamorphism in two-dimensional simple fluids, and electrostatic mechanisms for two-dimensional chiral symmetry breaking during growth. The study of polytypism will focus on applying ideas from the theory of language and automata to the analysis of experimentally observed structures in a range of layered materials. The study of polyamorphism will continue current work that revealed the existence of hexatic and isotropic types of structural glasses in these systems. The third project is motivated by the recent experimental observations of novel two-dimensional chiral growth forms in thin films of TCNQ and TCNQ+C60. %%% This award supports theoretical research in disorder and patterns in materials away from equilibrium. The project is constructed in three main thrust areas. In the first the PI will apply developments in mathematical models of one-dimensional, discrete systems to analyze the experimental diffraction measurements of layered materials. Potential systems of applicability include a range of materials with layered structures from superconducting materials to minerals such as mica and clays. The other topics will study model glassy phases in materials of reduced dimensionality and growth mechanisms of materials in systems with reduced dimensionality. ***
