Interest in macromolecules composed of carbon atoms has stimulated a great deal of recent research in materials science and physics. Much of this work has focused on carbon nanotubes and, more recently, on the basic structural element of a nanotube---graphene. Graphene is a single-atom-thick sheet of bonded carbon atoms. Despite many decades of effort, only within the last six years have scientists discovered methods for producing isolated individual graphene sheets. This discovery has stimulated a flurry of experimental and theoretical work on the exceptional mechanical, thermal, and electronic properties of graphene. Exploiting these properties could lead to significant advances in many technologies and yield, for example, more efficient solar cells, faster microprocessors, or lighter, stronger composite materials. The principal goal of this project is to employ mathematical modeling to gain a better fundamental understanding of how atomic-scale forces between layers of a carbon nanostructure influence its mechanical and thermal characteristics. The project investigators are developing and analyzing comprehensive multiscale models of interacting graphene layers by utilizing ideas at the forefront of existing theories as well as by introducing new mathematical tools.