The investigators in this FRG project develop and study the theory of objective structures. By definition, these are structures composed of identical molecules having the property that corresponding atoms in each molecule see precisely the same environment up to an orthogonal transformation. Objective structures generalize classical crystal structures, and include many of the most intensely studied structures in science today, including carbon nanotubes, buckyballs, viral capsids and other parts (necks, tails, baseplates), many common proteins, bilayers, and many other nanostructures now being synthesized, especially via the process of self-assembly. The investigators exploit the symmetries of these structures to develop computational numerical methods for molecular dynamics, a mathematical theory for the self-assembly of objective structures, a quasicontinuum numerical method for defective objective structures, and simpler first-principles calculations of the energy of these structures.
Nanostructures are becoming increasingly important in a variety of scientific and technological applications. Objective structures are the building blocks of nanostructures, both organic and inorganic. A comprehensive and unified mathematical treatment of such structures has the potential to lead to the discovery of new structures with unusual forms of ferromagnetism and ferroelectricity and unexpected transport properties. The detailed investigation of the self-assembly of objective structures can lead to new methods of synthesis of such structures, especially methods that produce nanostructures of desired dimensions and molecular arrangement. These, in turn, could lead to new strategies to combat viral infections, and new methods for the templated growth of particular nanostructures such as carbon nanotubes. The quasicontinuum mathematical methods deliver a general strategy for the systematic investigation of the process of nucleation and growth of defects in nanostructures. These methods are expected to give a systematic new tool for the discovery of exceptionally strong molecular structures.
