FRG: Modeling and Computation of Objective Structures in Materials Science and Biology

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LuskinDMS-0757355 The investigators in this FRG project develop and study thetheory of objective structures. By definition, these arestructures composed of identical molecules having the propertythat corresponding atoms in each molecule see precisely the sameenvironment up to an orthogonal transformation. Objectivestructures generalize classical crystal structures, and includemany of the most intensely studied structures in science today,including carbon nanotubes, buckyballs, viral capsids and otherparts (necks, tails, baseplates), many common proteins, bilayers,and many other nanostructures now being synthesized, especiallyvia the process of self-assembly. The investigators exploit thesymmetries of these structures to develop computational numericalmethods for molecular dynamics, a mathematical theory for theself-assembly of objective structures, a quasicontinuum numericalmethod for defective objective structures, and simplerfirst-principles calculations of the energy of these structures. Nanostructures are becoming increasingly important in avariety of scientific and technological applications. Objectivestructures are the building blocks of nanostructures, bothorganic and inorganic. A comprehensive and unified mathematicaltreatment of such structures has the potential to lead to thediscovery of new structures with unusual forms of ferromagnetismand ferroelectricity and unexpected transport properties. Thedetailed investigation of the self-assembly of objectivestructures can lead to new methods of synthesis of suchstructures, especially methods that produce nanostructures ofdesired dimensions and molecular arrangement. These, in turn,could lead to new strategies to combat viral infections, and newmethods for the templated growth of particular nanostructuressuch as carbon nanotubes. The quasicontinuum mathematicalmethods deliver a general strategy for the systematicinvestigation of the process of nucleation and growth of defectsin nanostructures. These methods are expected to give asystematic new tool for the discovery of exceptionally strongmolecular structures.