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

这个FRG项目的研究人员发展和研究客观结构理论。根据定义，这些结构是由相同的分子组成的，其性质是每个分子中相应的原子在正交变换中看到完全相同的环境。客观结构概括了经典晶体结构，包括许多当今科学研究最深入的结构，包括碳纳米管、巴基球、病毒衣壳和其他部分（颈、尾、基板）、许多常见的蛋白质、双层结构和许多其他正在合成的纳米结构，特别是通过自组装的过程。研究人员利用这些结构的对称性来发展分子动力学的计算数值方法，目标结构自组装的数学理论，缺陷目标结构的准连续体数值方法，以及这些结构能量的更简单的第一性原理计算。纳米结构在各种科技应用中发挥着越来越重要的作用。客观结构是有机和无机纳米结构的基本组成部分。对这种结构进行全面和统一的数学处理有可能导致发现具有不寻常形式的铁磁性和铁电性以及意想不到的输运性质的新结构。对目标结构的自组装的详细研究可以导致合成这些结构的新方法，特别是产生所需尺寸和分子排列的纳米结构的方法。反过来，这可能会导致对抗病毒感染的新策略，以及特定纳米结构（如碳纳米管）模板化生长的新方法。准连续统数学方法为系统研究纳米结构中缺陷的成核和生长过程提供了一种通用策略。这些方法有望为发现异常强分子结构提供系统的新工具。

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.