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

Luskin DMS-0757355是该FRG项目的研究人员，他们发展和研究了客观结构理论。根据定义，这些结构是由相同的分子组成的，具有这样的性质，即每个分子中的相应原子准确地看到相同的环境，直到进行正交变换。目的结构概括了经典的晶体结构，包括许多当今科学中研究最深入的结构，包括碳纳米管、巴克球、病毒衣壳和其他部分(脖子、尾巴、基板)、许多常见的蛋白质、双层和许多其他目前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，发展了分子动力学的计算数值方法，目标结构自组装的数学理论，缺陷目标结构的拟连续数值方法，以及这些结构能量的更简单的第一原理计算。纳米结构在各种科学技术应用中正变得越来越重要。目标结构是纳米结构的基础，包括有机和无机结构。对这类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。对目标结构自组装的详细研究可以导致合成这类结构的新方法，特别是产生所需尺寸和分子排列的纳米结构的方法。这些反过来可能导致对抗病毒感染的新战略，以及用于特定纳米结构(如碳纳米管)模板化生长的新方法。准连续的数学方法为系统研究纳米结构中缺陷的形核和生长过程提供了一般策略。这些方法有望为发现异常强的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.