Variational Modeling of Molecular Geometries

更广泛的研究背景：受其迷人的电子和机械性能的驱动，对低维材料（如石墨烯）的研究呈指数级增长。从基本概念到应用，新的发现总是以越来越快的速度出现。与目前丰富的实验和数值证据相比，关于局部和全局晶体几何形状的严格数学结果很少，对分子结构中不同尺度出现的研究仍处于起步阶段。目的：我们专注于分子力学框架内分子几何的变分建模：有效构型被确定为经典构型势的最小化。该项目旨在获得对分子几何的新的数学理解，并研究跨尺度尺度效应的出现。方法：从纳米尺度到宏观尺度，我们处理分子化合物的结晶，局部分子特征（包括缺陷和刚性）的描述，全局几何特征（如三维平面和分层）的发生，以及从离散到连续理论的过渡。以原子模型的变分方法为基础，该方法将整合离散数学和随机学的技术。创新：项目从严谨的数学角度出发，瞄准材料科学领域的多个热点研究前沿。与模拟相比，理论方法具有系统大小无关的优势，这是研究跨尺度效应的关键资产。参与的研究人员：<s:1>国家科学技术大学和维也纳大学之间的新国际研究小组将由曼努埃尔·弗里德里希和乌利斯·斯特凡内利协调，并将受益于当地和国际合作者的网络，包括实验和计算小组。

Wider research context: Driven by their fascinating electronic and mechanical properties, research on low-dimensional materials (such as graphene) is exponentially growing. New findings are emerging at an always increasing pace, ranging from fundamental concepts to applications. In contrast to the wealth of experimental and numerical evidence currently available, rigorous mathematical results on local and global crystalline geometries are scant and the study of the emergence of different scales within molecular structures is still in its infancy. Objectives: We focus on the variational modeling of molecular geometries within the frame of Molecular Mechanics: effective configurations are identified as minimizers of classical configurational potentials. The project aims at obtaining new mathematical understanding of molecular geometries and at investigating the emergence of scale effects across scales.Approach: Ranging from the nano to the macroscale, we address crystallization for molecular compounds, the description of local molecular features including defects and rigidity, the occurrence of global geometric characteristics such as flatness in 3d and stratification, and the passage from discrete to continuum theories. Grounded on variational methods for atomistic models, the methodology will integrate techniques from discrete mathematics and stochastics as well.Innovation: The project targets a number of hot research fronts in Materials Science from the rigorous mathematical standpoint. Compared with simulations, the theoretical approach bears the advantage of being system-size independent, a crucial asset for investigating effects across scales.Researchers involved: The new international research team between Münster and Vienna will be coordinated by Manuel Friedrich and Ulisse Stefanelli and will benefit from a network of local and international collaborators, including experimental and computational groups.