Variational Modeling of Molecular Geometries

分子几何的变分建模

• 批准号: 427980274
• 负责人: Professor Dr. Manuel Friedrich
• 金额: --
• 依托单位: Professur für Angewandte Analysis
• 依托单位国家: 德国
• 项目类别: Research Grants
• 财政年份: 2019
• 资助国家: 德国
• 起止时间: 2018-12-31 至 2023-12-31
• 项目状态: 已结题
• 来源: https://gepris.dfg.de/gepris/projekt/427980274?language=en
• 关键词: Variational; Modeling; Molecular; Geometries

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.

更广泛的研究背景：在其迷人的电子和机械性能的推动下，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，新的发现一直在以越来越快的速度出现。与目前可用的丰富的实验和数字证据相比，关于局部和全局晶体几何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初级阶段。目标：在分子力学的框架内，我们专注于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：从纳米到宏观尺度，我们讨论了分子化合物的结晶，包括缺陷和刚性的局部分子特征的描述，整体几何特征的发生，如三维平坦度和层化，以及从离散理论到连续理论的过渡。以原子模型的变分方法为基础，该方法还将整合离散数学和随机学的技术。创新：该项目从严格的数学观点出发，瞄准了材料科学的一些热门研究前沿。与模拟相比，理论方法具有独立于系统大小的优势，这是研究跨尺度影响的关键资产。参与研究的人员：明斯特和维也纳之间的新国际研究团队将由曼努埃尔·弗里德里希和乌利斯·斯特凡内利协调，并将受益于包括实验和计算小组在内的当地和国际合作者网络。