Discrete applied geometry

离散应用几何

• 批准号: 147637-2010
• 负责人: Whiteley, Walter
• 金额: $ 1.46万
• 依托单位: York University
• 依托单位国家: 加拿大
• 项目类别: Discovery Grants Program - Individual
• 财政年份: 2013
• 资助国家: 加拿大
• 起止时间: 2013-01-01 至 2014-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=522513
• 关键词: Discrete; applied; geometry

The rigidity and flexibility of structures are central to their function and their design. This holds for biomolecules (protein flexibility for predicting function and for drug design), material science (e.g. artificial zeolites for refining heavy oil), for human build structures, for designed mechanisms (paths of mechanisms), and for independence of geometric configurations in CAD (impacting the design of stable and efficient CAD programs) and computer graphics (how geometric constraints are handled inside a computer). This study uses combinatorics and geometry to analyze what portions of a structure are rigid and which are flexible. In some situations, we desire more than minimal rigidity - we desire stability or global rigidity. This is true in the study of small fluctuations in molecules, or avoiding alternative forms of molecules (which can cause disease or drug reactions) as well as built structures which should not fail if one bracing member is weak.

结构的刚性和灵活性是其功能和设计的核心。这适用于生物分子（用于预测功能和药物设计的蛋白质灵活性）、材料科学（例如用于精炼重油的人工沸石）、人体建筑结构、设计机制（机制路径）以及CAD中几何构型的独立性（影响稳定和高效的CAD程序的设计）和计算机图形学（如何在计算机内部处理几何约束）。这项研究使用组合学和几何学来分析结构的哪些部分是刚性的，哪些是柔性的。在某些情况下，我们需要的不仅仅是最小限度的刚性——我们需要稳定或全局刚性。在研究分子的微小波动，或避免分子的替代形式（这可能导致疾病或药物反应），以及在一个支撑构件薄弱时不应失败的建筑结构中，都是如此。