Mathematical Sciences: Surface Wave Mode Interactions with Explicit and Hidden Symmetry

数学科学：表面波模式与显式和隐式对称性的相互作用

• 批准号: 9201028
• 负责人: John Crawford
• 金额: $ 2.5万
• 依托单位: University of Pittsburgh
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1992
• 资助国家: 美国
• 起止时间: 1992-07-01 至 1994-12-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9201028&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Surface; Wave; Mode

The principal investigator will study a variety of problems raised by current experiments on parametrically driven surface waves performed in circular and square geometries. Several models for physical systems appear to exhibit bifurcations that are non-generic in the context of their natural geometric symmetry in that the effective symmetry of the bifurcation is larger than the natural symmetry. These studies will attempt to explain these apparent hidden symmetries. The analysis of nonlinear hydrodynamic waves is important because of their wide spread occurrence in nature and because such analyses can serve as a prototype for other situations.

首席研究员将研究各种问题 参数驱动曲面的现有实验提出 波在圆形和方形几何形状中执行。 几 物理系统的模型似乎表现出分叉， 在其自然的几何结构中是非通用的 对称性，因为分叉的有效对称性是 比自然的对称性更大。 这些研究将试图 解释这些明显隐藏的对称性。 非线性水动力波的分析具有重要意义 因为它们在自然界中广泛分布， 这种分析可以作为其他情况的原型。