Mathematical Sciences: Transport for Symplectic Mapping

数学科学：辛映射的传输

• 批准号: 9001103
• 负责人: James Meiss
• 金额: $ 6.08万
• 依托单位: University of Colorado at Boulder
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1990
• 资助国家: 美国
• 起止时间: 1990-06-15 至 1993-05-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9001103&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Transport; Symplectic; Mapping

This project will study transport phenomena in symplectic mappings of four or more dimensions. The goal is to partition phase space into regions bounded by partial barriers through which flux occurs. A candidate for such a region is a resonance, defined as a volume in the neighborhood of an elliptic point; its boundary will be obtained from limits of librational periodic orbits. Resonance volumes will be computed and we will determine whether resonances partition phase space. The correlation function for orbits in the neighborhood of a resonance boundary well be studied to determine whether the series for the diffusion tensor converges. Transport will be defined in terms of the flux across resonance boundaries, including branching ratios for transitions from one resonance to a neighboring one, as well as drift along a commensurability channel. To compute the latter a restricted symplectic map will be introduced and studied. Numerical techniques will include frequency filtering and finding periodic orbits.

这个项目将研究辛中的输运现象 四维或多维映射。 我们的目标是分割 相空间划分为由部分障碍物包围的区域， 产生磁通量。 这种区域的候选者是共振， 定义为椭圆点附近的体积;其 边界将从振动周期的极限获得 轨道 共振体积将被计算，我们将 确定共振是否划分相空间。 的 轨道附近的相关函数 共振边界以及研究，以确定是否 扩散张量的级数收敛。 运输将 根据穿过谐振边界的通量来定义， 包括从一个共振到另一个共振的跃迁的分支比， 一个相邻的，以及漂移沿着一个可扩展性 频道 为了计算后者，限制辛映射将 加以介绍和研究。 数字技术将包括 频率滤波和寻找周期轨道。