Postdoc: Extensive Spatiotemporal Chaos in Extended Nonequillibrium Systems

博士后：扩展非平衡系统中的广泛时空混沌

• 批准号: 9503963
• 负责人: Eberhard Bodenschatz
• 金额: $ 4.62万
• 依托单位: Cornell University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1995
• 资助国家: 美国
• 起止时间: 1995-07-01 至 1997-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9503963&HistoricalAwards=false
• 关键词: Postdoc; Extensive; Spatiotemporal; Chaos; Extended

9503963 Bodenchatz The objective of this proposal is to study numerical and analytically the microscopic equations describing certain experimental systems. This research will take three directions, it will make quantitative comparisons between simulations experiments, study lengthscale and order parameters in experimental systems, and examine the appearance and role of topological defects. A specific goal of this proposal is to use the powerful parallel computing facilities to explore new physical regimes which are described by the Boussinesq equations. Although the equations have been simulated before, the simulations have been limited to small systems, short integration times, limited fixed resolution, or particular boundary conditions. By comparing a code using spectral methods to one based on iterative methods, such as multigrid or conjugate-gradient-like methods, we will develop a general scalable Boussinesq solver optimized for parallel computers that will allow long integrations of large systems with aspect ratios greater than 100 and with adjustable resolution in all directions. This next generation convection code will allow this research to perform exhaustive explorations of spatiotemporal chaos in extended convection systems, and, hopefully, these explorations will constitute a significant step toward a formalism similar to equilibrium thermodynamics.

这个提议的目的是研究描述某些实验系统的数值和解析微观方程。本研究将从三个方向展开：模拟实验之间的定量比较，实验系统中长度尺度和有序参数的研究，拓扑缺陷的出现和作用的研究。本提案的一个具体目标是使用强大的并行计算设备来探索由Boussinesq方程描述的新物理状态。虽然以前已经模拟了这些方程，但模拟仅限于小系统、短积分时间、有限的固定分辨率或特定的边界条件。通过比较使用谱方法的代码与基于迭代方法的代码（如多网格或共轭梯度方法），我们将开发一个通用的可扩展的Boussinesq求解器，该求解器针对并行计算机进行了优化，该求解器将允许长时间集成长宽比大于100的大型系统，并且在所有方向上具有可调分辨率。下一代对流代码将允许本研究对扩展对流系统中的时空混沌进行详尽的探索，并且，希望这些探索将构成类似于平衡热力学的形式主义的重要一步。