Parsing complex spatio-temporal dynamics in physical and physiological applications

拟议的研究涉及复杂的行为，发生在空间扩展的系统。这种系统的一个重要例子是流体湍流。尽管在过去的世纪里，湍流一直是物理学家、数学家和工程师的研究对象，但许多基本问题仍然没有得到解决。对这一问题缺乏理解的一个重要原因是，Navier和Stokes的控制方程在数值实验中用于模拟湍流，但通常不用于分析结果。这通常是通过统计手段来完成的，它模糊了流动的内在结构，并丢弃了重要的动力学细节。然而，最近，随着计算机能力的提高和一系列新的理论思想的出现，我们可以用动力系统理论的工具来研究控制方程的解。这种分析使我们对相干结构（如涡管和涡面）在建立湍流观测统计中的作用有了前所未有的了解。我们将使用新颖的计算方法，结合对基本物理过程的详细分析，解决各向同性和剪切湍流中的几个悬而未决的问题。

The proposed research concerns complex behaviour which occurs in spatially extended systems. One important example of such a system is fluid turbulence. Although turbulence has been on the menu of physicists, mathematicians and engineers alike over the past century, many fundamental problems remain unsolved. One important reason for this tantalizing lack of understanding is the fact that the governing equations, due to Navier and Stokes, are used to simulate turbulence in numerical experiments, but not usually to analyse the results. This is commonly done by statistical means, which blur the intantaneous structure of the flow and discard important dynamical detail. Recently, however, increased computer power and a string of fresh theoretical ideas have enabled us to study solutions to the governing equations with the tools of dynamical systems theory. This kind of analysis gives us an unprecedented insight in the role of coherent structures, such as vortex tubes and sheets, in establishing the observed statistics of turbulence. We will address several open questions in isotropic and shear turbulence, using novel computational methods in conjunction with a detailed analysis of the elementary physical processes.