This project will investigate the precise analytic form of the complex singularities of the Lorenz system, the figure-eight solution of the three-body problem, and signals obtained from the Navier-Stokes boundary layer. Both analytic and numerical techniques will be used. Research on the Lorenz system has the aim of understanding the analytic continuation of the Lorenz solutions to the entire complex plane. With regard to the figure-eight solution, the project will show that the complex singularities of this system have an appealingly simple structure. The Navier-Stokes boundary layer has been studied primarily using techniques from spectral analysis. We will locate and elucidate singularities of the analytic continuation of the signal in the complex plane, and and obtain a measurement as well as an understanding of the time scales imposed by the outer flow.
This project endeavors to benefit the public in two respects. Firstly, we aim to obtain new insights into the Navier-Stokes boundary layer which is of immense importance in engineering and meteorology. As an example of its importance, we mention that a major part of the energy intake of automobiles is dissipated in the boundary layer. Secondly, we will write a new book that puts computer architecture at the heart of scientific computing. This book will introduce a style of scientific computing that is deeply informed by recent progress in computer architecture to a wider audience.