Homotopy continuation methods, intrinsic localized modes, and cooperative robotic workspaces
This dissertation considers three topics that are united by the theme of application of geometric and nonlinear mechanics to practical problems. Firstly we consider the parallel implementation of numerical solution of nonlinear polynomial systems depending on parameters. The program written to do this is called Paramotopy, and uses the Message Passing Interface to distribute homotopy continuation solves in another program called Bertini across a supercomputer. Paramotopy manages writing of Bertini input files, allows automatic re-solution of the system at points at which paths failed, and makes ...