University of Exeter

Faculty Member, Peninsula College of Medicine and Dentistry

ARF

Thesis Title: Many body symmetrical dynamical systems with close encounters

About

The central theme of my PhD level research is to develop a global regularization algorithm to study symmetrically reduced four and five body gravitational problems which allow numerical explorations of the system as they pass through two body close encounters. This work comprises of a study of the Caledonian Symmetric Four Body Problem (CSFBP) which is a restricted four body system with a symmetrically reduced phase space. The collisional singularities were of fundamental interest to us, as they caused the numerical integration algorithm to fail as the system approaches the close encounters. We have numerically investigated the close encounters in the model with the help of regularized codes and the effectiveness of the codes were tested for different families of orbits. The PhD project also involved a detailed investigation of the topological and hierarchical stability, the chaotic and regular behavior of the phase space using fast chaos detection methods and the periodic orbits of the four body and five body symmetrical dynamical systems using the regularized equations of motion to allow the systems to
pass through near two body collisions. All aspects of my PhD level research have entailed advanced level mathematical modelling and numerical simulations, using software packages such as FORTRAN, C++, and MATLAB on a High Performance Computing(HPC) platform.

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