Research objectives and content
Asymptotic expansions of the solutions for the dynamics of a viscoelastic link model with transcritical bifurcation have been determined using multiple time-scale expansions and matched asymptotic expansions. I have located the transition layers. There are further aspects of the model that need investigation. The objective of the proposed research is to study the problem using modern mathematical tools of Dynamical Systems Theory and Numerical Bifurcation Theory. The center-unstable manifold will be investigated and numerically calculated. Similar results will be obtained for the dynamics of other models corresponding to static pitchfork and hysteresis bifurcations. This work would be new and extend my current research to a Ph.D. standard.
Training content (objective, benefit and expected impact)
The objective of the training is to provide me with expertise in modern Dynamical Systems Theory and Numerical Methods and extend my current research. Part of the M.Sc. in Nonlinear Mathematics would provide me with training in dynamical systems, bifurcation theory, numerical bifurcation theory and nonlinear elasticity. Bath's series of industrial workshops and its hosting of the European Study Group with Industry would give me significant traning in the application of mathematics to industrial problems.
Links with industry / industrial relevance (22)
The proposed training involves participation in a series of industrial workshops and the European Study Group with Industry.