Doctor Andrew Burbanks

General Research Interests

Nonlinear dynamics in systems of coupled units; localisation, ratchets, collective phenomena, transport in phase space.

As described below, the prototypical model is one-dimensional particle motion in a tilted spatially periodic potential. Corresponding experimental realisations include Josephson junctions, charge density waves, superionic conductors, rotation of dipoles in external fields, phase-locked loops and diffusion of dimers on surfaces. Particle interactions can lead to cooperative effects not found in situations of individual particle motion. The objective of the current work is to investigate the conditions under which it is possible to generate a directed flow along with collective motion in systems of coupled particles and in systems subject to driving forces.

Dynamically-evolving networks.

Networks in which evolution of the network topology and the dynamics taking place on the network influence each other. Adaptation of classic problems such as Gambler's ruin / Prisoner's Dilemma to evolving networks. Potential for evolving global computation from local interaction rules on networks with both regular and irregular topology.

Other Interests

Visualisation of Mathematical Structures. Use of computational homology to examine transport in Hamiltonian systems. Natural independence phenomena in logic.