Statistical Physics of Complex systems

Complex systems are systems composed of many interacting entities in which interesting system-wide behaviour emerges from the interaction at the micro-level. These emergent phenomena cannot be explained by looking at individuals constituents alone, but are intrinsically a property of the system as a whole. Complex behaviour can be found in physical systems (e.g. turbulence, electronic transport, superconductivity, plasma physics), but also in a number of other disciplines. The constituents of a complex systems can therefore be electrons or particles in physics, but also traders in a financial market, genes or proteins in a biological system, or speakers in a model of language evolution.

In this project we will use ideas and methods from statistical physics to investigate stochastic complex systems. The work will focus on so-called `individual-based systems' of interacting agents. We will study such systems from a theoretical point of view, identify their characteristic behavior, and we will develop methods for the characterization of such systems. This includes approximation methods and simulation tools.

One particular initial focus will be on models in the class of the so-called `voter model'. This describes the spreading and spatial ordering of multiple traits, similar to models of biological evolution. The objective is to characterize the approach to spatial order and disorder. The student will use numerical simulations and tools from statistical physics to do this. In later stages of the project we will expand this to applications for example in language dynamics and biological evolution (e.g. anti-microbial resistance, evolutionary game theory). The project will branch out and be adapted as we go along and as new applications and ideas arise. The focus will always remain on stochastic processes, statistical physics, nonlinear dynamics, and the modelling and analysis of complex systems.

The project sits firmly in the EPSRC remit, as the main objective is to develop new mathematical and computational methods for the study of complex systems. The thesis will advance the field of non-equilibrium statistical physics and emergence.