In this thesis we study the statistical physics of social dynamics and spreading phenomena. We first demonstrate how the formation of regional dialects in birdsong can be related to the physical process of magnetic domain formation and coarsening. We show that the death rate of the species is analogous to the thermodynamic temperature in physical systems, and compute the death rate at which dialects cannot form due to a transition to a disordered state. We then investigate interface motion in a two dimensional lattice model of opinion spread. In our model sites have memories for the states of their neighbours and change state when this memory reaches a threshold. We consider the impact of surface roughening on the rate of spread and construct multiple approximation techniques to understand how varying the configuration of site thresholds can control the speed of the interface. We then investigate the motion of an opinion wave spreading via threshold dynamics in a one dimensional random network. We present a method for enumerating site connections and understanding what causes the wave to become arrested, and how long we expect to wait for this to occur. Our method makes use of martingale stopping sequences, and provides upper bounds on the time until the wave stops. We also develop a coarse-grained cluster method for estimating the expected stopping time. This is analogous to the well known (n,m) cluster approximation, but may be systematically derived from our dynamics. Finally we claim that this system of one dimensional spread is analogous to a branching and coalescing random walk process and we formulate mean field equations to describe this.
|Date of Award||Jun 2020|
|Supervisor||James Burridge (Supervisor), Michal Gnacik (Supervisor) & Andrew Harold Osbaldestin (Supervisor)|