CANCELLED: The unreasonable effectiveness of cluster scaling
This event is part of the Preliminary Oral Exam.
Equilibrium statistical mechanics requires assumptions such as a Hamiltonian description and ergodicity. Nevertheless, the tools of statistical mechanics have been successfully applied to models in biology and economics. I will focus on a specific example.
The Fisher-Stauffer scaling method has been applied to models of percolation and the Ising model. I generalize the Fisher-Stauffer cluster scaling to study the avalanches in the nearest-neighbor stochastic Olami-Feder-Christensen (OFC) model, which is believed to be a non-equilibrium system. The OFC model is a two-dimensional lattice of leaky integrate-and-fire sites. The strength of the noise determines if the model is effectively ergodic or non-ergodic. I show that the limit of vanishing dissipation corresponds to a critical point. I show that the Fisher-Stauffer scaling holds when the OFC model is effectively ergodic. The scale invariant behavior is consistent with the derived scaling laws. I derive universal scaling functions for the avalanche distributions and dynamics. However, Fisher-Stauffer scaling breaks down when the OFC model is non-ergodic. These results indicates that effective ergodicity may be a sufficient criterion for the validity of certain equilibrium tools such as cluster scaling.
Meeting ID: 954 2115 5441 Passcode: 112015