Theory and Simulation of Nucleation

Abstract

Nucleation is the process where a stable nucleus spontaneously emerges in a metastable environment. Examples of nucleation abound, for instance the formation of droplets in undercooled gasses and of crystals in undercooled liquids. The process is thermally activated and is key to understanding various subjects in biophysics, polymer physics and chemistry. The physics behind it has long been studied and the simplest version is known as classical nucleation theory. This thesis reveals a serious shortcoming of this classical theory, namely the assumption that nucleation is described by a memoryless stochastic process. A method to test for this so-called Markov property is developed and is applied to the nucleation process in the Ising model. To overcome this shortcoming, a non-Markovian theory for droplet growth is developed. This theory is validated with simulation results of the mass of growing droplets in the Ising model. More interesting quantities, of course, include the time scale and rate at which stable droplets arise. These times are typically very long, so that brute force simulations do not give useful results. Therefore, an efficient Monte Carlo method, called pathway recombination, is developed to measure transition times over large energy barriers. An adapted version of this method is used to determine nucleation rates of Ising models with various dynamics. These rates are then compared to the rates predicted by both the non-Markovian droplet theory and the classical one. Finally, a different activated process is discussed, namely the reversal of the Earth's magnetic field. Various time series of geomagnetic dipole moments are analyzed and theoretical, simulation and experimental results are compared.