There are an enormous number of physical phenomenons in this world that appear to behave randomly but are not random: such as the bouncing ball in a pinball machine or a physical device called the Galton board; a rock or any object rolling or sliding down a mountainside or slope. This thesis investigates whether or not one can predict the further dynamics of such systems. We formulate five Galton board models, also known as quincunx, and two ski slope models. The discussion includes a brief description of the systems, the important physical processes, the assumptions employed, the derivation of the governing equations, and a comparison between the quincunx models and the ski-slope models. The quincunx models are converted into maps, called quincunx maps, that enable a straight-forward analysis of the symbolic dynamics of the maps. While Galton and others suggested that a small ball falling through a quincunx would exhibits random walk; the results of the symbolic dynamics analysis demonstrate that this is not the case. Regarding our final aim of forecasting, we consider five examples of model-system pairs and study how well the more sophisticated model(system) can be forecasted with a simpler model. In reality one often faces the problem that the state of a system is effected by noise.
|Qualification||Doctor of Philosophy|
|Publication status||Unpublished - 2011|