An investigation of the spatiotemporal dynamics of complex pattern forming systems

Complex pattern forming systems form patterns that can be highly initial-condition dependent. In addition, these patterns take very long to reach a steady-state. Commonly used statistical measures to analyze such patterns do not utilize the local pattern variations. In this work, we introduce two local measures based on the curvature of the input field. It is shown how the use of these measures offers new insights into the pattern-forming process of some canonical pattern forming systems. The latter half of the dissertation is devoted to a study of a model of monolayer self-assembly. We use this model in conjunction with some special initial conditions to generate long-range perfect dot and stripe arrays, very useful from the viewpoint of ultrahigh density data storage and nanoelectronic circuitry, respectively. The study of how defects influence self-assembly reveals that even the presence of a small number of defects may drastically change the observed patterns. Using linear stability calculations, we extract hard-to-obtain material properties of the monolayer.