Pattern Formation in Micro and Nanosystems

Part I: We describe aspects of metal-semiconductor bonding in gold-linked Ge$_6$ cages in gas phase. Using total energy calculations and short molecular dynamics simulations, we examine the relative stability of Au$_n$Ge$_{12}$ where n = 0, 1, 2, 3 and classify cluster geometries with bondlengths, angles, bonding strength. We evaluate neutral and ionic charge states and calculate partial and total density of states. In agreement with previous experiment, our work suggests that linear Ge-Au-Ge bonds stabilize linked cluster systems. We predict favorable bond geometries in the Au-Ge system with a focus on the structure Au$_2$Ge$_{12}$ and evaluate the Ge$_6$ cluster as an alternate building block to Ge9 in the synthesis of germanium solids. Part II: Using large scale numerical simulations, we examine the ordering of colloidal particles on a rigid square periodic lattice. We explore static regimes where specific ratios of colloids to optic traps produce ordered and disordered patterns. We focus primarily on patterns which form from interacting grain-boundaries in an otherwise hexagonal lattice. After classifying groundstate patterns, we apply driving forces to the colloids. While the trapped colloids remain fixed throughout the simulation, the interstitial particles reveal distinct dynamical responses based on the overall static pattern. This reveals the relative pinning strength of the static pattern to the substrate. Furthermore it shows how topological defects such as solitons move and interact with one another.