Perrine, RandallThis dissertation is primarily focused on exploring whether weak cohesion among icy particles in Saturn's dense rings is consistent with observations--and if so, what limits can be placed on the strength of such cohesive bonds, and what dynamical or observable consequences might arise out of cohesive bonding. Here I present my numerical method that allows for N-body particle sticking within a local rotating frame ("patch")--an approach capable of modeling hundreds of thousands or more colliding bodies. Impacting particles can stick to form non-deformable but breakable aggregates that obey equations of rigid body motion. I then apply the method to Saturn's icy rings, for which laboratory experiments suggest that interpenetration of thin, frost-coated surface layers may lead to weak bonding if the bodies impact at low speeds--speeds that happen to be characteristic of the rings. This investigation is further motivated by observations of structure in the rings that could be formed through bottom-up aggregations of particles (i.e., "propellers" in the A ring, and large-scale radial structure in the B ring). This work presents the implementation of the model, as well as results from a suite of 100 simulations that investigate the effects of five parameters on the equilibrium characteristics of the rings: speed-based merge and fragmentation limits, bond strength, ring surface density, and patch orbital distance (specifically the center of either the A or B ring), some with both monodisperse and polydisperse particle comparison cases. I conclude that the presence of weak cohesion is consistent with observations of the A and B rings, and present a range of parameters that reproduce the observed size distribution and maximum particle size. The parameters that match observations differ between the A and B rings, and I discuss the potential implications of this result. I also comment on other observable consequences of cohesion for the rings, such as optical depth and scale height effects, and discuss the unlikelihood that very large objects are grown bottom-up from cohesion of smaller ring particles. Lastly, I include a brief summary of other projects in ring dynamics I have undertaken before and during my thesis work.DissertationAstronomyAstrophysicsComputer scienceCollisional physicsNumerical methodsOrbital dynamicsSaturn's rings