Study of interface dynamics in nonequilibrium growth models.

We study the dynamics of growth at the interface level for two different kinetic models. Both of these are simple kinetic models of growth with rules that are local, stochastic, and with a parameter p that indicates the probability to add a particle to a growth site. The first model is an epidemic model, and it appears to have the same critical behavior as percolation at the point where growth becomes marginal and the cluster fractal-like. At p$\sb{c}$ =.54, the cluster size distribution will scale as a power law with the same exponent as for percolation, $\tau$ = 2.0. The second model is a ballistic deposition model that has a nonzero flux density of incoming particles. We were able to describe both models by stochastic maps that iterate the whole lattice. The limit cycles of this map correspond, in the epidemic model, to multiperiodic oscillations in various growth quantities. We observed these oscillations by averaging over an ensemble of moderate-sized clusters. Moreover, as the control parameter p is lowered to p$\sb{c}$, limit cycle behavior becomes fixed point behavior. This allowed us to conclude that kinetic fractal growth is growth at the trivial fixed point of the stochastic map. In the case of the deposition model, the description by a stochastic map enabled us to prove that the bulk is compact and allowed us to derive a relation between the geometrical surface of the deposit and the width of the active region of growth. The latter relation defines a constant that measures the screening of the incoming particles. These results are true for models where the active zone is locked to the surface of the deposit. For both models we studied the roughness using Monte Carlo simulations. This quantity was measured by the interfacial width $\xi$. It is found that its scaling with time for the deposition model does not depend on p, and is the same as $\xi$ found in a variety of other, related models. For short times $\xi \propto t\sp{1/3}$ for a one dimensional substrate and $\xi\propto t\sp{.22}$ for two dimensional ones. The latter is not consistent with various theoretical predictions. Rough numerical estimates for the long-time exponent are also presented. For the epidemic model, the effective exponent depends on the position as we go from smooth straight facets to rough rounded segments. It does increase as we lower p and it becomes equal to 1 isotropically for $p=p\sb{c}$, as expected for a fractal.Ph.D.Condensed matter physicsPhysicsPure SciencesUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/128304/2/8920499.pd