Persistence in cluster-cluster aggregation.

Persistence is considered in one-dimensional diffusion-limited cluster-cluster aggregation when the diffusion coefficient of a cluster depends on its size s as D(s) approximately s(gamma). The probabilities that a site has been either empty or covered by a cluster all the time define the empty and filled site persistences. The cluster persistence gives the probability of a cluster remaining intact. The empty site and cluster persistences are universal whereas the filled site depends on the initial concentration. For gamma>0 the universal persistences decay algebraically with the exponent 2/(2-gamma). For the empty site case the exponent remains the same for gamma<0 but the cluster persistence shows a stretched exponential behavior as it is related to the small s behavior of the cluster size distribution. The scaling of the intervals between persistent regions demonstrates the presence of two length scales: the one related to the distances between clusters and that between the persistent regions.

Coarsening of sand ripples in mass transfer models.

Coarsening of sand ripples is studied in a one-dimensional stochastic model, where neighboring ripples exchange mass with algebraic rates, Gamma(m) approximately m(gamma), and ripples of zero mass are removed from the system. For gamma<0, ripples vanish through rare fluctuations and the average ripple mass grows as (t) approximately -gamma(-1)ln(t). Temporal correlations decay as t(-1/2) or t(-2/3) depending on the symmetry of the mass transfer, and asymptotically the system is characterized by a product measure. The stationary ripple mass distribution is obtained exactly. For gamma>0, ripple evolution is linearly unstable, and the noise in the dynamics is irrelevant. For gamma=1, the problem is solved on the mean-field level, but the mean-field theory does not adequately describe the full behavior of the coarsening. In particular, it fails to account for the numerically observed universality with respect to the initial ripple size distribution. The results are not restricted to sand ripple evolution since the model can be mapped to zero range processes, urn models, exclusion processes, and cluster-cluster aggregation.

Cluster persistence in one-dimensional diffusion-limited cluster-cluster aggregation.

The persistence probability, P(C)(t), of a cluster to remain unaggregated is studied in cluster-cluster aggregation, when the diffusion coefficient of a cluster depends on its size s as D(s) approximately s(gamma). In the mean field the problem maps to the survival of three annihilating random walkers with time-dependent noise correlations. For gamma> or =0 the motion of persistent clusters becomes asymptotically irrelevant and the mean-field theory provides a correct description. For gamma<0 the spatial fluctuations remain relevant and the persistence probability is overestimated by the random walk theory. The decay of persistence determines the small size tail of the cluster size distribution. For 0