We present a microscopic description of interface growth with power-law noise distriiurion in the iorm P(qjiiq!'", which exhibits non-universai roughening. For the p = d + 1 case in d + 1 dimensions, the existence of a fractal pattern in the bulk of the aggregate is explained, leading trivially to the proof of the identity a + i = 2 for the roughening and the dynamical scaling exponents a and i...

Limited dispersal distance, whether associated with vegetative growth or localized reproduction, induces spatial clustering and, in turn, focuses ecological interactions at the neighborhood scale. In particular, most invasive plants are clonal, cluster through vegetative propagation, and compete locally. Dispersal limitation implies that invasive spread occurs as advance of an ecological interf...

We study the competition interface between two clusters growing over a random vacant sector of the plane in a simple setup which allows us to perform formal computations and obtain analytical solutions. We demonstrate that a phase transition occurs for the asymptotic inclination of this interface when the final macroscopic shape goes from curved to noncurved. In the first case it is random whil...

Results of experiments on the dynamics and kinetic roughening of one-dimensional slow-combustion fronts in three grades of paper are reported. Extensive averaging of the data allows a detailed analysis of the spatial and temporal development of the interface fluctuations. The asymptotic scaling properties, on long length and time scales, are well described by the Kardar-Parisi-Zhang (KPZ) equat...

We investigate by exact optimization methods the roughening of two and three-dimensional systems of elastic lines with point disorder and hard-core repulsion with open boundary conditions. In 2d we find logarithmic behavior whereas in 3d simple random walk -like behavior. The line ’forests’ become asymptotically completely entangled as the system height is increased at fixed line density due to...

Surface roughening instabilities driven by a competition between elastic and surface energy contributions are shown to be saturated by plastic energy dissipation. It is shown that these morphological instabilities do not experience unbounded growth as predicted by consideration of elastic energy alone and that their growth is limited by dislocation emission from higher curvature grooves. © 2008...

We study the dynamical exponent z for the directed percolation depinning (DPD) class of models for surface roughening in the presence of quenched disorder. We argue that z for d 1 1 dimensions is equal to the exponent dmin characterizing the shortest path between two sites in an isotropic percolation cluster in d dimensions. To test the argument, we perform simulations and calculate z for DPD, ...