Collision of two interfaces of different roughnesses: a numerical study

In the classical Eden model (EM) the growing sites have the same probabilit y of becoming occupied and the growing process in (1 + 1) dimensions leads to the formation of a self-affine aggregate with a growing exponent beta (E M) = 1/3 and a roughness exponent alpha (EM) = 1/2. A generalization of the EM is proposed and studied, such that the growing probability now depends on the distance to the interface. This new model is called the unstable Ede n model (UEM) because, within the short time regime, it exhibits an unstabl e growth mode with a growing exponent beta (UEM) > 1/2. However, in the asy mptotic time regime the interface becomes stabilized and a roughness expone nt alpha (UEM) = 1 can be defined. In contrast to the EM, the interface of the UEM is no longer self-affine. Based on extensive numerical simulations it is concluded that the interface generated by the collision between the E M and the UEM is characterized by a roughness exponent alpha (coll) = alpha (UEM) = 1.