PROPAGATION AND KINETIC ROUGHENING OF WAVE-FRONTS IN DISORDERED LATTICES

The dynamics of a wave front propagating in diluted square lattices of elastic beams is analyzed. We concentrate on the propagation of the f irst maximum of a semi-infinite wave train. Two different limits are f ound for the velocity depending on the bending stiffness of the beams. If it vanishes, a one-dimensional chain model is derived for the velo city and the amplitude is found to decrease exponentially. The first m aximum is localized and the average width of the wave front is always finite. For very stiff beams an effective-medium model gives the corre ct velocity and the amplitude of the first maximum decays according to a power law. No localization of the first maximum is observed in the simulations. In this limit scaling arguments based on Huygen's princip le suggest a growth exponent of 1/2, and a roughness exponent of 2/3. The growth exponent fits the simulation data well, but a considerably lower roughness exponent (0.5) is obtained. There is a crossover regio n for the bending stiffness, wherein the wave-front behavior cannot be explained by these limiting cases.