Numerical simulation of a continuum model of growth of thin composite films

We present the results of extensive numerical integration in (1+1) dimensions of a set of equations that couple the Kardar-Parisi-Zhang (KPZ) equation to the time-dependent Ginzburg-Landau (TDGL) equation, recently proposed for modeling the growth of thin composite solid films. We find that for times t shorter than a crossover time t(c) the mean domain size L(t) grows logarithmically with the time, whereas for tmuch greater thant(c) L(t) grows as t(m)(1/z), with z(m) being nonuniversal and depending on the parameters of the model. The roughness exponent is also found to be nonuniversal. Thus, neither the dynamics of the domains' growth is governed by the TDGL equation, nor is the scaling of the surface roughness described by the KPZ equation.