Competition of growth patterns in directed growth

A new class of non-equilibrium critical phenomena is defined, which can appear during the growth of one phase at the expense of a second phase. We assume that the growing phase consists of several sub-phases or species or even of several dynamically defined growth patterns, and that the growth takes place by the propagation of an extended front which separates the growing from the shrinking phase. A coarsening process then takes place during growth, leaving a decreasing number of species or sub-phases immediately behind the front as time increases. This directional coarsening process can be described as a critical phenomenon in terms of a scaling theory. We define the relevant parameters, critical exponents and scaling functions, and give explicit values for these quantities for M-species front-growth in two dimensions. The results are compared with Monte-Carlo simulations and implications for experiments are discussed.