One-dimensional interfaces with curvature-driven growth kinetics are investigated. We calculate the steady-state distribution P(w2) of the square of the width of the interface w2 and show that, as in the case for random-walk interfaces, the result can be written in a scaling form w2P(w2)=(w2/w2), where w2 is the average of w2. The scaling function (x) is found to be distinct from that of random-walk interfaces, but, as our Monte Carlo simulations indicate, this function is universal for curvature-driven growth. It is argued that comparison of scaling functions can be a useful method for distinguishing between universality classes of growth processes.
ASJC Scopus subject areas
- Statistical and Nonlinear Physics
- Statistics and Probability
- Condensed Matter Physics