Exact results for curvature-driven coarsening in two dimensions.
We consider the statistics of the areas enclosed by domain boundaries ("hulls") during the curvature-driven coarsening dynamics of a two-dimensional nonconserved scalar field from a disordered initial state. We show that the number of hulls per unit area that enclose an area greater than A has, for large time t, the scaling form Nh(A,t)=2c/(A+lambdat), demonstrating the validity of dynamical scaling in this system, where c=1/8pisquare root 3 is a universal constant. Domain areas (regions of aligned spins) have a similar distribution up to very large values of A/lambdat. Identical forms are obtained for coarsening from a critical initial state, but with c replaced by c/2.
Arenzon
Jeferson J
JJ
Instituto de Física, Universidade Federal do Rio Grande do Sul, CP 15051, 91501-970 Porto Alegre RS, Brazil.
Bray
Alan J
AJ
Cugliandolo
Leticia F
LF
Sicilia
Alberto
A