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, nh(A, t)dA, with enclosed area in the range (A,A + dA), is described, for large time t, by the scaling form nh(A, t) = 2ch/(A + λht)2, demonstrating the validity of dynamical scaling in this system. Here ch = 1/8π √ 3 is a universal constant associated with the enclosed area distribution of percolation hulls at the percolation threshold, and λh is a material parameter. The distribution of domain areas, nd(A, t), is apparently very similar to that of hull areas up to very large values of A/λht. Identical forms are obtained for coarsening from a critical initial state, but with ch replaced by ch/2. The similarity of the two distributions (of areas enclosed by hulls, and of domain areas) is accounted for by the smallness of ch. By applying a ‘mean-field’ type of approximation we obtain the form nd(A, t) 2cd[λd(t+t0)]τ2/[A+λd(t+t0)]τ, where t0 is a microscopic timescale and τ = 187/91 2.055, for a disordered initial state, and a similar result for a critical initial state but with cd → cd/2 and τ → τc = 379/187 2.027. We also find that cd = ch + O(c2 h) and λd = λh(1 + O(ch)). These predictions are checked by extensive numerical simulations and found to be in good agreement with the data.
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