Domain growth morphology in curvature-driven two-dimensional coarsening

We study the distribution of domain areas, areas enclosed by domain boundaries (hulls), and perimeters for curvature-driven two-dimensional coarsening, employing a combination of exact analysis and numerical studies, for various initial conditions. We show that the number of hulls per unit area, n(h)(A,t)dA, with enclosed area in the interval (A,A+dA), is described, for a disordered initial condition, by the scaling function n(h)(A,t)=2c(h)/(A+lambda(h)t)(2), where c(h)=1/8 pi root 3 approximate to 0.023 is a universal constant and lambda(h) is a material parameter. For a critical initial condition, the same form is obtained, with the same lambda(h) but with c(h) replaced by c(h)/2. For the distribution of domain areas, we argue that the corresponding scaling function has, for random initial conditions, the form n(d)(A,t)=2c(d)(lambda(d)t)(tau')-2/(A+lambda(d)t)(tau'), where c(d) and lambda(d) are numerically very close to c(h) and lambda(h), respectively, and tau(')=187/91 approximate to 2.055. For critical initial conditions, one replaces c(d) by c(d)/2 and the exponent is tau=379/187 approximate to 2.027. These results are extended to describe the number density of the length of hulls and domain walls surrounding connected clusters of aligned spins. These predictions are supported by extensive numerical simulations. We also study numerically the geometric properties of the boundaries and areas.