Domain and hull-enclosed area distributions in two-dimensional coarsening

We obtain the exact distribution of the areas enclosed by domain boundaries (“hulls”) during the coarsening dynamics of a two-dimensional nonconserved scalar field. We prove that the number of hulls per unit area that enclose an area greater than A   has the form Nh(A,t)=2c/(A+λt)Nh(A,t)=2c/(A+λt), where c=18π3. This result is also a demonstration of the validity of the dynamical scaling hypothesis in this system. We also show that domain areas (regions of aligned spins) have a similar distribution.