2007/06/30 by Alberto Sicilia, Jeferson J. Arenzon, Alan J. Bray +1 · 8 citations
Materials Science · Physics and Astronomy · #Block Copolymer Self-Assembly #Magnetic properties of thin films #Theoretical and Computational Physics #cond-mat.stat-mech
paper · pdf · doi:10.1103/physreve.76.061116
published as Phys. Rev. E 76, 061116 (2007) · 27 pages, 35 figures
arxiv created 2007/11/08 · openalex publication_date 2007/12/17 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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, nh(A,t)dA, with enclosed area in the interval (A,A+dA), is described, for a disordered initial condition, by the scaling function nh(A,t)=2ch∕(A+\ensuremathλht)2, where ch=1∕8\ensuremathπ√(3)\ensuremath≈0.023 is a universal constant and \ensuremathλh is a material parameter. For a critical initial condition, the same form is obtained, with the same \ensuremathλh but with ch replaced by ch∕2. For the distribution of domain areas, we argue that the corresponding scaling function has, for random initial conditions, the form nd(A,t)=2cd(\ensuremathλdt)^\ensuremathτ^\ensuremath'\ensuremath-2∕(A+\ensuremathλdt)^\ensuremathτ^\ensuremath', where cd and \ensuremathλd are numerically very close to ch and \ensuremathλh, respectively, and \ensuremathτ^\ensuremath'=187∕91\ensuremath≈2.055. For critical initial conditions, one replaces cd by cd∕2 and the exponent is \ensuremathτ=379∕187\ensuremath≈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.