%0 Book Section %1 statphys23_0092 %A Arenzon, J.J. %A Bray, A.J. %A Cugliandolo, L.F. %A Sicilia, A. %B Abstract Book of the XXIII IUPAP International Conference on Statistical Physics %C Genova, Italy %D 2007 %E Pietronero, Luciano %E Loreto, Vittorio %E Zapperi, Stefano %K coarsening curvature-driven dynamical growth scaling statphys23 topic-3 %T Exact results in two-dimensional coarsening %U http://st23.statphys23.org/webservices/abstract/preview_pop.php?ID_PAPER=92 %X 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, $n_h(A,t)dA$, with enclosed area in the range $(A,A+dA)$ is described, for large time $t$, by the scaling form $n_h(A,t) = 2c_h/(A+łambda_h t)^2$, demonstrating the validity of dynamical scaling in this system. Here $c_h=1/8\pi3$ is a universal constant associated with the enclosed-area distribution of percolation hulls at the percolation threshold, and $łambda_h$ is a material parameter. The distribution, $n_d(A,t)$, of domain areas is apparently very similar to that of hull areas up to very large values of $A/łambda_h t$. Identical forms are obtained for coarsening from a critical initial state, but with $c_h$ replaced by $c_h/2$. The similarity of the two distributions (of areas enclosed by hulls, and of domain areas) is accounted for by the smallness of the parameter $c_h$. By applying a `mean-field' type of approximation, we obtain the form $n_d(A,t) c_dłambda_d(t+t_0)^\tau-2/A+łambda_d(t+t_0)^\tau$, where $t_0$ is a microscopic time scale and $= 187/91 2.055$, for a disordered initial state, and a similar result for a critical initial state but with $c_d c_d/2$ and $= 379/187 2.027$. We also find that $c_d=c_h + O(c_h^2)$ and $łambda_d = łambda_h(1 + O(c_h))$. These predictions are checked by extensive numerical simulations and found to be in good agreement with the data.

@incollection{statphys23_0092, abstract = {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, $n_h(A,t)dA$, with enclosed area in the range $(A,A+dA)$ is described, for large time $t$, by the scaling form $n_h(A,t) = 2c_h/(A+\lambda_h t)^2$, demonstrating the validity of dynamical scaling in this system. Here $c_h=1/8\pi\sqrt{3}$ is a universal constant associated with the enclosed-area distribution of percolation hulls at the percolation threshold, and $\lambda_h$ is a material parameter. The distribution, $n_d(A,t)$, of domain areas is apparently very similar to that of hull areas up to very large values of $A/\lambda_h t$. Identical forms are obtained for coarsening from a critical initial state, but with $c_h$ replaced by $c_h/2$. The similarity of the two distributions (of areas enclosed by hulls, and of domain areas) is accounted for by the smallness of the parameter $c_h$. By applying a `mean-field' type of approximation, we obtain the form $n_d(A,t) \simeq c_d[\lambda_d(t+t_0)]^{\tau-2}/[A+\lambda_d(t+t_0)]^\tau$, where $t_0$ is a microscopic time scale and $\tau = 187/91 \simeq 2.055$, for a disordered initial state, and a similar result for a critical initial state but with $c_d \to c_d/2$ and $\tau = 379/187 \simeq 2.027$. We also find that $c_d=c_h + O(c_h^2)$ and $\lambda_d = \lambda_h(1 + O(c_h))$. These predictions are checked by extensive numerical simulations and found to be in good agreement with the data.}, added-at = {2007-06-20T10:16:09.000+0200}, address = {Genova, Italy}, author = {Arenzon, J.J. and Bray, A.J. and Cugliandolo, L.F. and Sicilia, A.}, biburl = {https://www.bibsonomy.org/bibtex/222a23454c6f7d769525c87b2caf262c7/statphys23}, booktitle = {Abstract Book of the XXIII IUPAP International Conference on Statistical Physics}, editor = {Pietronero, Luciano and Loreto, Vittorio and Zapperi, Stefano}, interhash = {b146b2cd016560d6af5b3bd93860fff7}, intrahash = {22a23454c6f7d769525c87b2caf262c7}, keywords = {coarsening curvature-driven dynamical growth scaling statphys23 topic-3}, month = {9-13 July}, timestamp = {2007-06-20T10:16:11.000+0200}, title = {Exact results in two-dimensional coarsening}, url = {http://st23.statphys23.org/webservices/abstract/preview_pop.php?ID_PAPER=92}, year = 2007 }