摘要翻译：
本文采用精确分析和数值研究相结合的方法，在不同初始条件下，研究了曲率驱动二维粗化的区域、区域边界所包围的区域（“壳”）和周长的分布。在无序初始条件下，单位面积的外壳数$n_h(A,t)da$由标度函数$n_h(A,t)=2c_h/(A+\lambda_ht)^2$描述，其中$c_h=1/8\pi\sqrt{3}\\0.023$是一个通用常数，$\lambda_h$是一个物质参数。对于一个临界初始条件，得到了相同的形式，相同的$\lambda_h$，但将$C_h$替换为$C_h/2$。对于区域面积的分布，我们认为，在随机初始条件下，相应的标度函数具有$n_d(A,t)=2c_d(\lambda_d t)^{\tau'-2}/(A+\lambda_d t)^{\tau'}$,其中$c_d=c_h+{\cal O}(c_h^2)$,$\lambda_d=\lambda_h+{\cal O}(c_h)$,$\tau'=187/91\约2.055$。对于临界初始条件，用$C_d/2$代替$C_d$（可能用${\cal O}(C_h^2)$),其指数为$\tau=379/187\约2.027$。这些结果被推广到描述围绕排列自旋的连通团簇的壳和畴壁长度的数密度。这些预测得到了大量数值模拟的支持。我们还对边界和区域的几何性质进行了数值研究。
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英文标题：
《Domain growth morphology in curvature driven two dimensional coarsening》
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作者：
Alberto Sicilia, Jeferson J. Arenzon, Alan J. Bray, Leticia F.
  Cugliandolo
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最新提交年份：
2007
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分类信息：

一级分类：Physics        物理学
二级分类：Statistical Mechanics        统计力学
分类描述：Phase transitions, thermodynamics, field theory, non-equilibrium phenomena, renormalization group and scaling, integrable models, turbulence
相变，热力学，场论，非平衡现象，重整化群和标度，可积模型，湍流
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英文摘要：
  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 $c_h=1/8\pi\sqrt{3} \approx 0.023$ 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 $c_d=c_h + {\cal O}(c_h^2)$, $\lambda_d=\lambda_h + {\cal O}(c_h)$, and $\tau' = 187/91 \approx 2.055$. For critical initial conditions, one replaces $c_d$ by $c_d/2$ (possibly with corrections of ${\cal O}(c_h^2)$) and the exponent is $\tau = 379/187 \approx 2.027$. 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.
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PDF链接：
https://arxiv.org/pdf/706.4314