Nonlinear growth of periodic patterns.
Nonlinear growth of periodic patterns.
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周期性模式的非线性增长。
DOI：
10.1103/physreve.66.036308
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发表时间：
2000
期刊：
影响因子：
--
通讯作者：
C. Josserand
中科院分区：
文献类型：
--
作者：
S. Villain;C. Josserand
我们研究了一个独立分解模型——Cahn-Hilliard方程的一维周期模式的生长。我们特别关注中间区域，在这里非线性不能再被忽视，并且在合并占主导地位之前。动力学是通过在特定的准静态溶液族上执行溶解度条件的标准技术捕获的。主要的结果是沿着这类解的动力学可以用一个简单的常微分方程来表示。在非线性生长结束时发现的平稳状态的密度分布也很好地表征了。通过三种不同的方法进行的数值模拟与分析结果相吻合，即使远离近似所处的区域，也能很好地恢复渐近动力学。
We study the growth of a periodic pattern in one dimension for a model of spinodal decomposition, the Cahn-Hilliard equation. We particularly focus on the intermediate region, where the nonlinearity cannot be neglected anymore, and before the coalescence dominates. The dynamics is captured through the standard technique of a solubility condition performed over a particular family of quasistatic solutions. The main result is that the dynamics along this particular class of solutions can be expressed in terms of a simple ordinary differential equation. The density profile of the stationary regime found at the end of the nonlinear growth is also well characterized. Numerical simulations correspond satisfactorily to the analytical results through three different methods and asymptotic dynamics are well recovered, even far from the region where the approximations hold.