Misbah Chaouqi, Politi Paolo
Laboratoire de Spectrométrie Physique, UMR, 140 Avenue de la Physique, Université Joseph Fourier Grenoble and CNRS, 38402 Saint Martin d'Heres, France.
Phys Rev E Stat Nonlin Soft Matter Phys. 2009 Sep;80(3 Pt 1):030106. doi: 10.1103/PhysRevE.80.030106. Epub 2009 Sep 15.
Instabilities and pattern formation is the rule in nonequilibrium systems. Selection of a persistent length scale or coarsening (increase in the length scale with time) are the two major alternatives. When and under which conditions one dynamics prevails over the other is a long-standing problem, particularly beyond one dimension. It is shown that the challenge can be defied in two dimensions, using the concept of phase diffusion equation. We find that coarsening is related to the lambda dependence of a suitable phase diffusion coefficient, D11(lambda) , depending on lattice symmetry and conservation laws. These results are exemplified analytically on prototypical nonlinear equations.
不稳定性和模式形成是非平衡系统中的规律。选择一个持续的长度尺度或粗化（长度尺度随时间增加）是两种主要的选择。何时以及在何种条件下一种动力学比另一种占优势是一个长期存在的问题，特别是在一维以上的情况下。结果表明，利用相扩散方程的概念可以在二维中克服这一挑战。我们发现粗化与合适的相扩散系数(D_{11}(\lambda))的(\lambda)依赖性有关，这取决于晶格对称性和守恒定律。这些结果在典型的非线性方程上进行了分析举例。
