Grupo Interdisciplinar de Sistemas Complejos (GISC) and DNL, Escuela Téc. Sup. de Ingeniería (ICAI), Universi dad Pontificia Comillas, E-28015 Madrid, Spain.
Departamento de Matemáticas and GISC, Universidad Carlos III de Madrid, E-28911 Leganés, Spain.
Phys Rev Lett. 2014 Mar 7;112(9):094103. doi: 10.1103/PhysRevLett.112.094103.
We report the experimental observation of a submicron cellular structure on the surface of silicon targets eroded by an ion plasma. Analysis by atomic force microscopy allows us to assess the time evolution and show that the system can be described quantitatively by the convective Cahn-Hilliard equation, found in the study of domain coarsening for a large class of driven systems. The space-filling trait of the ensuing pattern relates it to evolving foams. Through this connection, we are actually able to derive the coarsening law for the pattern wavelength from the nontrivial topological dynamics of the cellular structure. Thus, the study of the topological properties of patterns in nonvariational spatially extended systems emerges as complementary to morphological approaches to their challenging coarsening properties.
我们报告了在被离子等离子体侵蚀的硅靶表面上观察到亚微米细胞结构的实验结果。原子力显微镜的分析使我们能够评估其时间演化，并表明该系统可以通过对流的 Cahn-Hilliard 方程进行定量描述，该方程在一大类驱动系统的畴细化研究中被发现。由此产生的图案的空间填充特性使其与演化泡沫相关。通过这种联系，我们实际上可以从细胞结构的非平凡拓扑动力学中推导出图案波长的粗化规律。因此，对非变分空间扩展系统中模式拓扑性质的研究与对其具有挑战性的粗化性质的形态学方法相辅相成。
