Three-dimensional interfacial wave theory of dendritic growth: (I). multiple variables expansion solutions ⁄
Three-dimensional interfacial wave theory of dendritic growth: (I). multiple variables expansion solutions ⁄
复制标题
DOI：
10.1088/1674-1056/18/2/046
复制
发表时间：
2009-02
影响因子：
1.7
通讯作者：
Yong-qiang Chen;Xiong-Xin Tang;Jian-Jun Xu
中科院分区：
文献类型：
--
作者：
Yong-qiang Chen;Xiong-Xin Tang;Jian-Jun Xu
液体和固体界面处的树枝状图案形成是晶体生长和凝固过程中常见的现象。枝晶生长的理论研究是界面图案形成、凝聚态物理和材料科学等广泛领域中最深刻和最具挑战性的课题之一，吸引了来自各个领域的许多研究人员。这一课题的一些长期悬而未决的关键问题终于在上世纪末通过基于对枝晶生长基本状态的系统全局稳定性分析的“界面波（IFW）理论”获得了突破。 IFW理论的最初形式主要集中于研究围绕树突生长系统的轴对称基本状态的各种轴对称非定常扰动模式解。实际上，系统可能允许各种非轴对称、不稳定的扰动状态。树突生长系统是否允许一些非轴对称生长模式？静止的树突图案是否会被某些此类非轴对称模式破坏？或者，一言以蔽之，一旦可以引发非轴对称模式，系统的稳定性特性是什么？这些问题的答案对于奠定 IFW 理论的坚实基础非常重要。目前的工作试图解决这些问题并发展树突生长的三维（3D）界面波理论。我们的研究证实，树突生长确实允许一组离散的非轴对称不稳定全局波模式，从而产生一组沿伊万佐夫抛物面传播的多臂螺旋波。
Dendritic pattern formation at the interface between liquid and solid is a commonly observed phenomenon in crystal growth and solidification process. The theoretical investigation of dendritic growth is one of the most profound and highly challenging subjects in the broad areas of interfacial pattern formation, condensed matter physics and materials science, preoccupying many researchers from various areas. Some longstanding key issues on this subject finally gained a breakthrough in the late of last century, via the 'Interfacial Wave (IFW) Theory' on the ground of systematical global stability analysis of the basic state of dendritic growth. The original form of the IFW theory mainly focus on the investigation of various axi-symmetric unsteady perturbed modes solutions around the axi-symmetric basic state of system of dendritic growth. In reality, the system may allow various non-axi-symmetric, unsteady perturbed states. Whether or not the system of dendritic growth allows some growing non-axi-symmetric modes? Will the stationary dendritic pattern be destroyed by some of such non-axi-symmetric modes? Or, in one word, what is the stability property of the system, once the non-axi-symmetric modes can be evoked? The answers for these questions are important for the solid foundation of IFW theory. The present work attempts to settle down these issues and develop a three-dimensional (3D) interfacial wave theory of dendritic growth. Our investigations verify that dendritic growth indeed allows a discrete set of non-axi-symmetric unstable global wave modes, which gives rise to a set of multiple arms spiral waves propagating along the Ivantsov's paraboloid.