论文标题
一种用各向异性表面能脱水的弥漫性接口方法
A diffuse-interface approach for solid-state dewetting with anisotropic surface energies
论文作者
论文摘要
我们为$ {\ Mathbb r}^d $ in \ in \ {2,3 \} $提供了各向异性表面能的固定状态易碎问题的漫差接口模型。引入的模型由各向异性cahn--hilliard方程组成，具有光滑或双凸电势，以及壁上的退化迁移率和适当的边界条件。在将引入的扩散界面模型正规化，并借助合适的渐近扩展，我们恢复了界面限制界面各向异性表面扩散流，以及各向异性Young的定律，以及在界面的接触线和固定外部边界处的零升华条件。此外，我们显示了正规化模型的弱解决方案的存在，无论是光滑和障碍物的潜力。提出了基于适当的有限元近似值的数值结果，以证明所提出的漫射界面模型与其尖锐地面限制之间的出色一致性。
We present a diffuse-interface model for the solid-state dewetting problem with anisotropic surface energies in ${\mathbb R}^d$ for $d\in\{2,3\}$. The introduced model consists of the anisotropic Cahn--Hilliard equation, with either a smooth or a double-obstacle potential, together with a degenerate mobility function and appropriate boundary conditions on the wall. Upon regularizing the introduced diffuse-interface model, and with the help of suitable asymptotic expansions, we recover as the sharp-interface limit the anisotropic surface diffusion flow for the interface together with an anisotropic Young's law and a zero-flux condition at the contact line of the interface with a fixed external boundary. Furthermore, we show the existence of weak solutions for the regularized model, for both smooth and obstacle potential. Numerical results based on an appropriate finite element approximation are presented to demonstrate the excellent agreement between the proposed diffuse-interface model and its sharp-interface limit.
