论文标题
在外延生长中的束束和渐近特性具有弹性效应：连续模型
Bunching instability and asymptotic properties in epitaxial growth with elasticity effects: continuum model
论文作者
论文摘要
我们研究了Xiang和E提出的弹性相互作用原子步骤的连续性外延模型（Xiang，Siam J.Appl。Math。63：241-258，2002; Xiang and E，Phys。B69：035409，2004）。非本地术语和奇异性使其PDE的分析变得复杂。在本文中，我们首先将此模型推广到步骤之间的Lennard-Jones（M，N）相互作用。基于非本地能量的几种重要配方，我们证明了在周期性环境中能量最小化器的存在，对称性，单型和规则性。特别是，最小化器的对称性和非模式性意味着它具有束曲线。此外，我们得出了原始连续性模型的最小能量缩放定律。所有结果均与Luo等人证明的离散模型证明的相应结果一致。 （Luo等人，多尺度模型。模拟14：737-771，2016）。
We study the continuum epitaxial model for elastic interacting atomic steps on vicinal surfaces proposed by Xiang and E (Xiang, SIAM J. Appl. Math. 63:241-258, 2002; Xiang and E, Phys. Rev. B 69:035409, 2004). The non-local term and the singularity complicate the analysis of its PDE. In this paper, we first generalize this model to the Lennard-Jones (m,n) interaction between steps. Based on several important formulations of the non-local energy, we prove the existence, symmetry, unimodality, and regularity of the energy minimizer in the periodic setting. In particular, the symmetry and unimodality of the minimizer implies that it has a bunching profile. Furthermore, we derive the minimum energy scaling law for the original continnum model. All results are consistent with the corresponding results proved for discrete models by Luo et al. (Luo et al., Multiscale Model. Simul. 14:737 - 771, 2016).
