AI 中文总结
该论文证明了一维莫尔材料原子尺度弛豫模型的极小元收敛到连续极限泛函的极小元，该连续极限耦合线性弹性与周期失配势，为莫尔弛豫建模提供了严格理论基础。
AI 中文摘要
我们建立了莫尔材料中一维原子尺度弛豫模型的极小元到一维连续极限泛函极小元的收敛性，该连续极限泛函与实践中常用的弛豫模型类似。原子尺度模型由每个公共晶胞含 $N$ 和 $N+1$ 个原子的两条周期链组成，并在原子尺度上精确地具有莫尔周期性。其能量将谐波最近邻层内相互作用与由具有多项式衰减的偶 $C^2$ 对势产生的非局域层间相互作用相结合。相应的连续能量将线性弹性与周期失配势耦合，该失配势通过对对势进行周期化得到，用于惩罚不利的局部堆垛。
英文摘要
We establish convergence of minimizers for a minimal one dimensional atomic-scale model for relaxation in moiré materials to those of a one-dimensional continuum limit functional analogous to those commonly used in practice to model relaxation. The atomic-scale model consists of two periodic chains containing $N$ and $N+1$ atoms per common cell and is exactly moiré-periodic at the atomic scale. Its energy combines harmonic nearest-neighbor intralayer interactions with nonlocal interlayer interactions generated by an even $C^2$ pair potential with polynomial decay. The associated continuum energy couples linear elasticity to a periodic misfit potential, obtained by periodizing the pair potential, which penalizes unfavorable local stackings.
Comments25 pages
