41 citations · 229 across the 27 of their papers we have counts for
4 papers · 1 filter
Bunching instability and asymptotic properties in epitaxial growth with elasticity effects: continuum model
Tao Luo, Yang Xiang, Nung Kwan Yip
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, P…
Convergence from Atomistic Model to Peierls-Nabarro Model for Dislocations in Bilayer System with Complex Lattice
Yahong Yang, Tao Luo, Yang Xiang
In this paper, we prove the convergence from the atomistic model to the Peierls--Nabarro (PN) model of two-dimensional bilayer system with complex lattice. We show that the displac…
Existence, uniqueness, and energy scaling of 2+1 dimensional continuum model for stepped epitaxial surfaces with elastic effects
Ganghua Fan, Tao Luo, Yang Xiang
We study the 2+1 dimensional continuum model for the evolution of stepped epitaxial surface under long-range elastic interaction proposed by Xu and Xiang (SIAM J. Appl. Math. 69, 1…
Mathematical validation of the Peierls--Nabarro model for edge dislocations
Yuan Gao, Jian-Guo Liu, Tao Luo +1
In this paper, we perform mathematical validation of the Peierls--Nabarro (PN) models, which are multiscale models of dislocations that incorporate the detailed dislocation core st…