Artificial boundary conditions for out-of-plane motion in penta-graphene

In this paper, artificial boundary conditions are designed for out-of-plane waves in penta-graphene, a newly proposed allotrope of carbon. By matching the dispersion relation for acoustic branch phonons in the long wave limit, we determine parameters in proposed linear constraints among displacements and velocities at the boundary and nearby atoms. Reflection analysis for normal incidences and a numerical test demonstrate the effectiveness of the artificial boundary conditions. These conditions may be used for studying mechanical behaviours of the novel complex lattice of penta-graphene. © 2017 The Chinese Society of Theoretical and Applied Mechanics; Institute of Mechanics, Chinese Academy of Sciences and Springer-Verlag Berlin Heidelberg

Stability of Atomic Simulations with Matching Boundary Conditions

.We explore the stability of matching boundary conditions in one space dimension,which were proposed recently for atomic simulations(Wang and Tang,Int.J.Numer.Mech.Eng.,93(2013),pp.1255–1285).For a finite segment of the linear harmonic chain,we construct explicit energy functionals that decay along with time.For a nonlinear atomic chain with its nonlinearity vanished around the boundaries,an energy functional is constructed for the first order matching boundary condition.Numerical verifications are also presented.