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Coupled Systems Mechanics
  Volume 7, Number 3, June 2018 , pages 255-268
DOI: https://doi.org/10.12989/csm.2018.7.3.255
 

Stability of matching boundary conditions for diatomic chain and square lattice
Songsong Ji and Shaoqiang Tang

 
Abstract
    Stability of MBC1, a specific matching boundary condition, is proved for atomic simulations of a diatomic chain. The boundary condition and the Newton equations that govern the atomic dynamics form a coupled system. Energy functions that decay along with time are constructed for both the boundary with the same type atoms and the one with different type atoms. For a nonlinear chain, MBC1 is also shown stable. Numerical verifications are presented. Moreover, MBC1 is proved to be stable for a two dimensional square lattice.
 
Key Words
    stability; matching boundary condition; diatomic chain; two-dimensional square lattice; energy function
 
Address
Songsong Ji: Department of Mechanics and Engineering Science, College of Engineering, Peking University, Beijing
100871, China
Shaoqiang Tang: HEDPS, CAPT and LTCS, College of Engineering, Peking University, Beijing 100871, China
 

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