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