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Volume 8, Issue 1
Unstable Surface Modes in Finite Chain Computations: Deficiency of Reflection Coefficient Approach

Shaoqiang Tang & Ming Fang

Commun. Comput. Phys., 8 (2010), pp. 143-158.

Published online: 2010-08

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  • Abstract

In this paper, we investigate the stability for a finite harmonic lattice under a certain class of boundary conditions. A rigorous eigenvalue study clarifies that the invalidity of Fourier modes as the basis results in the deficiency of standard reflection coefficient approach for stability analysis. In a certain parameter range, unstable surface modes exist in the form of exponential decay in space, and exponential growth in time. An approximate eigen-polynomial is proposed to ease the stability analysis. Moreover, the eigenvalues with small positive real part quantitatively explain the long time instability in wave propagation computations. Numerical results verify the analysis.

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@Article{CiCP-8-143, author = {}, title = {Unstable Surface Modes in Finite Chain Computations: Deficiency of Reflection Coefficient Approach}, journal = {Communications in Computational Physics}, year = {2010}, volume = {8}, number = {1}, pages = {143--158}, abstract = {

In this paper, we investigate the stability for a finite harmonic lattice under a certain class of boundary conditions. A rigorous eigenvalue study clarifies that the invalidity of Fourier modes as the basis results in the deficiency of standard reflection coefficient approach for stability analysis. In a certain parameter range, unstable surface modes exist in the form of exponential decay in space, and exponential growth in time. An approximate eigen-polynomial is proposed to ease the stability analysis. Moreover, the eigenvalues with small positive real part quantitatively explain the long time instability in wave propagation computations. Numerical results verify the analysis.

}, issn = {1991-7120}, doi = {https://doi.org/10.4208/cicp.2009.09.065}, url = {http://global-sci.org/intro/article_detail/cicp/7566.html} }
TY - JOUR T1 - Unstable Surface Modes in Finite Chain Computations: Deficiency of Reflection Coefficient Approach JO - Communications in Computational Physics VL - 1 SP - 143 EP - 158 PY - 2010 DA - 2010/08 SN - 8 DO - http://doi.org/10.4208/cicp.2009.09.065 UR - https://global-sci.org/intro/article_detail/cicp/7566.html KW - AB -

In this paper, we investigate the stability for a finite harmonic lattice under a certain class of boundary conditions. A rigorous eigenvalue study clarifies that the invalidity of Fourier modes as the basis results in the deficiency of standard reflection coefficient approach for stability analysis. In a certain parameter range, unstable surface modes exist in the form of exponential decay in space, and exponential growth in time. An approximate eigen-polynomial is proposed to ease the stability analysis. Moreover, the eigenvalues with small positive real part quantitatively explain the long time instability in wave propagation computations. Numerical results verify the analysis.

Shaoqiang Tang & Ming Fang. (2020). Unstable Surface Modes in Finite Chain Computations: Deficiency of Reflection Coefficient Approach. Communications in Computational Physics. 8 (1). 143-158. doi:10.4208/cicp.2009.09.065
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