Unstable Surface Modes in Finite Chain Computations: Deficiency of Reflection Coefficient Approach

Unstable Surface Modes in Finite Chain Computations: Deficiency of Reflection Coefficient Approach

Year:    2010

Communications in Computational Physics, Vol. 8 (2010), Iss. 1 : pp. 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.

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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/cicp.2009.09.065

Communications in Computational Physics, Vol. 8 (2010), Iss. 1 : pp. 143–158

Published online:    2010-01

AMS Subject Headings:    Global Science Press

Copyright:    COPYRIGHT: © Global Science Press

Pages:    16

Keywords: