Localized modes in a two dimensional lattice

Mathews, P. M. ; Seshadri, M. S. ; Vijayalakshmi, R. (1965) Localized modes in a two dimensional lattice Journal of Applied Mathematics and Mechanics, 45 (4). pp. 209-215. ISSN 0044-2267

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Official URL: http://onlinelibrary.wiley.com/doi/10.1002/zamm.19...

Related URL: http://dx.doi.org/10.1002/zamm.19650450406


The simplest non-trivial model of a two-dimensional monatomic lattice-one with nearest neighbour central and noncentral interactions-containing an isotopic impurity is considered. A characteristic equation is obtained for the frequency of the localized mode by the generating function method. The characteristic equation involves a complete elliptic integral of the first kind. The variation of the impurity frequency with the mass of the impurity and with the strength of noncentral interactions is studied. An asymptotic expression for the vibrational amplitude of the localized mode is derived, using the saddle-point approximation.

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Deposited On:04 Feb 2012 11:23
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