D. J. Colquitt, M. J. Nieves, I. S. Jones, A. B. Movchan, N. V. Movchan
Localised defect modes generated by a finite line defect composed of several masses, contained inside an infinite square cell lattice, are analysed using the linear superposition of Green's function for a single mass defect. For a nontrivial solution, it is shown that this problem can be reduced to a characteristic equation involving the eigenfrequencies for the defect and the mass of the particles composing the defect. An example is presented where eigenfrequencies linked to this system and the corresponding eigenmodes are computed for a defect composed of several particles. An infinite chain of defects contained in the infinite square lattice is also considered and an explicit dispersion relation is obtained. For the case when the number of masses within the line defect is large, it is shown that the range of the eigenfrequencies can be predicted using the dispersion diagram for the infinite chain.
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http://arxiv.org/abs/1208.1871
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