ISSN:
1572-9613
Keywords:
Disordered harmonic crystal
;
energy transport
;
fractional linear transformation
;
localization
;
self-inverse fractal
;
transmission coefficient
Source:
Springer Online Journal Archives 1860-2000
Topics:
Physics
Notes:
Abstract We reexamine the calculation of the transmission coefficient of a random array ofN isotopic defects in an otherwise perfect, harmonic, one-dimensional crystal lattice. The thermal conductivity of this model system has been studied under steady state conditions in which there is a kinetic temperature difference across, and an associated energy flux through, the array of defects. An exact expression for the transmission coefficient is obtained in terms of the magnitude of anNth-order determinant. Rubin reduced the evaluation of the determinant to the evaluation of a sequence ofN−1 nonlinear transformations drawn from a set of transformations parametrized by the nearest-neighbor spacing of the isotopic defects. These transformations are self-inverse and provide an example of what Mandelbrot has termed aself-inverse fractal. The variety of limiting distributions of values obtained under these transformations will be illustrated.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF01012926
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