Discontinuous behavior of effective transport coefficients in quasiperiodic media |
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Authors: | K Golden S Goldstein J L Lebowitz |
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Institution: | (1) Department of Mathematics, Rutgers University, 08903 New Brunswick, New Jersey;(2) Present address: Department of Mathematics, Princeton University, 08544 Princeton, New Jersey;(3) Department of Physics, Rutgers University, New Brunswick, New Jersey |
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Abstract: | We investigate the effective conductivity
* of a quasiperiodic medium in
d
and the discontinuous dependence, found in ref. 1, of
* on the wavelengths of the system. It was shown there, for example, that the effective conductivity
*(k) for a layered medium with a one-dimensional local conductivity
k
(x)=A+cosx+coskx, A>2, is discontinuous ink. An explicit class of higherdimensional examples which exhibit the discontinuity is constructed here. The conductivity
*(k, L) of a sample of lengthL in one dimension asL![rarr](/content/w96mh35650v80033/xxlarge8594.gif) is also analyzed and shown to have a plateau structure for any irrationalk well approximated by rationals. |
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Keywords: | Quasiperiodic media effective conductivity discontinuous dependence on wavelengths sample-size dependence |
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