Abstract
We investigate the effective conductivityσ * of a quasiperiodic medium in ℝd and the discontinuous dependence, found in ref. 1, ofσ * on the wavelengths of the system. It was shown there, for example, that the effective conductivityσ *(k) for a layered medium with a one-dimensional local conductivityσ k (x)=A+cosx+coskx, A>2, is discontinuous ink. An explicit class of higherdimensional examples which exhibit the discontinuity is constructed here. The conductivityσ *(k, L) of a sample of lengthL in one dimension asL→∞ is also analyzed and shown to have a plateau structure for any irrationalk well approximated by rationals.
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Golden, K., Goldstein, S. & Lebowitz, J.L. Discontinuous behavior of effective transport coefficients in quasiperiodic media. J Stat Phys 58, 669–684 (1990). https://doi.org/10.1007/BF01112770
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DOI: https://doi.org/10.1007/BF01112770