Localization of Photons in Random and Quasiperiodic Media

Quasiperiodic media is a class of almost periodic media which is generated from periodic media through a ‘cut and project’ procedure. Quasiperiodic media displays some extraordinary optical, electronic and conductivity properties which call for the development of methods to analyse their microstructures and effective behaviour. In this paper, we develop the method of Bloch wave homogenisation for quasiperiodic media. Bloch waves are typically defined through a direct integral decomposition of periodic operators. A suitable direct integral decomposition is not available for almost periodic operators. To remedy this, we lift a quasiperiodic operator to a degenerate periodic operator in higher dimensions. Approximate Bloch waves are obtained for a regularised version of the degenerate operator. Homogenised coefficients for quasiperiodic media are obtained from the first Bloch eigenvalue of the regularised operator in the limit of regularisation parameter going to zero. A notion of quasiperiodic Bloch transform is defined and employed to obtain homogenisation limit for an equation with highly oscillating quasiperiodic coefficients.

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Propagation of electromagnetic waves in one-dimensional quasiperiodic media

Astrophysics ◽

10.1007/s10511-006-0052-9 ◽

2006 ◽

Vol 49 (4) ◽

pp. 538-542

Author(s):

V. D. Badalyan

Keyword(s):

Electromagnetic Waves ◽

One Dimensional ◽

Quasiperiodic Media

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WAVE PROPAGATION IN QUASIPERIODIC MEDIA

Quasicrystals ◽

10.1142/9789812793201_0014 ◽

2000 ◽

Cited By ~ 3

Author(s):

D. MAYOU

Keyword(s):

Wave Propagation ◽

Quasiperiodic Media

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Stochastic webs and continuum percolation in quasiperiodic media

Chaos An Interdisciplinary Journal of Nonlinear Science ◽

10.1063/1.166055 ◽

1994 ◽

Vol 4 (1) ◽

pp. 35-46 ◽

Cited By ~ 4

Author(s):

A. A. Chernikov ◽

A. V. Rogalsky

Keyword(s):

Continuum Percolation ◽

Quasiperiodic Media

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The Method Based on Series Solution for Identifying an Unknown Source Coefficient on the Temperature Field in the Quasiperiodic Media

International Journal of Differential Equations ◽

10.1155/2021/2893299 ◽

2021 ◽

Vol 2021 ◽

pp. 1-8

Author(s):

Bingxian Wang ◽

Chuanzhi Bai ◽

M. Xu ◽

L. P. Zhang

Keyword(s):

Inverse Problem ◽

Series Solution ◽

Iteration Process ◽

One Dimensional ◽

Exact Data ◽

Unknown Source ◽

Convergence Results ◽

Quasiperiodic Media ◽

Iteration Processes ◽

Heat Field

In this paper, we consider the reconstruction of heat field in one-dimensional quasiperiodic media with an unknown source from the interior measurement. The innovation of this paper is solving the inverse problem by means of two different homotopy iteration processes. The first kind of homotopy iteration process is not convergent. For the second kind of homotopy iteration process, a convergent result is proved. Based on the uniqueness of this inverse problem and convergence results of the second kind of homotopy iteration process with exact data, the results of two numerical examples show that the proposed method is efficient, and the error of the inversion solution r t is given.

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