| Abstract: |
| Quasiperiodic geometry is characterized by a long-range order in the absence of periodicity. Quasiperiodic structures can be modeled using the cut-and-projection method that restricts or projects a periodic function in a higher dimensional space to a lower dimensional subspace cut at an irrational projection angle. We derive the homogenized equations for the effective electromagnetic properties of a quasiperiodic composite using cut-and-projection method applied to periodic homogenization in a higher dimensional space. We use equations for the local cell problem in the higher dimensional space established in the homogenization process to develop the Herglotz analytic representation for the effective properties of quasiperiodic materials. This integral representation determines the spectral characteristics of fields in quasicrystalline composites and can be used to derive bounds for the effective properties. A joint work with Niklas Wellander and Sebastien Guenneau. |
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