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The phenomena of band gaps and propagation of water waves over one-dimensional periodic bottoms and combination bottoms is investigated by the transfer matrix method. For the periodic bottoms (PBs), the effect of the steps' numbers, their height and width on the band gaps are discussed, respectively. For two kinds of combination periodic-bottoms (CPBs), namely height-CPBs and width-CPBs, both corresponding...
Quasiperiodic structures can be generated by cluster covering approach. In a decagonal covering pattern there are nine nearest neighbor configurations. These basic configurations exhibit certain correlations in the whole system and will develop to higher order configurations, which reflect the local structures concerning the neighbors beyond the nearest ones.
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