The Planar Inverse Problem of Dynamics

Anisiu, Mira-Cristiana

doi:10.1007/978-1-4939-1124-0_1

Cited by 1 publication

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“…Independently of their physical impact, local symmetries in 1D aperiodic sequences have been extensively studied under the name 'palindromes' in the combinatorics of words [11][12][13][14][15][16][17][18][19]. Here, the minimal reflection symmetric structural units are encoded as symbolic elements (the letters) of a set of given cardinality (the alphabet), out of which discrete lattices (the words) are constructed by concatenation.…”

Section: Introductionmentioning

confidence: 99%

Local symmetry dynamics in one-dimensional aperiodic lattices: a numerical study

et al. 2014

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A unifying description of lattice potentials generated by aperiodic one-dimensional sequences is proposed in terms of their local reflection or parity symmetry properties. We demonstrate that the ranges and axes of local reflection symmetry possess characteristic distributional and dynamical properties which can be determined for every aperiodic binary lattice. A striking aspect of such a property is given by the return maps of sequential spacings of local symmetry axes, which typically traverse few-point symmetry orbits. This local symmetry dynamics allows for a classification of inherently different aperiodic lattices according to fundamental symmetry principles. Illustrating the local symmetry distributional and dynamical properties for several representative binary lattices, we further show that the renormalized axis spacing sequences follow precisely the particular type of underlying aperiodic order. Our analysis thus reveals that the long-range order of aperiodic lattices is characterized in a compellingly simple way by its local symmetry dynamics.

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