We show how measuring real space properties such as the charge density in a quasiperiodic system can be used to gain insight into their topological properties. In particular, for Fibonacci chain, we that total onsite oscillates when plotted appropriate coordinates, and number of oscillations is given by Chern gap which Fermi level lies. these have two distinct interpretations, obtained extrapol...

Penrose tiling is an example of the two-dimensional quasicrystal tessellation model, which British mathematician Roger first proposed in 1974. In this paper, we investigate construction rules P3 theoretical model. We successfully generate seven generations complete using self-similar transformation method.

– From relaxation simulations of decoration-based quasicrystal structure models using microscopically based interatomic pair potentials, we have calculated the (usually neglected) phonon-phason coupling constant. Its sign is opposite for the two alloys studied, i-AlMn and i-(Al,Cu)Li; a dimensionless measure of its magnitude relative to the phonon and phason elastic constants is of order 1/10, ...

In this paper we are concerned with the reconstruction of a class of measures on the square from the sampling of its Fourier coefficients on some sparse set of points. We show that the exact reconstruction of a weighted Dirac sum measure is still possible when one knows a finite number of non-adaptive linear measurements of the spectrum. Surprisingly, these measurements are defined on a model s...

A switch in symmetry from fivefold to tenfold has been observed at the surface of a monograin icosahedral AlPdMn quasicrystal cut perpendicularly to a fivefold axis as a function of annealing temperature and/or annealing time at a constant temperature. A continuous change in stoichiometry was simultaneously monitored by X-ray photoelectron spectroscopy. The surface structure study was performed...