Related papers: Image Sampling with Quasicrystals
Kirigami, the art of introducing cuts in thin sheets to enable articulation and deployment, has become an inspiration for a novel class of mechanical metamaterials with unusual properties. Here we complement the use of periodic tiling…
Some of the most remarkable tilings and discrete quasiperiodic sets used in quasicrystal physics can be obtained by using strip projection method in a superspace of dimension four, five or six, and the projection of a unit hypercube as a…
In recent years, there has been a proliferation of wide-field sky surveys to search for a variety of transient objects. Using relatively short focal lengths, the optics of these systems produce undersampled stellar images often marred by a…
Image segmentation aims at identifying regions of interest within an image, by grouping pixels according to their properties. This task resembles the statistical one of clustering, yet many standard clustering methods fail to meet the basic…
A problem is addressed of minimization of the number of measurements needed for digital image acquisition and reconstruction with a given accuracy. A sampling theory based method of image sampling and reconstruction is suggested that allows…
In this paper the problem of the theory of a quasicrystal structures - the determination of coordinates of each atom of quasicrystal in analytical form - is solved. Within the framework of the proposed model a periodic crystal can be…
A geometric form of information theory allows for reasonable, i.e. probabilistic, evidence-ranking based, and generalized noise-level dependent, classifications of the crystallographic and quasicrystallographic symmetries in noisy digital…
Quasicrystals are characterized by quasi-periodic arrangements of atoms. The description of their mechanics involves deformation and a (so called phason) vector field accounting at macroscopic scale of local phase changes, due to atomic…
Crystals are the materials which can be described by uniform periodic lattices. Traditionally, only the 1-, 2-, 3-, 4- and 6-fold rotation symmetries are allowed in crystals because other n-fold rotation symmetries are forbidden by the…
Quasicrystals remain among the most intriguing materials in physics and chemistry. Their structure results in many unusual properties including anomalously low friction as well as poor electrical and thermal conductivity but it also…
Quasicrystals possess long-range order but lack the translational symmetry of crystalline solids. In solid state physics, periodicity is one of the fundamental properties that prescribes the electronic band structure in crystals. In the…
Periodic approximations of quasicrystals are a powerful tool in analyzing spectra of Schr\"odinger operators arising from quasicrystals, given the known theory for periodic crystals. Namely, we seek periodic operators whose spectra…
Understanding the growth of quasicrystals poses a challenging problem, not the least because the quasiperiodic order present in idealized mathematical models of quasicrystals prohibit simple local growth algorithms. This can only be…
Randomly sampling points on surfaces is an essential operation in geometry processing. This sampling is computationally straightforward on explicit meshes, but it is much more difficult on other shape representations, such as widely-used…
Recent developments of imaging techniques enable researchers to visualize materials at the atomic resolution to better understand the microscopic structures of materials. This paper aims at automatic and quantitative characterization of…
Quantum image processing employs quantum computing to capture, manipulate, and recover images in various formats. This requires representations of encoded images using the quantum mechanical composition of any potential computing hardware.…
The surprising recent discoveries of quasicrystals and their approximants in soft matter systems poses the intriguing possibility that these structures can be realized in a broad range of nano- and micro-scale assemblies. It has been…
We present a scheme to identify quasicrystals based on powder diffraction data and to provide a standardized indexing. We apply our scheme to a large catalog of powder diffraction patterns, including natural minerals, to look for new…
Quasicrystals are long-range ordered and yet non-periodic. This interplay results in a wealth of intriguing physical phenomena, such as the inheritance of topological properties from higher dimensions, and the presence of non-trivial…
We introduce a construction to embed a quasiperiodic lattice of obstacles into a single unit cell of a higher-dimensional space, with periodic boundary conditions. This construction transparently shows the existence of channels in these…