Properties of microcavities in two-dimensional photonic quasicrystals with octagonal rotational symmetry

2007 ◽  
Vol 54 (6) ◽  
pp. 881-893 ◽  
Author(s):  
D. M. Beggs ◽  
M. A. Kaliteevski ◽  
R. A. Abram
Keyword(s):  
Rotational Symmetry ◽  
Two Dimensional ◽  
Photonic Quasicrystals

Comparison of Calculated and Recorded Electron Energy-Loss Spectra of Aluminium and Carbon

1990 ◽  
Vol 48 (2) ◽  
pp. 64-65
Author(s):  
L. Reimer ◽  
R. Oelgeklaus
Keyword(s):  
Fourier Transform ◽  
Energy Loss ◽  
Electron Energy ◽  
Rotational Symmetry ◽  
Mean Free Path ◽  
Single Scattering ◽  
Specimen Thickness ◽  
Two Dimensional ◽  
Image Position ◽  
Electron Energy Loss

Quantitative electron energy-loss spectroscopy (EELS) needs a correction for the limited collection aperture α and a deconvolution of recorded spectra for eliminating the influence of multiple inelastic scattering. Reversely, it is of interest to calculate the influence of multiple scattering on EELS. The distribution f(w,θ,z) of scattered electrons as a function of energy loss w, scattering angle θ and reduced specimen thickness z=t/Λ (Λ=total mean-free-path) can either be recorded by angular-resolved EELS or calculated by a convolution of a normalized single-scattering function ϕ(w,θ). For rotational symmetry in angle (amorphous or polycrystalline specimens) this can be realised by the following sequence of operations :(1)where the two-dimensional distribution in angle is reduced to a one-dimensional function by a projection P, T is a two-dimensional Fourier transform in angle θ and energy loss w and the exponent -1 indicates a deprojection and inverse Fourier transform, respectively.

scholarly journals General up to next-nearest-neighbour elasticity of triangular lattices in three dimensions

2006 ◽  
Vol 462 (2073) ◽  
pp. 2695-2713 ◽  
Author(s):  
Cyril Dubus ◽  
Ken Sekimoto ◽  
Jean-Baptiste Fournier
Keyword(s):  
Blood Cell ◽  
Red Blood Cell ◽  
Triangular Lattice ◽  
Soft Matter ◽  
Rotational Symmetry ◽  
Three Dimensions ◽  
Nearest Neighbour ◽  
Two Dimensional ◽  
Biological Physics ◽  
Crystalline System

We establish the most general form of the discrete elasticity of a two-dimensional triangular lattice embedded in three dimensions, taking into account up to next-nearest-neighbour interactions. Besides crystalline system, this is relevant to biological physics (e.g. red blood cell cytoskeleton) and soft matter (e.g. percolating gels, etc.). In order to correctly impose the rotational invariance of the bulk terms, it turns out to be necessary to take into account explicitly the elasticity associated with the vertices located at the edges of the lattice. We find that some terms that were suspected in the literature to violate rotational symmetry are, in fact, admissible.

scholarly journals Two-dimensional quasicrystal with eightfold rotational symmetry

1987 ◽  
Vol 59 (9) ◽  
pp. 1010-1013 ◽  
Author(s):  
N. Wang ◽  
H. Chen ◽  
K. H. Kuo
Keyword(s):  
Rotational Symmetry ◽  
Two Dimensional

Arabic Astronomical Tables in China: Tabular Layout and its Implications for the Transmission and Use of the Huihui lifa

2016 ◽  
Vol 44 (1) ◽  
pp. 21-68
Author(s):  
Li Liang
Keyword(s):  
Rotational Symmetry ◽  
Single Type ◽  
Two Dimensional ◽  
Specific Nature ◽  
Intended Audience ◽  
One Dimensional ◽  
Dimensional Array

This paper examines the early transmission and translation of Arabic astronomical tables in China by comparing the layouts of parallax correction tables. After comparing the layouts of equation tables in various Huihui lifa works, this paper concludes that the characteristics of tabular layout are related to the specific nature of each work, and these adjustments thereto may reflect changes in their intended audience and purpose. Comparison of a single type of table that appears in Huihui lifa works of different eras in one-dimensional array, two-dimensional array, and rotational symmetry layouts illustrates that Chinese astronomical tables continually absorbed and adapted the advantages offered by Arabic and European counterparts, flexibly adapting them to their own purposes on the basis of their own tradition and habits.

scholarly journals Dirac electrons in a dodecagonal graphene quasicrystal

Science ◽  
2018 ◽  
Vol 361 (6404) ◽  
pp. 782-786 ◽  
Author(s):  
Sung Joon Ahn ◽  
Pilkyung Moon ◽  
Tae-Hoon Kim ◽  
Hyun-Woo Kim ◽  
Ha-Chul Shin ◽  
...  
Keyword(s):  
Silicon Carbide ◽  
Rotation Angle ◽  
Rotational Symmetry ◽  
Interlayer Coupling ◽  
Quantum States ◽  
Translational Symmetry ◽  
Two Dimensional ◽  
Ambient Conditions ◽  
Entire Sample ◽  
Twisted Bilayer Graphene

Quantum states of quasiparticles in solids are dictated by symmetry. We have experimentally demonstrated quantum states of Dirac electrons in a two-dimensional quasicrystal without translational symmetry. A dodecagonal quasicrystalline order was realized by epitaxial growth of twisted bilayer graphene rotated exactly 30°. We grew the graphene quasicrystal up to a millimeter scale on a silicon carbide surface while maintaining the single rotation angle over an entire sample and successfully isolated the quasicrystal from a substrate, demonstrating its structural and chemical stability under ambient conditions. Multiple Dirac cones replicated with the 12-fold rotational symmetry were observed in angle-resolved photoemission spectra, which revealed anomalous strong interlayer coupling with quasi-periodicity. Our study provides a way to explore physical properties of relativistic fermions with controllable quasicrystalline orders.

The design of two-dimensional photonic quasicrystals by means of a Fourier transform method

2001 ◽  
Vol 48 (1) ◽  
pp. 9-14 ◽  
Author(s):  
M. A. Kaliteevski ◽  
Brand S. ◽  
R. A. Abram ◽  
T. F. Krauss ◽  
R. De La Rue ◽  
...  
Keyword(s):  
Fourier Transform ◽  
Two Dimensional ◽  
Transform Method ◽  
Fourier Transform Method ◽  
Photonic Quasicrystals
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