原创力文档- 1、本文档共6页，可阅读全部内容。
- 2、原创力文档（book118）网站文档一经付费（服务费），不意味着购买了该文档的版权，仅供个人/单位学习、研究之用，不得用于商业用途，未经授权，严禁复制、发行、汇编、翻译或者网络传播等，侵权必究。
- 3、本站所有内容均由合作方或网友上传，本站不对文档的完整性、权威性及其观点立场正确性做任何保证或承诺！文档内容仅供研究参考，付费前请自行鉴别。如您付费，意味着您自己接受本站规则且自行承担风险，本站不退款、不进行额外附加服务；查看《如何避免下载的几个坑》。如果您已付费下载过本站文档，您可以点击 这里二次下载。
- 4、如文档侵犯商业秘密、侵犯著作权、侵犯人身权等，请点击“版权申诉”（推荐），也可以打举报电话：400-050-0827(电话支持时间：9:00-18:30)。
查看更多
Discrete quasiperiodic sets with predefined covering cluster
a
r
X
i
v
:
m
a
t
h
-
p
h
/
0
5
0
5
0
0
5
v
2
1
7
J
u
l
2
0
0
5
Discrete quasiperiodic sets with predefined covering
cluster
N. COTFAS
Faculty of Physics, University of Bucharest, E-mail: ncotfas@
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 window of selection. We present some mathematical results which allow one
to use this very elegant method in superspaces of dimension much higher, and
to generate discrete quasiperiodic sets with a more complicated local structure
by starting from the corresponding covering cluster. Hundreds of points of these
sets can be obtained in only a few minutes by using our computer programs.
Keywords: Strip projection method; quasiperiodic point set; covering cluster.
1. Introduction
Quasicrystals are materials with perfect long-range order, but with no three-
dimensional translational periodicity. The discovery of these solids in the early
1980’s and the challenge to describe their structure led to a great interest in
discrete quasiperiodic sets and their coverings ([9] and references therein).
The diffraction image of a quasicrystal often contains a set of sharp Bragg
peaks invariant under a finite non-crystallographic group of symmetriesG, called
the symmetry group of quasicrystal (in reciprocal space). In the case of qua-
sicrystals with no translational periodicity this group is the icosahedral group
Y and in the case of quasicrystals periodic along one direction (two-dimensional
quasicrystals) G is one of the dihedral groups D8 (octagonal quasicrystals),
D10 (decagonal quasicrystals) and D12 (dodecagonal quasicrystals). Real struc-
ture information obtained by high resolution transmission electron microscopy
suggests us that a quasicrystal with symmetry group G can be regarded as a
quasiperiodic packing of copies of a well-defined G-inv
您可能关注的文档
- Contact angle hysteresis of cylindrical drops on chemically heterogeneous striped surfaces.pdf
- Contactless 360° absolute angular CMOS microsystem based on vertical Hall sensors.pdf
- Contents Title ”Operator Theory Arising from Systems Engineering”.pdf
- Context Sensitive Anomaly Monitoring of Process Control Flow to Detect Mimicry ￡ Attacks a.pdf
- Context Shadow A Person-Centric Infrastructure for Context Aware Computing.pdf
- Context-Sensitive Referencing for Ontology Mapping Disambiguation.pdf
- Context-Sensitive Binding by the Laminar Circuits of V1 and V2 Unified Model Perceptual Gro.pdf
- Context-Sensitive Spoken Dialogue Processing with the DOP Model.pdf
- Continuity of the Complex Monge-Ampere Operator on Compact Kahler Manifolds.pdf
- Continuum Field Model of Street Canyon Theoretical Description Part I.pdf
文档评论（0）