Affine Symmetry Semi-Groups for Quasi-Crystals

1994 ◽  
Vol 25 (6) ◽  
pp. 435-440 ◽  
Author(s):  
D Barache ◽  
S. de Bievre ◽  
J. P Gazeau
Keyword(s):  
Affine Symmetry ◽  
Quasi Crystals

A Structural Model for a Quasi-Crystalline Material Derived from TEM

1990 ◽  
Vol 48 (1) ◽  
pp. 48-49
Author(s):  
Jan-Olov Bovin ◽  
Osamu Terasaki ◽  
Jan-Olle Malm ◽  
Sven Lidin ◽  
Sten Andersson
Keyword(s):  
High Resolution ◽  
Electron Diffraction ◽  
Structural Model ◽  
Image Intensifier ◽  
Crystalline Materials ◽  
Icosahedral Phases ◽  
Transmission Electron ◽  
Electron Microscopes ◽  
Diffraction Patterns ◽  
Quasi Crystals

High resolution transmission electron microscopy (HRTEM) is playing an important role in identifying the new icosahedral phases. The selected area diffraction patterns of quasi crystals, recorded with an aperture of the radius of many thousands of Ångströms, consist of dense arrays of well defined sharp spots with five fold dilatation symmetry which makes the interpretation of the diffraction process and the resulting images different from those invoked for usual crystals. The atomic structure of the quasi crystals is not established even if several models are proposed. The correct structure model must of course explain the electron diffraction patterns with 5-, 3- and 2-fold symmetry for the phases but it is also important that the HRTEM images of the alloys match the computer simulated images from the model. We have studied quasi crystals of the alloy Al65Cu20Fe15. The electron microscopes used to obtain high resolution electro micrographs and electron diffraction patterns (EDP) were a (S)TEM JEM-2000FX equipped with EDS and PEELS showing a structural resolution of 2.7 Å and a IVEM JEM-4000EX with a UHP40 high resolution pole piece operated at 400 kV and with a structural resolution of 1.6 Å. This microscope is used with a Gatan 622 TV system with an image intensifier, coupled to a YAG screen. It was found that the crystals of the quasi crystalline materials here investigated were more sensitive to beam damage using 400 kV as electron accelerating voltage than when using 200 kV. Low dose techniques were therefore applied to avoid damage of the structure.

ELECTRON DIFFRACTION AND MICROSCOPY OF INCOMMENSURATE PHASES AND QUASI-CRYSTALS

1986 ◽  
Vol 47 (C3) ◽  
pp. C3-437-C3-446 ◽  
Author(s):  
J. W. STEEDS ◽  
R. AYER ◽  
Y. P. LIN ◽  
R. VINCENT
Keyword(s):  
Electron Diffraction ◽  
Quasi Crystals ◽  
Incommensurate Phases

scholarly journals Integrable and Chaotic Systems Associated with Fractal Groups

Entropy ◽  
2021 ◽  
Vol 23 (2) ◽  
pp. 237
Author(s):  
Rostislav Grigorchuk ◽  
Supun Samarakoon
Keyword(s):  
Operator Algebras ◽  
Probabilistic Approach ◽  
Schur Complement ◽  
Automata Theory ◽  
Random Schrödinger Operators ◽  
Rational Maps ◽  
Holomorphic Dynamics ◽  
Von Neumann ◽  
Intermediate Growth ◽  
Quasi Crystals

Fractal groups (also called self-similar groups) is the class of groups discovered by the first author in the 1980s with the purpose of solving some famous problems in mathematics, including the question of raising to von Neumann about non-elementary amenability (in the association with studies around the Banach-Tarski Paradox) and John Milnor’s question on the existence of groups of intermediate growth between polynomial and exponential. Fractal groups arise in various fields of mathematics, including the theory of random walks, holomorphic dynamics, automata theory, operator algebras, etc. They have relations to the theory of chaos, quasi-crystals, fractals, and random Schrödinger operators. One important development is the relation of fractal groups to multi-dimensional dynamics, the theory of joint spectrum of pencil of operators, and the spectral theory of Laplace operator on graphs. This paper gives a quick access to these topics, provides calculation and analysis of multi-dimensional rational maps arising via the Schur complement in some important examples, including the first group of intermediate growth and its overgroup, contains a discussion of the dichotomy “integrable-chaotic” in the considered model, and suggests a possible probabilistic approach to studying the discussed problems.

scholarly journals Infinite approximate subgroups of soluble Lie groups

2021 ◽  
Author(s):  
Simon Machado
Keyword(s):  
Lie Groups ◽  
Structure Theorem ◽  
Quasi Crystals

AbstractWe study infinite approximate subgroups of soluble Lie groups. We show that approximate subgroups are close, in a sense to be defined, to genuine connected subgroups. Building upon this result we prove a structure theorem for approximate lattices in soluble Lie groups. This extends to soluble Lie groups a theorem about quasi-crystals due to Yves Meyer.

Quasi-crystals studied with convergent-beam electron diffraction

1988 ◽  
Vol 24 (4) ◽  
pp. 440-441
Author(s):  
S. Last ◽  
P.M. Bronsveld ◽  
G. Boom ◽  
J.Th.M. de Hosson
Keyword(s):  
Electron Diffraction ◽  
Convergent Beam Electron Diffraction ◽  
Beam Electron ◽  
Quasi Crystals ◽  
Convergent Beam

scholarly journals Quantum affine symmetry as generalized supersymmetry

1993 ◽  
Vol 401 (1-2) ◽  
pp. 413-454 ◽  
Author(s):  
André LeClair ◽  
Cumrun Vafa
Keyword(s):  
Affine Symmetry

Contributions of Time Dependent and Cyclic Crack Growth to the Crack Growth Behavior of Non Strain-Crystallizing Elastomers

2002 ◽  
Vol 75 (4) ◽  
pp. 643-656 ◽  
Author(s):  
J. J. C. Busfield ◽  
K. Tsunoda ◽  
C. K. L. Davies ◽  
A. G. Thomas
Keyword(s):  
Crack Growth ◽  
Growth Behavior ◽  
Time Dependent ◽  
Crack Growth Behavior ◽  
Wide Range ◽  
Dependent Component ◽  
Tearing Energy ◽  
Quasi Crystals ◽  
Crack Growth Rates ◽  
Time Dependent Crack Growth

Abstract Engineering components are observed to fail more rapidly under cyclic loading than under static loading. This reflects features of the underlying crack growth behavior. This behavior is characterized by the relation between the tearing energy, T, and the crack growth per cycle, dc/dn. The increment of crack growth during each cycle is shown here to result from the sum of time dependent and cyclic crack growth components. The time dependent component represents the crack growth behavior that would be present in a conventional constant T crack growth test. Under repeated stressing additional crack growth, termed the cyclic crack growth component, occurs. For a non-crystallizing elastomer, significant effects of frequency have been found on the cyclic crack growth behavior, reflecting the presence of this cyclic element of crack growth. The cyclic crack growth behavior over a wide range of frequencies was investigated for unfilled and swollen SBR materials. The time dependent crack growth component was calculated from constant T crack growth tests and the cyclic contribution derived from comparison with the observed cyclic growth. It is shown that decreasing the frequency or increasing the maximum tearing energy during a cycle results in the cyclic crack growth behavior being dominated by time dependent crack growth. Conversely at high frequency and at low tearing energy, cyclic crack growth is dominated by the cyclic crack growth component. A large effect of frequency on cyclic crack growth behavior was observed for highly swollen SBR. The cyclic crack growth behavior was dominated by the time dependent crack growth component over the entire range of tearing energy and/or crack growth rate. The origin of the cyclic component may be the formation/melting of quasi crystals at the crack tip, which is absent at fast crack growth rates in the unswollen SBR and is absent at all rates in the swollen SBR.

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