Description and symmetry of aperiodic crystals

2018 ◽  
Author(s):  
Ted Janssen ◽  
Gervais Chapuis ◽  
Marc de Boissieu
Keyword(s):  
Time Reversal ◽  
Mathematical Concept ◽  
New Materials ◽  
Magnetic Systems ◽  
Atomic Structures ◽  
Modulated Phases ◽  
Quasiperiodic Functions ◽  
Aperiodic Crystals ◽  
Superspace Description

This chapter first introduces the mathematical concept of aperiodic and quasiperiodic functions, which will form the theoretical basis of the superspace description of the new recently discovered forms of matter. They are divided in three groups, namely modulated phases, composites, and quasicrystals. It is shown how the atomic structures and their symmetry can be characterized and described by the new concept. The classification of superspace groups is introduced along with some examples. For quasicrystals, the notion of approximants is also introduced for a better understanding of their structures. Finally, alternatives for the descriptions of the new materials are presented along with scaling symmetries. Magnetic systems and time-reversal symmetry are also introduced.

scholarly journals Aperiodic Crystals

2014 ◽  
Vol 70 (a1) ◽  
pp. C1-C1 ◽  
Author(s):  
Ted Janssen ◽  
Aloysio Janner
Keyword(s):  
Physical Properties ◽  
Dimensional Space ◽  
X Rays ◽  
New Techniques ◽  
New Family ◽  
Modulated Phases ◽  
Open Questions ◽  
Higher Dimensional ◽  
Lattice Periodicity ◽  
Aperiodic Crystals

2014 is the International Year of Crystallography. During at least fifty years after the discovery of diffraction of X-rays by crystals, it was believed that crystals have lattice periodicity, and crystals were defined by this property. Now it has become clear that there is a large class of compounds with interesting properties that should be called crystals as well, but are not lattice periodic. A method has been developed to describe and analyze these aperiodic crystals, using a higher-dimensional space. In this lecture the discovery of aperiodic crystals and the development of the formalism of the so-called superspace will be described. There are several classes of such materials. After the incommensurate modulated phases, incommensurate magnetic crystals, incommensurate composites and quasicrystals were discovered. They could all be studied using the same technique. Their main properties of these classes and the ways to characterize them will be discussed. The new family of aperiodic crystals has led also to new physical properties, to new techniques in crystallography and to interesting mathematical questions. Much has been done in the last fifty years by hundreds of crystallographers, crystal growers, physicists, chemists, mineralogists and mathematicians. Many new insights have been obtained. But there are still many questions, also of fundamental nature, to be answered. We end with a discussion of these open questions.

scholarly journals Definition Extraction from Generic and Mathematical Domains with Deep Ensemble Learning

Mathematics ◽  
2021 ◽  
Vol 9 (19) ◽  
pp. 2502
Author(s):  
Natalia Vanetik ◽  
Marina Litvak
Keyword(s):  
Semantic Information ◽  
State Of The Art ◽  
Binary Classification ◽  
Ensemble Model ◽  
Classification Models ◽  
New Materials ◽  
Educational Materials ◽  
Efficient Learning ◽  
Mathematical Definitions

Definitions are extremely important for efficient learning of new materials. In particular, mathematical definitions are necessary for understanding mathematics-related areas. Automated extraction of definitions could be very useful for automated indexing educational materials, building taxonomies of relevant concepts, and more. For definitions that are contained within a single sentence, this problem can be viewed as a binary classification of sentences into definitions and non-definitions. In this paper, we focus on automatic detection of one-sentence definitions in mathematical and general texts. We experiment with different classification models arranged in an ensemble and applied to a sentence representation containing syntactic and semantic information, to classify sentences. Our ensemble model is applied to the data adjusted with oversampling. Our experiments demonstrate the superiority of our approach over state-of-the-art methods in both general and mathematical domains.

scholarly journals Researches on a complex of archeological sites Toropovo-7A

2020 ◽  
Vol 15 ◽  
pp. 40-45
Author(s):  
A. M. Ilyushin ◽  
◽  
M. G. Suleymenov ◽  
Keyword(s):  
Comparative Analysis ◽  
Middle Ages ◽  
Ceramic Ware ◽  
New Materials ◽  
Time Intervals ◽  
Late Middle Ages ◽  
Typological Classification

The article materials of excavation on a medieval complex of archeological sites Toropovo-7A are considered. In a form and figuration of ceramic ware typological classification of new materials is carried out. Comparative analysis with medieval monuments of Kuznetsk Depression allowed to reveal analogies to finds in the wide chronological range of the developed and late Middle Ages. It allowed to create a hypothesis of use of the cult family platform in two time intervals the developed and late Middle Ages.

scholarly journals Construction processes of roof structures: a systematic review

2020 ◽  
Vol 6 (4) ◽  
pp. 0520-0527
Author(s):  
Thaisa Lana Pilz ◽  
Mayara Scheuer ◽  
Marcell Mariano Corrêa Maceno ◽  
Thalyta Genaro ◽  
Nicolle Christine Sotsek
Keyword(s):  
Systematic Review ◽  
Environmental Impact ◽  
Construction Industry ◽  
New Materials ◽  
Construction Techniques ◽  
New Ideas ◽  
Research Questions ◽  
Quality Tool ◽  
Selection Of

Despite the fact that the construction industry in Brazil is traditionally recognized for the use of craft construction techniques, in the last few years, there has been a growth in the search for new materials, processes, and technologies for this segment.  This is mainly due to the great environmental impact that this sector causes. Based on this context, this article aimed to map the constructive processes of existing roofs in the literature, to raise its advantages, disadvantages and previous cases. To achieve this aim, the systematic review method based on three phases –  research questions, selection of documents and classification of selected documents, and the 5W2H quality tool were used. Thus, this research could contribute to the literature on this topic, as well as encourage the idealization of new ideas of roof construction processes.

An elementary introduction to superspace crystallography

2004 ◽  
Vol 219 (11) ◽  
Author(s):  
Sander van Smaalen
Keyword(s):  
Crystalline State ◽  
X Ray Diffraction ◽  
X Ray ◽  
Atomic Structures ◽  
Basic Concepts ◽  
State Of Matter ◽  
Aperiodic Crystals ◽  
Composite Crystals ◽  
Basis Vectors ◽  
Acta Crystallogr

AbstractAperiodic crystals are defined as a crystalline state of matter, that has atomic structures with long-range order but without translational symmetry. Experimentally, they are characterized by sharp Bragg reflections in the X-ray diffraction, that can be indexed by integers, if four or more reciprocal basis vectors are used. An introduction is given to the basic concepts of the superspace theory for structural analysis of incommensurately modulated crystals and incommensurate composite crystals [De Wolff, Janner and Janssen, Acta Crystallogr.

scholarly journals Exactly solvable spin chain models corresponding to BDI class of topological superconductors

2016 ◽  
Vol 6 (1) ◽  
Author(s):  
S. A. Jafari ◽  
Farhad Shahbazi
Keyword(s):  
Time Reversal ◽  
Solvable Models ◽  
Topological Superconductors ◽  
Spin Interactions ◽  
Detailed Classification ◽  
Exactly Solvable ◽  
Solvable Extension ◽  
Xy Chain ◽  
Topological Phase Transitions

Abstract We present an exactly solvable extension of the quantum XY chain with longer range multi-spin interactions. Topological phase transitions of the model are classified in terms of the number of Majorana zero modes, n M which are in turn related to an integer winding number, n W . The present class of exactly solvable models belong to the BDI class in the Altland-Zirnbauer classification of topological superconductors. We show that time reversal symmetry of the spin variables translates into a sliding particle-hole (PH) transformation in the language of Jordan-Wigner fermions – a PH transformation followed by a π shift in the wave vector which we call it the πPH. Presence of πPH symmetry restricts the n W (n M ) of time-reversal symmetric extensions of XY to odd (even) integers. The πPH operator may serve in further detailed classification of topological superconductors in higher dimensions as well.

scholarly journals Phase diagrams of superconducting topological surface states

2021 ◽  
Vol 24 (4) ◽  
pp. 43701
Author(s):  
W. Zhao ◽  
L. Ding ◽  
B. Zhou ◽  
J. Wu ◽  
Y. Bai ◽  
...  
Keyword(s):  
Phase Diagrams ◽  
Time Reversal ◽  
Mirror Symmetry ◽  
Surface States ◽  
Time Reversal Symmetry ◽  
And Topology ◽  
Topological Surface ◽  
Iron Based ◽  
Crystalline Symmetry

In this paper, we present a detailed study on the phase diagrams of superconducting topological surface states, especially, focusing on the interplay between crystalline symmetry and topology of the effective BdG Hamiltonian. We show that for the 4 x 4 kinematic Hamiltonian of the normal state, a mirror symmetry M can be defined, and for the M-odd pairings, the classification of the 8 x 8 BdG Hamiltonian is ℤ⊕ℤ, and the time-reversal symmetry is broken intrinsically. The topological non-trivial phase can support chiral Majorana edge modes, and can be realized in the thin films of iron-based superconductor such as FeSeTe.

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