Physical properties

2018 ◽  
Author(s):  
Ted Janssen ◽  
Gervais Chapuis ◽  
Marc de Boissieu
Keyword(s):  
Physical Properties ◽  
Dimensional Space ◽  
Three Dimensional ◽  
Waller Factor ◽  
Hydrodynamic Theory ◽  
Dimensional Representation ◽  
Debye Waller Factor ◽  
Higher Dimensional ◽  
Experimental Findings ◽  
Aperiodic Crystals

Physical properties of aperiodic crystals present some theoretical challenges due to the lack of three-dimensional periodicity. For the description of the structure there is a periodic representation in higher-dimensional space. For physical properties, however, this scheme cannot be used because the mapping between interatomic forces and the high-dimensional representation is not straightforward. In this chapter methods are described to deal with these problems. First, the hydrodynamic theory of aperiodic crystals and then the phonons and phasons theory are developed and illustrated with some examples. The properties of electrons in aperiodic crystals are also presented. Finally, the experimental findings of phonon and phason modes for modulated and quasicrystals are presented. The chapter also discusses diffuse scattering, the Debye–Waller factor, and electrical conductivity.

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 Structure determinations for random-tiling quasicrystals

2000 ◽  
Vol 215 (10) ◽  
Author(s):  
C.L. Henley ◽  
V. Elser ◽  
M. Mihalkovic
Keyword(s):  
Structural Information ◽  
Direct Method ◽  
Dimensional Space ◽  
Waller Factor ◽  
Data Set ◽  
3 Dimensional ◽  
Random Tiling ◽  
Debye Waller Factor ◽  
Higher Dimensional ◽  
Structure Determinations

How, in principle, could one solve the atomic structure of a quasicrystal, modeled as a random tiling decorated by atoms, and what techniques are available to do it? One path is to solve the phase problem first, obtaining the density in a higher dimensional space which yields the averaged scattering density in 3-dimensional space by the usual construction of an incommensurate cut. A novel direct method for this is summarized and applied to an i(AlPdMn) data set. This averaged density falls short of a true structure determination (which would reveal the typical unaveraged atomic patterns.) We discuss the problematic validity of inferring an ideal structure by simply factoring out a "perp-space" Debye-Waller factor, and we test this using simulations of rhombohedral tilings. A second, "unified" path is to relate the measured and modeled intensities directliy, by adjusting parameters in a simulation to optimize the fit. This approach is well suited for unifying structural information from diffraction and from minimizing total energies derived ultimately from ab-initio calculations. Finally, we discuss the special pitfalls of fitting random-tiling decagonal phases.

Has a fully three-dimensional space map never evolved in any species? A comparative imperative for studies of spatial cognition

2013 ◽  
Vol 36 (5) ◽  
pp. 557-557 ◽  
Author(s):  
Cynthia F. Moss
Keyword(s):  
Spatial Cognition ◽  
Dimensional Space ◽  
Large Body ◽  
Three Dimensional ◽  
Comparative Data ◽  
Dimensional Representation ◽  
Three Dimensional Representation ◽  
Space Coding ◽  
Three Dimensional Space

AbstractI propose that it is premature to assert that a fully three-dimensional map has never evolved in any species, as data are lacking to show that space coding in all animals is the same. Instead, I hypothesize that three-dimensional representation is tied to an animal's mode of locomotion through space. Testing this hypothesis requires a large body of comparative data.

scholarly journals Celestial Spheres

2018 ◽  
Vol 2 (2) ◽  
pp. 168-186
Author(s):  
Austin M. Freeman
Keyword(s):  
Dimensional Space ◽  
Three Dimensional ◽  
Good Evidence ◽  
Medieval Period ◽  
The Bible ◽  
Higher Dimensional ◽  
Spatial Dimensions ◽  
Modern Physics ◽  
The Subject ◽  
Three Dimensional Space

Angels probably have bodies. There is no good evidence (biblical, philosophical, or historical) to argue against their bodiliness; there is an abundance of evidence (biblical, philosophical, historical) that makes the case for angelic bodies. After surveying biblical texts alleged to demonstrate angelic incorporeality, the discussion moves to examine patristic, medieval, and some modern figures on the subject. In short, before the High Medieval period belief in angelic bodies was the norm, and afterwards it is the exception. A brief foray into modern physics and higher spatial dimensions (termed “hyperspace”), coupled with an analogical use of Edwin Abbott’s Flatland, serves to explain the way in which appealing to higher-dimensional angelic bodies matches the record of angelic activity in the Bible remarkably well. This position also cuts through a historical equivocation on the question of angelic embodiment. Angels do have bodies, but they are bodies very unlike our own. They do not have bodies in any three-dimensional space we can observe, but are nevertheless embodied beings.

scholarly journals A Temperature Variation of Debye-Waller Factor for Alkali and Noble Metals

1983 ◽  
Vol 38 (5) ◽  
pp. 503-508 ◽  
Author(s):  
A. R. Jani ◽  
V. B. Gohel
Keyword(s):  
Experimental Data ◽  
Temperature Variation ◽  
Phenomenological Model ◽  
Noble Metals ◽  
Experimental Information ◽  
Waller Factor ◽  
Critical Examination ◽  
Debye Waller Factor ◽  
Different Temperatures ◽  
Experimental Findings

Debye-Waller factors at different temperatures of four alkali and three noble metals have been computed on the basis of a screened shell phenomenological model. The theoretical values are compared with existing experimental data. Particularly for lithium and potassium, most recent experimental information has been included. A critical examination of the results reveals a satis­factory agreement between the theoretical and experimental findings.

scholarly journals Synthetic Weyl Points of the Shear Horizontal Guided Waves in One-Dimensional Phononic Crystal Plates

2021 ◽  
Vol 12 (1) ◽  
pp. 167
Author(s):  
Hongbo Zhang ◽  
Shaobo Zhang ◽  
Jiang Liu ◽  
Bilong Liu
Keyword(s):  
Guided Waves ◽  
Dimensional Space ◽  
Phononic Crystal ◽  
Phase Interface ◽  
Three Dimensional ◽  
Interface States ◽  
Geometrical Parameters ◽  
One Dimensional ◽  
Higher Dimensional ◽  
Shear Horizontal

Weyl physics in acoustic and elastic systems has drawn extensive attention. In this paper, Weyl points of shear horizontal guided waves are realized by one-dimensional phononic crystal plates, in which one physical dimension plus two geometrical parameters constitute a synthetic three-dimensional space. Based on the finite element method, we have not only observed the synthetic Weyl points but also explored the Weyl interface states and the reflection phase vortices, which have further proved the topological phase interface states. As the first realization of three-dimensional topological phases through one-dimensional phononic crystal plates in the synthetic dimension, this research demonstrates the great potential of applicable one-dimensional plate structural systems in detecting higher-dimensional topological phenomena.

Higher-Dimensional Space of Nanoworld

2021 ◽  
pp. 1-30
Keyword(s):  
Fundamental Domain ◽  
Dimensional Space ◽  
Golden Section ◽  
Convex Bodies ◽  
Three Dimensional ◽  
Geometrical Model ◽  
Parallel Lines ◽  
Higher Dimensional ◽  
Diffraction Patterns ◽  
Fifth Order

In this chapter, a geometrical model to accurately describe the distribution of light points in diffraction patterns of quasicrystals is proposed. It is shown that the proposed system of parallel lines has axes of the fifth order and periodically repeating the fundamental domain of the quasicrystals. This fundamental domain is 4D-polytope, called the golden hyper-rhombohedron. It consists of eight rhombohedrons densely filling the 4D space. Faces of the hyper-rhombohedron are connected by the golden section; they can be scaled as needed. On this universal lattice of the vertices of the golden hyper-rhombohedrons, famous crystallographic lattices—Bravais, Delone, Voronoi, etc.—can be embedded. On the lattice of the vertices of the golden hyper-rhombohedrons, projections of all regular three-dimensional convex bodies—Plato's bodies—can be constructed.

scholarly journals THE SANSEVERO CHAPEL, A THREE-DIMENSIONAL POINT OF VIEW

2019 ◽  
Vol XLII-2/W15 ◽  
pp. 299-304
Author(s):  
V. Cera ◽  
D. Marcos González ◽  
L. A. Garcia
Keyword(s):  
Dimensional Space ◽  
Three Dimensional ◽  
Point Of View ◽  
Two Dimensional ◽  
Dimensional Representation ◽  
Survey Techniques ◽  
Representation Systems ◽  
Representation Of Space ◽  
Special Relevance ◽  
Three Dimensional Space

<p><strong>Abstract.</strong> In this article, the importance of the three-dimensional survey in architectural spaces will be studied, taking special relevance in the study of the perception of perspective, since three-dimensional space would not be understood from a two-dimensional representation of space. The project aims to develop a comparison between the representation systems based on the automatic acquisition of various data by different 3D survey techniques. In particular, the document reports the results of an analysis based on the Sansevero Chapel in Naples.</p>

Non-periodic Space Structures

1987 ◽  
Vol 2 (2) ◽  
pp. 93-108 ◽  
Author(s):  
Haresh Lalvani
Keyword(s):  
Dimensional Space ◽  
Three Dimensional ◽  
Space Structures ◽  
Infinite Class ◽  
Space Filling ◽  
Higher Dimensional ◽  
Centrally Symmetric ◽  
Interesting Class ◽  
Periodic Space ◽  
Three Dimensional Space

An interesting class of two- and three-dimensional space structures can be derived from projections of higher-dimensional structures. Regular polygons and regular-faced polyhedra provide the geometry of families of n-stars from which two- and three-dimensional projections of n-dimensional grids can be derived. These projections are rhombic space grids composed of all-space filling rhombi and rhombohedra with edges parallel to n directions. An infinite class of single-, double- and multi-layered grids can be derived from n-sided polygons and prisms, and a finite class of multi-directional grids from the polyhedral symmetry groups. The grids can be periodic, centrally symmetric or non-periodic, and act as skeletons to generate corresponding classes of space-filling, packings and labyrinths.

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