scholarly journals Structural transformations in quasicrystals induced by higher dimensional lattice transitions

2012 ◽  
Vol 468 (2141) ◽  
pp. 1452-1471 ◽  
Author(s):  
Giuliana Indelicato ◽  
Tom Keef ◽  
Paolo Cermelli ◽  
David G. Salthouse ◽  
Reidun Twarock ◽  
...  
Keyword(s):  
Three Dimensional ◽  
Higher Dimensions ◽  
Structural Transformations ◽  
Icosahedral Symmetry ◽  
Local Transformation ◽  
Project Method ◽  
Higher Dimensional ◽  
Transformation Mechanisms ◽  
Transition Paths ◽  
Penrose Tilings

We study the structural transformations induced, via the cut-and-project method, in quasicrystals and tilings by lattice transitions in higher dimensions, with a focus on transition paths preserving at least some symmetry in intermediate lattices. We discuss the effect of such transformations on planar aperiodic Penrose tilings, and on three-dimensional aperiodic Ammann tilings with icosahedral symmetry. We find that locally the transformations in the aperiodic structures occur through the mechanisms of tile splitting, tile flipping and tile merger, and we investigate the origin of these local transformation mechanisms within the projection framework.

scholarly journals Group-theoretical analysis of aperiodic tilings from projections of higher-dimensional latticesBn

2015 ◽  
Vol 71 (2) ◽  
pp. 175-185 ◽  
Author(s):  
Mehmet Koca ◽  
Nazife Ozdes Koca ◽  
Ramazan Koc
Keyword(s):  
Three Dimensional ◽  
Lattice Points ◽  
Icosahedral Symmetry ◽  
The Novel ◽  
Voronoi Cells ◽  
Aperiodic Tilings ◽  
Coxeter Number ◽  
Hypercubic Lattice ◽  
Higher Dimensional ◽  
Coxeter Plane

A group-theoretical discussion on the hypercubic lattice described by the affine Coxeter–Weyl groupWa(Bn) is presented. When the lattice is projected onto the Coxeter plane it is noted that the maximal dihedral subgroupDhofW(Bn) withh= 2nrepresenting the Coxeter number describes theh-fold symmetric aperiodic tilings. Higher-dimensional cubic lattices are explicitly constructed forn= 4, 5, 6. Their rank-3 Coxeter subgroups and maximal dihedral subgroups are identified. It is explicitly shown that when their Voronoi cells are decomposed under the respective rank-3 subgroupsW(A3),W(H2) ×W(A1) andW(H3) one obtains the rhombic dodecahedron, rhombic icosahedron and rhombic triacontahedron, respectively. Projection of the latticeB4onto the Coxeter plane represents a model for quasicrystal structure with eightfold symmetry. TheB5lattice is used to describe both fivefold and tenfold symmetries. The latticeB6can describe aperiodic tilings with 12-fold symmetry as well as a three-dimensional icosahedral symmetry depending on the choice of subspace of projections. The novel structures from the projected sets of lattice points are compatible with the available experimental data.

scholarly journals GRAVITY-WAVE DETECTORS AS PROBES OF EXTRA DIMENSIONS

2005 ◽  
Vol 14 (12) ◽  
pp. 2347-2353 ◽  
Author(s):  
CHRIS CLARKSON ◽  
ROY MAARTENS
Keyword(s):  
Black Holes ◽  
String Theory ◽  
Gravity Wave ◽  
Gravity Waves ◽  
Extra Dimensions ◽  
State Of The Art ◽  
Three Dimensional ◽  
Observable Universe ◽  
Dimensional Spacetime ◽  
Higher Dimensional

If string theory is correct, then our observable universe may be a three-dimensional "brane" embedded in a higher-dimensional spacetime. This theoretical scenario should be tested via the state-of-the-art in gravitational experiments — the current and upcoming gravity-wave detectors. Indeed, the existence of extra dimensions leads to oscillations that leave a spectroscopic signature in the gravity-wave signal from black holes. The detectors that have been designed to confirm Einstein's prediction of gravity waves, can in principle also provide tests and constraints on string theory.

scholarly journals Crystal Structure of an Aquabirnavirus Particle: Insights into Antigenic Diversity and Virulence Determinism

2009 ◽  
Vol 84 (4) ◽  
pp. 1792-1799 ◽  
Author(s):  
Fasséli Coulibaly ◽  
Christophe Chevalier ◽  
Bernard Delmas ◽  
Félix A. Rey
Keyword(s):  
Crystal Structure ◽  
Three Dimensional ◽  
Salient Feature ◽  
Infectious Pancreatic Necrosis Virus ◽  
Antigenic Determinants ◽  
Binding Motif ◽  
Icosahedral Symmetry ◽  
Fold Axis ◽  
Cell Internalization ◽  
Pancreatic Necrosis Virus

ABSTRACT Infectious pancreatic necrosis virus (IPNV), a pathogen of salmon and trout, imposes a severe toll on the aquaculture and sea farming industries. IPNV belongs to the Aquabirnavirus genus in the Birnaviridae family of bisegmented double-stranded RNA viruses. The virions are nonenveloped with a T=13l icosahedral capsid made by the coat protein VP2, the three-dimensional (3D) organization of which is known in detail for the family prototype, the infectious bursal disease virus (IBDV) of poultry. A salient feature of the birnavirus architecture is the presence of 260 trimeric spikes formed by VP2, projecting radially from the capsid. The spikes carry the principal antigenic sites as well as virulence and cell adaptation determinants. We report here the 3.4-Å resolution crystal structure of a subviral particle (SVP) of IPNV, containing 20 VP2 trimers organized with icosahedral symmetry. We show that, as expected, the SVPs have a very similar organization to the IBDV counterparts, with VP2 exhibiting the same overall 3D fold. However, the spikes are significantly different, displaying a more compact organization with tighter packing about the molecular 3-fold axis. Amino acids controlling virulence and cell culture adaptation cluster differently at the top of the spike, i.e., in a central bowl in IBDV and at the periphery in IPNV. In contrast, the spike base features an exposed groove, conserved across birnavirus genera, which contains an integrin-binding motif. Thus, in addition to revealing the viral antigenic determinants, the structure suggests that birnaviruses interact with different receptors for attachment and for cell internalization during entry.

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.

Intercalation of pentane into the stage 2 to 4 cesium graphitides: Relation between cesium density in the intercalated layers and the stage of the parent binary

1993 ◽  
Vol 8 (9) ◽  
pp. 2288-2298 ◽  
Author(s):  
H. Pillière ◽  
M. Goldmann ◽  
F. Béguin
Keyword(s):  
Room Temperature ◽  
Three Dimensional ◽  
Structural Transformations ◽  
Layer Model ◽  
Simultaneous Formation ◽  
Ternary Compounds ◽  
Second Stage ◽  
The Third ◽  
Cesium Ions ◽  
Third Stage

Isotherms (at 300 K and 328 K) and isobars (in the range 300 to 400 K) of n-pentane intercalation in CsC24 and CsC36 were established. With CsC24, three plateaus were identified at 0.52, 0.7, and 1.0 n-pentane/24 C, whereas only two plateaus at 0.8 and 0.97 n-pentane/36 C were found with CsC36. The progress of the reaction between n-pentane and CsC24, CsC36, and CsC56 (stage 2 to 4) was monitored by real-time neutron diffraction. The intercalation of n-pentane in CsC24 results in the simultaneous formation of a second stage ternary and a first stage binary “CsC8”, whereas, from the third stage CsC36 or the fourth stage CsC56, only pure second stage or third stage ternary compounds are formed, respectively. Owing to the formation of binary domains rich in alkali metal (CsC8) or to stage lowering produced by the ternarization, the in-plane cesium density is smaller in the ternary layer than in the starting binary. The electrostatic repulsion between the cesium ions, provoked by the sorption of n-pentane, is believed to be at the origin of the increased coverage. During the intercalation or de-intercalation processes, three-dimensional segregation occurs in each grain. A pleated layer model with canted fronts is presented. It accounts for the various phases present within each grain and for the structural transformations caused by pressure variations. At room temperature, the ternary layer seems to be disordered. The order-disorder transition appearing either by decreasing the temperature or by increasing the n-pentane pressure is correlated to a hindered motion of the intercalated molecules.

Spatial Models of Sugars and Their Compounds

2021 ◽  
Vol 11 (2) ◽  
pp. 9-22
Author(s):  
Gennadiy Vladimirovich Zhizhin
Keyword(s):  
Convex Bodies ◽  
Three Dimensional ◽  
Spatial Models ◽  
Higher Dimensions ◽  
Three Dimensional Images

The images of saccharide and polysaccharide molecules in spaces of various dimensions are considered. A method has been developed for obtaining simplified three-dimensional images of sugar molecules and their chains based on their images in spaces of higher dimensions. It was found that three-dimensional images of furanose and pyranose molecules fundamentally differ from each other to form convex and, accordingly, non-convex bodies. This leads to fundamental differences in the structure of polysaccharides from these molecules.

scholarly journals Three-Dimensional Organization of Rift Valley Fever Virus Revealed by Cryoelectron Tomography

2008 ◽  
Vol 82 (21) ◽  
pp. 10341-10348 ◽  
Author(s):  
Alexander N. Freiberg ◽  
Michael B. Sherman ◽  
Marc C. Morais ◽  
Michael R. Holbrook ◽  
Stanley J. Watowich
Keyword(s):  
Rift Valley ◽  
Rift Valley Fever ◽  
Rift Valley Fever Virus ◽  
Three Dimensional ◽  
Average Diameter ◽  
Fever Virus ◽  
Icosahedral Symmetry ◽  
Valley Fever ◽  
Virus Family ◽  
Virus Surface

ABSTRACT Rift Valley fever virus (RVFV) is a member of the Bunyaviridae virus family (genus Phlebovirus) and is considered to be one of the most important pathogens in Africa, causing viral zoonoses in livestock and humans. Here, we report the characterization of the three-dimensional structural organization of RVFV vaccine strain MP-12 by cryoelectron tomography. Vitrified-hydrated virions were found to be spherical, with an average diameter of 100 nm. The virus glycoproteins formed cylindrical hollow spikes that clustered into distinct capsomeres. In contrast to previous assertions that RVFV is pleomorphic, the structure of RVFV MP-12 was found to be highly ordered. The three-dimensional map was resolved to a resolution of 6.1 nm, and capsomeres were observed to be arranged on the virus surface in an icosahedral lattice with clear T=12 quasisymmetry. All icosahedral symmetry axes were visible in self-rotation functions calculated using the Fourier transform of the RVFV MP-12 tomogram. To the best of our knowledge, a triangulation number of 12 had previously been reported only for Uukuniemi virus, a bunyavirus also within the Phlebovirus genus. The results presented in this study demonstrate that RVFV MP-12 possesses T=12 icosahedral symmetry and suggest that other members of the Phlebovirus genus, as well as of the Bunyaviridae family, may adopt icosahedral symmetry. Knowledge of the virus architecture may provide a structural template to develop vaccines and diagnostics, since no effective anti-RVFV treatments are available for human use.

Insulin Receptor: Structure Via 3D EM Reconstruction, Crystallography and NMR Reveals Details of Ligand Binding and Mechanism of Transmembrane Signalling

2000 ◽  
Vol 6 (S2) ◽  
pp. 274-275
Author(s):  
F.P. Ottensmeyer ◽  
R.Z.T. Luo ◽  
D.R. Beniac ◽  
A.B. Fernandes ◽  
C.C. Yip
Keyword(s):  
Low Dose ◽  
Rotational Symmetry ◽  
Three Dimensional ◽  
Helical Structure ◽  
Dimensional Structure ◽  
Icosahedral Symmetry ◽  
Great Success ◽  
Single Particles ◽  
Radiation Induced ◽  
3D Em

For over 25 years a major effort in electron microscopy of macromolecules has been the determination of the three dimensional structure from the two-dimensional electron micrographs of such specimens. Great success has been realized when the macromolecule or complex takes the form of an array such as a 2D crystal (1,2), a helical structure (3,4) or one with icosahedral symmetry (5,6). However, for molecules which do not form such arrays, and in the limit only exist as single particles, a number of challenges have had to be addressed. No easy averaging of noisy low dose images is possible due to the lack of lateral and rotational symmetry. Random unknown orientations of the particles have to be determined, a process exacerbated by noise if low dose images are used as input. Alternatively, higher dose images result in radiation-induced structural alterations of the macromolecule.

TIME LOWER BOUNDS FOR PERMUTATION ROUTING ON MULTI-DIMENSIONAL BUSED MESHES

1993 ◽  
Vol 03 (02) ◽  
pp. 129-138
Author(s):  
STEVEN CHEUNG ◽  
FRANCIS C.M. LAU
Keyword(s):  
Lower Bound ◽  
Lower Bounds ◽  
Three Dimensional ◽  
Dimensional Case ◽  
Routing Problem ◽  
Higher Dimensional ◽  
Low Dimensional ◽  
Permutation Routing

We present time lower bounds for the permutation routing problem on three- and higher-dimensional n x…x n meshes with buses. We prove an (r–1)n/r lower bound for the general case of an r-dimensional bused mesh, r≥2, which is not as strong for low-dimensional as for higher-dimensional cases. We then use a different approach to construct a 0.705n lower bound for the three-dimensional case.

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