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 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 Explicit construction of the Voronoi and Delaunay cells ofW(An) andW(Dn) lattices and their facets

2018 ◽  
Vol 74 (5) ◽  
pp. 499-511 ◽  
Author(s):  
Mehmet Koca ◽  
Nazife Ozdes Koca ◽  
Abeer Al-Siyabi ◽  
Ramazan Koc
Keyword(s):  
Voronoi Cell ◽  
Explicit Construction ◽  
Weyl Groups ◽  
Root Lattice ◽  
Coxeter Number ◽  
Aperiodic Tiling ◽  
Higher Dimensional ◽  
The Face ◽  
Coxeter Plane ◽  
Root Polytope

Voronoi and Delaunay (Delone) cells of the root and weight lattices of the Coxeter–Weyl groupsW(An) andW(Dn) are constructed. The face-centred cubic (f.c.c.) and body-centred cubic (b.c.c.) lattices are obtained in this context. Basic definitions are introduced such as parallelotope, fundamental simplex, contact polytope, root polytope, Voronoi cell, Delone cell,n-simplex,n-octahedron (cross polytope),n-cube andn-hemicube and their volumes are calculated. The Voronoi cell of the root lattice is constructed as the dual of the root polytope which turns out to be the union of Delone cells. It is shown that the Delone cells centred at the origin of the root latticeAnare the polytopes of the fundamental weights ω1, ω2,…, ωnand the Delone cells of the root latticeDnare the polytopes obtained from the weights ω1, ωn−1and ωn. A simple mechanism explains the tessellation of the root lattice by Delone cells. It is proved that the (n−1)-facet of the Voronoi cell of the root latticeAnis an (n−1)-dimensional rhombohedron and similarly the (n−1)-facet of the Voronoi cell of the root latticeDnis a dipyramid with a base of an (n−2)-cube. The volume of the Voronoi cell is calculatedviaits (n−1)-facet which in turn can be obtained from the fundamental simplex. Tessellations of the root lattice with the Voronoi and Delone cells are explained by giving examples from lower dimensions. Similar considerations are also worked out for the weight latticesAn* andDn*. It is pointed out that the projection of the higher-dimensional root and weight lattices on the Coxeter plane leads to theh-fold aperiodic tiling, wherehis the Coxeter number of the Coxeter–Weyl group. Tiles of the Coxeter plane can be obtained by projection of the two-dimensional faces of the Voronoi or Delone cells. Examples are given such as the Penrose-like fivefold symmetric tessellation by theA4root lattice and the eightfold symmetric tessellation by theD5root lattice.

scholarly journals Twelvefold symmetric quasicrystallography from the latticesF4,B6andE6

2014 ◽  
Vol 70 (6) ◽  
pp. 605-615 ◽  
Author(s):  
Nazife O. Koca ◽  
Mehmet Koca ◽  
Ramazan Koc
Keyword(s):  
Weyl Group ◽  
Coxeter Groups ◽  
Three Dimensional ◽  
Weyl Groups ◽  
Dimensional Euclidean Space ◽  
General Technique ◽  
Dimensional Lattice ◽  
Coxeter Number ◽  
Higher Dimensional ◽  
Group Play

One possible way to obtain the quasicrystallographic structure is the projection of the higher-dimensional lattice into two- or three-dimensional subspaces. Here a general technique applicable to any higher-dimensional lattice is introduced. The Coxeter number and the integers of the Coxeter exponents of a Coxeter–Weyl group play a crucial role in determining the plane onto which the lattice is to be projected. The quasicrystal structures display the dihedral symmetry of order twice that of the Coxeter number. The eigenvectors and the corresponding eigenvalues of the Cartan matrix are used to determine the set of orthonormal vectors inn-dimensional Euclidean space which lead to suitable choices for the projection subspaces. The maximal dihedral subgroup of the Coxeter–Weyl group is identified to determine the symmetry of the quasicrystal structure. Examples are given for 12-fold symmetric quasicrystal structures obtained by projecting the higher-dimensional lattices determined by the affine Coxeter–Weyl groupsWa(F4),Wa(B6) andWa(E6). These groups share the same Coxeter numberh= 12 with different Coxeter exponents. The dihedral subgroupD12of the Coxeter groups can be obtained by defining two generatorsR1andR2as the products of generators of the Coxeter–Weyl groups. The reflection generatorsR1andR2operate in the Coxeter planes where the Coxeter elementR1R2of the Coxeter–Weyl group represents the rotation of order 12. The canonical (strip, equivalently, cut-and-project technique) projections of the lattices determine the nature of the quasicrystallographic structures with 12-fold symmetry as well as the crystallographic structures with fourfold and sixfold symmetry. It is noted that the quasicrystal structures obtained from the latticesWa(F4) andWa(B6) are compatible with some experimental results.

scholarly journals Topological correlators and surface defects from equivariant cohomology

2020 ◽  
Vol 2020 (9) ◽  
Author(s):  
Rodolfo Panerai ◽  
Antonio Pittelli ◽  
Konstantina Polydorou
Keyword(s):  
Quantum Mechanics ◽  
Equivariant Cohomology ◽  
Surface Defects ◽  
Star Product ◽  
Three Dimensional ◽  
Three Dimensions ◽  
Dimensional System ◽  
The Novel ◽  
One Dimensional ◽  
Dual Quantum

Abstract We find a one-dimensional protected subsector of $$ \mathcal{N} $$ N = 4 matter theories on a general class of three-dimensional manifolds. By means of equivariant localization we identify a dual quantum mechanics computing BPS correlators of the original model in three dimensions. Specifically, applying the Atiyah-Bott-Berline-Vergne formula to the original action demonstrates that this localizes on a one-dimensional action with support on the fixed-point submanifold of suitable isometries. We first show that our approach reproduces previous results obtained on S3. Then, we apply it to the novel case of S2× S1 and show that the theory localizes on two noninteracting quantum mechanics with disjoint support. We prove that the BPS operators of such models are naturally associated with a noncom- mutative star product, while their correlation functions are essentially topological. Finally, we couple the three-dimensional theory to general $$ \mathcal{N} $$ N = (2, 2) surface defects and extend the localization computation to capture the full partition function and BPS correlators of the mixed-dimensional system.

scholarly journals Organotrialkoxysilane-Functionalized Prussian Blue Nanoparticles-Mediated Fluorescence Sensing of Arsenic(III)

Nanomaterials ◽  
2021 ◽  
Vol 11 (5) ◽  
pp. 1145
Author(s):  
Prem. C. Pandey ◽  
Shubhangi Shukla ◽  
Roger J. Narayan
Keyword(s):  
Prussian Blue ◽  
Chemical Reduction ◽  
Low Cost ◽  
Three Dimensional ◽  
Heterogeneous Systems ◽  
Lattice Points ◽  
Radiative Energy ◽  
Fluorescence Sensing ◽  
Emission Signal ◽  
Prussian Blue Nanoparticles

Prussian blue nanoparticles (PBN) exhibit selective fluorescence quenching behavior with heavy metal ions; in addition, they possess characteristic oxidant properties both for liquid–liquid and liquid–solid interface catalysis. Here, we propose to study the detection and efficient removal of toxic arsenic(III) species by materializing these dual functions of PBN. A sophisticated PBN-sensitized fluorometric switching system for dosage-dependent detection of As3+ along with PBN-integrated SiO2 platforms as a column adsorbent for biphasic oxidation and elimination of As3+ have been developed. Colloidal PBN were obtained by a facile two-step process involving chemical reduction in the presence of 2-(3,4-epoxycyclohexyl)ethyl trimethoxysilane (EETMSi) and cyclohexanone as reducing agents, while heterogeneous systems were formulated via EETMSi, which triggered in situ growth of PBN inside the three-dimensional framework of silica gel and silica nanoparticles (SiO2). PBN-induced quenching of the emission signal was recorded with an As3+ concentration (0.05–1.6 ppm)-dependent fluorometric titration system, owing to the potential excitation window of PBN (at 480–500 nm), which ultimately restricts the radiative energy transfer. The detection limit for this arrangement is estimated around 0.025 ppm. Furthermore, the mesoporous and macroporous PBN-integrated SiO2 arrangements might act as stationary phase in chromatographic studies to significantly remove As3+. Besides physisorption, significant electron exchange between Fe3+/Fe2+ lattice points and As3+ ions enable complete conversion to less toxic As5+ ions with the repeated influx of mobile phase. PBN-integrated SiO2 matrices were successfully restored after segregating the target ions. This study indicates that PBN and PBN-integrated SiO2 platforms may enable straightforward and low-cost removal of arsenic from contaminated water.

Numerical and experimental investigation for enhancing the energy absorption capacity of the novel three-dimensional printed sandwich structures

2021 ◽  
pp. 146442072199749
Author(s):  
H Geramizadeh ◽  
S Dariushi ◽  
S Jedari Salami
Keyword(s):  
Energy Absorption ◽  
Sandwich Structures ◽  
Three Dimensional ◽  
Absorption Capacity ◽  
The Novel ◽  
Energy Absorption Capacity ◽  
Fused Deposition ◽  
Honeycomb Sandwich ◽  
Out Of Plane ◽  
Vertical Walls

The current study focuses on designing the optimal three-dimensional printed sandwich structures. The main goal is to improve the energy absorption capacity of the out-of-plane honeycomb sandwich beam. The novel Beta VI and Alpha VI were designed in order to achieve this aim. In the Beta VI, the connecting curves (splines) were used instead of the four diagonal walls, while the two vertical walls remained unchanged. The Alpha VI is a step forward on the Beta VI, which was promoted by filleting all angles among the vertical walls, created arcs, and face sheets. The two offered sandwich structures have not hitherto been provided in the literature. All models were designed and simulated by the CATIA and ABAQUS, respectively. The three-dimensional printer fabricated the samples by fused deposition modeling technique. The material properties were determined under tensile, compression, and three-point bending tests. The results are carried out by two methods based on experimental tests and finite element analyses that confirmed each other. The achievements provide novel insights into the determination of the adequate number of unit cells and demonstrate the energy absorption capacity of the Beta VI and Alpha VI are 23.7% and 53.9%, respectively, higher than the out-of-plane honeycomb sandwich structures.

scholarly journals Hydrothermal Synthesis and Structural Investigation of a Crystalline Uranyl Borosilicate

Inorganics ◽  
2021 ◽  
Vol 9 (4) ◽  
pp. 25
Author(s):  
Kristen A. Pace ◽  
Vladislav V. Klepov ◽  
Mark D. Smith ◽  
Travis Williams ◽  
Gregory Morrison ◽  
...  
Keyword(s):  
Synthesis Method ◽  
Three Dimensional ◽  
Dimensional Structure ◽  
Exploratory Research ◽  
The Novel ◽  
Orthorhombic Space Group ◽  
Crystalline Materials ◽  
Waste Remediation ◽  
And Storage ◽  
X Ray Absorption

The relevance of multidimensional and porous crystalline materials to nuclear waste remediation and storage applications has motivated exploratory research focused on materials discovery of compounds, such as actinide mixed-oxoanion phases, which exhibit rich structural chemistry. The novel phase K1.8Na1.2[(UO2)BSi4O12] has been synthesized using hydrothermal methods, representing the first example of a uranyl borosilicate. The three-dimensional structure crystallizes in the orthorhombic space group Cmce with lattice parameters a = 15.5471(19) Å, b = 14.3403(17) Å, c = 11.7315(15) Å, and V = 2615.5(6) Å3, and is composed of UO6 octahedra linked by [BSi4O12]5− chains to form a [(UO2)BSi4O12]3− framework. The synthesis method, structure, results of Raman, IR, and X-ray absorption spectroscopy, and thermal stability are discussed.

scholarly journals Cinematic rendering of a burst sagittal suture caused by an occipito-frontal gunshot wound

2021 ◽  
Author(s):  
Dominic Gascho ◽  
Michael J. Thali ◽  
Rosa M. Martinez ◽  
Stephan A. Bolliger
Keyword(s):  
Gunshot Wound ◽  
Three Dimensional ◽  
The Novel ◽  
Sagittal Suture ◽  
Resonance Imaging ◽  
Cinematic Rendering ◽  
Reconstruction Methods ◽  
Dimensional Reconstruction ◽  
Magnetic Resonance Imaging Mri ◽  
The Brain

AbstractThe computed tomography (CT) scan of a 19-year-old man who died from an occipito-frontal gunshot wound presented an impressive radiating fracture line where the entire sagittal suture burst due to the high intracranial pressure that arose from a near-contact shot from a 9 mm bullet fired from a Glock 17 pistol. Photorealistic depictions of the radiating fracture lines along the cranial bones were created using three-dimensional reconstruction methods, such as the novel cinematic rendering technique that simulates the propagation and interaction of light when it passes through volumetric data. Since the brain had collapsed, depiction of soft tissue was insufficient on CT images. An additional magnetic resonance imaging (MRI) examination was performed, which enabled the diagnostic assessment of cerebral injuries.

scholarly journals Nanofiber-Mâché Hollow Ball Mimicking the Three-Dimensional Structure of a Cyst

Polymers ◽  
2021 ◽  
Vol 13 (14) ◽  
pp. 2273
Author(s):  
Wan-Ying Huang ◽  
Norichika Hashimoto ◽  
Ryuhei Kitai ◽  
Shin-ichiro Suye ◽  
Satoshi Fujita
Keyword(s):  
Three Dimensional ◽  
Hollow Structure ◽  
Dimensional Structure ◽  
The Novel ◽  
Fibrous Scaffold ◽  
Hydrogel Beads ◽  
Inner Surface ◽  
Intracranial Epidermoid ◽  
Hollow Ball

The occasional malignant transformation of intracranial epidermoid cysts into squamous cell carcinomas remains poorly understood; the development of an in vitro cyst model is urgently needed. For this purpose, we designed a hollow nanofiber sphere, the “nanofiber-mâché ball.” This hollow structure was fabricated by electrospinning nanofiber onto alginate hydrogel beads followed by dissolving the beads. A ball with approximately 230 mm3 inner volume provided a fibrous geometry mimicking the topography of the extracellular matrix. Two ducts located on opposite sides provided a route to exchange nutrients and waste. This resulted in a concentration gradient that induced oriented migration, in which seeded cells adhered randomly to the inner surface, formed a highly oriented structure, and then secreted a dense web of collagen fibrils. Circumferentially aligned fibers on the internal interface between the duct and hollow ball inhibited cells from migrating out of the interior, similar to a fish bottle trap. This structure helped to form an adepithelial layer on the inner surface. The novel nanofiber-mâché technique, using a millimeter-sized hollow fibrous scaffold, is excellently suited to investigating cyst physiology.

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.

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