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

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.

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Acoustic wave frequency filtering in constant total length phononic crystals of Al/Pb multilayer

International Journal of Modern Physics B ◽

10.1142/s0217979221503008 ◽

2021 ◽

Author(s):

Chittaranjan Nayak ◽

Mehdi Solaimani ◽

Alireza Aghajamali ◽

Arafa H. Aly

Keyword(s):

Acoustic Wave ◽

Phononic Crystal ◽

Phononic Crystals ◽

Geometrical Parameters ◽

One Dimensional ◽

Internal Geometry ◽

Total Length ◽

Acoustic Filters ◽

System Length ◽

Phononic Band Gaps

In this study, we have scrutinized the frequency gap generation by changing the geometrical parameters of a one-dimensional phononic crystal. For this purpose, we have calculated the transmission coefficient of an incident acoustic wave by using the transfer matrix method. We have retained and fixed the total length of the system and changed the system internal geometry not to increase the system length too much. Another reason was to adjust the phononic band gaps and get the desired transmission properties by finding the optimum internal geometry without increasing or decreasing the total length of phononic crystals. In addition, we also propose few structures with the opportunity of applications in acoustical devices such as sonic reflectors. Our results can also be of high interest to design acoustic filters in the case that transmission of certain frequencies is necessary.

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Celestial Spheres

TheoLogica An International Journal for Philosophy of Religion and Philosophical Theology ◽

10.14428/thl.v2i2.1883 ◽

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.

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Chaotic Attractor Generation via Space Function Controls

Discrete Dynamics in Nature and Society ◽

10.1155/2011/454636 ◽

2011 ◽

Vol 2011 ◽

pp. 1-11

Author(s):

Hong Shi ◽

Guangming Xie ◽

Desheng Liu

Keyword(s):

Linear Systems ◽

Chaotic Attractor ◽

Dimensional Space ◽

Three Dimensional ◽

Underlying Mechanism ◽

Two Dimensional ◽

One Dimensional ◽

Suitable Space ◽

Space Function ◽

Three Dimensional Space

The analysis of chaotic attractor generation is given, and the generation of novel chaotic attractor is introduced in this paper. The underlying mechanism involves two simple linear systems with one-dimensional, two-dimensional, or three-dimensional space functions. Moreover, it is demonstrated by simulation that various attractor patterns are generated conveniently by adjusting suitable space functions' parameters and the statistic behavior is also discussed.

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Coordination Polymers with a Bulky Perylene-Based Tetracarboxylate Ligand: Syntheses, Crystal Structures, and Luminescent Properties

Australian Journal of Chemistry ◽

10.1071/ch09411 ◽

2010 ◽

Vol 63 (3) ◽

pp. 463 ◽

Cited By ~ 8

Author(s):

Chun-Sen Liu ◽

Min Hu ◽

Song-Tao Ma ◽

Qiang Zhang ◽

Li-Ming Zhou ◽

...

Keyword(s):

Coordination Polymers ◽

Three Dimensional ◽

Luminescent Properties ◽

Supramolecular Interactions ◽

Polymeric Chain ◽

Stacking Interactions ◽

One Dimensional ◽

Π Stacking ◽

Higher Dimensional ◽

Interchain Interactions

To explore the coordination possibilities of perylene-based ligands with a larger conjugated π-system, four ZnII, MnII, and CoII coordination polymers with perylene-3,4,9,10-tetracarboxylate (ptc) and the chelating 1,10-phenanthroline (phen) ligands were synthesized and characterized: {[Zn2(ptc)(phen)2](H2O)10}∞ (1), {[Zn3(ptc)(OH)2(phen)2](H2O)3}∞ (2), {[Mn(ptc)0.5(phen)(H2O)2](H2O)1.5}∞ (3), and {[Co(ptc)0.5(phen)(H2O)2](H2O)2.5}∞ (4). Structural analysis reveals that complexes 1 and 2 both take one-dimensional polymeric chain structures with dinuclear and trinuclear units as nodes, respectively, which are further extended via the accessorial secondary interchain interactions, such as C–H···O H-bonding or aromatic π···π stacking interactions, to give rise to the relevant higher-dimensional frameworks. Compound 3 has a two-dimensional sheet structure that is further assembled to form a three-dimensional framework by interlayer π···π stacking interactions. Complex 4 is a one-dimensional ribbon-like array structure that is interlinked by the co-effects of intermolecular π···π stacking and C–H···π supramolecular interactions, resulting in a higher-dimensional framework from the different crystallographic directions. Moreover, complexes 1–4 exhibit strong solid-state luminescence emissions at room temperature, which mainly originate from intraligand π→π* transitions of ptc.

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Coupling of Shear Acoustic Waves by Gratings: Analytical and Experimental Analysis of Spatial Periodicity Effects

Acta Acustica united with Acustica ◽

10.3813/aaa.918451 ◽

2011 ◽

Vol 97 (5) ◽

pp. 717-727 ◽

Cited By ~ 2

Author(s):

T. Valier-Brasier ◽

C. Potel ◽

M. Bruneau ◽

D. Leduc ◽

B. Morvan ◽

...

Keyword(s):

Experimental Analysis ◽

Acoustic Waves ◽

Analytical Approach ◽

Optical Methods ◽

Geometrical Parameters ◽

One Dimensional ◽

Isotropic Solid ◽

Spatial Periodicity ◽

Shear Horizontal ◽

Modes Coupling

A model, presented in a previous paper [J. App. Phys. 108 (2010) 074910], describing the modes coupling due to scattering on small one-dimensional irregularities (parallel ridges) of the surface of isotropic solid plates, when shear horizontal waves polarized along the ridges propagate perpendicularly to them, appears to be a convenient tool to tackle the effects of the shape profile of the ridges (including the depth and the slope). Being concerned by the use of this analytical approach not utilised until now, several results, yet typical of applications, are presented below and compared with some experimental and numerical results, even analytical results (from an alternative analytical model for particular cases). These comparisons permit to highlight the effects of spatial periodicities of the ridges and show that the method could provide information on geometrical parameters characterising the profile of the roughness, which could be of interest when other methods like optical methods cannot be used.

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Working Capability Analysis of Stewart Platforms

Journal of Mechanical Design ◽

10.1115/1.2826873 ◽

1996 ◽

Vol 118 (2) ◽

pp. 220-227 ◽

Cited By ~ 38

Author(s):

Chi-Mei Luh ◽

F. A. Adkins ◽

E. J. Haug ◽

C. C. Qiu

Keyword(s):

Numerical Methods ◽

Motion Control ◽

Dimensional Space ◽

Three Dimensional ◽

Unilateral Constraints ◽

Dimensional Solution ◽

One Dimensional ◽

Capability Analysis ◽

Working Capability ◽

Stewart Platforms

Working capability analysis of planar and spatial Stewart platforms with unilateral constraints on actuator length is carried out using numerical methods based on analytical criteria for the boundary of the accessible output set. Restrictions on achievable motion at singular configurations associated with points interior to the accessible output set are also analyzed. Since movement of the working point on a spatial Stewart platform occurs in three-dimensional space, the boundary of the accessible output set is a two-dimensional surface. Numerical methods used in this analysis map one-dimensional solution sets, permitting the boundary of the accessible output set to be characterized by a family of one dimensional generators. Motion control restrictions inside the accessible output set are similarly characterized by families of interior singular curves, and barriers to motion control across surfaces defined are analyzed.

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Higher-Dimensional Space of Nanoworld

Nanotechnologies and Clusters in the Spaces of Higher Dimension - Advances in Chemical and Materials Engineering ◽

10.4018/978-1-7998-3784-8.ch001 ◽

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.

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ACOUSTIC ATTENUATION CHARACTERISTICS OF STRAIGHT-THROUGH PERFORATED TUBE SILENCERS AND RESONATORS

Journal of Computational Acoustics ◽

10.1142/s0218396x08003622 ◽

2008 ◽

Vol 16 (03) ◽

pp. 361-379 ◽

Cited By ~ 6

Author(s):

Z. L. JI

Keyword(s):

Performance Prediction ◽

Transmission Loss ◽

Three Dimensional ◽

Geometrical Parameters ◽

Mean Flow ◽

Acoustic Attenuation ◽

One Dimensional ◽

The One ◽

Attenuation Characteristics ◽

Perforated Tube

The one-dimensional analytical solutions are derived and three-dimensional substructure boundary element approaches are developed to predict and analyze the acoustic attenuation characteristics of straight-through perforated tube silencers and folded resonators without mean flow, as well as to examine the effect of nonplanar waves in the silencers and resonators on the acoustic attenuation performance. Comparisons of transmission loss predictions with the experimental results for prototype straight-through perforated tube silencers demonstrated that the three-dimensional approach is needed for accurate acoustic attenuation performance prediction at higher frequencies, while the simple one-dimensional theory is sufficient at lower frequencies. The BEM is then used to investigate the effects of geometrical parameters on the acoustic attenuation characteristics of straight-through perforated tube silencers and folded resonators in detail.

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Cubic Hybrid Mechanism Based on S[T] Output Base and P/R Input Base

Advanced Materials Research ◽

10.4028/www.scientific.net/amr.430-432.1725 ◽

2012 ◽

Vol 430-432 ◽

pp. 1725-1728

Author(s):

Jian Guo Luo ◽

Mao Yan He

Keyword(s):

Parallel Mechanism ◽

Dimensional Space ◽

Three Dimensional ◽

One Dimensional ◽

Hybrid Mechanism ◽

Hybrid Manipulator ◽

New Type ◽

The Stability ◽

Serial Mechanism ◽

Three Dimensional Space

Based on the flexibility of single couple of serial mechanism and the stability of multi couples of parallel mechanism, a new type of S[T] output base of hybrid mechanism presented, component of sphere joint run through the tiger joint, this component still the output one with the capability of rotate in three dimensional space. Add serial branch including three translation couple P or/and rotation couple R to the new type of S[T] output base, put these members on one cubic frame, twenty seven configurations obtained with 3-DOF(degree of freedom) allow of three dimensional rotation, twenty seven configurations belong to three conditions obtained with 4-DOF allow of three dimensional rotation and one dimensional translation, nine configurations belong to three conditions obtained with 5-DOF allow of three dimensional rotation and two dimensional translation, one configuration obtained with 6-DOF allow of three dimensional rotation and three dimensional translation, all those sixty four configurations have no more than six translation couple or rotation couple, and the sum of two kind of couple is equal to six. Developing new type of hybrid manipulator based on the hybrid cubic mechanism constructed with S[T] output base and P/R input base will be possible in theory and useful.

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