Topological nodal line states in three-dimensional ball-and-stick sonic crystals

2019 ◽  
Vol 100 (22) ◽  
Author(s):  
Zhi-Guo Geng ◽  
Yu-Gui Peng ◽  
Ya-Xi Shen ◽  
Zhen Ma ◽  
Rui Yu ◽  
...  
Keyword(s):  
Three Dimensional ◽  
Nodal Line ◽  
Dimensional Ball ◽  
Sonic Crystals

scholarly journals Dirac and Nodal Line Magnons in Three-Dimensional Antiferromagnets

2017 ◽  
Vol 119 (24) ◽  
Author(s):  
Kangkang Li ◽  
Chenyuan Li ◽  
Jiangping Hu ◽  
Yuan Li ◽  
Chen Fang
Keyword(s):  
Three Dimensional ◽  
Nodal Line

scholarly journals A three dimensional ball quotient

2013 ◽  
Vol 276 (1-2) ◽  
pp. 345-370
Author(s):  
Eberhard Freitag ◽  
Riccardo Salvati Manni
Keyword(s):  
Three Dimensional ◽  
Dimensional Ball

scholarly journals FOUR-DIMENSIONAL BALL IN A GRAPHIC REPRESENTATION

2021 ◽  
pp. 37-46
Author(s):  
Helena Bidnichenko
Keyword(s):  
Dimensional Space ◽  
Three Dimensional ◽  
Geometric Modelling ◽  
Vector Model ◽  
Original Position ◽  
Two Dimensional ◽  
Axis Of Rotation ◽  
Dimensional Ball ◽  
Three Dimensional Space ◽  
Horizontal Vector

The paper presents a method for geometric modelling of a four-dimensional ball. For this, the regularities of the change in the shape of the projections of simple geometric images of two-dimensional and three-dimensional spaces during rotation are considered. Rotations of a segment and a circle around an axis are considered; it is shown that during rotation the shape of their projections changes from the maximum value to the degenerate projection. It was found that the set of points of the degenerate projection belongs to the axis of rotation, and each n-dimensional geometric image during rotation forms a body of a higher dimension, that is, one that belongs to (n + 1) -dimensional space. Identified regularities are extended to the four-dimensional space in which the ball is placed. It is shown that the axis of rotation of the ball will be a degenerate projection in the form of a circle, and the ball, when rotating, changes its size from a volumetric object to a flat circle, then increases again, but in the other direction (that is, it turns out), and then in reverse order to its original position. This rotation is more like a deformation, and such a ball of four-dimensional space is a hypersphere. For geometric modelling of the hypersphere and the possibility of its projection image, the article uses the vector model proposed by P.V. Filippov. The coordinate system 0xyzt is defined. The algebraic equation of the hypersphere is given by analogy with the three-dimensional space along certain coordinates of the center a, b, c, d. A variant of hypersection at t = 0 is considered, which confirms by equations obtaining a two-dimensional ball of three-dimensional space, a point (a ball of zero radius), which coincides with the center of the ball, or an imaginary ball. For the variant t = d, the equation of a two-dimensional ball is obtained, in which the radius is equal to R and the coordinates of all points along the 0t axis are equal to d. The variant of hypersection t = k turned out to be interesting, in which the equation of a two-dimensional sphere was obtained, in which the coordinates of all points along the 0t axis are equal to k, and the radius is . Horizontal vector projections of hypersection are constructed for different values of k. It is concluded that the set of horizontal vector projections of hypersections at t = k defines an ellipse.  

Square-root-like higher-order topological states in three-dimensional sonic crystals

2021 ◽  
Author(s):  
Zhiguo Geng ◽  
Huanzhao Lv ◽  
Zhan Xiong ◽  
Yu-Gui Peng ◽  
Zhaojiang Chen ◽  
...  
Keyword(s):  
Three Dimensional ◽  
Surface States ◽  
Higher Order ◽  
Square Root ◽  
Root Lattice ◽  
Third Order ◽  
Topological Materials ◽  
Topological States ◽  
Sonic Crystal ◽  
Sonic Crystals

Abstract The square-root descendants of higher-order topological insulators were proposed recently, whose topological property is inherited from the squared Hamiltonian. Here we present a three-dimensional (3D) square-root-like sonic crystal by stacking the 2D square-root lattice in the normal (z) direction. With the nontrivial intralayer couplings, the opened degeneracy at the K-H direction induces the emergence of multiple acoustic localized modes, i.e., the extended 2D surface states and 1D hinge states, which originate from the square-root nature of the system. The square-root-like higher order topological states can be tunable and designed by optionally removing the cavities at the boundaries. We further propose a third-order topological corner state in the 3D sonic crystal by introducing the staggered interlayer couplings on each square-root layer, which leads to a nontrivial bulk polarization in the z direction. Our work sheds light on the high-dimensional square-root topological materials, and have the potentials in designing advanced functional devices with sound trapping and acoustic sensing.

scholarly journals Engineering Topological Nodal Line Semimetals in Rashba Spin-Orbit Coupled Atomic Chains

2019 ◽  
Vol 4 (1) ◽  
pp. 25 ◽  
Author(s):  
Paola Gentile ◽  
Vittorio Benvenuto ◽  
Carmine Ortix ◽  
Canio Noce ◽  
Mario Cuoco
Keyword(s):  
Three Dimensional ◽  
Nodal Line ◽  
Spin Orbit Coupling ◽  
Spin Orbit ◽  
Atomic Chain ◽  
Nodal Lines ◽  
Rashba Spin ◽  
Charge Potential ◽  
Atomic Chains ◽  
Two Phases

In this paper, we study an atomic chain in the presence of modulated charge potential and modulated Rashba spin-orbit coupling (RSOC) of equal periods. We show that for commensurate periodicities, λ = 4 n with integer n, the three-dimensional synthetic space obtained by sliding the two phases of the charge potential and RSOC features a topological nodal-line semimetal protected by an anti-unitary particle-hole symmetry. The location and shape of the nodal lines strongly depend on the relative amplitude between the charge potential and RSOC.

scholarly journals Three-dimensionally deformable, highly stretchable, permeable, durable and washable fabric circuit boards

2014 ◽  
Vol 470 (2171) ◽  
pp. 20140472 ◽  
Author(s):  
Qiao Li ◽  
Xiao Ming Tao
Keyword(s):  
Fatigue Life ◽  
Three Dimensional ◽  
Circuit Boards ◽  
Electrical Stability ◽  
Resistance Change ◽  
Structural Conversion ◽  
Punch Test ◽  
Dry Conditions ◽  
Highly Stretchable ◽  
Dimensional Ball

This paper reports fabric circuit boards (FCBs), a new type of circuit boards, that are three-dimensionally deformable, highly stretchable, durable and washable ideally for wearable electronic applications. Fabricated by using computerized knitting technologies at ambient dry conditions, the resultant knitted FCBs exhibit outstanding electrical stability with less than 1% relative resistance change up to 300% strain in unidirectional tensile test or 150% membrane strain in three-dimensional ball punch test, extraordinary fatigue life of more than 1 000 000 loading cycles at 20% maximum strain, and satisfactory washing capability up to 30 times. To the best of our knowledge, the performance of new FCBs has far exceeded those of previously reported metal-coated elastomeric films or other organic materials in terms of changes in electrical resistance, stretchability, fatigue life and washing capability as well as permeability. Theoretical analysis and numerical simulation illustrate that the structural conversion of knitted fabrics is attributed to the effective mitigation of strain in the conductive metal fibres, hence the outstanding mechanical and electrical properties. Those distinctive features make the FCBs particularly suitable for next-to-skin electronic devices. This paper has further demonstrated the application potential of the knitted FCBs in smart protective apparel for in situ measurement during ballistic impact.

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