scholarly journals Chiral Majorana Edge Modes and Vortex MajoranaZero Modes in Superconducting Antiferromagnetic TopologicalInsulator

2021 ◽  
Author(s):  
Beibing Huang ◽  
Xiaosen Yang ◽  
Qinfang Zhang ◽  
Ning Xu
Keyword(s):  
Local Density ◽  
Three Dimensional ◽  
Chern Number ◽  
Theoretic Model ◽  
S Wave ◽  
Topological Stability ◽  
Surface Layers ◽  
New Era ◽  
Vortex Phase ◽  
Chern Numbers

Abstract The antiferromagnetic topological insulator (AFTI) is topologically protected by the combined time-reversal and translational symmetry $\mathcal{T}_c$. In this paper we investigate the effects of the $s$-wave superconducting pairings on the multilayers of AFTI, which breaks $\mathcal{T}_c$ symmetry and can realize quantum anomalous Hall insulator with unit Chern number. For the weakly coupled pairings, the system corresponds to the topological superconductor (TSC) with the Chern number $C=\pm 2$. We answer the following questions whether the local Chern numbers and chiral Majorana edge modes of such a TSC distribute around the surface layers. By the numerical calculations based on a theoretic model of AFTI, we find that when the local Chern numbers are always dominated by the surface layers, the wavefunctions of chiral Majorana edge modes must not localize on the surface layers and show a smooth crossover from spatially occupying all layers to only distributing near the surface layers, similar to the hinge states in a three dimensional second-order topological phases. The latter phase, denoted by the hinged TSC, can be distinguished from the former phase by the measurements of the local density of state. In addition we also study the superconducting vortex phase transition in this system and find that the exchange field in the AFTI not only enlarges the phase space of topological vortex phase but also enhances its topological stability. These conclusions will stimulate the investigations on superconducting effects of AFTI and drive the studies on chiral Majorana edge modes and vortex Majorana zero modes into a new era.

Acoustic receptivity and evolution of two-dimensional and oblique disturbances in a Blasius boundary layer

2001 ◽  
Vol 432 ◽  
pp. 69-90 ◽  
Author(s):  
RUDOLPH A. KING ◽  
KENNETH S. BREUER
Keyword(s):  
Boundary Layer ◽  
Surface Roughness ◽  
Acoustic Wave ◽  
Three Dimensional ◽  
Two Dimensional ◽  
Surface Waviness ◽  
S Wave ◽  
Boundary Layer Instability ◽  
Blasius Boundary Layer ◽  
Tollmien Schlichting

An experimental investigation was conducted to examine acoustic receptivity and subsequent boundary-layer instability evolution for a Blasius boundary layer formed on a flat plate in the presence of two-dimensional and oblique (three-dimensional) surface waviness. The effect of the non-localized surface roughness geometry and acoustic wave amplitude on the receptivity process was explored. The surface roughness had a well-defined wavenumber spectrum with fundamental wavenumber kw. A planar downstream-travelling acoustic wave was created to temporally excite the flow near the resonance frequency of an unstable eigenmode corresponding to kts = kw. The range of acoustic forcing levels, ε, and roughness heights, Δh, examined resulted in a linear dependence of receptivity coefficients; however, the larger values of the forcing combination εΔh resulted in subsequent nonlinear development of the Tollmien–Schlichting (T–S) wave. This study provides the first experimental evidence of a marked increase in the receptivity coefficient with increasing obliqueness of the surface waviness in excellent agreement with theory. Detuning of the two-dimensional and oblique disturbances was investigated by varying the streamwise wall-roughness wavenumber αw and measuring the T–S response. For the configuration where laminar-to-turbulent breakdown occurred, the breakdown process was found to be dominated by energy at the fundamental and harmonic frequencies, indicative of K-type breakdown.

scholarly journals The New Era of Three-Dimensional Histoarchitecture of the Human Endometrium

2021 ◽  
Vol 11 (8) ◽  
pp. 713
Author(s):  
Manako Yamaguchi ◽  
Kosuke Yoshihara ◽  
Nozomi Yachida ◽  
Kazuaki Suda ◽  
Ryo Tamura ◽  
...  
Keyword(s):  
3D Imaging ◽  
Relevant Literature ◽  
3D Structure ◽  
Three Dimensional ◽  
Human Endometrium ◽  
Tissue Structure ◽  
New Era ◽  
Whole Mount ◽  
Uterine Glands

The histology of the endometrium has traditionally been established by observation of two-dimensional (2D) pathological sections. However, because human endometrial glands exhibit coiling and branching morphology, it is extremely difficult to obtain an entire image of the glands by 2D observation. In recent years, the development of three-dimensional (3D) reconstruction of serial pathological sections by computer and whole-mount imaging technology using tissue clearing methods with high-resolution fluorescence microscopy has enabled us to observe the 3D histoarchitecture of tissues. As a result, 3D imaging has revealed that human endometrial glands form a plexus network in the basalis, similar to the rhizome of grass, whereas mouse uterine glands are single branched tubular glands. This review summarizes the relevant literature on the 3D structure of mouse and human endometrium and discusses the significance of the rhizome structure in the human endometrium and the expected role of understanding the 3D tissue structure in future applications to systems biology.

Local Density of States of a Three-Dimensional Conductor in the Extreme Quantum Limit

2001 ◽  
Vol 86 (8) ◽  
pp. 1582-1585 ◽  
Author(s):  
D. Haude ◽  
M. Morgenstern ◽  
I. Meinel ◽  
R. Wiesendanger
Keyword(s):  
Density Of States ◽  
Local Density ◽  
Three Dimensional ◽  
Quantum Limit ◽  
Local Density Of States

Three-dimensional lithospheric S wave velocity model of the NE Tibetan Plateau and western North China Craton

2017 ◽  
Vol 122 (8) ◽  
pp. 6703-6720 ◽  
Author(s):  
Xingchen Wang ◽  
Yonghua Li ◽  
Zhifeng Ding ◽  
Lupei Zhu ◽  
Chunyong Wang ◽  
...  
Keyword(s):  
Tibetan Plateau ◽  
Wave Velocity ◽  
North China Craton ◽  
North China ◽  
Three Dimensional ◽  
Velocity Model ◽  
S Wave ◽  
Ne Tibetan Plateau

scholarly journals Measuring Chern numbers in Hofstadter strips

2017 ◽  
Vol 3 (2) ◽  
Author(s):  
Samuel Mugel ◽  
Alexandre Dauphin ◽  
Pietro Massignan ◽  
Leticia Tarruell ◽  
Maciej Lewenstein ◽  
...  
Keyword(s):  
Boundary Conditions ◽  
Periodic Boundary Conditions ◽  
Chern Number ◽  
Open Boundary ◽  
Topological Invariants ◽  
Transverse Displacement ◽  
Open Boundary Conditions ◽  
Open Questions ◽  
Chern Numbers ◽  
Spatial Dimensions

Topologically non-trivial Hamiltonians with periodic boundary conditions are characterized by strictly quantized invariants. Open questions and fundamental challenges concern their existence, and the possibility of measuring them in systems with open boundary conditions and limited spatial extension. Here, we consider transport in Hofstadter strips, that is, two-dimensional lattices pierced by a uniform magnetic flux which extend over few sites in one of the spatial dimensions. As we show, an atomic wave packet exhibits a transverse displacement under the action of a weak constant force. After one Bloch oscillation, this displacement approaches the quantized Chern number of the periodic system in the limit of vanishing tunneling along the transverse direction. We further demonstrate that this scheme is able to map out the Chern number of ground and excited bands, and we investigate the robustness of the method in presence of both disorder and harmonic trapping. Our results prove that topological invariants can be measured in Hofstadter strips with open boundary conditions and as few as three sites along one direction.

scholarly journals Chern Class Inequalities on Polarized Manifolds and Nef Vector Bundles

2020 ◽  
Author(s):  
Ping Li ◽  
Fangyang Zheng
Keyword(s):  
Chern Class ◽  
Vector Bundles ◽  
Euler Number ◽  
Type Inequality ◽  
Chern Number ◽  
Kähler Manifolds ◽  
Kahler Manifolds ◽  
Bisectional Curvature ◽  
Chern Numbers ◽  
Nef Vector Bundles

Abstract This article is concerned with Chern class and Chern number inequalities on polarized manifolds and nef vector bundles. For a polarized pair $(M,L)$ with $L$ very ample, our 1st main result is a family of sharp Chern class inequalities. Among them the 1st one is a variant of a classical result and the equality case of the 2nd one is a characterization of hypersurfaces. The 2nd main result is a Chern number inequality on it, which includes a reverse Miyaoka–Yau-type inequality. The 3rd main result is that the Chern numbers of a nef vector bundle over a compact Kähler manifold are bounded below by the Euler number. As an application, we classify compact Kähler manifolds with nonnegative bisectional curvature whose Chern numbers are all positive. A conjecture related to the Euler number of compact Kähler manifolds with nonpositive bisectional curvature is proposed, which can be regarded as a complex analogue to the Hopf conjecture.

scholarly journals Antarctic Upper Mantle Rheology

2021 ◽  
pp. M56-2020-19
Author(s):  
E. R. Ivins ◽  
W. van der Wal ◽  
D. A. Wiens ◽  
A. J. Lloyd ◽  
L. Caron
Keyword(s):  
Wave Velocity ◽  
Upper Mantle ◽  
Effective Viscosity ◽  
Seismic Velocity ◽  
Imaging Techniques ◽  
Three Dimensional ◽  
Velocity Model ◽  
Mantle Flow ◽  
S Wave ◽  
Velocity Changes

AbstractThe Antarctic mantle and lithosphere are known to have large lateral contrasts in seismic velocity and tectonic history. These contrasts suggest differences in the response time scale of mantle flow across the continent, similar to those documented between the northeastern and southwestern upper mantle of North America. Glacial isostatic adjustment and geodynamical modeling rely on independent estimates of lateral variability in effective viscosity. Recent improvements in imaging techniques and the distribution of seismic stations now allow resolution of both lateral and vertical variability of seismic velocity, making detailed inferences about lateral viscosity variations possible. Geodetic and paleo sea-level investigations of Antarctica provide quantitative ways of independently assessing the three-dimensional mantle viscosity structure. While observational and causal connections between inferred lateral viscosity variability and seismic velocity changes are qualitatively reconciled, significant improvements in the quantitative relations between effective viscosity anomalies and those imaged by P- and S-wave tomography have remained elusive. Here we describe several methods for estimating effective viscosity from S-wave velocity. We then present and compare maps of the viscosity variability beneath Antarctica based on the recent S-wave velocity model ANT-20 using three different approaches.

Investigation of Sintering of Spherical Copper Powder by Micro Focus Computed Tomography (μCT) and Synchrotron Tomography

2007 ◽  
Vol 539-543 ◽  
pp. 2657-2662 ◽  
Author(s):  
Michael Nöthe ◽  
Matthias Schulze ◽  
Rainer Grupp ◽  
Bernd Kieback ◽  
A. Haibel
Keyword(s):  
Computed Tomography ◽  
Copper Powder ◽  
Local Density ◽  
Three Dimensional ◽  
Particle Model ◽  
Metal Powders ◽  
Particle Rotation ◽  
Depth Analysis ◽  
Recent Developments ◽  
Interparticle Contacts

The two-particle model describes the approach of particle centres and the growth of the interparticle contacts during sintering of metal powders. Unfortunately the comprehensive description of processes inside of three dimensional specimens must consider the contribution of particle rearrangements. The recent developments of combined micro focus computed tomography (CT) and 3D photogrammetric image analyzing give the opportunity to obtain the experimental data required to overcome the shortcomings of sintering theories based on the two-particle model. The analysis of spherical poly and single crystalline copper powder was performed by CT. In addition a single crystal specimen was analyzed by high resolution synchrotron radiation tomography - a more sophisticated analysis method with very limited availability. The analysis of the 3D tomographic image by photogrammetric image analyzing yielded the positions and radii of all particles and their contact partners as well. A statistical analysis of the retrieved data was performed. The formation and breaking of necks during sintering could be observed. An in-depth analysis of the particle rotation with respect to the coordination number and local density will be presented.

On the ratio of P-wave to S-wave corner frequencies for shallow earthquake sources

1974 ◽  
Vol 64 (4) ◽  
pp. 1159-1180 ◽  
Author(s):  
F. A. Dahlen
Keyword(s):  
Single Point ◽  
Three Dimensional ◽  
P Wave ◽  
Corner Frequency ◽  
S Wave ◽  
Earthquake Sources ◽  
Kinematical Model ◽  
Self Similar ◽  
Smooth Deceleration ◽  
Shallow Focus

abstract We construct a theoretical three-dimensional kinematical model of shallow-focus earthquake faulting in order to investigate the ratio of the P- and S-wave corner frequencies of the far-field elastic radiation. We attempt to incorporate in this model all of the important gross kinematical features which would arise if ordinary mechanical friction should be the dominant traction resisting fault motion. These features include a self-similar nucleation at a single point, a subsonic spreading of rupture away from that point, and a termination of faulting by smooth deceleration. We show that the ratio of the P-wave corner frequency to the S-wave corner frequency for any model which has these features will be less than unity at all points on the focal sphere.

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