TOPOLOGICAL STRUCTURE AND EVOLUTION OF SPACE–TIME DISLOCATIONS AND DISCLINATIONS

2007 ◽  
Vol 22 (07) ◽  
pp. 1335-1351 ◽  
Author(s):  
Y. S. DUAN ◽  
L. ZHAO
Keyword(s):  
Topological Structure ◽  
Order Parameter ◽  
Space Time ◽  
Gauge Potential ◽  
Topological Properties ◽  
Decomposition Theory ◽  
Bifurcation Points ◽  
Parameter Field ◽  
Limit Points ◽  
Mapping Theory

By making use of the gauge potential decomposition theory and ϕ-mapping theory, the topological structure and the topological quantization of dislocations and disclinations are studied in the framework of Riemann–Cartan space–time manifold. The evolution of dislocation strings and disclination points is also studied from the topological properties of the order parameter field. The dislocations and disclinations are found generating or annihilating at the limit points and encountering, splitting, or merging at the bifurcation points of the order parameter field.

scholarly journals TOPOLOGICAL STRUCTURE OF THE MANY VORTICES SOLUTION IN JACKIW–PI MODEL

2008 ◽  
Vol 23 (14) ◽  
pp. 1055-1066 ◽  
Author(s):  
XI-GUO LEE ◽  
ZI-YU LIU ◽  
YONG-QING LI ◽  
PENG-MING ZHANG
Keyword(s):  
Topological Structure ◽  
The Self ◽  
Gauge Potential ◽  
Topological Properties ◽  
Dual Equation ◽  
The Many ◽  
Chern Simons ◽  
Topological Number

By using the gauge potential decomposition, we discuss the self-dual equation and its solution in Jackiw–Pi model. We obtain a new concrete self-dual equation and find relationship between Chern–Simons vortices solution and topological number which is determined by Hopf indices and Brouwer degrees of Ψ-mapping. To show the meaning of topological number we give several figures with different topological numbers. In order to investigate the topological properties of many vortices, we use five parameters (two positions, one scale, one phase per vortex and one charge of each vortex) to describe each vortex in many vortices solutions in Jackiw–Pi model. For many vortices, we give three figures with different topological numbers to show the effect of the charge on the many vortices solutions. We also study the quantization of flux of those vortices related to the topological numbers in this case.

TOPOLOGICAL ASPECTS OF THE PROTON VORTEX CLUSTERS IN THE CORE OF A NEUTRON STAR

2009 ◽  
Vol 18 (12) ◽  
pp. 1839-1849
Author(s):  
JUN LIANG ◽  
YISHI DUAN
Keyword(s):  
Neutron Star ◽  
Topological Structure ◽  
Order Parameter ◽  
Current Theory ◽  
Bifurcation Points ◽  
The Core ◽  
Topological Current ◽  
London Equation ◽  
Zero Points ◽  
Topological Charges

Based on the ϕ mapping topological current theory, the proton vortex clusters in the core of a neutron star are investigated. We derive rigorously the London equation with topological structure for superconducting protons. We also show that the proton vortices can only stem from the zero points of the vector order parameter. The evolution of the proton vortices is discussed, the proton vortices are found generating or annihilating at the limit points and splitting or merging at the bifurcation points of the vector order parameter, and the total topological charges remain invariant during the evolution.

scholarly journals Geometrically nonlinear analysis of the stability of the stiffened plate taking into account the interaction of eigenforms of buckling

2021 ◽  
Vol 17 (1) ◽  
pp. 3-18
Author(s):  
Gaik A. Manuylov ◽  
Sergey B. Kositsyn ◽  
Irina E. Grudtsyna
Keyword(s):  
Numerical Solution ◽  
Nonlinear Analysis ◽  
Critical Loads ◽  
Wave Formation ◽  
Geometrically Nonlinear ◽  
Stiffened Plate ◽  
Geometrically Nonlinear Analysis ◽  
Initial Imperfections ◽  
Bifurcation Points ◽  
Limit Points

The aims of this work are a detailed consideration in a geometrically nonlinear formulation of the stages of the equilibrium behavior of a compressed stiffened plate, taking into account the interaction of the general form of buckling and local forms of wave formation in the plate or in the reinforcing ribs, comparison of the results of the semi-analytical solution of the system of nonlinear equations with the results of the numerical solution on the Patran-Nastran FEM complex of the problem of subcritical and postcritical equilibrium of a compressed stiffened plate. Methods. Geometrically-nonlinear analysis of displacement fields, deformations and stresses, calculation of eigenforms of buckling and construction of bifurcation solutions and solutions for equilibrium curves with limit points depending on the initial imperfections. An original method is proposed for determining critical states and obtaining bilateral estimates of critical loads at limiting points. Results. An algorithm for studying the equilibrium states of a stiffened plate near critical points is described in detail and illustrated by examples, using the first nonlinear (cubic terms) terms of the potential energy expansion, the coordinates of bifurcation points and limit points, as well as the corresponding values of critical loads. The curves of the critical load sensitivity are plotted depending on the value of the initial imperfections of the total deflection. Equilibrium curves with characteristic bifurcation points of local wave formation are constructed using a numerical solution. For the case of action of two initial imperfections, an algorithm is proposed for obtaining two-sided estimates of critical loads at limiting points.

scholarly journals Fractional Dp-branes with transverse and tangential dynamics in the presence of background fluxes

2018 ◽  
Vol 33 (18n19) ◽  
pp. 1850107
Author(s):  
Shiva Heidarian ◽  
Davoud Kamani
Keyword(s):  
Long Range ◽  
Space Time ◽  
Gauge Potential ◽  
Boundary States ◽  
Range Force

We shall construct two boundary states which are corresponding to a dynamical fractional D[Formula: see text]-brane in the presence of the fluxes of the Kalb–Ramond field and a [Formula: see text] gauge potential in the partially orbifold space–time [Formula: see text]. These states accurately describe the D[Formula: see text]-brane in the twisted and untwisted sectors under the orbifold projection. We use them to compute the interaction of two parallel fractional D[Formula: see text]-branes with the transverse velocities, tangential rotations and tangential linear motions. Various properties of the interaction, such as its long-range force, will be discussed.

Geometrical particles and Legendrian dualities related to null curves

2020 ◽  
Vol 35 (09) ◽  
pp. 2050051
Author(s):  
Chunxiao Wang ◽  
Qingxin Zhou ◽  
Zhigang Wang
Keyword(s):  
Topological Structure ◽  
Space Time ◽  
De Sitter ◽  
Contact Manifolds ◽  
Frenet Equations ◽  
Dual Relationship ◽  
Null Curves

In this paper, we investigate the special properties of geometrical particles with null paths in de Sitter 3-space–time, new Frenet equations and an important invariant associated with null paths are presented. By means of unfolding theory, the local topological structure of the lightlike dual surfaces is revealed. It is found that the lightlike dual surface has some singularities whose types can be determined by the invariant. Based on the theory of Legendrian dualities on pseudospheres and the theory of contact manifolds, it is shown that there exists the [Formula: see text]-dual relationship between the lightlike transversal trajectory of the particle and the lightlike dual surface. In addition, an interesting and important fact mentioned is that the contact of lightlike transversal trajectory with lightcone quadric and the contact of lightlike transversal trajectory with null hyperplane have the same order when they are related to the same type of singularities of the lightlike dual surface.

Skyrmion Excitations in Graphene

2014 ◽  
Vol 887-888 ◽  
pp. 960-965 ◽  
Author(s):  
Bu Da Zhao ◽  
Ming Xiang
Keyword(s):  
Potential Theory ◽  
Limit Point ◽  
Bifurcation Theory ◽  
Current Theory ◽  
Gauge Potential ◽  
Topological Current ◽  
Mapping Theory

By making use of theφ-mapping topological current theory and the decomposition of gauge potential theory, we investigate the skyrmion excitations of (2+1)-dimensional graphene. It is shown that the topological numbers are Hopf indices and Brower degrees. Based on the bifurcation theory of theφ-mapping theory, it is founded that the skyrmions can be generated or annihilated at the limit point (the generation and annihilation of skyrmion-antiskyrmion pairs).

ϕ-MAPPING TOPOLOGICAL THEORY IN TWO-GAP SUPERCONDUCTOR

2004 ◽  
Vol 18 (09) ◽  
pp. 1309-1318 ◽  
Author(s):  
YISHI DUAN ◽  
XUGUANG SHI
Keyword(s):  
Magnetic Field ◽  
Topological Structure ◽  
Topological Theory ◽  
Topological Current ◽  
Composite Vortex ◽  
Mapping Theory ◽  
The Magnetic Field ◽  
Zero Points

In this paper, the topological structure of the two-gap superconductor is discussed in detail based on the ϕ-mapping theory. The expression of the vorticity ∇×V of the composite vortex is given and the relation between the vorticity and the magnetic field which is carried by the composite vortex is discussed. The curl of velocity ∇×V has important relation to δ2(ϕ) or we can say that ∇×V has an important relation to the zero points of ϕ. The inner structure of the topological current is characterized by the ϕ-mapping topological numbers Hopf-index and Brouwer degrees.

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