Singularity properties of null killing magnetic curves in Minkowski 3-space

2020 ◽  
Vol 17 (09) ◽  
pp. 2050141 ◽  
Author(s):  
Jianguo Sun
Keyword(s):  
Vector Field ◽  
Magnetic Vector ◽  
Geometrical Properties ◽  
Singular Loci ◽  
Magnetic Curve

We reconstruct the Cartan Equations of null Killing magnetic curve [Formula: see text] in [Formula: see text] with Killing magnetic vector field [Formula: see text] under the new Cartan frame [Formula: see text], which describe some new geometrical properties of [Formula: see text]. The singularity properties of the rectifying surfaces and the binormal osculating surfaces of null Killing magnetic curves are given. As an application, two examples are given to explain the main results, where the singular loci of null Killing magnetic curves are obtained.

Singularity properties of killing magnetic curves in Minkowski 3-space

2019 ◽  
Vol 16 (08) ◽  
pp. 1950123 ◽  
Author(s):  
Jianguo Sun
Keyword(s):  
Vector Field ◽  
Magnetic Vector ◽  
Geometrical Properties

We define the coordinate equations of killing magnetic curves [Formula: see text] in [Formula: see text] with the magnetic vector field [Formula: see text] under the frame [Formula: see text]. In particular, this yields to describe the geometrical properties and singularities of the magnetic curves and the magnetic normal binormal surfaces. Meanwhile, we establish the relationships between singularity types of the magnetic normal binormal surfaces and geometrical invariants of the magnetic curves. As an application, we give an example to explain the main results in this paper, where we give the classification of singularity types of the magnetic curves.

Frictional magnetic curves in 3D Riemannian manifolds

2018 ◽  
Vol 15 (02) ◽  
pp. 1850020 ◽  
Author(s):  
Talat Korpinar ◽  
Ridvan Cem Demirkol
Keyword(s):  
Magnetic Field ◽  
Riemannian Manifold ◽  
Charged Particle ◽  
Vector Field ◽  
Riemannian Manifolds ◽  
Frictional Force ◽  
Magnetic Vector ◽  
Geometrical Properties ◽  
Physical Consequences ◽  
The Magnetic Field

In this study, we investigate the special type of magnetic trajectories associated with a magnetic field [Formula: see text] defined on a 3D Riemannian manifold. First, we consider a moving charged particle under the action of a frictional force, [Formula: see text], in the magnetic field [Formula: see text]. Then, we assume that trajectories of the particle associated with the magnetic field [Formula: see text] correspond to frictional magnetic curves ([Formula: see text]-magnetic curves[Formula: see text] of magnetic vector field [Formula: see text] on the 3D Riemannian manifold. Thus, we are able to investigate some geometrical properties and physical consequences of the particle under the action of frictional force in the magnetic field [Formula: see text] on the 3D Riemannian manifold.

Study on the Geometrical Properties and Existence of Orbit Homoclinic to a Saddle Point in n-Dimensional Autonomous Vector Field with Polynomials

2018 ◽  
Vol 28 (14) ◽  
pp. 1850169
Author(s):  
Lingli Xie
Keyword(s):  
Vector Field ◽  
Saddle Point ◽  
Equilibrium Point ◽  
Necessary Conditions ◽  
Continuous System ◽  
Homoclinic Bifurcation ◽  
Stable And Unstable Manifolds ◽  
Geometrical Properties ◽  
Unstable Manifolds

According to the theory of stable and unstable manifolds of an equilibrium point, we firstly find out some geometrical properties of orbits on the stable and unstable manifolds of a saddle point under some brief conditions of nonlinear terms composed of polynomials for [Formula: see text]-dimensional time continuous system. These properties show that the orbits on stable and unstable manifolds of the saddle point will stay on the corresponding stable and unstable subspaces in the [Formula: see text]-neighborhood of the saddle point. Furthermore, the necessary conditions of existence for orbit homoclinic to a saddle point are exposed. Some examples including homoclinic bifurcation are given to indicate the application of the results. Finally, the conclusions are presented.

Magnetic Vector-field of Optical Antennas from Electromagnetic Duality

2012 ◽  
Author(s):  
Robert L. Olmon ◽  
Xiaoji G. Xu ◽  
Kseniya S. Deryckx ◽  
Brian A. Lail ◽  
Markus B. Raschke
Keyword(s):  
Vector Field ◽  
Optical Antennas ◽  
Magnetic Vector

scholarly journals Relativistic segnificance of curvature tensors

1982 ◽  
Vol 5 (1) ◽  
pp. 133-139 ◽  
Author(s):  
G. P. Pokhariyal
Keyword(s):  
Electromagnetic Field ◽  
Vector Field ◽  
Electric Field ◽  
Gravitational Waves ◽  
Einstein Space ◽  
Geometrical Properties ◽  
Projective Curvature ◽  
Cyclic Property ◽  
Projective Curvature Tensor ◽  
Curvature Tensors

In thi paper new curvature tensors have been defined on the lines of Weyl's projective curvature tensor and it has been shown that the “distribution” (order in which the vectors in question are arranged before being acted upon by the tensor in question) of vector field over the metric potentials and matter tensors plays an important role in shaping the various physical and geometrical properties of a tensor viz the formulation of gravitational waves, reduction of electromagnetic field to a purely electric field, vanishing of the contracted tensor in an Einstein Space and the cyclic property.

High resolution magnetic vector-field imaging with cold atomic ensembles

2011 ◽  
Vol 98 (7) ◽  
pp. 074101 ◽  
Author(s):  
M. Koschorreck ◽  
M. Napolitano ◽  
B. Dubost ◽  
M. W. Mitchell
Keyword(s):  
Vector Field ◽  
High Resolution ◽  
Atomic Ensembles ◽  
Magnetic Vector ◽  
Field Imaging
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