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.

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.

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.

scholarly journals Clifford algebra-based structure filtering analysis for geophysical vector fields

2013 ◽  
Vol 20 (4) ◽  
pp. 563-570 ◽  
Author(s):  
Z. Yu ◽  
W. Luo ◽  
L. Yi ◽  
Y. Hu ◽  
L. Yuan
Keyword(s):  
Vector Field ◽  
Clifford Algebra ◽  
El Niño ◽  
Vector Fields ◽  
El Nino ◽  
Field Analysis ◽  
Directional Information ◽  
Filtering Method ◽  
Additional Information

Abstract. A new Clifford algebra-based vector field filtering method, which combines amplitude similarity and direction difference synchronously, is proposed. Firstly, a modified correlation product is defined by combining the amplitude similarity and direction difference. Then, a structure filtering algorithm is constructed based on the modified correlation product. With custom template and thresholds applied to the modulus and directional fields independently, our approach can reveal not only the modulus similarities but also the classification of the angular distribution. Experiments on exploring the tempo-spatial evolution of the 2002–2003 El Niño from the global wind data field are used to test the algorithm. The results suggest that both the modulus similarity and directional information given by our approach can reveal the different stages and dominate factors of the process of the El Niño evolution. Additional information such as the directional stability of the El Niño can also be extracted. All the above suggest our method can provide a new powerful and applicable tool for geophysical vector field analysis.

scholarly journals Classification of generalized Yamabe solitons in Euclidean spaces

2021 ◽  
pp. 2150022
Author(s):  
Shunya Fujii ◽  
Shun Maeta
Keyword(s):  
Vector Field ◽  
Position Vector ◽  
Euclidean Spaces ◽  
Yamabe Solitons ◽  
Gradient Solitons

In this paper, we consider generalized Yamabe solitons which include many notions, such as Yamabe solitons, almost Yamabe solitons, [Formula: see text]-almost Yamabe solitons, gradient [Formula: see text]-Yamabe solitons and conformal gradient solitons. We completely classify the generalized Yamabe solitons on hypersurfaces in Euclidean spaces arisen from the position vector field.

scholarly journals Lie Derivatives and Ricci Tensor on Real Hypersurfaces in Complex Two-plane Grassmannians

2018 ◽  
Vol 61 (3) ◽  
pp. 543-552
Author(s):  
Imsoon Jeong ◽  
Juan de Dios Pérez ◽  
Young Jin Suh ◽  
Changhwa Woo
Keyword(s):  
Vector Field ◽  
Differential Operator ◽  
Ricci Tensor ◽  
Real Hypersurface ◽  
Real Hypersurfaces ◽  
Reeb Vector ◽  
Reeb Vector Field ◽  
Lie Derivatives ◽  
Lie Derivation

AbstractOn a real hypersurface M in a complex two-plane Grassmannian G2() we have the Lie derivation and a differential operator of order one associated with the generalized Tanaka–Webster connection . We give a classification of real hypersurfaces M on G2() satisfying , where ξ is the Reeb vector field on M and S the Ricci tensor of M.

scholarly journals On the predictability of economic structural change by the Poincaré–Bendixson theory

foresight ◽  
2019 ◽  
Vol 21 (2) ◽  
pp. 250-265 ◽  
Author(s):  
Denis Stijepic
Keyword(s):  
Structural Change ◽  
Design Methodology ◽  
Economic Structure ◽  
Content Type ◽  
Geometrical Properties ◽  
Modeling Methods ◽  
Modeling And Prediction ◽  
Long Run ◽  
Topological Modeling

Purpose The three-sector framework (relating to agriculture, manufacturing and services) is one of the major concepts for studying the long-run change of the economic structure. This paper aims to discuss the system-theoretical classification of the structural change in the three-sector framework and, in particular, its predictability by the Poincaré–Bendixson theory. Design/methodology/approach This study compares the assumptions of the Poincaré–Bendixson theory to the typical axioms of structural change modeling, the empirical evidence on the geometrical properties of structural change trajectories and the methodological arguments referring to the laws of structural change. Findings The findings support the assumption that the structural change phenomenon is representable by a dynamical system that is predictable by the Poincaré–Bendixson theory. This result implies, among others, that in the long run, structural change is either transitory or cyclical and can be used in further geometrical/topological long-run structural change modeling and prediction. Originality/value Although widespread in mathematics, geometrical/topological modeling methods have not been used in modeling and prediction of long-run structural change, despite the fact that they seem to be predestined for this purpose owing to their global, system-theoretical nature, allowing for a reduction of ideology content of predictions and greater robustness of results.

scholarly journals Finitely curved orbits of complex polynomial vector fields

2007 ◽  
Vol 79 (1) ◽  
pp. 13-16
Author(s):  
Albetã C. Mafra
Keyword(s):  
Vector Field ◽  
Gaussian Curvature ◽  
Algebraic Curve ◽  
Vector Fields ◽  
Complex Polynomial ◽  
Holomorphic Foliations ◽  
Holomorphic Curve ◽  
Polynomial Vector ◽  
Polynomial Vector Fields

This note is about the geometry of holomorphic foliations. Let X be a polynomial vector field with isolated singularities on C². We announce some results regarding two problems: 1. Given a finitely curved orbit L of X, under which conditions is L algebraic? 2. If X has some non-algebraic finitely curved orbit L what is the classification of X? Problem 1 is related to the following question: Let C <FONT FACE=Symbol>Ì</FONT> C² be a holomorphic curve which has finite total Gaussian curvature. IsC contained in an algebraic curve?

Classification of Visual Strategies in Physics Vector Field Problem-solving

2020 ◽  
Author(s):  
Saleh Mozaffari ◽  
Mohammad Al-Naser ◽  
Pascal Klein ◽  
Stefan Küchemann ◽  
Jochen Kuhn ◽  
...  
Keyword(s):  
Vector Field ◽  
Problem Solving ◽  
Field Problem ◽  
Visual Strategies
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