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.

Gravitational magnetic curves on 3D Riemannian manifolds

2018 ◽  
Vol 15 (11) ◽  
pp. 1850184 ◽  
Author(s):  
Talat Körpınar ◽  
Ridvan Cem Demirkol
Keyword(s):  
Magnetic Field ◽  
Riemannian Manifold ◽  
Charged Particle ◽  
Riemannian Manifolds ◽  
Magnetic Force ◽  
Gravitational Force ◽  
Magnetic Vector ◽  
Magnetic Curve ◽  
Physical Features ◽  
The Magnetic Field

In this paper, we study a special type of magnetic trajectories associated with a magnetic field [Formula: see text] defined on a 3D Riemannian manifold. First, we assume that we have a moving charged particle which is supposed to be under the action of a gravitational force [Formula: see text] in the magnetic field [Formula: see text] on the 3D Riemannian manifold. Then, we determine trajectories of the charged particle associated with the magnetic field [Formula: see text] and we define gravitational magnetic curves ([Formula: see text]-magnetic curves) of the magnetic vector field [Formula: see text] on the 3D Riemannian manifold. Finally, we investigate some geometrical and physical features of the moving charged particle corresponding to the [Formula: see text]-magnetic curve. Namely, we compute the energy, magnetic force, and uniformity of the [Formula: see text]-magnetic curve.

Pseudo null curve variations for Bishop frame in 3D semi-Riemannian manifold

2019 ◽  
Vol 16 (03) ◽  
pp. 1950043 ◽  
Author(s):  
Zehra Özdemi̇r
Keyword(s):  
Magnetic Field ◽  
Riemannian Manifold ◽  
Riemannian Manifolds ◽  
Vector Fields ◽  
Space Form ◽  
Charged Particles ◽  
Null Curve ◽  
Null Curves ◽  
The Magnetic Field ◽  
Killing Equations

In the present paper, the relation between invariants of the pseudo null curves and the variational vector fields of semi-Riemannian manifolds is introduced. After that, the Killing equations are written in terms of the Bishop curvatures along the pseudo null curve. By means of this approach, Killing equations make allow to interpret the movement of charged particles within the magnetic field. Afterwards, as an application, pseudo null magnetic curves are defined using the Killing variational vector field. The parametric representations of all pseudo null magnetic curves are determined in semi-Riemannian space form. Moreover, various examples of pseudo null magnetic curves are illustrated.

scholarly journals Self-adjoint Extensions of Schrödinger Operators with ?-magnetic Fields on Riemannian Manifolds

10.14311/1271 ◽  
2010 ◽  
Vol 50 (5) ◽  
Author(s):  
T. Mine
Keyword(s):  
Magnetic Field ◽  
Riemannian Manifold ◽  
Magnetic Fields ◽  
Boundary Conditions ◽  
Riemannian Manifolds ◽  
Complete Characterization ◽  
The Self ◽  
Minimal Operator ◽  
The Magnetic Field

We consider the magnetic Schr¨odinger operator on a Riemannian manifold M. We assume the magnetic field is given by the sum of a regular field and the Dirac δ measures supported on a discrete set Γ in M. We give a complete characterization of the self-adjoint extensions of the minimal operator, in terms of the boundary conditions. The result is an extension of the former results by Dabrowski-Šťoviček and Exner-Šťoviček-Vytřas.

scholarly journals Photoelectric Measurements of Sunspot Magnetic Fields

1971 ◽  
Vol 43 ◽  
pp. 190-191
Author(s):  
F.-L. Deubner ◽  
R. Göhring
Keyword(s):  
Magnetic Field ◽  
Vector Field ◽  
Magnetic Fields ◽  
Linear Polarization ◽  
Field Vector ◽  
Two Dimensional ◽  
Magnetic Vector ◽  
Umbral Dots ◽  
Photoelectric Measurements ◽  
The Magnetic Field

Photoelectric polarization measurements in a stable sunspot (type H) with a particularly dark umbra, where ‘umbral dots’ were virtually lacking, have been carried out with the Capri magnetograph. The measurements were evaluated in terms of Unno's theory to give the value and direction of the magnetic field vector. The parameters η0 = 5, β0 = 2.5 and ΔλD = 40mÅ have been adopted for the Fe I 5250 line. Taking the configuration of the sunspot into account as well as simple conditions of steadiness of the distributions to be obtained, it is possible to derive the magnetic vector field from two-dimensional records of circular and linear polarization without ambiguities.

A Proposed Experiment of Direct Detecting of the Vector Potential within Classical Electrodynamics

1997 ◽  
Vol 11 (12) ◽  
pp. 531-540
Author(s):  
V. Onoochin
Keyword(s):  
Magnetic Field ◽  
Electromagnetic Field ◽  
Charged Particle ◽  
Vector Potential ◽  
Energy Exchange ◽  
Short Pulse ◽  
Classical Electrodynamics ◽  
Direct Influence ◽  
Ultra Short Pulse ◽  
The Magnetic Field

An experiment within the framework of classical electrodynamics is proposed, to demonstrate Boyer's suggestion of a change in the velocity of a charged particle as it passes close to a solenoid. The moving charge is replaced by an ultra-short pulse (USP), whose characteristics should depend on the current in the coil. This dependence results from the exchange of energy between the electromagnetic field of the pulse and the magnetic field within the solenoid. This energy exchange could only be explained, by assuming that the vector potential of the solenoid has a direct influence on the pulse.

scholarly journals Classification of Ricci solitons on Euclidean hypersurfaces

2014 ◽  
Vol 25 (11) ◽  
pp. 1450104 ◽  
Author(s):  
Bang-Yen Chen ◽  
Sharief Deshmukh
Keyword(s):  
Riemannian Manifold ◽  
Vector Field ◽  
Riemannian Manifolds ◽  
Potential Field ◽  
Vector Fields ◽  
Ricci Soliton ◽  
Position Vector ◽  
Ricci Solitons ◽  
Euclidean Submanifolds

A Ricci soliton (M, g, v, λ) on a Riemannian manifold (M, g) is said to have concurrent potential field if its potential field v is a concurrent vector field. Ricci solitons arisen from concurrent vector fields on Riemannian manifolds were studied recently in [Ricci solitons and concurrent vector fields, preprint (2014), arXiv:1407.2790]. The most important concurrent vector field is the position vector field on Euclidean submanifolds. In this paper we completely classify Ricci solitons on Euclidean hypersurfaces arisen from the position vector field of the hypersurfaces.

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