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.

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.

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.

A new approach for inextensible flows of binormal spherical indicatrices of magnetic curves

2019 ◽  
Vol 16 (02) ◽  
pp. 1950020 ◽  
Author(s):  
Talat Korpinar ◽  
Selçuk Baş
Keyword(s):  
Magnetic Field ◽  
Riemannian Manifold ◽  
Charged Particle ◽  
Partial Differential Equations ◽  
Differential Equations ◽  
Partial Differential ◽  
New Approach ◽  
Inextensible Flows ◽  
Physical Features

In this study, we obtain the special type of magnetic trajectories associated with a magnetic field [Formula: see text] defined on a 3D Riemannian manifold. We investigate a new representation of binormal spherical indicatrices of magnetic curves. Thus, we study [Formula: see text]-magnetic curves terms of inextensible flows. Furthermore, we give some new characterizations of curvatures in terms of some partial differential equations. Finally, we examine some geometrical and physical features of the moving charged particle corresponding to the [Formula: see text]-magnetic curves. Namely, we compute uniformity of the [Formula: see text]-magnetic curves.

Study of MFM Application in Semiconductor Failure Analysis

2004 ◽  
Author(s):  
Way-Jam Chen ◽  
Lily Shiau ◽  
Ming-Ching Huang ◽  
Chia-Hsing Chao
Keyword(s):  
Magnetic Field ◽  
Failure Analysis ◽  
Magnetic Force Microscopy ◽  
Magnetic Force ◽  
Current Flow ◽  
Force Microscopy ◽  
The Magnetic Field ◽  
A Current

Abstract In this study we have investigated the magnetic field associated with a current flowing in a circuit using Magnetic Force Microscopy (MFM). The technique is able to identify the magnetic field associated with a current flow and has potential for failure analysis.

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.

Fragmentation of a Filamentary Cloud Threaded by Perpendicular Magnetic Field

2018 ◽  
Vol 14 (A30) ◽  
pp. 105-105
Author(s):  
Tomoyuki Hanawa ◽  
Takahiro Kudoh ◽  
Kohji Tomisaka
Keyword(s):  
Magnetic Field ◽  
Magnetic Force ◽  
Outer Boundary ◽  
Radial Distance ◽  
Radial Density ◽  
Radial Density Distribution ◽  
Model Cloud ◽  
Moderate Magnetic Field ◽  
Self Gravity ◽  
The Magnetic Field

AbstractFilamentary molecular clouds are thought to fragment to form clumps and cores. However, the fragmentation may be suppressed by magnetic force if the magnetic fields run perpendicularly to the cloud axis. We evaluate the effect using a simple model. Our model cloud is assumed to have a Plummer like radial density distribution, $\rho = {\rho _{\rm{c}}}{\left[ {1 + {r^2}/(2p{H^2})} \right]^{2p}}$ , where r and H denote the radial distance from the cloud axis and the scale length, respectively. The symbols, ρc and p denote the density on the axis and radial density index, respectively. The initial magnetic field is assumed to be uniform and perpendicular to the cloud axis. The model cloud is assumed to be supported against the self gravity by gas pressure and turbulence. We have obtained the growth rate of the fragmentation instability as a function of the wavelength, according to the method of Hanawa, Kudoh & Tomisaka (2017). The instability depends crucially on the outer boundary. If the displacement vanishes in regions very far from the cloud axis, cloud fragmentation is suppressed by a moderate magnetic field. If the displacement is constant along the magnetic field in regions very far from the cloud, the cloud is unstable even when the magnetic field is infinitely strong. The wavelength of the most unstable mode is longer for smaller index, p.

scholarly journals The diffusion and mobility of ions in a magnetic field

1912 ◽  
Vol 86 (590) ◽  
pp. 571-577 ◽  
Keyword(s):  
Magnetic Field ◽  
Free Path ◽  
Magnetic Force ◽  
Mean Free Path ◽  
Electric Force ◽  
Mobility Of Ions ◽  
The Mean ◽  
The Magnetic Field

1. When the motion of ions in a gas takes place in a magnetic field the rates of diffusion and the velocities due to an electric force may be determined by methods similar to those given in a previous paper. The effect of the magnetic field may be determined by considering the motion of each ion between collisions with molecules. The magnetic force causes the ions to be deflected in their free paths, and when no electric force is acting the paths are spirals, the axes being along the direction of the magnetic force. If H be the intensity of the magnetic field, e the charge, and m the mass of an ion, then the radius r of the spiral is mv /He, v being the velocity in the direction perpendicular to H. The distance that the ion travels in the interval between two collisions in a direction normal to the magnetic force is a chord of the circle of radius r . The average lengths of these chords may be reduced to any fraction of the projection of the mean free path in the direction of the magnetic force, so that the rate of diffusion of ions in the directions perpendicular to the magnetic force is less than the rate of diffusion in the direction of the force.

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