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Kinematic modeling of Rytov's law and electromagnetic curves in the optical fiber based on elliptical quaternion algebra
(Elsevier Gmbh, 2021)
In this paper, we aim a kinematic method to investigate the behavior of polarized light in an optical fiber. Geometric phase equations are obtained using elliptic quaternions. The behavior of polarized light is studied for ...
Electromagnetic curves and Rytov curves based on the hyperbolic split quaternion algebra
(Elsevier Gmbh, 2022)
This paper aims to investigate the hyperbolically the motion of the polarization plane traveling along the linearly polarized light wave in the optical fiber via the hyperbolic split quaternion algebra. The motion of the ...
Accretive Darboux growth in Lorentz-Minkowski spacetime
(Wiley, 2021)
It is known that the geometric methods are used in most fields in natural sciences. Kinematics on curves and surfaces as one of these methods is an essential tool for investigating the growth of some biological objects. ...
Elliptical kinematics of the accretive surface growth
(Tubitak Scientific & Technological Research Council Turkey, 2022)
The stresses within the soft tissue are not constant for some shell surfaces. They vary with position along the mantle edge. In this paper, we show that elliptical geometry is more convenient to describe this type of ...
A Geometric Interpretation of Polarized Light and Electromagnetic Curves Along an Optical Fiber with Surface Kinematics
(Springer Basel Ag, 2022)
In this study, we research the behavior of a linearly polarized light wave coupling into an optical fiber on a surface in E-3 via geometric phase equations. The geometric phase has applications in many areas from ...
Variational equations and Killing magnetic trajectories on timelike surfaces in semi-Riemannian manifolds
(Hacettepe Univ, Fac Sci, 2022)
In this article, Darboux frame variations for timelike surfaces in semi-Riemannian manifolds are discussed. In addition, the Killing equations are examined by using the Darboux frame curvature variations. Then, magnetic ...
Null Cartan curve variations in 3D semi-Riemannian manifold
(Hacettepe Univ, Fac Sci, 2021)
The aim of this study is to investigate the variations of the Bishop frame curvatures for null Cartan curves in semi-Riemannian manifolds. The Killing equations in terms of the variations of the Bishop curvatures along the ...
Kinematical modeling of circular and elliptical polarization of the polarized light via screw transformation
(Iop Publishing Ltd, 2022)
In this paper, it is shown that the motion of a polarized light wave in an optical fiber has a special meaning that relates the scalar and vector part of the dual quaternion to the kinematics concept of a screw. We describe ...
Kinematic equations of Lorentzian magnetic flux tubes based on split quaternion algebra
(Springer Heidelberg, 2021)
The aim of the paper is to present a new geometric viewpoint for magnetic flux tubes (MFTs) in the three-dimensional Lorentzian space through split quaternion algebra. For this, we prove that an MFT can be completely ...
The 2-ruled hypersurfaces in Minkowski 4-space and their constructions via octonions
(Wiley, 2023)
In this paper, we define three types of 2-ruled hypersurfaces in the Minkowski 4-space E-1(4). We obtain Gaussian and mean curvatures of the 2-ruled hypersurfaces of type-1 and type-2 and some characterizations about its ...
