Soliton propagation of electromagnetic field vectors of polarized light ray traveling in a coiled optical fiber in Minkowski space with Bishop equations

Demi̇rkol²,

et al. 2021

Rev. Mex. Fís.

Self Cite

Motivated by recent researches in magnetic curves and their flows in different types of geometric manifolds and physical spacetime structures, we compute Lorentz force equations associated with the magnetic b-lines in the binormal direction. Evolution equations of magnetic b-lines due to inextensible Heisenberg antiferromagnetic flow are computed to construct the soliton surface associated with the inextensible Heisenberg antiferromagnetic flow. Then, their explicit solutions are investigated in terms of magnetic and geometric quantities via the conformable fractional derivative method. By considering arc-length and time-dependent orthogonal curvilinear coordinates, we finally determine the necessary and sufficient conditions that have to be satisfied by these quantities to define the Lorentz magnetic flux surfaces based on the inextensible Heisenberg antiferromagnetic flow model.

“…Now, if basic compatibility conditions and properties of the inner product are applied to Eqs. (5,31,32) then we may write that…”

Section: Inextensible Heisenberg Antiferromagnetic Flow Model In the Binormal Directionmentioning

confidence: 99%

Section: Inextensible Heisenberg Antiferromagnetic Flow Model In the Binormal Directionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Fractional solutions for the inextensible Heisenberg antiferromagnetic fow and solitonic magnetic flux surfaces in the binormal direction

Demi̇rkol²,

et al. 2021

Rev. Mex. Fís.

Self Cite

“…Moreover, it contributes to investigate a deeper understanding of the physical and geometric model of the Hall effect 12 . It also gives a useful connection between the integrable evolution equations and associated geometric evolution problems including localized induction equation, Betchov–Da Rios equation, binormal motion, and Hasimoto evolution 13–18 …”

Section: Introductionmentioning

confidence: 97%

Elastic magnetic curves of ferromagnetic and superparamagnetic models

Demi̇rkol

Math Methods in App Sciences

2021

Self Cite

In this paper, new energy functionals are described via the variational approach method. By doing this, a new class of elastic curves is described in the three‐dimensional ordinary space. An alternative method is also investigated to compute critical points of the bending energy functionals acting on a class of magnetic curves. Then, classifications of these critical curves are presented as elastic magnetic curves of the Frenet–Serret vectors family. Moreover, the dynamics of the elastic magnetic curves of ferromagnetic and superparamagnetic models are discussed with their numerical and analytical analysis.

“…Haldane defined the geometric rotation of the polarization angle in an ideal cylindrical optical fiber without birefringence for arbitrary fiber paths in terms of the image of the path in the tangent vector space [5]. Apart from previous researches, we proposed some new approaches to compute the electromagnetic phase with an antiferromagnetic chain [6][7][8][9][10].…”

Section: Introductionmentioning

confidence: 99%

New magnetic flux flows with Heisenberg ferromagnetic spin of optical quasi velocity magnetic flows with flux density

Körpınar¹,

Demi̇rkol²,

Körpınar³

et al. 2021

Rev. Mex. Fís.

In this article, we first offer the approach of quasi magnetic Lorentz flux of quasi velocity magnetic flows of particles by the quasi frame in 3D space. Eventually, we obtain new optical conditions of quasi magnetic Lorentz flux by using directional quasi fields. Moreover, we determine quasi magnetic Lorentz flux for quasi vector fields. Also, we give new constructions for quasi curvatures of quasi velocity magnetic flows by considering Heisenberg ferromagnetic spin. Finally, magnetic flux surface is demonstrated in a static and uniform magnetic surface by using the analytical and numerical results.