Quasi uniformly accelered motion of quasi normal magnetic biharmonic particles in Heisenberg space with cold plasma

Authors

  • Zeliha Körpınar
  • Talat Körpınar

DOI:

https://doi.org/10.31349/RevMexFis.68.020708

Keywords:

biharmonic particle, quasi plasma, Heisenberg space, magnetic field, magnetic flux density, electrical energy.

Abstract

In this paper, we firstly review the quasi uniformly accelerated motion (QUAM) with Fermi derivative by cold plasma in Heisenberg space. We define new quasi uniformly accelerated potential electric energy of quasi normal magnetic biharmonic particles and some Lorentz fields. Moreover, we design the new relationship between the quasi uniformly accelerated motion and the Fermi parallel transportation in cold plasma. Also, we collect new physical geometric designs for a quasi uniformly accelerated motion of normal magnetic biharmonic particles in Heisenberg space. Finally, we construct quasi uniformly accelerated potential electric energy with respect to its electric field and some quasi curvatures.

References

J.L. Synge, Relativity: The General Theory. North Holland, Amsterdam (1960).

B. Mashhoon, U. Muench, Length measurement in accelerated systems. Annalen der Physik 11 (2002) 532, https://doi.org/10.1002/1521-3889(200208) 11:7h532::AID-ANDP532i3.0.CO;2-3.

D. de la Fuente, A. Romero, Uniformly accelerated motion in General Relativity: completeness of inextensible trajectories.

Gen. Relativ. Gravit. 47 (2015) 33, https://doi.org/10.1007/s10714-015-1879-3.

D. de la Fuente, A. Romero, and P. Torres, Unchanged direction motion in General Relativity: the problems of prescribing acceleration and the extensibility of trajectories. J. Math. Phys. 56 (2015) 112501, https://doi.org/10.1063/1.4935854.

Y. Friedman, and T. Scarr, Uniform acceleration in general relativity. Gen. Relativ. and Gravit. 47 (2015) 121, DOI: https://doi.org/10.1007/s10714-015-1966-5.

Y. Friedman, T. Scarr, Making the relativistic dynamics equation covariant: explicit solutions for motion under a constant force, Phys. Scr. 86 (2012) 065008, https://doi.org/10.1088/0031-8949/86/06/065008.

B. O’Neill, Semi-Riemannian Geometry. Academic Press, Massachusetts (1983).

K. Takenaka, A.D. Setyawan, P. Sharma, N. Nishiyama, A. Makino, Industrialization of nanocrystalline Fe–Si–B–P–Cu alloys for high magnetic flux density cores, J. Magn. Magn. Mater, 401 (2016) 479, https://doi.org/10.1016/j.jmmm.2015.10.091.

M. Li, T. Bien, G. Rose, Construction of a conductive distortion reduced electromagnetic tracking system for computer assisted image-guided interventions, Med. Eng. Phys. 36 (2014) 1496, DOI: https://doi.org/10.1016/j.medengphy.2014.07.018.

A.M. Franz, T. Haidegger, W. Birkfellner, K. Cleary, T.M. Peters, L. Maier-Hein, Electromagnetic tracking in medicine - a review of technology, validation and applications, IEEE Trans. Med. Imag. 33 (2014) 1702, https://doi.org/10.1109/TMI.2014.2321777.

A. De Lambert, S. Esneault, A. Lucas, P. Haigron, P. Cinquin, J.L. Magne, Electromagnetic tracking for registration and navigation in endovascular aneurysm repair: a phantom study, Eur. J. Vasc. Endovasc. Surg. 43 (2012) 684, https://doi.org/10.1016/j.ejvs.2012.03.007.

M. Sha, Y. Wang, N. Ding, X. Wu, Z. Fang, An electromagnetic tracking method based on fast determination of the maximum magnetic flux density vector represented by two azimuth angles, Measurement, 109 (2017) 160, https://doi.org/10.1016/j.measurement.2017.04.027.

E. Turhan, T. Korpınar, On Characterization Canal Surfaces around Timelike Horizontal Biharmonic Curves in Lorentzian

Heisenberg Group Heis3, Z. Naturforsch. 66a (2011) 441, https://doi.org/10.5560/ZNA.2011.66a0441.

E. Turhan, T. Korpınar, On Characterization of Time-Like Horizontal Biharmonic Curves in the Lorentzian Heisenberg Group

Heis3, Z. Naturforsch. 65a (2010) 641, https://doi.org/10.1515/zna-2010-8-904.

A. Altin, On the energy and Pseduoangle of Frenet Vector Fields in R n v . Ukranian Mathematical J. 63 (2011), 969,

https://doi.org/10.1007/s11253-011-0556-2.

V. Asil, Velocities of Dual Homothetic Exponential Motions in D3, Iranian Journal of Science & Tecnology Transaction A,

Science 31 (2007) 265, https://doi.org/10.22099/IJSTS.2008.2301.

T. Korpınar, R.C. Demirkol, A new approach on the curvature ¨dependent energy for elastic curves in a Lie Group. Honam

Mathematical J. 39 (2017), 637, https://doi.org/10.5831/HMJ.2017.39.4.637.

T. Korpınar, R.C. Demirkol, A New characterization on the energy of elastica with the energy of Bishop vector fields in

Minkowski space. Journal of Advanced Physics. 6 (2017) 562, https://doi.org/10.1166/jap.2017.1375.

T. Korpınar, R.C. Demirkol, Energy on a timelike particle in dynamical and electrodynamical force fields in De-Sitter space.

Rev. Mex. Fis. 63 (2017) 560-568.

T. Adachi, Kahler magnetic on a complex projective space. Proc. Japan Acad. Ser. A: Math Sci. 70 (1994) 12, https://doi.org/10.3792/pjaa.70.12.

M. Barros, A. Romero, J.L. Cabrerizo, M. Fernandez, The Gauss–Landau–Hall problem on Riemannian surfaces, J. Math. Phys. 46 (2005) 112905, https://doi.org/10.1063/1.2136215.

J.L. Cabrerizo, M. Fernandez, J.S. Gomez, The contact magnetic flow in 3D Sasakian manifolds, J. Phys. A 42 (2009) 195201, https://doi.org/10.1088/1751-8113/42/19/195201.

J.L. Cabrerizo, Magnetic fields in 2D and 3D sphere. Journal of Nonlinear Mathematical Physics 20 (2013), 440, https://doi.org/10.1080/14029251.2013.855052.

T. Korpınar, R. C. Demirkol, Frictional magnetic curves in 3D Riemannian manifolds, International Journal of Geometric Methods in Modern Physics, 15 (2018) 1850020, https://doi.org/10.1142/S0219887818500202.

T. Korpınar, On T-Magnetic Biharmonic Particles with Energy and Angle in the Three Dimensional Heisenberg Group H, Adv.

Appl. Clifford Algebras, 28 (2018) 1, https://doi.org/10.1007/s00006-018-0834-2.

S. Rahmani, Metriqus de Lorentz sur les groupes de Lie unimodulaires, de dimension trois, Journal of Geometry and Physics 9 (1992), 295, https://doi.org/10.1016/0393-0440(92)90033-W.

M. Dede, C. Ekici, H. Tozak, Directional Tubular Surfaces, International Journal of Algebra, 9 (2015), 527, http://dx.doi.org/10.12988/ija.2015.51274.

E. Pina, Lorentz transformation and the motion of a charge in a constant electromagnetic field. Rev. Mex. Fis. 16 (1967) 233.

H. Ringermacher, Intrinsic geometry of curves and the Minkowski force, Phys. Lett. A 74 (1979) 381, https://doi.org/10.1016/0375-9601(79)90229-9.

B. M. Barbashov and V. Nesterenko, Introduction to the relativistic string theory (World Scientific, 1990).

T. Korpınar, A new characterization of quasi velocity magnetic biharmonic particles in the Heisenberg space with cold plasma, Rev. Mex. Fis.. Accepted.

T. Korpınar, Z. Korpınar, Y-M. Chu, M A Akinlar and M. Inc, New Uniform Motion and Fermi–Walker Derivative of Normal Magnetic Biharmonic Particles in Heisenberg Space, Symmetry, 12 (2020) 1017, https://doi.org/10.3390/sym12061017.

T. Korpınar, R. C. Demirkol and Z. K ¨ orpınar, Soliton propagation of electromagnetic field vectors of polarized light ray

traveling in a coiled optical fiber in the ordinary space, International Journal of Geometric Methods in Modern Physics 16 (8)(2019) 1950117, https://doi.org/10.1142/S0219887819501172.

T. Korpınar R. C. Demirkol, On the uniform motion of a relativistic charged particle in a homogeneous electromagnetic field

in Minkowski space E4 2, Math Meth Appl Sci. 42 (2019) 3069, https://doi.org/10.1002/mma.5567.

T. Korpınar, Optical directional binormal magnetic flows with geometric phase: Heisenberg ferromagnetic model, Optik - International Journal for Light and Electron Optics 219 (2020) 165134, https://doi.org/10.1016/j.ijleo.2020.165134.

Downloads

Published

2022-03-01

How to Cite

[1]
Z. Körpınar and T. Körpınar, “Quasi uniformly accelered motion of quasi normal magnetic biharmonic particles in Heisenberg space with cold plasma”, Rev. Mex. Fís., vol. 68, no. 2 Mar-Apr, pp. 020708 1–, Mar. 2022.

Issue

Section

07 Gravitation, Mathematical Physics and Field Theory