Skip to main content
SpringerLink
Log in

Optical normalized microscale for optical total recursion electromagnetic flux on Heisenberg space \({\mathbb {S}}_{{\mathbb {H}}}^{2}\)

  • Published:
Optical and Quantum Electronics Aims and scope Submit manuscript

Abstract

In this article, we construct a new design for optical spherical Heisenberg total recursion flux with a normalized microscale in spherical Heisenberg space. Moreover, we demonstrate spherical Heisenberg normalized microscale by Heisenberg recursion operator for some magnetic fibers. Thus, we obtain optical spherical Heisenberg ferromagnetic recursion flux by using optical spherical Heisenberg ferromagnetic normalized microscale in spherical Heisenberg space.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3

Similar content being viewed by others

References

  • Adali, S.: Variational principles for transversely vibrating multiwalled carbon nanotubes based on nonlocal Euler -Bernoulli beam model. Nano Lett. 9, 1737–1741 (2009)

    Article  ADS  Google Scholar 

  • Aghababaei, R., Reddy, J.: Nonlocal third-order shear deformation plate theory with application to bending and vibration of plates. J. Sound Vib. 326, 277–289 (2009)

    Article  ADS  Google Scholar 

  • Akbaş, ŞD.: Forced vibration analysis of functionally graded nanobeams. Int. J. Appl. Mech. 9, 1750100 (2017)

    Article  Google Scholar 

  • Akbaş, ŞD.: Free vibration of edge cracked functionally graded microscale beams based on the modified couple stress theory. Int. J. Struct. Stab. Dyn. 17, 1750033 (2017)

    Article  MathSciNet  Google Scholar 

  • Akinyemi, L., Inc, M., Khater, M.M.A., Rezazadeh, H.: Dynamical behaviour of Chiral nonlinear Schrödinger equation. Optical Quant. Elect. 54(3), 1–15 (2022)

    Article  Google Scholar 

  • Al-Basyouni, K., Tounsi, A., Mahmoud, S.: Size dependent bending and vibration analysis of functionally graded micro beams based on modified couple stress theory and neutral surface position. Compos. Struct. 125, 621–630 (2015)

    Article  Google Scholar 

  • Ali, K.K., Zabihi, A., Rezazadeh, H., Ansari, R., Inc, M.: Optical soliton with Kudryashov’s equation via sine-Gordon expansion and Kudryashov methods. Opt. Quant. Electron. 53(7), 1–15 (2021)

    Article  Google Scholar 

  • Almaas, E., Brevik, I.: Possible sorting mechanism for microparticles in an evanescent field. Phys. Rev. A 87, 063826 (2013)

    Article  ADS  Google Scholar 

  • Anco, S.C., Myrzakulov, R.: Integrable generalizations of Schr ödinger maps and Heisenberg spin models from Hamiltonian flows of curves and surfaces. J. Geom. Phys. 60(10), 1576–1603 (2010)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  • Ashkin, A.: Acceleration and trapping of particles by radiation pressure. Phys. Rev. Lett. 24, 156–159 (1970)

    Article  ADS  Google Scholar 

  • Ashkin, A., Dziedzic, J.M., Bjorkholm, J.E., Chu, S.: Observation of a single-beam gradient force optical trap for dielectric particles. Opt. Lett. 11, 288–290 (1986)

    Article  ADS  Google Scholar 

  • Assadi, A., Farshi, B., Alinia-Ziazi, A.: Size dependent dynamic analysis of nanoplates. J. Appl. Phys. 107, 124310 (2010)

    Article  ADS  Google Scholar 

  • Attia, M.A.: On the mechanics of functionally graded nanobeams with the account of surface elasticity. Int. J. Eng. Sci. 115, 73–101 (2017)

    Article  MathSciNet  MATH  Google Scholar 

  • Aydogdu, M.: Longitudinal wave propagation in nanorods using a general nonlocal unimodal rod theory and calibration of nonlocal parameter with lattice dynamics. Int. J. Eng. Sci. 56, 17–28 (2012)

    Article  Google Scholar 

  • Balakrishnan, R., Bishop, A.R., Dandoloff, R.: Geometric phase in the classical continuous antiferromagnetic Heisenberg spin chain. Phys. Rev. Lett. 64(18), 2107 (1990)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  • Balakrishnan, R., Bishop, A.R., Dandoloff, R.: Anholonomy of a moving space curve and applications to classical magnetic chains. Phys. Rev. B 47(6), 3108 (1993)

    Article  ADS  Google Scholar 

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

    Book  Google Scholar 

  • Barros, M., Ferrández, A., Lucas, P., Merono, M.: Hopf cylinders, B-scrolls and solitons of the Betchov-Da Rios equation in the 3-dimensional anti-De Sitter space. CR Acad. Sci. Paris, Série I 321, 505–509 (1995)

    MATH  Google Scholar 

  • Barros, M., Ferrández, A., Lucas, P., Meroño, M.A.: Solutions of the Betchov-Da Rios soliton equation: a Lorentzian approach. J. Geom. Phys. 31(2–3), 217–228 (1999)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  • Bliokh, K.Y.: Geometrodynamics of polarized light: Berry phase and spin Hall effect in a gradient-index medium. J. Optics A: Pure Appl. Optics 11(9), 094009 (2009)

    Article  ADS  Google Scholar 

  • Bliokh, K.Y., Niv, A., Kleiner, V., Hasman, E.: Geometrodynamics of spinning light. Nat. Photonics 2(12), 748 (2008)

    Article  ADS  Google Scholar 

  • Burns, M.M., Fournier, J.-M., Golovchenko, J.A.: Optical binding. Phys. Rev. Lett. 63, 1233–1236 (1989)

    Article  ADS  Google Scholar 

  • Calini, A., Ivey, T.: Finite-gap solutions of the vortex filament equation genus one solutions and symmetric solutions. J. Nonlinear Sci. 1(5), 321–361 (2005)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  • Calini, A., Ivey, T., Marí Beffa, G.: Remarks on KdV-type flows on star-shaped curves. Phys. D 238, 788–797 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  • Chaumet, P.C., Nieto-Vesperinas, M.: Optical binding of particles with or without the presence of a flat dielectric surface. Phys. Rev. B 64, 035422 (2001)

    Article  ADS  Google Scholar 

  • Chen, X., Iwamoto, M., Shi, Z., Zhang, L., Wang, Z.L.: Self-powered trace memorization by conjunction of contact-electrification and ferroelectricity. Adv. Funct. Mater. 25, 739–747 (2015)

    Article  Google Scholar 

  • Cheng, T.S., Chao, Y.C., Wu, C.Y., Li, Y.H., Nakamura, Y., Lee, K.Y., et al.: Experimental and numerical investigation of microscale hydrogen diffusion flames. Proc. Combust. Inst. 30, 2489–97 (2005)

    Article  Google Scholar 

  • Chou, K.S., Qu, C.Z.: The KdV equation and motion of plane curves. J. Phys. Soc. Jan. 7, 1912–1916 (2001)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  • Coppi, B., Greene, J.M., Johnson, J.L.: Resistive instabilities in a diffuse linear pinch. Nucl. Fusion 6(2), 101 (1966)

    Article  Google Scholar 

  • Dai, H., Wang, Y., Wang, L.: Nonlinear dynamics of cantilevered microbeams based on modified couple stress theory. Int. J. Eng. Sci. 94, 103–112 (2015)

    Article  MathSciNet  MATH  Google Scholar 

  • Danesh, M., Farajpour, A., Mohammadi, M.: Axial vibration analysis of a tapered nanorod based on nonlocal elasticity theory and differential quadrature method. Mech. Res. Commun. 39, 23–27 (2012)

    Article  MATH  Google Scholar 

  • Daneshmehr, A., Rajabpoor, A.: Stability of size dependent functionally graded nanoplate based on nonlocal elasticity and higher order plate theories and different boundary conditions. Int. J. Eng. Sci. 82, 84–100 (2014)

    Article  Google Scholar 

  • De Andrade, L.G.: Vortex filaments in MHD. Phys. Scr. 73(5), 484 (2006)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  • Dholakia, K., Zemánek, P.: Colloquium: gripped by light: Optical binding. Rev. Mod. Phys. 82, 1767–1791 (2010)

    Article  ADS  Google Scholar 

  • Farajpour, A., Farokhi, H., Ghayesh, M.H., Hussain, S.: Nonlinear mechanics of nanotubes conveying fluid. Int. J. Eng. Sci. 133, 132–143 (2018)

    Article  MathSciNet  MATH  Google Scholar 

  • Farajpour, A., Yazdi, M.H., Rastgoo, A., Loghmani, M., Mohammadi, M.: Nonlocal nonlinear plate model for large amplitude vibration of magneto-electro-elastic nanoplates. Compos. Struct. 140, 323–336 (2016)

    Article  Google Scholar 

  • Farokhi, H., Ghayesh, M.H.: Nonlinear size-dependent dynamics of microarches with modal interactions. J. Vib. Control 22, 3679–3689 (2016)

    Article  MathSciNet  Google Scholar 

  • Gilmore, R.: Length and curvature in the geometry of thermodynamics. Phys. Rev. A 30(4), 1994 (1984)

    Article  ADS  MathSciNet  Google Scholar 

  • Greene, J.M., Johnson, J.L.: Stability criterion for arbitrary hydromagnetic equilibria. Phys. Fluids 5(5), 510–517 (1962)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  • Guo, B., Ding, S.: Landau-Lifshitz Equations. World Scientific, UK (2008)

    Book  MATH  Google Scholar 

  • Gürbüz, N.: The differantial formula of Hasimoto transformation in Minkowski 3-space. Int. J. Math. Math. Sci. 2005, 542381 (2005)

    Article  Google Scholar 

  • Hasimoto, H.: A soliton on a vortex filament. J. Fluid Mech. 51(3), 477–485 (1972)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  • Inan, I.E., Inc, M., Rezazadeh, H., Akinyemi, L.: Optical solitons of (3+ 1) dimensional and coupled nonlinear Schrodinger equations. Opt. Quant. Electron. 54(4), 1–15 (2022)

    Article  Google Scholar 

  • Khater, M., Jhangeer, A., Rezazadeh, H., Akinyemi, L., Akbar, M.A., Inc, M., Ahmad, H.: New kinds of analytical solitary wave solutions for ionic currents on microtubules equation via two different techniques. Opt. Quant. Electron. 53(11), 1–27 (2021)

    Article  Google Scholar 

  • Khodadad, F.S., Mirhosseini-Alizamini, S.M., Günay, B., Akinyemi, L., Rezazadeh, H., Inc, M.: Abundant optical solitons to the Sasa-Satsuma higher-order nonlinear Schrödinger equation. Opt. Quant. Electron. 53(12), 1–17 (2021)

    Article  Google Scholar 

  • Körpınar, T.: Optical directional binormal magnetic flows with geometric phase: Heisenberg ferromagnetic model. Optik 219, 165134 (2020)

    Article  ADS  Google Scholar 

  • Körpınar, T., Demirkol, R.C., Asil, V., Körpınar, Z.: Magnetic flux surfaces by the fractional Heisenberg antiferromagnetic flow of magnetic b-lines in binormal direction in Minkowski space. J. Magn. Mag. Mater. 549, 168952 (2022)

    Article  Google Scholar 

  • Körpınar, T., Demirkol, R.C., Körpınar, Z.: Soliton propagation of electromagnetic field vectors of polarized light ray traveling along with coiled optical fiber on the unit 2-sphere \({\mathbb{S} } ^{2}\). Rev. Mex. Fis. 65(6), 626–633 (2019)

    Article  MATH  Google Scholar 

  • Körpınar, T., Demirkol, R.C., Körpınar, Z.: Soliton propagation of electromagnetic field vectors of polarized light ray traveling in a coiled optical fiber in Minkowski space with Bishop equations. Eur. Phys. J. D 73(9), 203 (2019)

    Article  ADS  MATH  Google Scholar 

  • Körpınar, T., Demirkol, R.C., Körpınar, Z.: Soliton propagation of electromagnetic field vectors of polarized light ray traveling in a coiled optical fiber in the ordinary space. Int. J. Geom. Methods Modern Phys. 16(8), 1950117 (2019)

    Article  MathSciNet  MATH  Google Scholar 

  • Körpınar, T., Demirkol, R.C., Körpınar, Z.: Optical magnetic helicity with binormal electromagnetic vortex filament flows in MHD. Optik 247, 167823 (2021)

    Article  ADS  Google Scholar 

  • Körpınar, T., Demirkol, R.C., Körpınar, Z.: Polarization of propagated light with optical solitons along the fiber in de-sitter space. Optik 226, 165872 (2021)

    Article  ADS  Google Scholar 

  • Körpınar, T., Demirkol, R.C., Körpınar, Z.: Approximate solutions for the inextensible Heisenberg antiferromagnetic flow and solitonic magnetic flux surfaces in the normal direction in Minkowski space. Optik 238, 166403 (2021)

    Article  ADS  Google Scholar 

  • Körpınar, T., Demirkol, R.C., Körpınar, Z.: Magnetic helicity and electromagnetic vortex filament flows under the influence of Lorentz force in MHD. Optik 242, 167302 (2021)

    Article  ADS  Google Scholar 

  • Körpınar, T., Demirkol, R.C., Körpınar, Z.: New analytical solutions for the inextensible Heisenberg ferromagnetic flow and solitonic magnetic flux surfaces in the binormal direction. Physica Scripta 96(8), 085219 (2021)

    Article  ADS  Google Scholar 

  • Körpınar, T., Demirkol, R.C., Körpınar, Z., Asil, V.: Maxwellian evolution equations along the uniform optical fiber in Minkowski space. Revista Mexicana de Física 66(4), 431–439 (2020)

    Article  Google Scholar 

  • Körpınar, T., Demirkol, R.C., Körpınar, Z., Asil, V.: Maxwellian evolution equations along the uniform optical fiber. Optik 217, 164561 (2020)

    Article  ADS  Google Scholar 

  • Körpınar, Z., Korpinar, T.: Optical spherical electroosmotic phase and optical energy for spherical \(\alpha\)-magnetic fibers. Optik 255, 168455 (2022)

    Article  ADS  Google Scholar 

  • Körpınar, Z., Korpinar, T.: Optical antiferromagnetic electric \({\mathbb{S} }\alpha\)-flux with electroosmotic velocity in Heisenberg \({\mathbb{S} }_{{\mathbb{H} }}^{2}\). Optik 252, 168206 (2022)

    Article  ADS  Google Scholar 

  • Körpınar, Z., Körpınar, T.: Optical hybrid electric and magnetic B\(_{1}\)-phase with Landau Lifshitz approach. Optik 247, 167917 (2021)

    Article  ADS  Google Scholar 

  • Körpınar, Z., Körpınar, T.: Optical tangent hybrid electromotives for tangent hybrid magnetic particle. Optik 247, 167823 (2021)

    Article  ADS  Google Scholar 

  • Körpınar, T., Körpınar, Z.: Optical spherical Ss-electric and magnetic phase with fractional q-HATM approach. Optik 243, 167274 (2021)

    Article  ADS  Google Scholar 

  • Körpınar, T., Körpınar, Z.: Timelike spherical magnetic \({\mathbb{S} }_{{\mathbf{N} }}\) flux flows with Heisenberg sphericalferromagnetic spin with some solutions. Optik 242, 166745 (2021)

    Article  ADS  Google Scholar 

  • Körpınar, T., Körpınar, Z.: Spherical electric and magnetic phase with Heisenberg spherical ferromagnetic spin by some fractional solutions. Optik 242, 167164 (2021)

    Article  ADS  Google Scholar 

  • Körpınar, T., Körpınar, Z.: New version of optical spherical electric and magnetic flow phase with some fractional solutions in \({\mathbb{S} }_{{\mathbb{H} }^{3}}^{2}\). Optik 243, 167378 (2021)

    Article  ADS  Google Scholar 

  • Körpınar, T., Körpınar, Z.: A new approach for fractional spherical magnetic flux flows with some fractional solutions. Optik 240, 166906 (2021)

    Article  ADS  Google Scholar 

  • Körpınar, T., Körpınar, Z.: Optical electromagnetic flux fibers with optical antiferromagnetic model. Optik 251, 168301 (2022)

    Article  ADS  Google Scholar 

  • Körpınar, T., Körpınar, Z., Asil, V.: New approach for optical electroostimistic phase with optical quasi potential energy. Optik 251, 168291 (2022)

    Article  ADS  Google Scholar 

  • Körpınar, T., Körpınar, Z., Asil, V.: Electric flux fibers with spherical antiferromagnetic approach with electroosmotic velocity. Optik 252, 168108 (2022)

    Article  ADS  Google Scholar 

  • Körpınar, T., Körpınar, Z., Demirkol, R.C.: Binormal schrodinger system of wave propagation field of light radiate in the normal direction with q-HATM approach. Optik 235, 166444 (2020)

    Article  ADS  Google Scholar 

  • Körpınar, T., Körpınar, Z., Yeneroğlu, M.: Optical energy of spherical velocity with optical magnetic density in Heisenberg sphere space \({\mathbb{S} }_{Heis^{3}}^{2}\). Optik 247, 167937 (2021)

    Article  ADS  Google Scholar 

  • Körpınar, T., Sazak, A., Körpınar, Z.: Optical effects of some motion equations on quasi-frame with compatible Hasimoto map. Optik 247, 167914 (2021)

    Article  ADS  Google Scholar 

  • Li, Y.Y., Qu, C.Z., Shu, S.C.: Integrable motions of curves in projective geometries. J. Geom. Phys. 6, 972–985 (2010)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  • Maruta, K., Park, J.K., Oh, K.C., Fujimori, T., Minaev, S.S., Fursenko, R.V.: Characteristics of microscale combustion in a narrow heated channel. Combus. Explos. Shock Waves 40(5), 516–23 (2004)

    Article  Google Scholar 

  • Marí Beffa, G., Sanders, J.A., Wang, J.P.: Integrable systems in three-dimensional Riemannian geometry. J. Nonlinear Sci. 12, 143–167 (2002)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  • Matta, L.M., Neumeier, Y., Lemon, B., Zinn, B.T.: Characteristics of microscale diffusion flames. Proc. Combust. Inst 29(1), 933–9 (2002)

    Article  Google Scholar 

  • Ohadi, M.M., Buckley, S.G.: High temperature heat exchangers and microscale combustion systems: applications to thermal system miniaturization. Experim. Thermal Fluid Sci. 25(5), 207–17 (2001)

    Article  Google Scholar 

  • Ricca, R.L.: Physical interpretation of certain invariants for vortex filament motion under LIA. Phys. Fluids A 4(5), 938–944 (1992)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  • Ricca, R.L.: Evolution and inflexional instability of twisted magnetic flux tubes. Sol. Phys. 172(1), 241–248 (1997)

    Article  ADS  Google Scholar 

  • Ricca, R.L.: Inflexional disequilibrium of magnetic flux-tubes. Fluid Dyn. Res. 36(4–6), 319 (2005)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  • Richecoeur, F., Kyritsis, D.C.: Experimental study of flame stabilization in low Reynolds and Dean number flows in curved mesoscale ducts. Proc. Combus. Inst. 30(2), 2419–27 (2005)

    Article  Google Scholar 

  • De Sabbata, V., Sivaram, C.: Spin and torsion in gravitation. World Scientific, UK (1994)

    Book  MATH  Google Scholar 

  • Schief, W.K., Rogers, C.: The Da Rios system under a geometric constraint: the Gilbarg problem. J. Geom. Phys. 54(3), 286–300 (2005)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  • Vieira, V.R., Horley, P.P.: The Frenet-Serret representation of the Landau-Lifshitz-Gilbert equation. J. Phys. A: Math. Theor. 45(6), 065208 (2012)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  • Wassmann, F., Ankiewicz, A.: Berry’s phase analysis of polarization rotation in helicoidal fibers. Applied optics 37(18), 3902–3911 (1998)

    Article  ADS  Google Scholar 

  • Wo, W.F., Qu, C.Z.: Integrable motions of curves in S1 R. J. Geom. Phys. 5(7), 1733–1755 (2007)

    Article  ADS  MATH  Google Scholar 

  • Zhou, T., Zhang, C., Han, C.B., Fan, F.R., Tang, W., Wang, Z.L.: Woven structured triboelectric nanogenerator for wearable devices. ACS Appl. Mater. Interfaces. 6, 14695–14701 (2014)

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, Muş Alparslan University, 49250, Muş, Turkey

    Talat Körpinar

  2. Department of Administration, Muş Alparslan University, 49250, Muş, Turkey

    Zeliha Körpinar

Authors
  1. Talat Körpinar
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Zeliha Körpinar
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Zeliha Körpinar.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Springer Nature or its licensor holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Körpinar, T., Körpinar, Z. Optical normalized microscale for optical total recursion electromagnetic flux on Heisenberg space \({\mathbb {S}}_{{\mathbb {H}}}^{2}\). Opt Quant Electron 54, 777 (2022). https://doi.org/10.1007/s11082-022-04058-z

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s11082-022-04058-z

Keywords

PACS

Search

Navigation