Abstract
The paper focuses on applying the algebra of octonions to explore the influence of electric-charge gradients on the electric-current derivatives, revealing some of major influence factors of high pulse electric-currents. J. C. Maxwell was the first scholar to utilize the algebra of quaternions to study the physical properties of electromagnetic fields. The contemporary scholars employ simultaneously the quaternions and octonions to investigate the physical properties of electromagnetic fields, including the octonion field strength, field source, linear momentum, angular momentum, torque, and force and so forth. When the octonion force is equal to zero, it is able to achieve eight equations independent of each other, including the fluid continuity equation, current continuity equation, force equilibrium equation, and second-force equilibrium equation and so on. One of inferences derived from the second-force equilibrium equation is that the charge gradient and current derivative are interrelated closely, two of them must satisfy the need of the second-force equilibrium equation synchronously. Meanwhile the electromagnetic strength and linear momentum both may exert an influence on the current derivative to a certain extent. The above states that the charge gradient and current derivative are two correlative physical quantities, they must meet the requirement of second-force equilibrium equation. By means of controlling the charge gradients and other physical quantities, it is capable of restricting the development process of current derivatives, reducing the damage caused by the instantaneous impact of high pulse electric-currents, enhancing the anti-interference ability of electronic equipments to resist the high pulse electric-currents and their current derivatives. Further the second-force equilibrium equation is able to explain two types of superconducting currents.
Similar content being viewed by others
References
J. Lekner, Chiral content of electromagnetic pulses. J. Opt. 20(10), 105605 (2018)
J.-X. Fang, J.-H. Mo, F.-M. Bai, H.-T. Wang, Experimental investigations of the electromagnetic pulse-assisted incremental drawing of aluminum alloy. Int. J. Adv. Manuf. Technol. 103(5–8), 2991–3001 (2019)
J. Borhanian, S. Sobhanian, I. Kourakis, R. Esfandyari, Evolution of linearly polarized electromagnetic pulses in laser plasmas. Phys. Plasmas 15(9), 093108 (2008)
J. Wu, Y.-H. Lu, F.-J. Sun, X.-W. Li, X.-F. Jiang, Z.-G. Wang, D.-Y. Zhang, A.-C. Qiu, S. Lebedev, Preconditioned wire array Z-pinches driven by a double pulse current generator. Plasma Phys. Control. Fusion 60(7), 075014 (2018)
B.-Y. Zhang, S. Inagaki, K. Hasamada, K. Yamasaki, F. Kin, Y. Nagashima, T. Yamada, A. Fujisawa, Study of turbulence intermittency in linear magnetized plasma. Plasma Phys. Control. Fusion 61(11), 115010 (2019)
W.-Q. Zhao, L.-Z. Wang, Z.-S. Yu, J.-S. Chen, J. Yang, A processing technology of grooves by picosecond ultrashort pulse laser in Ni alloy: enhancing efficiency and quality. Opt. Laser Technol. 111(4), 214–221 (2019)
M.F. Garcia, C. Gallrapp, M. Moll, D. Muenstermann, Radiation hardness studies of neutron irradiated CMOS sensors fabricated in the ams H18 high voltage process. J. Instrum. 11(2), P02016 (2016)
N.R.N. Idris, A.H. Yatim, Direct torque control of induction machines with constant switching frequency and reduced torque ripple. IEEE Trans. Ind. Electron. 51(4), 758–767 (2004)
O. Mokin, The synthesis of optimum current obtained by mathematical models for an electrically propelled truck drive electromotor. Prz. Elektrotech. 1(3), 75–80 (2017)
X.-W. Yang, H.-T. Hu, Y.-B. Ge, S. Aatif, Z.-Y. He, S.-B. Gao, An improved droop control strategy for VSC-based MVDC traction power supply system. IEEE Trans. Ind. Appl. 54(5), 5173–5186 (2018)
S. Ouni, M.R. Zolghadri, J. Rodriguez, M. Shahbazi, H. Oraee, P. Lezana, A.U. Schmeisser, Quick diagnosis of short circuit faults in cascaded H-bridge multilevel inverters using FPGA. J. Power Electron. 17(1), 56–66 (2017)
W.-Y. Chen, E. Rosenbaum, M.-D. Ker, Diode-triggered silicon-controlled rectifier with reduced voltage overshoot for CDM ESD protection. IEEE Trans. Device Mater. Reliab. 12(1), 10–14 (2012)
P. Bansal, A. Srivastava, A. Zaya, B. Sharma, A. Upadhyay, Design and fabrication of automatic speed controller for automobile. Int. J. Trend Sci. Res. Dev. 3(4), 524–527 (2019)
Q.-C. Zhang, Analysis and design of PLL motor speed control system. Telkomnika 11(10), 5662–5668 (2013)
E. Torres, A.J. Mazon, E. Fernandez, I. Zamora, J.C. Prez, Thermal performance of back-up current-limiting fuses. Electr. Power Syst. Res. 80(12), 1469–1476 (2010)
Y.V. Siniavskii, A.S. Fedylov, M.I. Dli, V.V. Borisov, Vacuum evaporator with the electrochemical generator on oxyhydrogen cell. Int. J. Hydrog. Energy 42(21), 14649–14655 (2017)
K. Gorecki, P. Gorecki, J. Zarebski, Measurements of parameters of the thermal model of the IGBT module. IEEE Trans. Instrum. Meas. 68(12), 1–22 (2019)
Y.-Z. Lu, A. Christou, Prognostics of IGBT modules based on the approach of particle filtering. Microelectron. Reliab. 92(1), 96–105 (2019)
V.L. Mironov, S.V. Mironov, Octonic representation of electromagnetic field equations. J. Math. Phys. 50(01), 012901 (2009)
S. De Leo, G. Ducati, The octonionic eigenvalue problem. J. Phys. A 45(31), 315203 (2012)
M. Gogberashvili, Octonionic version of Dirac equations. Int. J. Mod. Phys. A 21(17), 3513–3523 (2006)
B.A. Bernevig, J.-Q. Hu, N. Toumbas, S.-C. Zhang, Eight dimensional quantum Hall effect and octonions. Phys. Rev. Lett. 91(23), 236803 (2003)
S. De Leo, K. Abdel-Khalek, Octonionic quantum mechanics and complex geometry. Prog. Theor. Phys. 96(04), 823–831 (1996)
S. De Leo, K. Abdel-Khalek, Octonionic Dirac equation, progress theoretical. Physics 96(04), 833–845 (1996)
S. De Leo, K. Abdel-Khalek, Octonionic representations of GL(8, R) and GL(4, C). J. Math. Phys. 38(02), 582–598 (1997)
G. Bossard, Octonionic black holes. J. High Energy Phys. 2012(05), 113 (2012)
S. Furui, The flavor symmetry in the standard model and the triality symmetry. Int. J. Mod. Phys. A 27(27), 1250158 (2012)
S. Majid, Gauge theory on nonassociative spaces. J. Math. Phys. 46(10), 103519 (2005)
J.M. Figueroa-O’Farrill, Gauge theory and the division algebras. J. Geom. Phys. 32(02), 227–240 (1999)
B.C. Chanyal, P.S. Bisht, T.-J. Li, O.P.S. Negi, Octonion quantum chromodynamics. Int. J. Theor. Phys. 51(11), 3410–3422 (2012)
C. Furey, Generations: three prints, in colour. J. High Energy Phys. 2014(10), 046 (2014)
S. Demir, M. Tanisli, Spacetime algebra for the reformulation of fluid field equations. Int. J. Geom. Methods Mod. Phys. 14(05), 1750075 (2017)
B.C. Chanyal, P.S. Bisht, O.P.S. Negi, Generalized octonion electrodynamics. J. Math. Phys. 49(06), 1333–1343 (2010)
S. Demir, M. Tanisli, E. Kansu, Generalized hyperbolic octonion formulation for the fields of massive dyons and gravito-dyons. Int. J. Theor. Phys. 52(10), 3696 (2013)
V.L. Mironov, S.V. Mironov, Octonic first-order equations of relativistic quantum mechanics. Int. J. Mod. Phys. A 24(22), 4157–4167 (2009)
J.C. Baez, The octonions. Bull. Am. Math. Soc. 39(02), 145–205 (2001)
Z.-H. Weng, Some properties of dark matter field in the complex octonion space. Int. J. Mod. Phys. A 30(35), 1550212 (2015)
Z.-H. Weng, Forces in the complex octonion curved space. Int. J. Geom. Methods Mod. Phys. 13(6), 1650076 (2016)
Y. Cao, V. Fatemi, S.-A. Fang, K. Watanabe, T. Taniguchi, E. Kaxiras, P. Jarillo-Herrero, Unconventional superconductivity in magic-angle graphene superlattices. Nature 556(7699), 43–50 (2018)
Y. Cao, V. Fatemi, A. Demir, S.-A. Fang, S.L. Tomarken, J.Y. Luo, J.D. Sanchez-Yamagishi, K. Watanabe, T. Taniguchi, E. Kaxiras, R.C. Ashoori, P. Jarillo-Herrero, Correlated insulator behaviour at half-filling in magic-angle graphene superlattices. Nature 556(7699), 80–84 (2018)
R.-Y. Han, J.-W. Wu, W.-D. Ding, Y. Jing, H.-B. Zhou, Q.-J. Liu, A.-C. Qiu, Hybrid PCB rogowski coil for measurement of nanosecond-risetime pulsed current. IEEE Trans. Plasma Sci. 43(10), 3555–3561 (2015)
Q.-Q. Sun, D.-H. Wang, Y.-N. Li, J.-H. Zhang, S.-J. Ye, J.-X. Cui, L.-Q. Chen, Z.-K. Wang, H.-J. Butt, D. Vollmer, X. Deng, Surface charge printing for programmed droplet transport. Nat. Mater. 18(9), 936–941 (2019)
Acknowledgements
The author is indebted to the anonymous referees for their valuable comments on the previous manuscripts. This project was supported partially by the National Natural Science Foundation of China under Grant Number 60677039.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Weng, ZH. Superconducting currents and charge gradients in the octonion spaces. Eur. Phys. J. Plus 135, 443 (2020). https://doi.org/10.1140/epjp/s13360-020-00477-7
Received:
Accepted:
Published:
DOI: https://doi.org/10.1140/epjp/s13360-020-00477-7