Biquaternionic reformulation of multifluid plasma equations. (English) Zbl 1539.35258
Summary: Extending the biquaternionic generalization of the Maxwell type equations of compressible fluids, an effort has been introduced for the reformulation of analogous multifluid plasma equations. With the help of an exact correlation between the equations of classical electrodynamics and multifluid plasma model, suitable and elegant biquaternionic expressions including corresponding matrix representations have been presented. The proposed model in this paper generalizes Maxwell type equations of multifluid plasma in a simple, compact and consistent manner. Finally, using the advantages of biquaternions, the wave equation for plasma is reformulated similarly to the compressible fluids.
MSC:
| 35Q61 | Maxwell equations |
| 78A25 | Electromagnetic theory (general) |
| 47S05 | Quaternionic operator theory |
References:
| [1] | Logan, J. G., Phys. Fluids, 5, 868, (1962) |
| [2] | Troshkin, O. V., Comp. Maths. Math. Phys., 33, 1613, (1993) · Zbl 0821.76038 |
| [3] | Marmanis, H., Phys. Fluids, 10, 1428, (1998) · Zbl 1185.76666 |
| [4] | Kambe, T., Fluid Dyn. Res., 42, 055502, (2010) · Zbl 1291.76270 |
| [5] | Kambe, T., On fluid maxwell equations, Frontiers of Fundamental Physics and Physics Education Research, vol. 145, 287-295, (2014), Springer Proceedings in Physics |
| [6] | Scofield, D. F.; Huq, P., Fluid Dyn. Res., 46, 055513, (2014) |
| [7] | Scofield, D. F.; Huq, P., Fluid Dyn. Res., 46, 055514, (2014) |
| [8] | Abreu, E. M.C.; Neto, J. A.; Mendes, A. C.R.; Sasaki, N., Phys. Rev. D, 91, 125011, (2015) |
| [9] | Thompson, R. J.; Moeller, T. M., Phys. Plasmas, 19, 010702, (2012) |
| [10] | Thompson, R. J.; Moeller, T. M., Phys. Plasmas, 19, 082116, (2012) |
| [11] | Hamilton, W. R., Elements of Quaternions, (1899), Chelsea · JFM 30.0093.03 |
| [12] | Imaeda, K., Nuovo Cimento B, 32, 138, (1976) |
| [13] | Colombo, F.; Loustaunau, P.; Sabadini, I.; Struppa, D. C., J. Geom. Phys., 26, 183, (1998) · Zbl 0973.83007 |
| [14] | Lambek, J., Math. Intelligencer, 17, 7, (1995) · Zbl 0836.01011 |
| [15] | Ward, J. P., Quaternions and Cayley Numbers, (1996), Kluwer |
| [16] | Kassandrov, V. V., Grav. Cosm., 3, 216, (1995) · Zbl 0957.83527 |
| [17] | Majernik, V., Adv. Appl. Clifford Alg., 9, 119, (1999) · Zbl 0943.35092 |
| [18] | Gsponer, A.; Hurni, J. P., Found. Phys. Lett., 14, 77, (2001) |
| [19] | Kravchenko, V. V., Z.f. Anal.u. ihre Anwend., 21, 21, (2002) · Zbl 0999.30033 |
| [20] | Vlaenderen, K. J.V.; Waser, A., Hadronic J., 27, 673, (2004) · Zbl 1062.81554 |
| [21] | Grudsky, S. M.; Khmelnytskaya, K. V.; Kravchenko, V. V., J. Phys. A, 37, 4641, (2004) · Zbl 1047.78003 |
| [22] | Tanışlı, M., Europhys. Lett., 74, 569, (2006) |
| [23] | Arbab, A. I., Prog. Phys., 2, 14, (2009) |
| [24] | Demir, S.; Özdaş, K., Acta Phys. Slovaca, 53, 429, (2003) |
| [25] | Demir, S.; Tanışlı, M.; Candemir, N., Adv. Appl. Clifford Alg., 20, 547, (2010) · Zbl 1203.78005 |
| [26] | Cafaro, C.; Ali, S. A., Adv. Appl. Clifford Alg., 17, 23, (2007) · Zbl 1113.78003 |
| [27] | Cafaro, C., Adv. Appl. Clifford Alg., 17, 617, (2007) · Zbl 1156.78002 |
| [28] | Dressel, J.; Bliokh, K. Y.; Nori, F., Phys. Rep., 589, 1, (2015) · Zbl 1357.15016 |
| [29] | Negi, O. P.S.; Bisht, S.; Bisht, P. S., Nuovo Cimento B, 113, 1449, (1998) |
| [30] | Bisht, P. S.; Negi, O. P.S., Int. J. Theor. Phys., 47, 3108, (2008) · Zbl 1173.78001 |
| [31] | Singh, J.; Bisht, P. S.; Negi, O. P.S., J. Phys. A, 40, 9137, (2007) · Zbl 1143.78003 |
| [32] | Bisht, P. S.; Singh, J.; Negi, O. P.S., J. Phys. A, 40, 11395, (2007) · Zbl 1128.78001 |
| [33] | Yefremov, A.; Smarandache, F.; Christianto, V., Prog. Phys., 3, 42, (2007) |
| [34] | Christianto, V.; Smarandache, F., Prog. Phys., 1, 40, (2008) |
| [35] | Christianto, V.; Smarandache, F.; Lichtenberg, F., Prog. Phys., 1, 40, (2009) |
| [36] | Singh, A., Lett. Nuovo Cimento, 32, 5, (1981) |
| [37] | Majernik, V., Astrophys. Space. Sci., 84, 191, (1982) · Zbl 0501.70002 |
| [38] | Demir, S.; Tanışlı, M., Eur. Phys. J. Plus, 126, 51, (2011) |
| [39] | Chanyal, B. C.; Bisht, P. S.; Negi, O. P.S., Int. J. Theor. Phys., 49, 1333, (2010) · Zbl 1194.81312 |
| [40] | Chanyal, B. C.; Bisht, P. S.; Negi, O. P.S., Int. J. Theor. Phys., 50, 1919, (2011) · Zbl 1225.81147 |
| [41] | Kansu, M. E.; Tanışlı, M.; Demir, S., Eur. Phys. J. Plus, 127, 69, (2012) |
| [42] | Demir, S., Int. J. Theor. Phys., 52, 105, (2013) · Zbl 1263.83059 |
| [43] | Demir, S.; Tanışlı, M.; Kansu, M. E., Int. J. Theor. Phys., 52, 3696, (2013) · Zbl 1274.81272 |
| [44] | Tanışlı, M.; Kansu, M. E.; Demir, S., Gen. Relativ. Gravit., 46, 1739, (2014) · Zbl 1291.83021 |
| [45] | Kansu, M. E.; Tanışlı, M.; Demir, S., Turk. J. Phys., 38, 155, (2014) |
| [46] | Chanyal, B. C.; Sharma, V. K.; Negi, O. P.S., Int. J. Theor. Phys., 54, 3516, (2015) · Zbl 1327.83266 |
| [47] | Chanyal, B. C., Rep. Math. Phys., 76, 1, (2015) · Zbl 1326.83063 |
| [48] | Chanyal, B. C., J. Math. Phys., 56, 051702, (2015) · Zbl 1317.83018 |
| [49] | Chanyal, B. C., Chin. J. Phys., 55, 432, (2017) · Zbl 1539.35262 |
| [50] | Rajput, B. S., J. Math. Phys., 25, 351, (1984) |
| [51] | Bisht, P. S.; Negi, O. P.S.; Rajput, B. S., Ind. J. Pure Appl. Phys., 24, 543, (1993) |
| [52] | Bisht, P. S.; Negi, O. P.S.; Rajput, B. S., Int. J. Theor. Phys., 32, 2099, (1993) |
| [53] | Dangwal, S.; Bisht, P. S.; Negi, O. P.S., Russ. Phys. J., 49, 1274, (2006) · Zbl 1258.81049 |
| [54] | Bisht, P. S.; Karnatak, G.; Negi, O. P.S., Int. J. Theor. Phys., 49, 1344, (2010) · Zbl 1194.81311 |
| [55] | Rawat, A. S.; Negi, O. P.S., Int. J. Theor. Phys., 51, 738, (2012) · Zbl 1241.83011 |
| [56] | Demir, S.; Tanışlı, M., Eur. Phys. J. Plus, 126, 115, (2011) |
| [57] | Kansu, M. E.; Tanışlı, M.; Demir, S., Turk J. Phys., 38, 155, (2014) |
| [58] | Weng, Z. H., Adv. Math. Phys., 2014, 450262, (2014) · Zbl 1307.78003 |
| [59] | Tanışlı, M.; Demir, S.; Şahin, N., J. Math. Phys., 56, 091701, (2015) · Zbl 1327.76119 |
| [60] | Demir, S.; Tanışlı, M., J. Korean Phys. Soc., 68, 616, (2016) |
| [61] | Demir, S.; Tanışlı, M., Int. J. Geom. Meth. Mod. Phys., 14, 1750075, (2017) · Zbl 1431.83028 |
| [62] | Demir, S.; Uymaz, A.; Tanışlı, M., Chin. J. Phys., 55, 115, (2017) · Zbl 1539.76185 |
| [63] | Chou, J. C.K., IEEE Trans. Robot. Autom., 8, 53, (1992) |
| [64] | Demir, S.; Tanışlı, M., Phys. Scr., 75, 630, (2007) · Zbl 1196.70012 |
| [65] | Wehage, R. A., Quaternions and euler parameters-a brief exposition, Computer Aided Analysis and Optimization of Mechanical System Dynamics, 147-180, (1984), Spring-Verlag · Zbl 0557.70005 |
| [66] | Maxwell, J. C., A Treatise on Electricity and Magnetism, (1873), Clarendon Press · JFM 05.0556.01 |
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