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Research Articles

Dynamics of particles in cold electrons plasma: fractional actionlike variational approach versus fractal spaces approach

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Pages 350-371 | Received 18 Aug 2020, Accepted 22 Mar 2021, Published online: 05 Apr 2021

References

  • Mandelbrot BB. The fractal geometry of nature. Vol. 1. San Francisco: WH Freeman; 1982.
  • Edgar G. Measure, topology, and fractal geometry. New York: Springer Science & Business Media; 2007.
  • Falconer K. Fractal geometry: mathematical foundations and applications. New York: John Wiley & Sons; 2004.
  • Dewey TG. Fractals in molecular biophysics. New York: Oxford University Press; 1998.
  • Pietronero L, Tosatti E. Fractals in physics. Boston: Elsevier; 2012.
  • Fernández-Martínez M, Sánchez-Granero M. Fractal dimension for fractal structures. Topology Appl. 2014;163:93–111.
  • Family F. Dynamics of fractal surfaces. Singapore: World Scientific; 1991.
  • Stillinger FH. Axiomatic basis for spaces with noninteger dimension. J Math Phys. 1977;18(6):1224–1234.
  • Balankin AS. A continuum framework for mechanics of fractal materials i: from fractional space to continuum with fractal metric. Eur Phys J B. 2015;88(4):1–13.
  • Zubair M, Mughal MJ, Naqvi QA. Electromagnetic fields and waves in fractional dimensional space. Berlin: Springer Science & Business Media; 2012.
  • Kigami J. Analysis on fractals. Cambridge: Cambridge University Press; 2001. 143.
  • Strichartz RS. Differential equations on fractals: a tutorial. Princeton: Princeton University Press; 2006.
  • Uchaikin VV. Fractional derivatives for physicists and engineers. Vol. 2, Berlin: Springer; 2013.
  • Kilbas AA, Srivastava HM, Trujillo JJ. Theory and applications of fractional differential equations. Vol. 204, Amsterdam: Elsevier; 2006.
  • Sandev T, Tomovski Ž. Fractional equations and models. Berlin: Springer; 2019.
  • Uchaikin VV, Sibatov RT. Fractional kinetics in space: anomalous transport models. Singapore: World Scientific; 2017.
  • Herrmann R. Fractional calculus: an introduction for physicists. Singapore: World Scientific; 2014.
  • Parvate A, Gangal AD. Calculus on fractal subsets of real line-I: formulation. Fractals. 2009;17(01):53–81.
  • Golmankhaneh AK, Balankin AS. Sub-and super-diffusion on cantor sets: beyond the paradox. Phys Lett A. 2018;382(14):960–967.
  • Golmankhaneh AK, Tunç C. Stochastic differential equations on fractal sets. Stochastics. 2020;92(8):1244–1260.
  • Golmankhaneh AK, Fernandez A. Random variables and stable distributions on fractal cantor sets. Fractal Fract. 2019;3(2):31.
  • Golmankhaneh AK, Cattani C. Fractal logistic equation. Fractal Fract. 2019;3(3):41.
  • Golmankhaneh AK, Tunç C, Nia SM, et al. A review on local and non-local fractal calculus. Num Com Meth Sci Eng. 2019;1:19–31.
  • Golmankhaneh AK. A review on application of the local fractal calculus. Num Com Meth Sci Eng. 2019;1:57–66.
  • Yang Y. Energy transfer and dissipation in plasma turbulence: from compressible mhd to collisionless plasma. Singapore: Springer; 2019.
  • Van Yen RN. Wavelet-based study of dissipation in plasma and fluid flows [dissertation]. Université Paris Sud-Paris XI; 2010.
  • Büchner J. Astrophysical reconnection and collisionless dissipation. Plasma Phys Control Fusion. 200749(12B):B325.
  • Du S, Zank GP, Li X, et al. Energy dissipation and entropy in collisionless plasma. Phys Rev E. 2020;101(3):033208.
  • Schekochihin AA, Cowley SC, Dorland W, et al. Astrophysical gyrokinetics: kinetic and fluid turbulent cascades in magnetized weakly collisional plasmas. Astrophys J Suppl Ser. 2009;182(1):310.
  • Meyrand R, Kanekar A, Dorland W, et al. Fluidization of collisionless plasma turbulence. Proc Natl Acad Sci. 2019;116(4):1185–1194.
  • Kanekar A, Schekochihin AA, Dorland W, et al. Fluctuation-dissipation relations for a plasma-kinetic langevin equation. J Plasma Phys. 2015;81(1).
  • El-Nabulsi RA. The fractional boltzmann transport equation. Comput Math. 2011;62(3):1568–1575.
  • Baumjohann W, Treumann R. Basic space plasma physics (revised edition). Singapore: World Scientific; 2012.
  • Chen FF. Introduction to plasma physics and controlled fusion. Vol. 1, New York: Springer; 1984.
  • Hauray M, Jabin PE. N-particles approximation of the vlasov equations with singular potential. Arch Ration Mech Anal. 2007;183(3):489–524.
  • Isliker H, Vlahos L, Constantinescu D. Fractional transport in strongly turbulent plasmas. Phys Rev Lett. 2017;119(4):045101.
  • Isliker H, Pisokas T, Vlahos L, et al. Particle acceleration and fractional transport in turbulent reconnection. Astrophys J. 2017;849(1):35.
  • Thamareerat N, Luadsong A, Aschariyaphotha N. Stability results of a fractional model for unsteady-state fluid flow problem. Adv Differ Equ. 2017;2017(1):1-–17.
  • Zubair M, Ang L. Fractional-dimensional child-langmuir law for a rough cathode. Phys Plasmas. 2016;23(7):072118.
  • Viana R, Da Silva E, Kroetz T, et al. Fractal structures in nonlinear plasma physics. Philos Trans R Soc A: Math Phys Eng Sci. 2011;369(1935):371–395.
  • Wit T, Krasnosel'Skikh V. Non-gaussian statistics in space plasma turbulence: fractal properties and pitfalls. Nonlinear Proc Geoph. 1996;3(4):262–273.
  • Mathias AC, Viana RL, Kroetz T, et al. Fractal structures in the chaotic motion of charged particles in a magnetized plasma under the influence of drift waves. Phys A. 2017;469:681–694.
  • Nocera L. Fractal mhd waves in the solar atmosphere. International astronomical union colloquium. Vol. 141. Cambridge: Cambridge University Press; 1993. p. 538–541
  • Domínguez M, Nigro G, Muñoz V, et al. Study of fractal features of magnetized plasma through an mhd shell model. Phys Plasmas. 2017;24(7):072308.
  • Chernyshov AA, Mogilevsky MM, Kozelov BV. Use of fractal approach to investigate ionospheric conductivity in the auroral zone. J Geophys Res Space Phys. 2013;118(7):4108–4118.
  • Mathias AC, Kroetz T, Caldas IL, et al. Chaotic magnetic field lines and fractal structures in a tokamak with magnetic limiter. Chaos, Solitons & Fractals. 2017;104:588–598.
  • Chai KB. Dynamics of nonspherical, fractal-like water-ice particles in a plasma environment. Sci Rep. 2018;8(1):1–7.
  • Budaev VP, Khimchenko LN. Fractal structure of films deposited in a tokamak. J Experiment Theoret Phys. 2007;104(4):629–643.
  • Rayneau-Kirkhope D, Mao Y, Farr R. Ultralight fractal structures from hollow tubes. Phys Rev Lett. 2012;109(20):204301.
  • Mathias A, Viana R, Kroetz T, et al. Fractal structures in the chaotic motion of charged particles in a magnetized plasma under the influence of drift waves. Phys A. 2017;469:681–694.
  • Torres DF, Malinowska AB. Introduction to the fractional calculus of variations. Singapore: World Scientific; 2012.
  • El-Nabulsi RA, Torres DF. Fractional actionlike variational problems. J Math Phys. 2008;49(5):053521.
  • El-Nabulsi RA. A fractional approach to non-conservative lagrangian dynamical systems. Fizika: A. 2005;14(4):289–298.
  • El-Nabulsi RA. A fractional action-like variational approach of some classical, quantum and geometrical dynamics. Int J Appl Math. 2005 ;17:299.
  • Novotnỳ T. Investigation of apparent violation of the second law of thermodynamics in quantum transport studies. Europhys Lett. 2002;59(5):648.
  • Wang GM, Sevick EM, Mittag E, et al. Experimental demonstration of violations of the second law of thermodynamics for small systems and short time scales. Phys Rev Lett. 2002;89(5):050601.
  • El-Nabulsi AR, Wu CG. Fractional complexified field theory from saxena–kumbhat fractional integral, fractional derivative of order (α, β) and dynamical fractional integral exponent. Afr Diaspora J Math. 2012;13(2):45–61.
  • El-Nabulsi RA. Fractional dirac operators and deformed field theory on clifford algebra. Chaos Solitons Fractals. 2009;42(5):2614–2622.
  • El-Nabulsi AR. Fractional action-like variational problems in holonomic, non-holonomic and semi-holonomic constrained and dissipative dynamical systems. Chaos Solitons Fractals. 2009;42(1):52–61.
  • Tasso H. Energy principle for dissipative two-fluid plasmas. Z Naturforsch A. 1978;33(3):257–260.
  • Caldas IL, Tasso H. Application of the two-fluid energy principle to large aspect ratio tokamaks. Plasma Phys. 1978;20(12):1299.
  • Miyamoto K. Plasma physics for nuclear fusion. Cambridge: The MIT Press; 1980.
  • Hutchinson IH. Electron velocity distribution instability in magnetized plasma wakes and artificial electron mass. J Geophys Res Space Phys. 2012117(A3)
  • Parra FI, Catto PJ. Transport of momentum in full f gyrokinetics. Phys Plasmas. 2010;17(5):056106.
  • Abraham-Shrauner B. Suppression of runaway of electrons in a lorentz plasma: I harmonically time varying electric field. J Plasma Phys. 1970;4(2):387–402.
  • Zhang W, Stone H. Oscillatory motions of circular disks and nearly spherical particles in viscous flows. J Fluid Mech. 1998;367:329–358.
  • Gourlay MR. Nonuniform alongshore currents and sediment transport: a one dimensional approach. 1982;
  • Bég OA, Sim L, Zueco J, et al. Numerical study of magnetohydrodynamic viscous plasma flow in rotating porous media with hall currents and inclined magnetic field influence. Commun Nonlinear Sci Numer Simul. 2010;15(2):345–359.
  • Roos Ov. Boltzmann-vlasov equation for a quantum plasma. Phys Rev. 1960;119(4):1174–1179.
  • Goldstein H, Poole C, Safko J. Classical mechanics. San Francisco: Addison Wesley; 2002.
  • Mendonça JT. Time refraction in expanding plasma bubbles. New J Phys. 2009;11(1):013029.
  • Qu K, Fisch NJ. Laser frequency upconversion in plasmas with finite ionization rates. Phys Plasmas. 2019;26(8):083105.
  • Woods BJ. Analytical solutions for nonlinear plasma waves with time-varying complex frequency. Plasma Res Express. 2019;1(4):045003.
  • Anderson MW, O'Neil T. Collisional damping of plasma waves on a pure electron plasma column. Phys Plasmas. 2007;14(11):112110.
  • Koutserimpas TT, Fleury R. Zero refractive index in time-floquet acoustic metamaterials. J Appl Phys. 2018;123(9):091709.
  • Sakai O, Sakaguchi T, Naito T, et al. Characteristics of metamaterials composed of microplasma arrays. Plasma Phys Control Fusion. 200749(12B):B453.
  • Lee DS, Sakai O, Tachibana K. Microplasma-induced deformation of an anomalous response spectrum of electromagnetic waves propagating along periodically perforated metal plates. Jpn J Appl Phys. 200948(6R):062004.
  • Litos M, Adli E, An W, et al. High-efficiency acceleration of an electron beam in a plasma wakefield accelerator. Nature. 2014;515(7525):92–95.
  • Chauhan VD P, Sajal V. Electron acceleration by surface plasma waves in the presence of static magnetic field. Laser Part Beams. 2015;33(1):109–115.
  • Verma P. Generation of low frequency plasma waves after the wave-breaking. Phys Lett A. 2017;381(48):4005–4010.
  • Gang Q, Jia-Fu W, Ming-Bao Y, et al. Lowering plasma frequency by enhancing the effective mass of electrons: A route to deep sub-wavelength metamaterials. Chin Phys B. 2013;22(8):087302.
  • Gurevich A. On the theory of runaway electrons. Sov Phys JETP. 1961;12(5):904–912.
  • Kovrizhnykh L. Velocity distribution of electrons in a strong electric field. Soviet Physics JETP. 1960;37(10
  • Welch K. A fractal topology of time: deepening into timelessness. Austin: Fox Finding Press; 2020.
  • Mohapatra KM, Panda B. Plasma dispersion in fractional-dimensional space. Modern Phys Lett B. 2014;28(20):1450161.
  • Mace R, Hellberg M. A dispersion function for plasmas containing superthermal particles. Phys Plasmas. 1995;2(6):2098–2109.
  • Abbasi H, Pajouh HH. Influence of trapped electrons on ion-acoustic solitons in plasmas with superthermal electrons. Phys Plasmas. 2007;14(1):012307.
  • Singhal A, Mohammad Sedighi H, Ebrahimi F, et al. Comparative study of the flexoelectricity effect with a highly/weakly interface in distinct piezoelectric materials (PZT-2, PZT-4, PZT-5H, LiNbO3, BaTiO3). Waves Random Complex Media. 2019;1–19. doi:10.1080/17455030.2019.1699676.
  • Saroj PK, Sahu SA, Singhal A, et al. On the transference of love-type waves in pre-stressed pzt-5h material stick on sio2 material with irregularity. Mater Res Express. 2019;6(12):125703.
  • Chaudhary S, Sahu SA, Singhal A. On secular equation of sh waves propagating in pre-stressed and rotating piezo-composite structure with imperfect interface. J Intel Mat Syst Str. 2018;29(10):2223–2235.
  • Ebrahimi F, Karimiasl M, Singhal A. Magneto-electro-elastic analysis of piezoelectric–flexoelectric nanobeams rested on silica aerogel foundation. Eng Comput. 2021;37:1007–1014.
  • Singhal A, Sahu SA, Chaudhary S, et al. Initial and couple stress influence on the surface waves transmission in material layers with imperfect interface. Mater Res Express. 2019;6(10):105713.
  • Singhal A, Sahu SA, Nirwal S, et al. Anatomy of flexoelectricity in micro plates with dielectrically highly/weakly and mechanically complaint interface. Mater Res Express. 2019;6(10):105714.
  • Chaudhary S, Sahu SA, Singhal A, et al. Interfacial imperfection study in pres-stressed rotating multiferroic cylindrical tube with wave vibration analytical approach. Mater Res Express. 2019;6(10):105704.
  • Nirwal S, Sahu SA, Singhal A, et al. Analysis of different boundary types on wave velocity in bedded piezo-structure with flexoelectric effect. Compos B Eng. 2019;167:434–447.
  • Sahu SA, Singhal A, Chaudhary S. Surface wave propagation in functionally graded piezoelectric material: an analytical solution. J Intel Mat Syst Str. 2018;29(3):423–437.
  • Singhal A, Sahu SA, Chaudhary S. Liouville–Green approximation: an analytical approach to study the elastic waves vibrations in composite structure of piezo material. Compos Struct. 2018;184:714–727.
  • Singhal A, Sahu SA. Transference of rayleigh waves in corrugated orthotropic layer over a pre-stressed orthotropic half-space with self weight. Procedia Eng. 2017;173:972–979.
  • Singhal A, Sahu SA, Chaudhary S. Approximation of surface wave frequency in piezo-composite structure. Compos B Eng. 2018;144:19–28.
  • Chaudhary S, Sahu SA, Dewangan N, et al. Stresses produced due to moving load in a prestressed piezoelectric substrate. Mech Adv Mater Struc. 2019;26(12):1028–1041.
  • Singh MK, Sahu SA, Singhal A, et al. Approximation of surface wave velocity in smart composite structure using wentzel–kramers–brillouin method. J Intel Mat Syst Str. 2018;29(18):3582–3597.
  • Ebrahimi F, Hosseini S, Singhal A. A comprehensive review on the modeling of smart piezoelectric nanostructures. Struct Eng Mech. 2020;74(5):611–633.
  • El-Nabulsi RA. Emergence of quasiperiodic quantum wave functions in hausdorff dimensional crystals and improved intrinsic carrier concentrations. J Phys Chem Solids. 2019;127:224–230.
  • El-Nabulsi RA. Path integral formulation of fractionally perturbed lagrangian oscillators on fractal. J Stat Phys. 2018;172(6):1617–1640.

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