Abstract
Plasma turbulence is ubiquitous in space and astrophysical flows. For example, the solar wind emitting from the sun into interplanetary space, one of the most studied natural plasmas, is in a turbulent state.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsReferences
Alexakis A, Bigot B, Politano H, Galtier S (2007) Anisotropic fluxes and nonlocal interactions in magnetohydrodynamic turbulence. Phys Rev E 76:056,313
Alexakis A, Mininni PD, Pouquet A (2005) Shell-to-shell energy transfer in magnetohydrodynamics. I. Steady state turbulence. Phys Rev E 72:046,301
Alexakis A, Mininni PD, Pouquet A (2007) Turbulent cascades, transfer, and scale interactions in magnetohydrodynamics. New J Phys 9:298
Alexandrova O, Lacombe C, Mangeney A, Grappin R, Maksimovic M (2012) Solar wind turbulent spectrum at plasma kinetic scales. Astrophys J 760(2):121
Alexandrova O, Saur J, Lacombe C, Mangeney A, Mitchell J, Schwartz SJ, Robert P (2009) University of solar wind turbulent spectrum from MHD to electron scales. Phys Rev Lett 103:165,003
Aluie H (2011) Compressible turbulence: the cascade and its locality. Phys Rev Lett 106:174,502
Aluie H, Eyink GL (2009) Localness of energy cascade in hydrodynamic turbulence. II. Sharp-spectral filter. Phys Fluids 21:115,108
Aluie H, Eyink GL (2010) Scale locality of magnetohydrodynamic turbulence. Phys Rev Lett 104:081,101
Anselmet F, Gagne Y, Hopfinger E, Antonia R (1984) High-order velocity structure functions in turbulent shear flows. J Fluid Mech 140:63–89
Axford W (1969) Acceleration of cosmic rays by shock waves. In: Invited Papers. Springer, pp 155–203
Balsara DS (2009) Divergence-free reconstruction of magnetic fields and WENO schemes for magnetohydrodynamics. J Comput Phys 228:5040–5056
Balsara DS, Kim J (2004) A comparison between divergence-cleaning and staggered-mesh formulations for numerical magnetohydrodynamics. Astrophys J 602:1079–1090
Balsara DS, Meyer C, Dumbser M, Du H, Xu Z (2013) Efficient implementation of ADER schemes for Euler and magnetohydrodynamical flows on structured meshes—speed comparisons with runge-kutta methods. J Comput Phys 235:934–969
Balsara DS, Rumpf T, Dumbser M, Munz CD (2009) Efficient, high accuracy ADER-WENO schemes for hydrodynamics and divergence-free magnetohydrodynamics. J Comput Phys 228:2480–2516
Balsara DS, Shu CW (2000) Monotonicity preserving weighted essentially non-oscillatory schemes with increasingly high order of accuracy. J Comput Phys 169:405–452
Balsara DS, Spicer DS (1999) A staggered mesh algorithm using high order Godunov fluxes to ensure solenoidal magnetic fields in magnetohydrodynamic simulations. J Comput Phys 149:270–292
Bandyopadhyay R, Chasapis A, Chhiber R, Parashar T, Maruca B, Matthaeus W, Schwartz S, Eriksson S, Le Contel O, Breuillard H et al (2018) Solar wind turbulence studies using mms fast plasma investigation data. Astrophys J 866(2):81
Bell A (1978) The acceleration of cosmic rays in shock fronts-i. Month Not Royal Astron Soc 182(2):147–156
Birdsall CK, Langdon AB (2004) Plasma physics via computer simulation. CRC Press
Biskamp D (2003) Magnetohydrodynamic turbulence. Cambridge University Press, Cambridge
Boldyrev S (2005) On the spectrum of magnetohydrodynamic turbulence. Astrophys J Lett 626(1):L37
Brackbill JU, Barnes DC (1980) The effect of nonzero \(\nabla \cdot \mathbf{B}\) on the numerical solution of the magnetohydrodynamic equations. J Comput Phys 35:426–430
Brio M, Wu CC (1988) An upwind differencing scheme for the equations of ideal magnetohydrodynamics. J Comput Phys 75:400–422
Carati D, Debliquy O, Knaepen B, Teaca B, Verma M (2006) Energy transfers in forced MHD turbulence. J Turbul 7:51
Chasapis A, Matthaeus W, Parashar T, Wan M, Haggerty C, Pollock C, Giles B, Paterson W, Dorelli J, Gershman D et al (2018) In situ observation of intermittent dissipation at kinetic scales in the earth’s magnetosheath. Astrophys J Lett 856(1):L19
Cho J (2010) Non-locality of hydrodynamic and magnetohydrodynamic turbulence. Astrophys J 725:1786–1791
Cho J, Vishniac ET (2000) The anisotropy of magnetohydrodynamic Alfvénic turbulence. Astrophys J 539:273–282
Christlieb AJ, Rossmanith JA, Tang Q (2014) Finite difference weighted essentially non-oscillatory schemes with constrained transport for ideal magnetohydrodynamics. J Comput Phys 268:302–325
Coburn JT, Forman MA, Smith CW, Vasquez BJ, Stawarz JE (2015) Third-moment descriptions of the interplanetary turbulent cascade, intermittency and back transfer. Phil Trans R Soc A 373:20140,150
Coleman PJ Jr (1968) Turbulence, viscosity, and dissipation in the solar-wind plasma. Astrophys J 153:371–388
Cook AW, Cabot WH (2004) A high-wavenumber viscosity for high-resolution numerical methods. J Comput Phys 195:594–601
Cook AW, Cabot WH (2005) Hyperviscosity for shock-turbulence interactions. J Comput Phys 203:379–385
Dai W, Woodward PR (1994) Extension of the piecewise parabolic method to multidimensional ideal magnetohydrodynamics. J Comput Phys 115:485–514
Dar G, Verma MK, Eswaran V (2001) Energy transfer in two-dimensional magnetohydrodynamic turbulence: formalism and numerical results. Phys D 157:207–225
Debliquy O, Verma MK, Carati D (2005) Energy fluxes and shell-to-shell transfers in three-dimensional decaying magnetohydrodynamics turbulence. Phys Plasmas 12:042,309
Dedner A, Kemm E, Kröner D, Munz CD, Schnitzer T, Wesenberg M (2002) Hyperbolic divergence cleaning for the MHD equations. J Comput Phys 175:645–673
Devore CR (1991) Flux-corrected transport techniques for multidimensional compressible magnetohydrodynamics. J Comput Phys 92:142–160
Dmitruk P, Matthaeus WH, Seenu N (2004) Test particle energization by current sheets and nonuniform fields in magnetohydrodynamic turbulence. Astrophys J 617:667–679
Domaradzki JA (1988) Analysis of energy transfer in direct numerical simulations of isotropic turbulence. Phys Fluids 31:2747
Domaradzki JA, Carati D (2007) An analysis of the energy transfer and the locality of nonlinear interactions in turbulence. Phys Fluids 19:085,112
Domaradzki JA, Carati D (2007) A comparison of spectral sharp and smooth filters in the analysis of nonlinear interactions and energy transfer in turbulence. Phys Fluids 19:085,111
Domaradzki JA, Rogallo RS (1990) Local energy transfer and nonlocal interactions in homogeneous, isotropic turbulence. Phys Fluids A 2:413
Domaradzki JA, Teaca B, Carati D (2010) Locality properties of the energy flux in magnetohydrodynamic turbulence. Phys Fluids 22:051,702
Drury LO (1983) An introduction to the theory of diffusive shock acceleration of energetic particles in tenuous plasmas. Reports Progress Phys 46(8):973
Ergun R, Goodrich K, Wilder F, Ahmadi N, Holmes J, Eriksson S, Stawarz J, Nakamura R, Genestreti K, Hesse M et al (2018) Magnetic reconnection, turbulence, and particle acceleration: Observations in the earth’s magnetotail. Geophys Res Lett 45(8):3338–3347
Evans CR, Hawley JF (1988) Simulation of magnetohydrodynamic flows: a constrained transport method. Astrophys J 332:659–677
Eyink GL (1994) Energy dissipation without viscosity in ideal hydrodynamics I. Fourier analysis and local energy transfer. Phys D 78:222–240
Eyink GL (2005) Locality of turbulent cascades. Phys D 207:91–116
Eyink GL, Aluie H (2009) Localness of energy cascade in hydrodynamic turbulence. I. Smooth coarse graining. Phys Fluids 21:115,107
Fisk LA, Gloeckler G (2012) Particle acceleration in the heliosphere: implications for astrophysics. Space Sci Rev 173:433–458
Frisch U (1995) Turbulence. The legacy of A. N, Kolmogorov
Frisch U, Sulem PL, Nelkin M (1978) A simple dynamical model of intermittent fully developed turbulence. J Fluid Mech 87(4):719–736
Fu H, Vaivads A, Khotyaintsev YV, André M, Cao J, Olshevsky V, Eastwood J, Retino A (2017) Intermittent energy dissipation by turbulent reconnection. Geophys Res Lett 44(1):37–43
Gaitonde DV (2001) Higher-order solution procedure for three-dimensional nonideal magnetogasdynamics. AIAA J 39:2111–2120
Gaitonde DV, Visbal MR (1998) High-order schemes for Navier-Stokes equations: algorithm and implementation into FDL3DI. Technical Report AFRL-VA-WP-TR-1998-3060, US Air Force Research Laboratory, Wright-Patterson AFB
Gary SP, Saito S (2003) Particle-in-cell simulations of alfvén-cyclotron wave scattering: proton velocity distributions. J Geophys Res 108:1194
Gary SP, Saito S, Li H (2008) Cascade of whistler turbulence: particle-in-cell simulations. Geophys Res Lett 35:L02,104
Giacalone J, Jokipii JR (2007) Magnetic field amplification by shocks in turbulent fluids. Astrophys J 663:L41–L44
Goldreich P, Sridhar S (1995) Toward a theory of interstellar turbulence. 2: Strong alfvenic turbulence. Astrophys J 438:763–775
Goldstein ML, Roberts DA, Matthaeus W (1995) Magnetohydrodynamic turbulence in the solar wind. Ann Rev Astron Astrophys 33(1):283–325
Grauer R, Krug J, Marliani C (1994) Scaling of high-order structure functions in magnetohydrodynamic turbulence. Phys Lett A 195(5–6):335–338
He J, Tu C, Marsch E, Chen CH, Wang L, Pei Z, Zhang L, Salem CS, Bale SD (2015) Proton heating in solar wind compressible turbulence with collisions between counter-propagating waves. Astrophys J Lett 813(2):L30
He J, Wang L, Tu C, Marsch E, Zong Q (2015) Evidence of landau and cyclotron resonance between protons and kinetic waves in solar wind turbulence. Astrophys J Lett 800(2):L31
He J, Zhu X, Chen Y, Salem C, Stevens M, Li H, Ruan W, Zhang L, Tu C (2018) Plasma heating and alfvénic turbulence enhancement during two steps of energy conversion in magnetic reconnection exhaust region of solar wind. Astrophys J 856(2):148
Hollweg JV (1986) Transition region, corona, and solar wind in coronal holes. J Geophys Res 91:4111–4125
Hollweg JV, Isenberg PA (2002) Generation of the fast solar wind: a review with emphasis on the resonant cyclotron interaction. J Geophys Res 107:1147
Horbury T, Balogh A (1997) Structure function measurements of the intermittent mhd turbulent cascade. Nonlinear Process Geophys 4(3):185–199
Howes G, Dorland W, Cowley S, Hammett G, Quataert E, Schekochihin A, Tatsuno T (2008) Kinetic simulations of magnetized turbulence in astrophysical plasmas. Phys Rev Lett 100(6):065,004
Howes GG, McCubbin AJ, Klein KG (2018) Spatially localized particle energization by landau damping in current sheets produced by strong alfvén wave collisions. J Plasma Phys 84(1)
Iroshnikov P (1964) Turbulence of a conducting fluid in a strong magnetic field. Sov Astron 7:566
Jeffrey A, Taniuti T (1964) Nonlinear wave propagation. ACADEMIC PR, New York
Jiang GS, Shu CW (1996) Efficient implementation of weighted ENO schemes. J Comput Phys 126:202–228
Jiang GS, Wu CC (1999) A high-order WENO finite difference scheme for the equations of ideal magnetohydrodynamics. J Comput Phys 150:561–594
Jokipii JR, Lee MA (2010) Compression acceleration in astrophysical plasmas and the production of \(f(v) \propto v^{-5}\) spectra in the heliosphere. Astrophys J 713:475–483
Kawai S (2013) Divergence-free-preserving high-order schemes for magnetohydrodynamics: an artificial magnetic resistivity method. J Comput Phys 251:292–318
Kim JW (2010) High-order compact filters with variable cut-off wavenumber and stable boundary treatment. Comput Fluids 39:1168–1182
Kishida K, Araki K, Kishiba S, Suzuki K (1999) Local or nonlocal? Orthonormal divergence-free wavelet analysis of nonlinear interactions in turbulence. Phys Rev Lett 83:5487
Kolmogorov AN (1941) Dissipation of energy in locally isotropic turbulence. Dokl Akad Nauk SSSR 32:16–18
Kolmogorov AN (1941) The local structure of turbulence in incompressible viscous fluid for very large reynolds numbers. Dokl Akad Nauk SSSR 30:299–303
Kolmogorov AN (1962) A refinement of previous hypotheses concerning the local structure of turbulence in a viscous incompressible fluid at high reynolds number. J Fluid Mech 13(1):82–85
Kraichnan RH (1965) Inertial-range spectrum of hydromagnetic turbulence. Phys Fluids 8(7):1385–1387
Kraichnan RH (1967) Inertial ranges in two-dimensional turbulence. Phys Fluids 10(7):1417–1423
Kraichnan RH (1971) Inertial-range transfer in two- and three-dimensional turbulence. J Fluid Mech 47(3):525–535
Larsson J, Cook A, Lele SK, Moin P, Cabot B, Sjögreen B, Yee H, Zhong X (2007) Computational issues and algorithm assessment for shock/turbulence interaction problems. J Phys Conf Ser 78:012,014
Lele SK (1992) Compact finite difference schemes with spectral-like resolution. J Comput Phys 103:16–42
MacBride BT, Smith CW (2008) The turbulent cascade at 1 AU: energy transfer and the third-order scaling for MHD. Astrophys J 679:1644–1660
Marino R, Sorrisovalvo L, Carbone V, Noullez A, Bruno R, Bavassano B (2008) Heating the solar wind by a magnetohydrodynamic turbulent energy cascade. Astrophys J 677(1):L71
Markovskii SA, Vasquez BJ, Smith CW, Hollweg JV (2006) Dissipation of th perpendicular turbulent cascade in the solar wind. Astrophys J 639:1177–1185
Matsumoto Y, Amano T, Kato TN, Hoshino M (2015) Stochastic electron acceleration during spontaneous turbulent reconnection in a strong shock wave. Science 347:974–978
Matthaeus WH, Goldstein ML (1982) Measurement of the rugged invariants of magnetohydrodynamic turbulence in the solar wind. J Geophys Res Space Phys 87(A8):6011–6028
Matthaeus WH, Zhou Y (1989) Extended inertial range phenomenology of magnetohydrodynamic turbulence. Phys Fluids B: Plasma Phys 1(9):1929–1931
Milano LJ, Matthaeus WH, Dmitruk P, Montgomery DC (2001) Local anisotropy in incompressible magnetohydrodynamic turbulence. Phys Plasmas 8:2673–2681
Monin AS, Yaglom AM (1975) Statistical fluid mechanics: machanics of turbulence, vol 2. MIT Press, Cambridge, MA
Montgomery D, Matthaeus WH (1995) Anisotropic modal energy transfer in interstellar turbulence. Astrophys J 447:706
Müller WC, Biskamp D (2000) Scaling properties of three-dimensional magnetohydrodynmaic turbulence. Phys Rev Lett 84:475
Müller WC, Grappin R (2005) Spectral energy dynamics in magnetohydrodynamic turbulence. Phys Rev Lett 95(11):114,502
Myong RS, Roe PL (1997) Shock waves and rarefaction waves in magnetohydrodynamics. Part 2. The MHD system. J Plasmas Phys 58:521–552
Obukhov A (1962) Some specific features of atmospheric tubulence. J Fluid Mech 13(1):77–81
Ohkitani K, Kida S (1992) Triad interactions in a forced turbulence. Phys Fluids A 4:794
Osman K, Kiyani K, Matthaeus W, Hnat B, Chapman S, Khotyaintsev YV (2015) Multi-spacecraft measurement of turbulence within a magnetic reconnection jet. Astrophys J Lett 815(2):L24
Parashar TN, Servidio S, Shay MA, Breech B, Matthaeus WH (2011) Effect of driving frequency on excitation of turbulence in a kinetic plasma. Phys Plasmas 18:092,302
Perri S, Goldstein ML, Dorelli JC, Sahraoui F (2012) Detection of small-scale structures in the dissipation regime of solar-wind turbulence. Phys Rev Lett 109:191,101
Pirozzoli S (2002) Conservative hybrid compact-WENO schemes for shock-turbulence interaction. J Comput Phys 178:81–117
Politano H, Pouquet A (1995) Model of intermittency in magnetohydrodynamic turbulence. Phys Rev E 52(1):636
Politano H, Pouquet A (1998) Dynamical length scales for turbulent magnetized flow. Geophys Res Lett 25:273–276
Politano H, Pouquet A (1998) Von Kármán-Howarth equation for magnetohydrodynamics and its consequences on third-order longitudinal structure and correlation functions. Phys Rev E 57:R21–R24
Powell K, Roe PL, Linde TJ, Gombosi TI, Zeeuw DLD (1999) A solution-adaptive upwind scheme for ideal magnetohydrodynamics. J Comput Phys 154:284–309
Powell K, Roe PL, Myong RS (1995) An upwind scheme for magnetohydrodynamics. AIAA Paper 95–1704
Ren YX, Liu M, Zhang H (2003) A characteristic-wise hybrid compact-WENO scheme for solving hyperbolic conservation laws. J Comput Phys 192:365–386
Retinò A, Sundkvist D, Vaivads A, Mozer F, André M, Owen CJ (2007) In situ evidence of magnetic reconnection in turbulent plasma. Nature Phys 3:235–238
Richardson JD, Paularena KI, Lazarus AJ, Belcher JW (1995) Radial evolution of the solar wind from imp 8 to voyager 2. Geophys Res Lett 22(4):325–328
Richardson LF (1922) Weather prediction by numerical process. Cambridge University Press, Cambridge
Sahraoui F, Goldstein ML, Belmont G, Canu P, Rezeau L (2010) Three dimensional anisotropic k spectra of turbulence at subproton scales in the solar wind. Phys Rev Lett 105(13):131,101
Sahraoui F, Goldstein ML, Robert P, Khotyaintsev YV (2009) Evidence of a cascade and dissipation of solar-wind turbulence at the electron gyroscale. Phys Rev Lett 102:231,102
Schekochihin AA, Cowley SC, Taylor SF, Maron JL, McWilliams JC (2004) Simulations of the small-scale turbulent dynamo. Astrophys J 612:276–307
Schilling O, Zhou Y (2002) Triadic energy transfers in non-helical magnetohydrodynamic turbulence. J Plasma Phys 68:389–406
She ZS, Lévêque E (1994) Universal scaling laws in fully developed turbulence. Phys Rev Lett 72:336
Shebalin JV, Matthaeus WH, Montgomery D (1983) Anisotropy in mhd turbulence due to a mean magnetic field. J Plasma Phys 29:525–547
Shen Y, Zha G, Huerta MA (2012) E-CUSP scheme for the equations of ideal magnetohydrodynamics with high order WENO scheme. J Comput Phys 231:6233–6247
Shu CW (2009) High order weighted essentially nonoscillatory schemes for convection dominated problems. SIAM Rev 51:82–126
Sjögreen B, Yee HC (2004) Multiresolution wavelet based adaptive numerical dissipation control for high order methods. J Sci Comput 20:211–255
Sorriso-Valvo L, Carbone V, Noullez A, Politano H, Pouquet A, Veltri P (2002) Analysis of cancellation in two-dimensional magnetohydrodynamic turbulence. Phys Plasmas 9:89–95
Sorriso-Valvo L, Marino R, Carbone V, Noullez A, Lepreti F, Veltri P, Bruno R, Bavassano B, Pietropaolo E (2007) Observation of inertial energy cascade in interplanetary space plasma. Phys Rev Lett 99:115,001
Stawarz JE, Smith CW, Vasquez BJ, Forman MA, MacBride BT (2009) The turbulent cascade and proton heating in the solar wind at 1 AU. Astrophys J 697:1119–1127
Sundkvist D, Retinò A, Vaivads A, Bale SD (2007) Dissipation in turbulent plasma due to reconnection in thin current sheets. Phys Rev Lett 99:025,004
Teaca B, Carati D, Domaradzki JA (2011) On the locality of magnetohydrodynamic turbulence scale fluxes. Phys Plasmas 18:112,307
TenBarge JM, Howes GG (2013) Current sheets and collisionless damping in kinetic plasma turbulence. Astrophys J Lett 771:L27
Tóth G (2000) The \(\nabla \cdot \mathbf{B}=0\) constraint in shock-capturing magnetohydrodynamics codes. J Comput Phys 161:605–652
Tu CY, Marsch E (1995) Mhd structures, waves and turbulence in the solar wind: observations and theories. Space Sci Rev 73:1–210
Verma MK (2004) Statistical theory of magnetohydrodynamic turbulence: recent results. Phys Rep 401:229–380
Verma MK, Ayyer A, Chandra AV (2005) Energy transfers and locality in magnetohydrodynamic turbulence. Phys Plasmas 12:082,307
Von Kármán T, Howarth L (1938) On the statistical theory of isotropic turbulence. Proc Roy Soc London Ser A 164:192
Wan M, Matthaeus WH, Karimabadi H, Roytershteyn V, Shay M, Wu P, Daughton W, Loring B, Chapman SC (2012) Intermittent dissipation at kinetic scales in collisionless plasma turbulence. Phys Rev Lett 109:195,001
Wan M, Matthaeus WH, Roytershteyn V, Karimabadi H, Parashar T, Wu P, Shay M (2015) Intermittent dissipation and heating in 3d kinetic plasma turbulence. Phys Rev Lett 114:175,002
Wang J, Shi Y, Wang LP, Xiao Z, He XT, Chen S (2012) Scaling and statistics in three-dimensional compressible turbulence. Phys Rev Lett 108:214,505
Wang J, Wang LP, Xiao Z, Shi Y, Chen S (2010) A hybrid numerical simulation of isotropic compressible turbulence. J Comput Phys 229:5257–5279
Wang J, Yang Y, Shi Y, Xiao Z, He XT, Chen S (2013) Cascade of kinetic energy in three-dimensional compressible turbulence. Phys Rev Lett 110:214,505
Warburton TC, Karniadakis GE (1999) A discontinuous Galerkin method for the viscous MHD equations. J Comput Phys 152:608–641
Whitham GB (2011) Linear and nonlinear waves, vol 42. John Wiley & Sons
Yaglom A (1949) On the local structure of a temperature field in a turbulent flow. Dokl Akad Nauk SSSR 69:743–746
Yao Z, Rae I, Guo R, Fazakerley A, Owen C, Nakamura R, Baumjohann W, Watt CE, Hwang K, Giles B et al (2017) A direct examination of the dynamics of dipolarization fronts using mms. J Geophys Res Space Phys 122(4):4335–4347
Yee HC, Sandham ND, Djomehri MJ (1999) Low-dissipative high-order shock-capturing methods using characteristic-based filters. J Comput Phys 150:199–238
Yee HC, Sjögreen B (2005) Efficient low dissipative high order schemes for multiscale MHD flows, II: minimization of \(\nabla \cdot \mathbf{B}\) numerical error. J Sci Comput 29:115–164
Yousef TA, Rincon F, Schekochihin AA (2007) Exact scaling laws and the local structure of isotropic magnetohydrodynamic turbulence. J Fluid Mech 575:111–120
Zhou Y (1993) Degrees of locality of energy transfer in the inertial range. Phys Fluids A 5:1092
Zhou Y (1993) Interacting scales and energy transfer in isotropic turbulence. Phys Fluids A 5:2511
Zhou Y, Matthaeus WH (1990) Models of inertial range spectra of interplanetary magnetohydrodynamic turbulence. J Geophys Res Space Phys 95(A9):14881–14892
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
Copyright information
© 2019 Springer Nature Singapore Pte Ltd.
About this chapter
Cite this chapter
Yang, Y. (2019). Introduction. In: Energy Transfer and Dissipation in Plasma Turbulence . Springer Theses. Springer, Singapore. https://doi.org/10.1007/978-981-13-8149-2_1
Download citation
DOI: https://doi.org/10.1007/978-981-13-8149-2_1
Published:
Publisher Name: Springer, Singapore
Print ISBN: 978-981-13-8148-5
Online ISBN: 978-981-13-8149-2
eBook Packages: Physics and AstronomyPhysics and Astronomy (R0)