Publications
N. W. Watkins (2024). Brownian motion as a mathematical superstructure to organise the science of climate and weather. In Foundational Papers in Complexity ScienceLink opens in a new window. Edited by David C. Krakauer. Volume 4. Santa Fe, NM: SFI Press. In press.
N. W. Watkins, R. Calel, S. C. Chapman, A. Chechkin, R. Klages and D. Stainforth, (2024).
The Challenge of Non-Markovian Energy Balance Models in Climate. Chaos. 34, 072105, DOI:10.1063/5.0187815
O. Allanson, D. Ma, A. Osmane, J. M. Albert, J. Bortnik, C. E.J. Watt, S. C. Chapman, J. Spencer, D. J. Ratliff, N. P. Meredith, T. Elsden, T. Neukirch, D. P. Hartley, R. Black, N. W. Watkins, and S. Elvidge (2024). The challenge to understand the zoo of particle transport regimes during resonant wave-particle interactions for given
survey-mode wave spectra. Frontiers in Astronomy and Space Science. 11. DOI: 10.3389/fspas.2024.1332931
A. Bergin, S. C. Chapman, N. W. Watkins, N. R. Moloney, J. W. Gjerloev (2023) Extreme event statistics in Dst, SYM-H and SMR geomagnetic indices, Space Weather, DOI: 10.1029/2022SW003304
A. Bergin, S. C. Chapman, N. Moloney, N. W. Watkins, Variation of geomagnetic index empirical distribution and burst statistics across successive solar cycles, J. Geophys. Res, doi:10.1029/2021JA029986 (2022)
S. C. Chapman, S. W. McIntosh, R. J. Leamon, N. W. Watkins, The Sun's magnetic (Hale) cycle and 27 day recurrences in the aa geomagnetic index. Ap. J. (2021) doi: 10.3847/1538-4357/ac069e
B. Hnat, S. C. Chapman, N. W. Watkins, Magnetic topology of actively evolving and passively convecting structures in the turbulent solar wind, Phys. Rev. Lett., 126, 125101 (2021) https://doi.org/10.1103/PhysRevLett.126.125101
N. W. Watkins, R. Klages, D. Stainforth, I. Ford, S. C. Chapman and A. Chechkin (2021). Generalized Langevin dynamics and the modeling of global mean temperature. pp. 433-441 in D. Braha et al. (eds.), Unifying Themes in Complex Systems X, Springer Proceedings in ComplexityLink opens in a new window
C. L. E. Franzke, S. Barbosa, R. Blender, Hege-Beate Fredriksen, T. Laepple, F. Lambert, T. Nilsen,
K. Rypdal, M. Rypdal, M. G. Scotto, S. Vannitsem, N. W. Watkins, L. Yang and N. Yuan (2020). The structure of climate variability across scales. Reviews of Geophysics. 58(2), e2019RG000657. DOI: 10.1029/2019RG000657
McIntosh, S.W., Chapman, S. C, Leamon, R.J. et al. Overlapping Magnetic Activity Cycles and the Sunspot Number: Forecasting Sunspot Cycle 25 Amplitude. Sol Phys 295, 163 (2020). https://doi.org/10.1007/s11207-020-01723-y
R. Calel, S. C. Chapman, D. A. Stainforth, N. W. Watkins Temperature variability implies greater economic damages from climate change, Nature Communications, 11, 5028 (2020). doi:10.1038/s41467-020-18797-8 the article is here
S. C. Chapman, S. W. McIntosh, R. J. Leamon, N. W. Watkins, Quantifying the solar cycle modulation of extreme space weather, Geophysical Research Letters, (2020) doi:10.1029/2020GL087795 the article is here
S. C. Chapman, E. J. Murphy, D. A. Stainforth, N. W. Watkins, Trends in Winter Warm Spells in the Central England Temperature Record, JAMC (2020) doi:10.1175/JAMC-D-19-0267.1 the article is here
R. J. Leamon, S. W. McIntosh, S. C. Chapman, N. W. Watkins, Timing Terminators: Forecasting Sunspot Cycle 25 Onset, Solar Phys. in 295:36 doi: 10.1007/s11207-020-1595-3 (2020)
S. C. Chapman, R. Horne, N. W. Watkins, Using the aa index over the last 14 solar cycles to characterize extreme geomagnetic activity. Geophys. Res. Lett.(2020) doi: 10.1029/2019GL086524 the article is here
S. C. Chapman, N. W. Watkins, D. A. Stainforth, Warming trends in summer heatwaves, GRL https://doi.org/10.1029/2018GL081004(2019) In top 10% of downloaded 2018-2019
N. W. Watkins (2019). Mandelbrot's stochastic time series models. Earth and Space Science. 6(11), 2044-2056. DOI:10.1029/2019EA000598. Invited for special issue on "Nonlinear Systems in Geophysics: Past Accomplishments and Future Challenges".
V. V. Palyulin, G. Blackburn, M. A. Lomholt, N. W. Watkins, R. Metzler, R. Klages, A. V. Chechkin (2019), First-passage and first-hitting times of Levy flights and Levy walks. New Journal of Physics. 21(10), 103028. DOI:10.1088/1367-2630/ab41bb
S.C. Chapman, P.T. Lang, R.O. Dendy, N.W. Watkins, M. Dunne, L. Giannone, ASDEX Upgrade Team and EUROfusion MST1 Team, Intrinsic ELMing in ASDEX Upgrade and global control system-plasma self-entrainment, Nucl. Fusion, 58 126003 (2018) the article is here
E. Tindale, S. C. Chapman, N. R. Moloney, and N.W. Watkins, The dependence of solar wind burst size on burst duration and its invariance across solar cycles 23 and 24, JGR, (2018) DOI: 10.1029/2018JA025740
S. C. Chapman, N. W. Watkins, E. Tindale, Reproducible aspects of the climate of space weather over the last five solar cycles, Space Weather, DOI:10.1029/2018SW001884 (2018) In top 10% of downloaded 2018-2019
S. C. Chapman, P. T. Lang, R. O. Dendy, L. Giannone, N. W. Watkins, ASDEX Upgrade Team, Control system-plasma synchronization and naturally occurring edge localized modes in a tokamak, Phys. Plasmas, 25, 062511 (2018) https://doi.org/10.1063/1.5025333 the article appeared here
E. Shepherd, E. Boyd, R. A. Calel, S. C. Chapman, S. Dessai, I. M. Dima-West, H. J. Fowler, R. James, D. Maraun, O. Martius, C. A. Senior, A. H. Sobel, D. A. Stainforth, S. F. B. Tett, K. E. Trenberth, B. J. J. M. van den Hurk, N. W. Watkins, R. L. Wilby, D. Zenghelis (2018). Storylines as an alternative approach for the construction and communication of climate information. Climatic Change. 151(3--4), 555--571. DOI:10.1007/s10584-018-2317-9
N. W. Watkins (2018), Aphantasia and severely deficient autobiographical memory: Scientific and personal perspectives. Cortex. 105, 41--52. DOI:10.1016/j.cortex.2017.10.010. Invited paper based on my talk at the AHRC-sponsored ``Eye’s Mind" conference at UEA.
S. C. Chapman, P. T. Lang, R. O. Dendy, L. Giannone, N. W. Watkins, ASDEX Upgrade Team, Eurofusion MST team, Global control system and synchronous natural ELMing in the ASDEX Upgrade tokamak, Proceedings, 44th EPS Conference on Plasma Physics, Vol. 41F ISBN: 979-10-96389-07, (2017), the article appeared here
J. Pratt, A. Busse, W.- C. Muller, S. C. Chapman, N. W. Watkins, Extreme-value statistics from Lagrangian convex hull analysis for homogeneous turbulent Boussinesq convection and MHD convection, New J. Phys. 19, 065006 (2017)
N. W. Watkins (2017). On the Continuing relevance of Mandelbrot's non-ergodic fractional renewal models of 1963 to 1967. The European Physical Journal B. 90(12), 241. DOI:10.1140/epjb/e2017-80357-3. Invited paper for special issue "Continuous Time Random Walk Still Trendy: Fifty-year History, Current State and Outlook", edited by R. Kutner and J. Masoliver.
S. C. Chapman, R. O. Dendy, P. T. Lang, N. W. Watkins, F. Calderon, M. Romanelli, T. N. Todd and JET Contributors, The global build-up to intrinsic ELM bursts and comparison with pellet precipitated ELMs seen in JET, Nucl. Fusion, 57, 022017, (2017) (published 2016) the article appeared here
T. Graves, R. B. Gramacy, N. W. Watkins and C. L. E. Franzke (2017). A brief history of long memory: Hurst, Mandelbrot and the road to ARFIMA. Entropy. 19(9), 437. DOI:10.3390/e19090437. Invited paper for special issue on ``Complex Systems, Non-Equilibrium Dynamics and Self-Organisation", edited by G. Pruessner.
T. Graves, C. Franzke, N. W. Watkins, R. Gramacy, E. Tindale (2017). Systematic inference of the long-range dependence and heavy-tail distribution parameters of ARFIMA models. Physica A: Statistical mechanics and its applications. 473, 60--71.
N. W. Watkins (2017). Fractional stochastic models for heavy tailed, and long-range dependent, fluctuations in physical systems. pp. 340--368 in "Nonlinear and Stochastic Climate Dynamics", T. O'Kane and C. L. E. Franzke (eds), Cambridge University Press. Invited chapter
S. C. Chapman, R. O. Dendy, P T Lang, N W Watkins, M Romanelli, T N Todd and JET Contributors, Global control system and plasma dynamics distinguish naturally occurring and pellet -precipitated edge localized modes in the JET tokamak, Proceedings, 43rd EPS Conference on Plasma Physics, (2016) the article appeared here
P. Hush, S. C. Chapman, M. W. Dunlop, N. W. Watkins, Robust statistical properties of the size of large burst events in AE, Geophys. Res. Lett.,42, (2015) doi: 10.1002/2015GL066277 the article appeared here
Chapman, S. C., Stainforth, D. A., Watkins, N. W. Limits to the quantification of local climate change, ERL,10, 094018 (2015) the article appeared here ERL monthly highlight
S C Chapman, R O Dendy, N W Watkins, T N Todd, F A Calderon and JET Contributors, ELM occurrence times in relation to the phase evolution of global measurements in JET, Proceedings, 42nd EPS Conference on Plasma Physics, EPS Vol. 39E ISBN 2-914771-98-3, the article appeared here, (2015)
S. C. Chapman, R. O. Dendy, T. N. Todd, N. W. Watkins, F. A. Calderon, J. Morris, and JET Contributors, The global build-up to intrinsic ELM bursts seen in divertor full flux loops in JET, Phys. Plasmas 22, 072506 (2015); the article can be found here: http://dx.doi.org/10.1063/1.4926592
N. W. Watkins, G. Pruessner, S. C. Chapman, N. B. Crosby, H. J. Jensen, 25 Years of SOC: Concepts and Controversies, Space Science Reviews, (2015) DOI 10.1007/s11214-015-0155-x. See also the commentary in Nature Physics by Mark Buchanan, vol11, p 442, June 2015, and erratum to our article at DOI: 10.1007/s11214-015-0155-x
T. Graves, R. B. Gramacy, C. L. E. Franzke and N. W. Watkins (2015). Efficient Bayesian inference for natural time series using ARFIMA processes. Nonlinear Processes in Geophysics. 22(6), 679--700.
C. L. E. Franzke, S. M. Osprey, P. Davini, and N. W. Watkins (2015). A dynamical systems explanation of the Hurst effect and atmospheric low frequency volatility. Scientific Reports. 5, 9068. DOI: 10.1038/srep09068
S. C. Chapman, R. O. Dendy, A. J. Webster, N. W. Watkins, T. N. Todd, J. Morris and JET EFDA Contributors, An apparent relation between ELM occurrence times and the prior phase evolution of divertor flux loop measurements in JET, Proceedings, 41st EPS Conference on Plasma Physics (2014); the article appeared here: EPS Vol. 38F, ISBN 2-914771-90-8
S. C. Chapman, R. O. Dendy. T. N. Todd, N. W. Watkins, A. J. Webster, F. A. Calderon, J. Morris, and JET EDFA Contributors, Relationship of ELM burst times with divertor flux loop signal phase in JET, Phys. Plasmas, 21, 062302 (2014); The article appeared here: DOI: 10.1063/1.4881474
D. A. Stainforth, S. C. Chapman, N. W. Watkins, Mapping climate change in European temperature distributions, Link opens in a new windowLink opens in a new windowEnviron. Res. Lett. 8, 034031 (2013) The article appeared here DOI:10.1088/1748-9326/8/3/034031 An ERL Monthly highlight.
V. Capparelli, C. Franzke, A. Vecchio, M. P. Freeman, N. W. Watkins, and V. Carbone (2013). A spatiotemporal analysis of US station temperature trends over the last century. Journal of Geophysical Research Atmospheres. 118(14), 7427--7434. DOI: 10.1002/jgrd.5055
N. W. Watkins, Bunched black (and grouped grey) Swans: Dissipative and non-dissipative models of correlated extreme fluctuations in complex geosystems (2013). Geophysical Research Letters. 8(3), 034031. DOI: 10.1002/grl.50103. Invited paper in Frontiers series, one of the top downloaded articles in GRL the week of its release, and chosen as a Research Spotlight.
Chapman, S. C., D. A. Stainforth, N. W. Watkins, On estimating long term local climate trendsLink opens in a new windowLink opens in a new window, Phil. Trans. Royal Soc., A,371 20120287;(2013) The article appeared here 
DOI:10.1098/rsta.2012.0287
N. W. Watkins, B. Hnat, S. C. Chapman, On Self-Similar and Multifractal Models for the Scaling of Extreme Bursty Fluctuations in Space Plasmas, Geophysical Monograph Series, 196, 299-313, (2012) The article appeared here DOI:10.1029/2011GM001084
S. Sharma, D. N. Baker, A. Bhattacharyya, A. Bunde, V. P. Dimri, H. K. Gupta, V. K. Gupta, S. Lovejoy, I. G. Main, D. Schertzer, H. von Storch, and N. W. Watkins (2012). pp. 1--16, Complexity and Extreme Events in Geosciences: An Overview, in Extreme Events and Natural Hazards: The Complexity Perspective, Geophysical Monograph volume 196, S. Sharma et al., (eds.)
C. L. E. Franzke, T. Graves, N. W. Watkins, R. B. Gramacy and C. Hughes (2012). Robustness of estimators of long-range dependence and self-similarity under non-Gaussianity. Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences. 370(1962), 1250--1267. DOI:10.1098/rsta.2011.0349
P. E. Vertes, R. M. Nicol, S. C. Chapman, N. W. Watkins, D. A. Robertson, E. T. Bullmore. Topological isomorphisms of human brain and financial market networks, Front. Syst. Neurosci., 5, 75, (2011)
S. C. Chapman, N. W. Watkins, Avalanching systems under intermediate driving rate, Plasma Phys. Cont. Fusion, 51, 124006, (2009) The article appears here DOI:10.1088/0741-333074100000741-3335/12/1240060741-3335/12/124006
N.W. Watkins, S.C. Chapman, and S. Rosenberg, Comment on "Coexistence of self-organized criticality and intermittent turbulence in the solar corona", Phys. Rev. Lett., 103, 039501, (2009) The article appears here DOI: 10.1103/PhysRevLett.103.039501
K. Kiyani, S. C. Chapman, N. W. Watkins, Pseudo-nonstationarity in the scaling exponents of finite interval time series, Phys Rev. E, 79, 036109, (2009) The article appeared here: DOI: http://dx.doi.org/10.1103/PhysRevE.79.036109
N. W. Watkins, D. Credgington, R. Sanchez, S. C. Chapman, Linear fractional stable motion: a new kinetic equation and applications to modelling the scaling of intermittent bursts, Phys. Rev. E, 79, 041124, (2009)
S. C. Chapman, G. Rowlands, N. W. Watkins, Macroscopic control parameter for avalanche models for bursty transport, Phys. Plasmas, 16, 012303, (2009) The article appears here DOI: 10.1063/1.3057392
N. W. Watkins, and Freeman, M. P. (2008). Natural complexity. Science. 320(5874), 323--324.
G. A. Abel, M. P. Freeman, G. Chisham and N. W. Watkins (2007). Investigating the turbulent structure of ionospheric plasma velocities on open and closed magnetic field lines. AIP Conference Proceedings, 2007. 932, 307--312.
B. Hnat, S. C. Chapman, K. Kiyani, G. Rowlands, N. W. Watkins, On the fractal nature of the magnetic field energy density in the solar wind, Geophys. Res. Lett., 34, L15108, (2007). The article appears here DOI: 10.1029/2007GL029531
A. M. Edwards, R. A. Phillips, N. W. Watkins, M. P. Freeman, E. J. Murphy, V. Afanasyev, S. V. Buldyrev, M. G. E. da Luz, E. P. Raposo, H. E. Stanley and G. M. Viswanathan (2007). Revisiting Levy flight search patterns of wandering albatrosses, bumblebees and deer. Nature. 449(7165), 1044--1048.
G. A. Abel, M. P. Freeman, G. Chisham and N. W. Watkins (2007). Investigating turbulent structure of ionospheric plasma velocity using the Halley SuperDARN radar. Nonlinear Processes in Geophysics. 14(6), 799--809.
N. W. Watkins, D. Credgington, B. Hnat, S. C. Chapman, M. P. Freeman, and J. Greenhough, Towards synthesis of solar wind and geomagnetic scaling exponents: a fractional Levy motion model, Space. Sci. Rev., 121, 269, (2006) The article appears here DOI:10.1007/s11214-006-4578-2
S. C. Chapman, B. Hnat, G.Rowlands, N. W. Watkins, Scaling collapse and structure functions: Identifying self-affinity in finite length time series, Nonlin. Proc. Geophys., 767-774, 1607-7946/npg/2005-12-767 (2005) The article appears here DOI: 10.5194/npg-12-767-2005
S. C. Chapman, G. Rowlands, N. W. Watkins, Scaling and commonality in anomalous fluctuation statistics in models for turbulence and ferromagnetism, J. Phys. A. Math. Gen. 38, 2289, (2005). The article appears here DOI: 10.1088/0305-4470/38/10/016
S C Chapman, R O Dendy and N W Watkins, Robustness and scaling: key observables in the complex dynamic magnetosphere Plasma Phys. Cont. Fusion, 46, B157, (2004) The article appears here DOI: 10.1088/0305-4470/38/10/016
B. Hnat, S. C. Chapman, G. Rowlands, N. W. Watkins, M. P. Freeman, Scaling in long term datasets of geomagnetic indices and solar wind epsilon as seen by WIND, Geophys. Res. Lett., 30, 2174, (2003). The article appears here DOI: 10.1029 /2003GLO18209
R. W. Clarke, M. P. Freeman and N. W. Watkins (2003). Application of computational mechanics to the analysis of natural data: An example in geomagnetism. Physical Review E--Statistical Physics, Plasmas, Fields, and Related Interdisciplinary Topics. 67, 016203
N.W. Watkins, S.C. Chapman, and G. Rowlands, Comment on ``Universal fluctuations in correlated systems, Bramwell et al,'', Phys. Rev. Lett., 89, 28901, (2002).
M. P. Freeman and N. W. Watkins (2002). The heavens in a pile of sand. Science. 298(5595), 979--980.
B. Hnat, S.C. Chapman, G. Rowlands, N.W. Watkins and M. P. Freeman, Scaling in solar wind epsilon and the AE, AL, and AU indices as seen by WIND, Geophys. Res. Lett., 29, 2078, (2002). To view the published open abstract, go to http://dx.doi.org and enter the DOI: 10.1029/2002GL016054 correction
B. Hnat, S. C. Chapman, G. Rowlands, N. W. Watkins, W. M. Farrell, Finite size scaling in the solar wind magnetic field energy density as seen by WIND, Geophys. Res. Lett, 29, 86, (2002). To view the published open abstract, go to http://dx.doi.org and enter the DOI: 10.1029/2001GL014587
N. W. Watkins (2002). Scaling in the space climatology of the auroral indices: Is SOC the only possible description ? Nonlinear Processes in Geophysics. 9(5--6), 389--397.
S. C. Chapman, N. W. Watkins, Avalanching and Self Organised Criticality: a paradigm for magnetospheric dynamics? Invited review paper for Space Science Reviews special issue "Challenge to Long-Standing Unsolved Space Physics Problems in the 20th Century", 95,293, (2001). The final publication is available at Springer via http://dx.doi.org/10.1023/A:1005236717469
S. C. Chapman, N. W. Watkins and G. Rowlands, Signatures of dual scaling regimes in a simple avalanche model for magnetospheric activity, J. Atmos. Solar Terres. Phys., 63, 1361, (2001).
N. W. Watkins, M. Freeman, S. C. Chapman, R. O. Dendy, Testing the SOC hypothesis for the magnetosphere, J. Atmos. Solar Terres. Phys., 63, 1435, (2001).
N. W. Watkins, M. P. Freeman, C. S. Rhodes and G. Rowlands (2001). Ambiguities in determination of self-affinity in the AE index time series. Fractals. 9(4), 471--480.
N. W. Watkins, S. Oughton and M. P. Freeman (2001). What can we infer about the underlying physics from burst distributions observed in an RMHD simulation ? Planetary and Space Science. 49(12), 1233--1237.
N. W. Watkins, N. A. Bharmal, M. A. Clilverd and A. J. Smith (2001). Comparison of VLF sferics intensity at Halley, Antarctica, with tropical lightning and temperature. Radio Science. 36(5), 1053--1064.
N. W. Watkins, M. A. Clilverd, A. J. Smith, C. J. Rodger, N. A. Bharmal and K. H. Yearby (2001). Lightning atmospherics count rates observed at Halley, Antarctica. Journal of Atmospheric and Solar-Terrestrial Physics. 63(10), 993--1003.
S. Tam, T. S. Chang, S. C. Chapman, N. W. Watkins, Analytical determination of power law index for the Chapman et al. sandpile (FSOC) analog for magnetospheric activity- renormalization group analysis, Geophys. Res. Lett., 27, 1367, (2000). To view the published open abstract, go to http://dx.doi.org and enter the DOI: 10.1029/2000GL000030
M. P. Freeman, N. W. Watkins and D. J. Riley (2000). Power law distributions of burst duration and interburst interval in the solar wind: Turbulence or dissipative self-organized criticality? Physical Review E--Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics. 62(6B), 8794--8797.
M. P. Freeman, N. W. Watkins and D. J. Riley (2000). Evidence for a solar wind origin of the power law burst lifetime distribution of the AE indices. Geophysical Research Letters. 27(8), 1087--1090.
N. W. Watkins, S. C. Chapman, R. O. Dendy, P. Helander, G. Rowlands, Robustness of collective behaviour in strongly driven avalanche models: magnetospheric implications, Geoph. Res. Lett., Vol. 26 , No. 16 , p. 2617, (1999). To view the published open abstract, go to http://dx.doi.org and enter the DOI: 10.1029/1999GL900586
M. A. Clilverd, N. W. Watkins, A. J. Smith and K. H. Yearby (1999). Diurnal and annual variations in 10-kHz radio noise. Radio Science. 34(4), 933--938.
P. Helander, S. C. Chapman, R. O. Dendy, G. Rowlands, N. W. Watkins, Exactly solvable sandpile with fractal avalanching, Phys. Rev. E, Vol 59, p 6356-6360, (1999).
N. W. Watkins, M. A. Clilverd, A. J. Smith and K. H. Yearby (1998). A 25-year Record of 10 kHz sferics noise in Antarctica: Implications for tropical lightning levels. Geophysical Research Letters. 25(23), 4353--4356.
S. C. Chapman, N. W. Watkins, R. Dendy, P. Helander and G. Rowlands, A simple avalanche model as an analogue for magnetospheric activity, Geophys. Res. Lett., 25, 2397, (1998). DOI: 10.1029/98GL51700
N. W. Watkins, S. C. Chapman, M. P. Gough and P. Forsberg (1998). In-situ spacecraft particle correlation: Theory and practice. pp 319--324 in Measurement Techniques for Space Plasma: Particles, Geophysical Monograph Series. 102, R. Pfaff et al., (eds.).
S. C. Chapman and N. W. Watkins, Scaling Parameters and Parametric Coordinates in Static and Time Dependent Magnetic Reversals, Adv. Space Res., 18, 8285, (1996). The article appeared here DOI: 10.1016/0273-1177(95)01001-7
S. C. Chapman and N. W. Watkins, Delay coordinate plots: a sensitive indicator of nonlinear dynamics in single charged particle motion in magnetic reversals, Ann. Geophysicae, 13, 836, (1995).
N. W. Watkins, J. A. Bather, S. C. Chapman, C. G. Mouikis, M. P.Gough, J. R. Wygant, D. A. Hardy, H. L. Collin, A. D. Johnstone, R. R. Anderson, Suspected Wave-Particle Interactions coincident with a Pancake Distribution as seen by the CRRES spacecraft, Adv. Space Res., 17, 1083-1087, (1995).
S. C. Chapman, and N. W. Watkins, Parameterization of chaotic particle dynamics in a simple time-dependent field reversal, J. Geophys. Res., 98, 165-177, (1993). The article appeared here DOI: 10.1029/92JA01548
N. W. Watkins (1989), The Dissipative Zener Tunnelling Problem, Sussex University D. Phil. Thesis. See also preprint: N. W. Watkins and D. Waxman, “Path integral derivation of Bloch-Redfield equations for a qubit weakly coupled to a heat bath: Application to nonadiabatic transitions”, arXiv:cond-mat/0411443[cond-mat.mes-hall]