Please wait a minute...
Frontiers of Physics

ISSN 2095-0462

ISSN 2095-0470(Online)

CN 11-5994/O4

Postal Subscription Code 80-965

2018 Impact Factor: 2.483

Front. Phys.    2020, Vol. 15 Issue (3) : 34601    https://doi.org/10.1007/s11467-020-0956-6
RESEARCH ARTICLE
A new approach to solar flare prediction
Michael L. Goodman1(), Chiman Kwan2, Bulent Ayhan2, Eric L. Shang2
1. Jacobs Space Exploration Group, Natural Environments Branch-EV44, NASA Marshall Space Flight Center, Huntsville, AL 35812, USA
2. Applied Research LLC, 9605 Medical Center Drive-Suite 127 E, Rockville, MD 20850, USA
 Download: PDF(6490 KB)  
 Export: BibTeX | EndNote | Reference Manager | ProCite | RefWorks
Abstract

All three components of the current density are required to compute the heating rate due to free magnetic energy dissipation. Here we present a first test of a new model developed to determine if the times of increases in the resistive heating rate in active region (AR) photospheres are correlated with the subsequent occurrence of M and X flares in the corona. A data driven, 3D, non-force-free magnetohydrodynamic model restricted to the near-photospheric region is used to compute time series of the complete current density and the resistive heating rate per unit volume [Q(t)] in each pixel in neutral line regions (NLRs) of 14 ARs. The model is driven by time series of the magnetic field B measured by the Helioseismic & Magnetic Imager on the Solar Dynamics Observatory (SDO) satellite. Spurious Doppler periods due to SDO orbital motion are filtered out of the time series for B in every AR pixel. For each AR, the cumulative distribution function (CDF) of the values of the NLR area integral Qi(t) of Q(t) is found to be a scale invariant power law distribution essentially identical to the observed CDF for the total energy released in coronal flares. This suggests that coronal flares and the photospheric Qiare correlated, and powered by the same process. The model predicts spikes in Qiwith values orders of magnitude above background values. These spikes are driven by spikes in the non-force free component of the current density. The times of these spikes are plausibly correlated with times of subsequent M or X flares a few hours to a few days later. The spikes occur on granulation scales, and may be signatures of heating in horizontal current sheets. It is also found that the times of relatively large values of the rate of change of the NLR unsigned magnetic flux are also plausibly correlated with the times of subsequent M and X flares, and spikes in Qi.

Keywords active regions      magnetic fields      flares      forecasting      heating      photosphere      models      magnetohydrodynamics     
Corresponding Author(s): Michael L. Goodman   
Issue Date: 13 April 2020
 Cite this article:   
Michael L. Goodman,Chiman Kwan,Bulent Ayhan, et al. A new approach to solar flare prediction[J]. Front. Phys. , 2020, 15(3): 34601.
 URL:  
https://academic.hep.com.cn/fop/EN/10.1007/s11467-020-0956-6
https://academic.hep.com.cn/fop/EN/Y2020/V15/I3/34601
1 M. J. Hagyard, D. Jr Smith, D. Teuber, and E. A. West, A quantitative study relating observed shear in photospheric magnetic fields to repeated flaring, Sol. Phys. 91(1), 115 (1984)
https://doi.org/10.1007/BF00213618
2 C. J. Schrijver, Driving major solar flares and eruptions: A review, Adv. Space Res. 43(5), 739 (2009)
https://doi.org/10.1016/j.asr.2008.11.004
3 L. Fletcher, B. R. Dennis, H. S. Hudson, S. Krucker, K. Phillips, A. Veronig, M. Battaglia, L. Bone, A. Caspi, Q. Chen, P. Gallagher, P. T. Grigis, H. Ji, W. Liu, R. O. Milligan, and M. Temmer, An observational overview of solar flares, Space Sci. Rev. 159(1–4), 19 (2011)
https://doi.org/10.1007/s11214-010-9701-8
4 H. S. Hudson, Global properties of solar flares, Space Sci. Rev. 158(1), 5 (2011)
https://doi.org/10.1007/s11214-010-9721-4
5 M. K. Georgoulis, V. S. Titov, and Z. Mikić, Nonneutralized electric current patterns in solar active regions: Origin of the shear-generating Lorentz force, Astrophys. J. 761(1), 61 (2012)
https://doi.org/10.1088/0004-637X/761/1/61
6 H. Wang and C. Liu, Structure and evolution of magnetic fields associated with solar eruptions, Res. Astron. Astrophys. 15(2), 145 (2015)
https://doi.org/10.1088/1674-4527/15/2/001
7 N. Gyenge, N. Ballai, and T. Baranyi, Statistical study of spatio-temporal distribution of precursor solar flares associated with major flares, Mon. Not. R. Astron. Soc. 459(4), 3532 (2016)
https://doi.org/10.1093/mnras/stw859
8 L. G. Balázs, N. Gyenge, M. B. ó, T. Baranyi, E. Forgács-Dajka, and I. Ballai, Statistical relationship between the succeeding solar flares detected by the RHESSI satellite, Mon. Not. R. Astron. Soc. 441(2), 1157 (2014)
https://doi.org/10.1093/mnras/stu609
9 D. L. Chesny, H. M. Oluseyi, and N. B. Orange, Heliumabundance and other composition effects on the properties of stellar surface convection in solar-like mainsequence stars, Astrophys. J. 778(2), 117 (2013)
https://doi.org/10.1088/0004-637X/778/2/117
10 T. Török, J. E. Leake, T. S. Titov, V. Archontis, Z. Mikić, M. G. Linton, K. Dalmasse, G. Aulanier, and B. Kliem, Distribution of electric currents in solar active regions, Astrophys. J. 782(1), L10 (2014)
https://doi.org/10.1088/2041-8205/782/1/L10
11 P. H. Scherrer, R. S. Bogart, R. I. Bush, J. T. Hoeksema, A. G. Kosovichev, J. Schou, W. Rosenberg, L. Springer, T. D. Tarbell, A. Title, C. J. Wolfson, and I. Zayer, The solar oscillations investigation- Michelson Doppler imager, Sol. Phys. 162(1–2), 129 (1995)
https://doi.org/10.1007/BF00733429
12 R. C. Canfield, 1993, NASA-CR-194729, Solar Imaging Vector Magnetograph, Final Technical Report for NASA Grant NAGW-1454, 1 Aug. 1988- 31 Jul. 1993 (Univ. of Hawaii)
13 D. A. Falconer, R. L. Moore, and G. A. Gary, Magnetic causes of solar coronal mass ejections: Dominance of the free magnetic energy over the magnetic twist alone, Astrophys. J. 644(2), 1258 (2006)
https://doi.org/10.1086/503699
14 D. A. Falconer, R. L. Moore, and G. A. Gary, Magnetogram measures of total nonpotentiality for prediction of solar coronal mass ejections from active regions of any degree of magnetic complexity, Astrophys. J. 689(2), 1433 (2008)
https://doi.org/10.1086/591045
15 D. Falconer, A. F. Barghouty, I. Khazanov, and M. Moore, A tool for empirical forecasting of major flares, coronal mass ejections, and solar particle events from a proxy of active-region free magnetic energy, Space Weather 9(4), S04003 (2011)
https://doi.org/10.1029/2009SW000537
16 D. A. Falconer, R. L. Moore, A. F. Barghouty, and I. Khazanov, Prior flaring as a complement to free magnetic energy for forecasting solar eruptions, Astrophys. J. 757(1), 32 (2012)
https://doi.org/10.1088/0004-637X/757/1/32
17 D. A. Falconer, R. L. Moore, A. F. Barghouty, and I. Khazanov, MAG4 versus alternative techniques for forecasting active region flare productivity, Space Weather 12(5), 306 (2014)
https://doi.org/10.1002/2013SW001024
18 C. J. Schrijver, A characteristic magnetic field pattern associated with all major solar flares and its use in flare forecasting, Astrophys. J. 655(2), L117 (2007)
https://doi.org/10.1086/511857
19 M. B. Korsós, T. Baranyi, and A. Ludmány, Pre-flare dynamics of sunspot groups, Astrophys. J. 789(2), 107 (2014)
https://doi.org/10.1088/0004-637X/789/2/107
20 M. B. Korsós, A. Ludmány, R. Erdélyi, and T. Baranyi, On flare predictability based on sunspot group evolution, Astrophys. J. 802(2), L21 (2015a)
https://doi.org/10.1088/2041-8205/802/2/L21
21 M. B. Korsós, N. Gyenge, T. Baranyi, and A. Ludmány, Dynamic precursors of flares in active region NOAA 10486, J. Astrophys. Astron. 36(1), 111 (2015b)
https://doi.org/10.1007/s12036-015-9329-x
22 M. B. Korsós and R. Erdélyi, On the state of a solar active region before flares and CMEs, Astrophys. J. 823(2), 153 (2016)
https://doi.org/10.3847/0004-637X/823/2/153
23 M. K. Georgoulis and D. M. Rust, Quantitative forecasting of major solar flares, Astrophys. J. 661(1), L109 (2007)
https://doi.org/10.1086/518718
24 M. K. Georgoulis, 2011, in Physics of Sun and Star Spots, Proceedings IAU Symposium No. 273, 2010, pg. 495 (International Astronomical Union 2011)
25 K. D. Leka and G. Barnes, Photospheric magnetic field properties of flaring versus flare-quiet active regions (I): Data, general approach, and sample results, Astrophys. J. 595(2), 1277 (2003a)
https://doi.org/10.1086/377511
26 K. D. Leka and G. Barnes, Photospheric magnetic field properties of flaring versus flare-quiet active regions (II): Discriminant analysis, Astrophys. J. 595(2), 1296 (2003b)
https://doi.org/10.1086/377512
27 K. D. Leka and G. Barnes, Photospheric magnetic field properties of flaring versus flare-quiet active regions (IV): A statistically significant sample, Astrophys. J. 656(2), 1173 (2007)
https://doi.org/10.1086/510282
28 G. Barnes, and K. D. Leka, Photospheric magnetic field properties of flaring versus flare-quiet active regions (III): Magnetic charge topology models, Astrophys. J. 646(2), 1303 (2006)
https://doi.org/10.1086/504960
29 , J. Wang, , Z. Shi, , H Wang. & , Y Lü. 1996, 456, 861
https://doi.org/10.1086/176703
30 Y. Lü, J. Wang, and H. Wang, Shear angle of magnetic fields, Sol. Phys. 148(1), 119 (1993)
https://doi.org/10.1007/BF00675538
31 G. Barnes, K. D. Leka, C. J. Schrijver, T. Colak, R. Qahwaji, O. W. Ashamari, Y. Yuan, J. Zhang, R. T. J. McAteer, D. S. Bloomfield, P. A. Higgins, P. T. Gallagher, D. A. Falconer, M. K. Georgoulis, M. S. Wheatland, C. Balch, T. Dunn, and E. L. Wagner, A comparison of flare forecasting methods (i): Results from the “all-clear” workshop, Astrophys. J. 829(2), 89 (2016)
https://doi.org/10.3847/0004-637X/829/2/89
32 P. H. Scherrer, J. Schou, R. I. Bush, A. G. Kosovichev, R. S. Bogart, J. T. Hoeksema, Y. Liu, T. L. Jr Duvall, J. Zhao, A. M. Title, C. J. Schrijver, T. D. Tarbell, and S. Tomczyk, The helioseismic and magnetic imager (HMI) investigation for the solar dynamics observatory (SDO), Sol. Phys. 275(1), 207 (2012)
https://doi.org/10.1007/s11207-011-9834-2
33 M. G. Bobra, X. Sun, J. T. Hoeksema, M. Turmon, Y. Liu, K. Hayashi, G. Barnes, and K. D. Leka, The helioseismic and magnetic imager (HMI) vector magnetic field pipeline: SHARPs – Space-weather HMI active region patches, Sol. Phys. 289(9), 3549 (2014)
https://doi.org/10.1007/s11207-014-0529-3
34 J. T. Hoeksema, Y. Liu, K. Hayashi, X. Sun, J. Schou, S. Couvidat, A. Norton, M. Bobra, R. Centeno, K. D. Leka, G. Barnes, and M. Turmon, The helioseismic and magnetic imager (HMI) vector magnetic field pipeline: Overview and performance, Sol. Phys. 289(9), 3483 (2014)
https://doi.org/10.1007/s11207-014-0516-8
35 Å. Nordlund, R. F. Stein, and M. Asplund, Solar Surface Convection, Living Rev. Sol. Phys. 6, 2 (2009)
https://doi.org/10.12942/lrsp-2009-2
36 B. W. Lites, K. D. Leka, A. Skumanich, V. Martínez Pillet, and T. Shimizu, Small-scale horizontal magnetic fields in the solar photosphere, Astrophys. J. 460, 1019 (1996)
https://doi.org/10.1086/177028
37 B. W. Lites, A. Skumanich, and V. Martínez Pillet, Astron. Astrophys. 333, 1053 (1998)
38 B. W. Lites, M. Kubo, H. Socas-Navarro, T. Berger, Z. Frank, R. Shine, T. Tarbell, A. Title, K. Ichimoto, Y. Katsukawa, S. Tsuneta, Y. Suematsu, T. Shimizu, and S. Nagata, The horizontal magnetic flux of the quiet- Sun internetwork as observed with the hinode spectropolarimeter, Astrophys. J. 672(2), 1237 (2008)
https://doi.org/10.1086/522922
39 D. Orozco Suárez, L. R. Bellot Rubio, J. C. del Toro Iniesta, S. Tsuneta, B. W. Lites, K. Ichimoto, Y. Katsukawa, S. Nagata, T. Shimizu, R. A. Shine, Y. Suematsu, T. D. Tarbell, and A. M. Title, Quiet-Sun internetwork magnetic fields from the inversion of Hinode measurements, Astrophys. J. 670(1), L61 (2007)
https://doi.org/10.1086/524139
40 B. W. Lites, The topology and behavior of magnetic fields emerging at the solar photosphere, Space Sci. Rev. 144(1–4), 197 (2009)
https://doi.org/10.1007/s11214-008-9437-x
41 S14 2014, Final Report for NASA Phase 1 SBIR Contract NNX14CG30P: “A New Class of Flare Prediction Algorithms: A Synthesis of Data, Pattern Recognition Algorithms, and First Principles Magnetohydrodynamics”, (Accepted by the NASA Technology Transfer System on December 22, 2014, Case No. GSC-17381-1). The report is available at goo.gl/jQh0YX. Note: The PI name on the report is not correct. The PI is Chiman Kwan. The report was written by the PI and M. L. Goodman. M. C. Cheung, and M. L. DeRosa, A method for data-driven simulations of evolving solar active regions, Astrophys. J. 757(2), 147 (2012)
42 X. Sun, On the coordinate system of space-weather HMI active region patches (SHARPs): A technical note, arxiv: 1309.2392 (2013)
43 M. G. Bobra, 2014, private communication
44 J. D. Jackson, Classical Electrodynamics, 3rd Ed., John Wiley & Sons, 1999
https://doi.org/10.1119/1.19136
45 M. L. Goodman, On the efficiency of plasma heating by Pedersen current dissipation from the photosphere to the lower corona, Astron. Astrophys. 416(3), 1159 (2004)
https://doi.org/10.1051/0004-6361:20031719
46 V. Smirnova, A. Richokainen, A. Solovev, J. Kallunki, A. Zhiltsov, and V. Ryzhov, Long quasi-periodic oscillations of sunspots and nearby magnetic structures, Astron. Astrophys. 552, A23 (2013a)
https://doi.org/10.1051/0004-6361/201219600
47 V. Smirnova, V. I. Efremov, L. D. Parfinenko, A. Riehokainen, and A. A. Solov’ev, Artifacts of SDO/HMI data and long-period oscillations of sunspots, Astron. Astrophys. 554, A121 (2013b)
https://doi.org/10.1051/0004-6361/201220825
48 P. V. Strekalova, Y. A. Nagovitsyn, A. Riehokainen, and V. V. Smirnova, Long-period variations in the magnetic field of small-scale solar structures., Geomagn. Aeron. 56(8), 1052 (2016)
https://doi.org/10.1134/S0016793216080211
49 S. Couvidat, J. Schou, J. T. Hoeksema, R. S. Bogart, R. I. Bush, T. L. Jr Duvall, Y. Liu, A. A. Norton, and P. H. Scherrer, Observables processing for the helioseismic and magnetic imager instrument on the solar dynamics observatory, Sol. Phys. 291(7), 1887 (2016)
https://doi.org/10.1007/s11207-016-0957-3
50 Y. Liu, J. T. Hoeksema, P. H. Scherrer, J. Schou, S. Couvidat, R. I. Bush, K. Jr Duvall, X. Hayashi, X. Sun, and X. Zhao, Comparison of line-of-sight magnetograms taken by the solar dynamics observatory/helioseismic and magnetic imager and solar and heliospheric observatory/ Michelson Doppler imager, Sol. Phys. 279(1), 295 (2012)
https://doi.org/10.1007/s11207-012-9976-x
51 A. G. de Wijn, J. O. Stenflo, S. K. Solanki, and S. Tsuneta, Small-scale solar magnetic fields, Space Sci. Rev. 144(1–4), 275 (2009)
https://doi.org/10.1007/s11214-008-9473-6
52 H. Peter, H. Tian, W. Curdt, D. Schmit, D. Innes, B. De Pontieu, J. Lemen, A. Title, P. Boerner, N. Hurlburt, T. D. Tarbell, J. P. Wuelser, J. Martinez-Sykora, L. Kleint, L. Golub, S. McKillop, K. K. Reeves, S. Saar, P. Testa, C. Kankelborg, S. Jaeggli, M. Carlsson, and V. Hansteen, Hot explosions in the cool atmosphere of the Sun, Science 346(6207), 1255726 (2014)
https://doi.org/10.1126/science.1255726
53 P. G. Judge, UV spectra, bombs, and the solar atmosphere, Astrophys. J. 808(2), 116 (2015)
https://doi.org/10.1088/0004-637X/808/2/116
54 G. R. Gupta and D. Tripathi, IRIS and SDO observations of recurrent explosive events, Astrophys. J. 809(1), 82 (2015)
https://doi.org/10.1088/0004-637X/809/1/82
55 G. J. M. Vissers, L. H. M. Rouppe van der Voort, R. J. Rutten, M. Carlsson, and B. De Pontieu, Ellerman bombs at high resolution (iii): Simultaneous observations with IRIS and SST, Astrophys. J. 812(1), 11 (2015)
https://doi.org/10.1088/0004-637X/812/1/11
56 Y. H. Kim, V. Yurchyshyn, S. C. Bong, I. H. Cho, K. S. Cho, J. Lee, E. K. Lim, Y. D. Park, H. Yang, K. Ahn, P. R. Goode, and B. H. Jang, Simultaneous observation of a hot explosion by NST and IRIS, Astrophys. J. 810(1), 38 (2015)
https://doi.org/10.1088/0004-637X/810/1/38
57 H. Tian, Z. Xu, J. He, and C. Madsen, Are IRIS bombs connected to Ellerman bombs? Astrophys. J. 824(2), 96 (2016)
https://doi.org/10.3847/0004-637X/824/2/96
58 R. J. Rutten, H features with hot onsets, Astron. Astrophys. 590, A124 (2016)
https://doi.org/10.1051/0004-6361/201526489
59 R. J. Rutten, Solar H-alpha features with hot onsets, Astron. Astrophys. 598, A89 (2017)
https://doi.org/10.1051/0004-6361/201629238
60 L. P. Chitta, H. Peter, P. R. Young, and Y. M. Huant, Compact solar UV burst triggered in a magnetic field with a fan-spine topology, Astron. Astrophys. 605, A49 (2017)
https://doi.org/10.1051/0004-6361/201730830
61 H. Tian, V. Yurchyshyn, H. Peter, S. K. Solanki, P. R. Young, L. Ni, W. Cao, K. Ji, Y. Zhu, J. Zhang, T. Samanta, Y. Song, J. He, L. Wang, and Y. Chen, Frequently occurring reconnection jets from Sunspot light bridges, Astrophys. J. 854(2), 92 (2018a)
https://doi.org/10.3847/1538-4357/aaa89d
62 H. Tian, X. Zhu, H. Peter, J. Zhao, T. Samanta, and Y. Chen, Magnetic reconnection at the earliest stage of solar flux emergence, Astrophys. J. 854(2), 174 (2018b)
https://doi.org/10.3847/1538-4357/aaaae6
63 N. W. Watkins, G. Pruessner, S. C. Chapman, N. B. Crosby, and H. J. Jensen, 25 years of self-organized criticality: Concepts and controversies, Space Sci. Rev. 198(1), 3 (2016)
https://doi.org/10.1007/s11214-015-0155-x
64 P. Bak, C. Tang, and K. Wiesenfeld, Self-organized criticality: An explanation of the 1/fnoise, Phys. Rev. Lett. 59(4), 381 (1987)
https://doi.org/10.1103/PhysRevLett.59.381
65 C. Tang, K. Wiesenfeld, P. Bak, S. Coppersmith, and P. Littlewood, Phase organization, Phys. Rev. Lett. 58(12), 1161 (1987)
https://doi.org/10.1103/PhysRevLett.58.1161
66 L. Kadanoff, in: Springer Proceedings in Physics, V. 57, Evolutionary Trends in the Physical Sciences, Eds. M. Suzuki and R. Kubo, Springer-Verlag Berlin Heidelberg, 1991
67 P. G. Drazin, Nonlinear Systems, Cambridge University Press, Cambridge Texts in Applied Mathematics, 1992
68 P. Bak, How Nature Works, Springer Science+ Business Media New York, 1996
https://doi.org/10.1007/978-1-4757-5426-1
69 M. E. J. Newman, Power laws, Pareto distributions and Zipf’s law, Contemp. Phys. 46(5), 323 (2005)
https://doi.org/10.1080/00107510500052444
70 D. W. Datlowe, M. J. Elcan, and H. S. Hudson, OSO-7 observations of solar X-rays in the energy range 10-100 keV, Sol. Phys. 39(1), 155 (1974)
https://doi.org/10.1007/BF00154978
71 M. S. Wheatland, Flare frequency-size distributions for individual active regions, Astrophys. J. 532(2), 1209 (2000)
https://doi.org/10.1086/308605
72 M. S. Wheatland, Evidence for departure from a powerlaw flare size distribution for a small solar active region, Astrophys. J. 710(2), 1324 (2010)
https://doi.org/10.1088/0004-637X/710/2/1324
73 H. S. Hudson, Solar flares, microflares, nanoflares, and coronal heating, Sol. Phys. 133(2), 357 (1991)
https://doi.org/10.1007/BF00149894
74 N. B. Crosby, M. J. Aschwanden, and B. R. Dennis, Frequency distributions and correlations of solar X-ray flare parameters, Sol. Phys. 143(2), 275 (1993)
https://doi.org/10.1007/BF00646488
75 T. Shimizu, Publ. Astron. Soc. Jpn. 47, 251 (1995)
76 M. J. Aschwanden, and C. E. Parnell, Nanoflare statistics from first principles: Fractal geometry and temperature synthesis, Astrophys. J. 572(2), 1048 (2002)
https://doi.org/10.1086/340385
77 M. J. Aschwanden, A statistical fractal-diffusive avalanche model of a slowly-driven self-organized criticality system, Astron. Astrophys. 539, A2 (2012)
https://doi.org/10.1051/0004-6361/201118237
78 M. J. Aschwnaden, in: Self Organized Criticality Systems, Ed. M. J. Aschwanden, Open Academic Press: Berlin, Warsaw, 2013,
79 M. J. Aschwanden, N. B. Crosby, M. Dimitropoulou, M. K. Georgoulis, S. Hergarten, J. McAteer, A. V. Milovanov, S. Mineshige, L. Morales, N. Nishizuka, G. Pruessner, R. Sanchez, A. S. Sharma, A. Strugarek, and V. Uritsky, 25 years of self-organized criticality: Solar and astrophysics, Space Sci. Rev. 198(1–4), 47 (2016)
https://doi.org/10.1007/s11214-014-0054-6
80 E. T. Lu and R. J. Hamilton, Avalanches and the distribution of solar flares, Astrophys. J. 380, L89 (1991)
https://doi.org/10.1086/186180
81 E. T. Lu, R. J. Hamilton, J. M. McTiernan, and K. R. Bromund, Solar flares and avalanches in driven dissipative systems, Astrophys. J. 412, 841 (1993)
https://doi.org/10.1086/172966
82 P. Charbonneau, S. W. McIntosh, H. Liu, and T. Bogdan, Avalanche models for solar flares, Sol. Phys. 203(2), 321 (2001)
https://doi.org/10.1023/A:1013301521745
83 S. W. McIntosh, P. Charbonneau, T. J. Bogdan, H. Liu, and J. P. Norman, Geometrical properties of avalanches in self-organized critical models of solar flares, Phys. Rev. E 65(4), 046125 (2002)
https://doi.org/10.1103/PhysRevE.65.046125
84 L. Vlahos and M. K. Georgoulis, On the self-similarity of unstable magnetic discontinuities in solar active regions, Astrophys. J. 603(1), L61 (2004)
https://doi.org/10.1086/383032
85 M. S. Wheatland and I. J. D. Craig, Toward a reconnection model for solar flare statistics, Astrophys. J. 595(1), 458 (2003)
https://doi.org/10.1086/377254
86 V. M. Uritsky, J. M. Davila, L. Ofman, and A. J. Coyner, Stochastic coupling of solar photosphere and corona, Astrophys. J. 769(1), 62 (2013)
https://doi.org/10.1088/0004-637X/769/1/62
87 V. M. Uritsky and J. M. Davila, Spatiotemporal organization of energy release events in the quiet solar corona, Astrophys. J. 795(1), 15 (2014)
https://doi.org/10.1088/0004-637X/795/1/15
88 R. A. Howard, J. D. Moses, A. Vourlidas, J. S. Newmark, D. G. Socker, et al., Sun earth connection coronal and heliospheric investigation (SECCHI), Space Sci. Rev. 136(1–4), 67 (2008)
[1] Ai-Yuan Hu, Huai-Yu Wang. Phase transition of the frustrated antiferromagntic J1-J2-J3 spin-1/2 Heisenberg model on a simple cubic lattice[J]. Front. Phys. , 2019, 14(1): 13605-.
[2] R. F. Casten. Approaching nuclei through multiple perspectives and diverse models: Patterns, symmetries, interactions[J]. Front. Phys. , 2018, 13(6): 132104-.
[3] Andrea Gabrieli, Marco Sant, Saeed Izadi, Parviz Seifpanahi Shabane, Alexey V. Onufriev, Giuseppe B. Suffritti. High-temperature dynamic behavior in bulk liquid water: A molecular dynamics simulation study using the OPC and TIP4P-Ew potentials[J]. Front. Phys. , 2018, 13(1): 138203-.
[4] C. Echeverria, K. Tucci, O. Alvarez-Llamoza, E. E. Orozco-Guillén, M. Morales, M. G. Cosenza. Mesoscopic model for binary fluids[J]. Front. Phys. , 2017, 12(5): 128703-.
[5] Xiao Xu, Junfeng Wang, Jian-Ping Lv, Youjin Deng. Simultaneous analysis of three-dimensional percolation models[J]. Front. Phys. , 2014, 9(1): 113-119.
[6] Ru HUANG (黄如), Run-sheng WANG (王润声). Investigation of gate-all-around silicon nanowire transistors for ultimately scaled CMOS technology from top–down approach[J]. Front Phys Chin, 2010, 5(4): 414-421.
[7] Vitaly N. MELNIKOV. Models of G time variations in diverse dimensions[J]. Front Phys Chin, 2009, 4(1): 75-93.
Viewed
Full text


Abstract

Cited

  Shared   
  Discussed