text: 6 105 Modified Shifted Gompertz |y| < 0.5 104 900 GeV ( x 102 ) pp 540 GeV ( x 101 ) 103 200 GeV ( x 100 ) 102 10 1 10- 1 10- 2 10- 3 10- 4 0 5 10 15 20 25 n 105 Modified Shifted Gompertz |y| < 1.5 104 900 GeV ( x 102 ) pp 540 GeV ( x 101 ) 103 200 GeV ( x 100 ) 102 10 1 10- 1 10- 2 10- 3 10- 4 10 20 30 40 50 60 n 105 Modified Shifted Gompertz |y| < 3.0 104 900 GeV ( x 102 ) pp 540 GeV ( x 101 ) 103 200 GeV ( x 100 ) 102 10 1 10- 1 10- 2 10- 3 10- 4 0 20 40 60 80 100 n 105 Modified Shifted Gompertz |y| < 5.0 104 900 GeV ( x 102 ) pp 540 GeV ( x 101 ) 103 200 GeV ( x 100 ) 102 10 1 10- 1 10- 2 10- 3 10- 4 0 20 40 60 80 100 n FIG. 3: Charged multiplicity distributions in pp collisions at diﬀerent energies and in four diﬀerent rapidity windows for modiﬁed shifted Gompertz distributions. 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text: 2 only when the distance between them is less than a critical value[13, 14]. Yang et al. proposed a random routing strategy on mobile networks, in which packets deliver to a randomly selected agent in the communication circle. They found an algebraic power law between the throughput and the communication range with an exponent determined by the speed[15]. Moreover, Yang and Tang proposed an adaptive routing strategy, in which incorporates geographical distance with local traﬃc information through a tunable parameter. They found there exists an optimal value of the parameter, leading to the maximum traﬃc throughput of the network[16]. In previous work, queue discipline has little attention in routing strategies. Queue discipline refers to the manner in which packets are selected when arrival packets exceed maximal processing capacity of agent[17]. The most common discipline is ﬁrst-in-ﬁrst-out. However, this is certainly not the only possible queue discipline. The second is last-in- ﬁrst-out discipline. A typical example is the last clicked information may be served ﬁrst in the World Wide Web. The third is priority schemes, in which packets are given priorities, the ones with higher priorities to be selected ahead of those with lower priorities, regardless of their time of arrival to the agent. For example, paid packets with high priority are delivered ﬁrst when downloaded from a certain web site. In most existing work, ﬁrst-in-ﬁrst-out discipline is widely used. It is simple and convenient, but far from optimal. AS our knowledge, only a few articles use other discipline. Tadi´c et al. study the web-graph model with last-in-ﬁrst- out discipline[18–21]. Kim et al. introduce a priority routing strategy, in which each packet is pre-set a priority. They found the traﬃc behavior is improved in the congestion region, but worsened in the free ﬂow region[22]. Tang and Zhou deﬁne an eﬀective distance by considering simultaneously the waiting time and remaining path-length to the destination, according to which the packets queue in a descending order of the eﬀective distance. They found it can remarkably enhance the network throughput[23]. Du et al. propose a shortest-remaining-path-ﬁrst queueing strategy in which a packet’s priority is determined by the distance between its current location and destination. They found the traﬃc eﬃciency is greatly improved, especially in the congestion state[24]. Zhang et al. introduce a dynamic- information-based queueing strategy, They found the network capacity has no obvious change, but it got signiﬁcant improvement for some traﬃc indexes such as average end-to-end delay, rate of queueing delay[25]. In previous studies, few researchers have applied priority discipline to routing strategy on mobile networks. However, in the real dynamic network, packets are often assign priority. For example, important military information often has a higher delivered priority on mobile ad hoc networks in the battleﬁeld environment. In this article, we propose a shortest-distance-ﬁrst(SDF) routing strategy on mobile networks, in which packet is delivered ﬁrst if the distance between location of neighbor agent and its destination is shortest. Compared with ﬁrst-in-ﬁrst-out queueing discipline, our strategy not only remarkably improves network throughout and the packet arriving rate, but also reduces average end-to-end delay and the rate of queueing delay. II. METHODS AND MATERIALS A. Network model and queueing strategy Traﬃc is simulated on a random network of mobile agents, i.e., N agents (numbered from 1 to N) move on a × square-shaped cell of size L L. Periodic boundary condition is used. Initially, agents distribute randomly in the area. At each time step ∆t, moving direction of an agent is re-directed randomly, while its speed v is selected to be a constant for simplicity. At the same time, a total of R packets are generated in the network, whose source and

label: paragraph

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text: critical

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text: al.

text: proposed

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text: random

text: routing

text: strategy

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text: mobile

text: networks,

text: in

text: which

text: packets

text: deliver

text: to

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text: randomly

text: selected

text: agent

text: in

text: the

text: communication

text: circle.

text: They

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text: Yang

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text: et

text: al.

text: study

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text: web-graph

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text: out

text: Kim

text: et

text: al.

text: introduce

text: a

text: priority

text: routing

text: strategy,

text: in

text: which

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text: pre-set

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text: traﬃc

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text: improved

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text: eﬀective

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text: the

text: destination,

text: according

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text: packets

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text: the

text: eﬀective

text: distance.

text: They

text: found

text: it

text: can

text: remarkably

text: enhance

text: the

text: network

text: Du

text: et

text: al.

text: propose

text: a

text: shortest-remaining-path-ﬁrst

text: queueing

text: strategy

text: in

text: which

text: a

text: packet’s

text: priority

text: is

text: determined

text: by

text: the

text: distance

text: between

text: its

text: current

text: location

text: and

text: destination.

text: They

text: found

text: the

text: traﬃc

text: eﬃciency

text: is

text: greatly

text: improved,

text: especially

text: in

text: the

text: congestion

text: Zhang

text: et

text: al.

text: introduce

text: a

text: dynamic-

text: information-based

text: queueing

text: strategy,

text: They

text: found

text: the

text: network

text: capacity

text: has

text: no

text: obvious

text: change,

text: but

text: it

text: got

text: signiﬁcant

text: improvement

text: for

text: some

text: traﬃc

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text: such

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text: average

text: end-to-end

text: delay,

text: rate

text: of

text: queueing

text: In

text: previous

text: studies,

text: few

text: researchers

text: have

text: applied

text: priority

text: discipline

text: to

text: routing

text: strategy

text: on

text: mobile

text: networks.

text: However,

text: in

text: the

text: real

text: dynamic

text: network,

text: packets

text: are

text: often

text: assign

text: priority.

text: For

text: example,

text: important

text: military

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text: often

text: has

text: a

text: higher

text: delivered

text: priority

text: on

text: mobile

text: ad

text: hoc

text: networks

text: in

text: the

text: battleﬁeld

text: environment.

text: In

text: this

text: article,

text: we

text: propose

text: a

text: shortest-distance-ﬁrst(SDF)

text: routing

text: strategy

text: on

text: mobile

text: networks,

text: in

text: which

text: packet

text: is

text: delivered

text: ﬁrst

text: if

text: the

text: distance

text: between

text: location

text: of

text: neighbor

text: agent

text: and

text: its

text: destination

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text: shortest.

text: Compared

text: with

text: ﬁrst-in-ﬁrst-out

text: queueing

text: discipline,

text: our

text: strategy

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text: remarkably

text: improves

text: network

text: throughout

text: and

text: the

text: packet

text: arriving

text: rate,

text: but

text: also

text: reduces

text: average

text: end-to-end

text: delay

text: and

text: the

text: rate

text: of

text: queueing

text: delay.

text: II.

text: METHODS

text: AND

text: MATERIALS

text: A.

text: Network

text: model

text: and

text: queueing

text: strategy

text: Traﬃc

text: is

text: simulated

text: on

text: a

text: random

text: network

text: of

text: mobile

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text: N

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text: move

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text: size

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text: L.

text: Periodic

text: boundary

text: condition

text: is

text: used.

text: Initially,

text: agents

text: distribute

text: randomly

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text: the

text: area.

text: At

text: each

text: time

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text: ∆t,

text: moving

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text: re-directed

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text: 6 1.1 1.0 0.9 SDF v=0.1 0.8 FIFO v=0.1 0.7 SDF v=1 0.6 FIFO v=1 0.5 Rc 0.4 0.3 0.2 0.1 0.0 -0.1 0 200 400 600 800 1000 R FIG. 1: Order parameter η versus R for diﬀerent values of speed v. The number of agents is 800, the size of the × × square region L L = 10 10, and the communication radius α = 1. Delivery capacity of each agent is C = 1. Each data point results from an average over 20 realizations. Error bar is not shown as the values of error are very small. 800 800 700 700 600 600 v=0.3 500 500 400 400 SDF 300 FIFO 300 200 200 100 100 0 0 0.0 0.5 1.0 1.5 2.0 0.0 0.5 1.0 1.5 2.0 V FIG. 2: (a) The critical value R as a function of the moving speed v for the communication radius α = 1. (b) The c critical value R as a function of α for moving speed v = 0.3. Here N = 800, L = 10, C = 1. c cR cR ##LTFigure## ##LTFigure## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine## ##LTLine##

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text: 9 [8] G. Yan, T. Zhou, B. Hu, Z.-Q. Fu, and B.-H. Wang, Phys. Rev. E 73 (2006) 046108. [9] R. Albert, H. Jeong, and A. L. Baraba´si, Nature 401 (1999) 130. [10] W.-X. Wang, B.-H. Wang, C.-Y. Yin, Y.-B. Xie, and T. Zhou, Phys. Rev. E 73 (2006) 026111. [11] F. Liu, H. Zhao, M. Li, F.-Y. Ren, and Y.-B. Zhu, Chin. Phys. B 19 (2010) 040513. [12] W.-X. Wang, C.-Y. Yin, G. Yan, and B.-H. Wang, Phys. Rev. E 74 (2006) 016101. [13] M. Abolhasan, T. Wysocki, and E. Dutkiewicz, Ad Hoc Netw. 2 (2004) 1. [14] T. Camp, J. Boleng, and V. Davies, Wirel. Commun. Mob. Comput. 2 (2002) 483. [15] H.-X. Yang, W.-X. Wang, Y.-B. Xie, Y.-C. Lai, and B.-H. Wang, Phys. Rev. E 83 (2011) 016102. [16] H.-X. Yang and M. Tang Physica A 402 (2014) 1. [17] D. Gross, J. F. Shortle, J. M. Thompson, and C. M. Harris, Fundamentals of Queueing Theory, John Wiley & Sons, Inc., Hoboken, 2008, p. 15. [18] B. Tadi´c and S. Thurner, Physica A 332 (2004) 566. [19] B. Tadi´c, S. Thurner, and G. J. Rodgers, Phys. Rev. E 69 (2004) 036102. [20] B. Tadi´c, G. J. Rodgers, and S. Thurner, INT. J. BIFURCAT. CHAOS 17 (2007) 2363. [21] M. Andjelkovi´c, N. Gupte, and B. Tadi´c, Phys. Rev. E 91 (2015) 052817. [22] K. Kim, B. Kahng, and D. Kim, Europhys. Lett. 86 (2009) 58002. [23] M. Tang and T. Zhou, Phys. Rev. E 84 (2011) 026116. [24] W.-B. Du, Z.-X. Wu, and K.-Q. Cai, Physica A 392 (2013) 3505. [25] X.-J. Zhang, X.-M. Guan, D.-F. Sun, and S.-T. Tang, Commun. Theor. Phys. 60 (2013) 496. [26] A. Arenas, A. D. Guilera, and R. Guimera`, Phys. Rev. Lett. 86 (2001) 3196. [27] C.-L Chen, X.-B Cao, and W.-B. Du, Physica A 389 (2010) 4571. [28] W.-B. Du, X.-B Cao, C.-L Chen, and G. Yan, Physica A 390 (2011) 3982. [29] A. Scheerer, Probability On Discrete Sample Spaces, International Textbook Co., Scranton, 1969, p. 227.

label: reference

text: G.

text: Yan,

text: T.

text: Zhou,

text: B.

text: Hu,

text: Z.-Q.

text: Fu,

text: and

text: B.-H.

text: Wang,

text: Phys.

text: Rev.

text: E

text: R.

text: Albert,

text: H.

text: Jeong,

text: and

text: A.

text: L.

text: Baraba´si,

text: Nature

text: W.-X.

text: Wang,

text: B.-H.

text: Wang,

text: C.-Y.

text: Yin,

text: Y.-B.

text: Xie,

text: and

text: T.

text: Zhou,

text: Phys.

text: Rev.

text: E

text: F.

text: Liu,

text: H.

text: Zhao,

text: M.

text: Li,

text: F.-Y.

text: Ren,

text: and

text: Y.-B.

text: Zhu,

text: Chin.

text: Phys.

text: B

text: W.-X.

text: Wang,

text: C.-Y.

text: Yin,

text: G.

text: Yan,

text: and

text: B.-H.

text: Wang,

text: Phys.

text: Rev.

text: E

text: M.

text: Abolhasan,

text: T.

text: Wysocki,

text: and

text: E.

text: Dutkiewicz,

text: Ad

text: Hoc

text: Netw.

text: T.

text: Camp,

text: J.

text: Boleng,

text: and

text: V.

text: Davies,

text: Wirel.

text: Commun.

text: Mob.

text: Comput.

text: H.-X.

text: Yang,

text: W.-X.

text: Wang,

text: Y.-B.

text: Xie,

text: Y.-C.

text: Lai,

text: and

text: B.-H.

text: Wang,

text: Phys.

text: Rev.

text: E

text: H.-X.

text: Yang

text: and

text: M.

text: Tang

text: Physica

text: A

text: D.

text: Gross,

text: J.

text: F.

text: Shortle,

text: J.

text: M.

text: Thompson,

text: and

text: C.

text: M.

text: Harris,

text: Fundamentals

text: of

text: Queueing

text: Theory,

text: John

text: Wiley

text: Sons,

text: Inc.,

text: Hoboken,

text: p.

text: B.

text: Tadi´c

text: and

text: S.

text: Thurner,

text: Physica

text: A

text: B.

text: Tadi´c,

text: S.

text: Thurner,

text: and

text: G.

text: J.

text: Rodgers,

text: Phys.

text: Rev.

text: E

text: B.

text: Tadi´c,

text: G.

text: J.

text: Rodgers,

text: and

text: S.

text: Thurner,

text: INT.

text: J.

text: BIFURCAT.

text: CHAOS

text: M.

text: Andjelkovi´c,

text: N.

text: Gupte,

text: and

text: B.

text: Tadi´c,

text: Phys.

text: Rev.

text: E

text: K.

text: Kim,

text: B.

text: Kahng,

text: and

text: D.

text: Kim,

text: Europhys.

text: Lett.

text: M.

text: Tang

text: and

text: T.

text: Zhou,

text: Phys.

text: Rev.

text: E

text: W.-B.

text: Du,

text: Z.-X.

text: Wu,

text: and

text: K.-Q.

text: Cai,

text: Physica

text: A

text: X.-J.

text: Zhang,

text: X.-M.

text: Guan,

text: D.-F.

text: Sun,

text: and

text: S.-T.

text: Tang,

text: Commun.

text: Theor.

text: Phys.

text: A.

text: Arenas,

text: A.

text: D.

text: Guilera,

text: and

text: R.

text: Guimera`,

text: Phys.

text: Rev.

text: Lett.

text: C.-L

text: Chen,

text: X.-B

text: Cao,

text: and

text: W.-B.

text: Du,

text: Physica

text: A

text: W.-B.

text: Du,

text: X.-B

text: Cao,

text: C.-L

text: Chen,

text: and

text: G.

text: Yan,

text: Physica

text: A

text: A.

text: Scheerer,

text: Probability

text: On

text: Discrete

text: Sample

text: Spaces,

text: International

text: Textbook

text: Co.,

text: Scranton,

text: p.


text: AR produced ﬂares without CME. If these properties found for the move- ment of the barycenters are generic pre-cursors of CME eruption (or lack of it), identifying them may serve as an excellent pre-condition for reﬁning the forecast of the lift-oﬀ of CMEs. Keywords: AR, Flare, CME, precursor parameters 1. Introduction There are many kinds of eruptions on the Sun and from these the solar ﬂares and coronal mass ejections (CMEs) are the most gigantic energy ex- plosions. These two major eruptions are powered by the free energy stored in the stressed magnetic ﬁelds in active regions (ARs). Sunspots appear as dark spots compared to surrounding regions on the photosphere and are considered as good markers of ARs. The concentration of magnetic ﬁeld ﬂuxes of AR, often modelled as ﬂux tubes, reduce the temperature in the photosphere by inhibiting convection. Strongly twisted magnetic ﬂux tubes and strongly sheared magnetic structures are candidates for facilitating the high intensity ﬂares and ﬂux rope eruption from AR. A number of spe- ciﬁc mechanisms are proposed to lead to ﬂare and CME occurrences, e.g. sunspot rotation (Yan & Qu, 2007; Zhang et al., 2007; Yan et al., 2009; Chandra et al., 2011; Hardersen et al., 2011; Vemareddy et al., 2016) and shearing motion of the sunspots at photosphere (Vemareddy et al., 2012) which contribute to helicity and accumulation of magnetic energy of an AR (To¨r¨ok & Kliem, 2003; D´emoulin, 2007; D´emoulin & Pariat, 2009). The magnetically complicated and highly dynamic delta-type sunspot groups are more likely for ﬂare and CME genesis than bipolar ARs, see e.g. Ku¨nzel (1960), Sammis & Zirin (2000). It is now also well known that solar ﬂares and CMEs occur close to the polarity inversion line (PIL) (Louis et al., 2015). The PIL can be deﬁned as the boundary separating positive and negative magnetic polarities (Babcock & Babcock, 1955). Flare and CME often accompany each other, but not always. Yashiro (2006) found that the probability of a low energetic ﬂare with CME oc- currence is much smaller than an intensive ﬂare being associated with a large CME. If these two phenomena do occur together then the pre-, rise- or decay-phase of a ﬂare is temporally associate with the initial-, impulsive acceleration- or propagation-phase of a CME (Zhang et al., 2001). A main diﬀerence between solar ﬂare and CME is the scale on which they occur. A ﬂare is small and more local compared to a CME. Flares occur Preprint submitted to Advances in Space Research May 30, 2020 ##LTLine##

text: AR

label: abstract

text: produced

text: ﬂares

text: without

text: CME.

text: If

text: these

text: properties

text: found

text: for

text: the

text: move-

text: ment

text: of

text: the

text: barycenters

text: are

text: generic

text: pre-cursors

text: of

text: CME

text: eruption

text: (or

text: lack

text: of

text: it),

text: identifying

text: them

text: may

text: serve

text: as

text: an

text: excellent

text: pre-condition

text: for

text: reﬁning

text: the

text: forecast

text: of

text: the

text: lift-oﬀ

text: of

text: CMEs.

text: Keywords:

text: AR,

text: Flare,

text: CME,

text: precursor

text: parameters

label: section

text: Introduction

text: There

text: are

text: many

text: kinds

text: of

text: eruptions

text: on

text: the

text: Sun

text: and

text: from

text: these

text: the

text: solar

text: ﬂares

text: and

text: coronal

text: mass

text: ejections

text: (CMEs)

text: are

text: the

text: most

text: gigantic

text: energy

text: ex-

text: plosions.

text: These

text: two

text: major

text: eruptions

text: are

text: powered

text: by

text: the

text: free

text: energy

text: stored

text: in

text: the

text: stressed

text: magnetic

text: ﬁelds

text: in

text: active

text: regions

text: (ARs).

text: Sunspots

text: appear

text: as

text: dark

text: spots

text: compared

text: to

text: surrounding

text: regions

text: on

text: the

text: photosphere

text: and

text: are

text: considered

text: as

text: good

text: markers

text: of

text: ARs.

text: The

text: concentration

text: of

text: magnetic

text: ﬁeld

text: ﬂuxes

text: of

text: AR,

text: often

text: modelled

text: as

text: ﬂux

text: tubes,

text: reduce

text: the

text: temperature

text: in

text: the

text: photosphere

text: by

text: inhibiting

text: convection.

text: Strongly

text: twisted

text: magnetic

text: ﬂux

text: tubes

text: and

text: strongly

text: sheared

text: magnetic

text: structures

text: are

text: candidates

text: for

text: facilitating

text: the

text: high

text: intensity

text: ﬂares

text: and

text: ﬂux

text: rope

text: eruption

text: from

text: AR.

text: A

text: number

text: of

text: spe-

text: ciﬁc

text: mechanisms

text: are

text: proposed

text: to

text: lead

text: to

text: ﬂare

text: and

text: CME

text: occurrences,

text: e.g.

text: sunspot

text: rotation

text: (Yan

text: Qu,

text: Zhang

text: et

text: al.,

text: Yan

text: et

text: al.,

text: Chandra

text: et

text: al.,

text: Hardersen

text: et

text: al.,

text: Vemareddy

text: et

text: al.,

text: and

text: shearing

text: motion

text: of

text: the

text: sunspots

text: at

text: photosphere

text: (Vemareddy

text: et

text: al.,

text: which

text: contribute

text: to

text: helicity

text: and

text: accumulation

text: of

text: magnetic

text: energy

text: of

text: an

text: AR

text: (To¨r¨ok

text: Kliem,

text: D´emoulin,

text: D´emoulin

text: Pariat,

text: The

text: magnetically

text: complicated

text: and

text: highly

text: dynamic

text: delta-type

text: sunspot

text: groups

text: are

text: more

text: likely

text: for

text: ﬂare

text: and

text: CME

text: genesis

text: than

text: bipolar

text: ARs,

text: see

text: e.g.

text: Ku¨nzel

text: Sammis

text: Zirin

text: It

text: is

text: now

text: also

text: well

text: known

text: that

text: solar

text: ﬂares

text: and

text: CMEs

text: occur

text: close

text: to

text: the

text: polarity

text: inversion

text: line

text: (PIL)

text: (Louis

text: et

text: al.,

text: The

text: PIL

text: can

text: be

text: deﬁned

text: as

text: the

text: boundary

text: separating

text: positive

text: and

text: negative

text: magnetic

text: polarities

text: (Babcock

text: Babcock,

text: Flare

text: and

text: CME

text: often

text: accompany

text: each

text: other,

text: but

text: not

text: always.

text: Yashiro

text: found

text: that

text: the

text: probability

text: of

text: a

text: low

text: energetic

text: ﬂare

text: with

text: CME

text: oc-

text: currence

text: is

text: much

text: smaller

text: than

text: an

text: intensive

text: ﬂare

text: being

text: associated

text: with

text: a

text: large

text: CME.

text: If

text: these

text: two

text: phenomena

text: do

text: occur

text: together

text: then

text: the

text: pre-,

text: rise-

text: or

text: decay-phase

text: of

text: a

text: ﬂare

text: is

text: temporally

text: associate

text: with

text: the

text: initial-,

text: impulsive

text: acceleration-

text: or

text: propagation-phase

text: of

text: a

text: CME

text: (Zhang

text: et

text: al.,

text: A

text: main

text: diﬀerence

text: between

text: solar

text: ﬂare

text: and

text: CME

text: is

text: the

text: scale

text: on

text: which

text: they

text: occur.

text: A

text: ﬂare

text: is

text: small

text: and

text: more

text: local

text: compared

text: to

text: a

text: CME.

text: Flares

text: occur

text: Preprint

text: submitted

text: to

text: Advances

text: in

text: Space

text: Research

text: May

text: ##LTLine##


text: occur, and only after the second converging-diverging motion there was a ﬂare. Two consecutive converging-diverging motions may be a pre-CME di- agnostic tool, but we need more ﬂares with fast CME occurrence examples for a further investigation and deﬁnite conclusion. Next, we investigated the predicted ﬂare(s) onset time of AR 12192. We followed the evolution of the distance parameter in time. First, we have identiﬁed the duration of converging and diverging motion of barycenters of opposite polarities before the ﬁrst X1.1-class eruption. Second, we also can see a further converging and diverging motion subsequently followed by X1.6, X3.1, X1.0, X2.0 and X2.0 class ﬂares. The ﬁrst predicted onset time of the X1.1 ﬂare is 10 hrs earlier than the actual observed ﬂare onset time. In the next step, we estimated the next expected ﬂare onset time from the second approaching and receding phases of the distance before the series of X1.6, X3.1, X1.0, X2.0 and X2.0-class energetic ﬂares. The second predicted onset time of the next ﬂare was at 02:00 on 21 September 2014, obtained by Equation 2, and the ﬁrst ﬂare (X1.6) occurred 12 hrs later after the second converging-diverging motion. Again, there seems to be an underestimate of onset time. Note that we cannot predict onset time of the subsequent ﬂares, but we used the percentage value of the maximum of W G to the M value of W G at the ﬂare onset for the prediction of intensity of the next M X3.1, X1.0, X2.0 and X2.0-class energetic ﬂares. In Kors´os et al. (2015), we proposed an empirical percentage that of W G that is a proxy of the available non-potential energy to be released M in a spot group. We determine this percentage value from the relationship of the maximum of W G and the value of W G at the ﬂare onset. In the M M case of AR 12192, the percentage of decrease is 28% at the X1.1 ﬂare onset, so more ﬂare is expected. Next, after the second maximum value of the W G , in the case of the X1.6-class ﬂare, the percentage is only 20% and M indeed more ﬂares (X3.1, X1.6, X1.0, X2.0 and X2.0) occurred during the decreasing phase of the W G . The percentage of the maximum of W G M M and the value of W G at the last X2.0-class energetic ﬂare is 38% but no M more ﬂares seemed to occur during the decreasing phase of the W G . Here, M we note that the AR 12192 turned out oﬀ the west limb becoming invisible. Perhaps the most interesting results of the present case studies are the movements (i.e. loci) of the area-weighted barycenters of the opposite po- larity sunspots before ﬂare and CME in the selected clusters. We have used the Carrington-coordinate system which is a ﬁxed solar coordinate system to clearly follow the evolution of the movements of barycenters of 15

text: occur,

text: and

text: only

text: after

text: the

text: second

text: converging-diverging

text: motion

text: there

text: was

text: a

text: ﬂare.

text: Two

text: consecutive

text: converging-diverging

text: motions

text: may

text: be

text: a

text: pre-CME

text: di-

text: agnostic

text: tool,

text: but

text: we

text: need

text: more

text: ﬂares

text: with

text: fast

text: CME

text: occurrence

text: examples

text: for

text: a

text: further

text: investigation

text: and

text: deﬁnite

text: conclusion.

text: Next,

text: we

text: investigated

text: the

text: predicted

text: ﬂare(s)

text: onset

text: time

text: of

text: AR

text: We

text: followed

text: the

text: evolution

text: of

text: the

text: distance

text: parameter

text: in

text: time.

text: First,

text: we

text: have

text: identiﬁed

text: the

text: duration

text: of

text: converging

text: and

text: diverging

text: motion

text: of

text: barycenters

text: of

text: opposite

text: polarities

text: before

text: the

text: ﬁrst

text: eruption.

text: Second,

text: we

text: also

text: can

text: see

text: a

text: further

text: converging

text: and

text: diverging

text: motion

text: subsequently

text: followed

text: by

text: and

text: class

text: ﬂares.

text: The

text: ﬁrst

text: predicted

text: onset

text: time

text: of

text: the

text: ﬂare

text: is

text: hrs

text: earlier

text: than

text: the

text: actual

text: observed

text: ﬂare

text: onset

text: time.

text: In

text: the

text: next

text: step,

text: we

text: estimated

text: the

text: next

text: expected

text: ﬂare

text: onset

text: time

text: from

text: the

text: second

text: approaching

text: and

text: receding

text: phases

text: of

text: the

text: distance

text: before

text: the

text: series

text: of

text: and

text: energetic

text: ﬂares.

text: The

text: second

text: predicted

text: onset

text: time

text: of

text: the

text: next

text: ﬂare

text: was

text: at

text: on

text: September

text: obtained

text: by

text: Equation

text: and

text: the

text: ﬁrst

text: ﬂare

text: occurred

text: hrs

text: later

text: after

text: the

text: second

text: converging-diverging

text: motion.

text: Again,

text: there

text: seems

text: to

text: be

text: an

text: underestimate

text: of

text: onset

text: time.

text: Note

text: that

text: we

text: cannot

text: predict

text: onset

text: time

text: of

text: the

text: subsequent

text: ﬂares,

text: but

text: we

text: used

text: the

text: percentage

text: value

text: of

text: the

text: maximum

text: of

text: W

text: G

text: to

text: the

text: M

text: value

text: of

text: W

text: G

text: at

text: the

text: ﬂare

text: onset

text: for

text: the

text: prediction

text: of

text: intensity

text: of

text: the

text: next

text: M

text: and

text: energetic

text: ﬂares.

text: In

text: Kors´os

text: et

text: al.

text: we

text: proposed

text: an

text: empirical

text: percentage

text: that

text: of

text: W

text: G

text: that

text: is

text: a

text: proxy

text: of

text: the

text: available

text: non-potential

text: energy

text: to

text: be

text: released

text: M

text: in

text: a

text: spot

text: group.

text: We

text: determine

text: this

text: percentage

text: value

text: from

text: the

text: relationship

text: of

text: the

text: maximum

text: of

text: W

text: G

text: and

text: the

text: value

text: of

text: W

text: G

text: at

text: the

text: ﬂare

text: onset.

text: In

text: the

text: M

text: M

text: case

text: of

text: AR

text: the

text: percentage

text: of

text: decrease

text: is

text: at

text: the

text: ﬂare

text: onset,

text: so

text: more

text: ﬂare

text: is

text: expected.

text: Next,

text: after

text: the

text: second

text: maximum

text: value

text: of

text: the

text: W

text: G

text: in

text: the

text: case

text: of

text: the

text: ﬂare,

text: the

text: percentage

text: is

text: only

text: and

text: M

text: indeed

text: more

text: ﬂares

text: and

text: occurred

text: during

text: the

text: decreasing

text: phase

text: of

text: the

text: W

text: G

text: The

text: percentage

text: of

text: the

text: maximum

text: of

text: W

text: G

text: M

text: M

text: and

text: the

text: value

text: of

text: W

text: G

text: at

text: the

text: last

text: energetic

text: ﬂare

text: is

text: but

text: no

text: M

text: more

text: ﬂares

text: seemed

text: to

text: occur

text: during

text: the

text: decreasing

text: phase

text: of

text: the

text: W

text: G

text: Here,

text: M

text: we

text: note

text: that

text: the

text: AR

text: turned

text: out

text: oﬀ

text: the

text: west

text: limb

text: becoming

text: invisible.

text: Perhaps

text: the

text: most

text: interesting

text: results

text: of

text: the

text: present

text: case

text: studies

text: are

text: the

text: movements

text: (i.e.

text: loci)

text: of

text: the

text: area-weighted

text: barycenters

text: of

text: the

text: opposite

text: po-

text: larity

text: sunspots

text: before

text: ﬂare

text: and

text: CME

text: in

text: the

text: selected

text: clusters.

text: We

text: have

text: used

text: the

text: Carrington-coordinate

text: system

text: which

text: is

text: a

text: ﬁxed

text: solar

text: coordinate

text: system

text: to

text: clearly

text: follow

text: the

text: evolution

text: of

text: the

text: movements

text: of

text: barycenters

text: of


text: the opposite polarity sunspots. In particular, Figures 5 and 6 reveal a very interesting feature: they capture some distinct patterns of the behavior of the negative and the positive polarity sunspots before ﬂares. There are two types of ﬁgures: one for the case with fast CME (see Figure 5), another ﬂare(s) without CME (see Figure 6). Even just a simple visual inspection of the trajectory of sunspot barycenter motion will unveil that one may ﬁnd distinct signatures of ﬂaring without fast CMEs, respectively, in the trajectories of sunspots. Furthermore, we have determined separately the evolution of negative and positive polarity displacement, i.e. as a function of time of the two ARs (AR 12158 and AR 12192). We have found, where there is a fast CME the negative polarity area-weighted barycenter has moved before the fast CME and the positive polarity “stayed” at the same coordinates. Otherwise, when the AR produced ﬂares but no CME, then the barycenters of both the negative and the positive polarity sunspots have moved around. This latter empirical relation may mean that the highly stressed region would relax itself via these unwinding motions, not leaving enough free energy there for a major mass uplift. The results are encour- aging but we need to conﬁrm statistically this latter statement by carrying out the study on much larger samples. 5. Acknowledgements MBK is grateful to the University of Sheﬃeld for the support received while carrying out research for some time there. RE and MSR are grateful to Science and Technology Facilities Council (STFC) UK and the Royal Society (UK). The authors also acknowledge the support received from the CAS Key Laboratory of Solar Activity, National Astronomical Observato- ries Commission for Collaborating Research Program. RE acknowledges the support received from the CAS Presidents International Fellowship Ini- tiative, Grant No. 2016VMA045. References Alicia N. Aarnio, Keivan G. Stassun, W. Jeﬀrey Hughes, Sarah L. McGregor, Solar Flares and Coronal Mass Ejections: A Statistically Determined Flare Flux-CME Mass Correlation, 2011, Solar Phys., 268, 195-212 Horace W Babcock, D. Harold Babcock, The Sun’s Magnetic Field, 1952-1954., 1955, The Astrophys. J., 121, 349-366 Baranyi, T., Gy˝ori, L., & Ludm´any, A., On-line Tools for Solar Data Compiled at the Debrecen Observatory and Their Extensions with the Greenwich Sunspot Data, 2016, Solar Phys., 291, 3081-3102 Chandra, R., Schmieder, B., Mandrini, C. H., Dmoulin, P., Pariat, E., T¨or¨ok, T, Uddin, W, Homologous Flares and Magnetic Field Topology in Active Region NOAA 10501 on 20 November 2003, 2011, Solar Phys., 269, 83-104 16

text: the

text: opposite

text: polarity

text: sunspots.

text: In

text: particular,

text: Figures

text: and

text: reveal

text: a

text: very

text: interesting

text: feature:

text: they

text: capture

text: some

text: distinct

text: patterns

text: of

text: the

text: behavior

text: of

text: the

text: negative

text: and

text: the

text: positive

text: polarity

text: sunspots

text: before

text: ﬂares.

text: There

text: are

text: two

text: types

text: of

text: ﬁgures:

text: one

text: for

text: the

text: case

text: with

text: fast

text: CME

text: (see

text: Figure

text: another

text: ﬂare(s)

text: without

text: CME

text: (see

text: Figure

text: Even

text: just

text: a

text: simple

text: visual

text: inspection

text: of

text: the

text: trajectory

text: of

text: sunspot

text: barycenter

text: motion

text: will

text: unveil

text: that

text: one

text: may

text: ﬁnd

text: distinct

text: signatures

text: of

text: ﬂaring

text: without

text: fast

text: CMEs,

text: respectively,

text: in

text: the

text: trajectories

text: of

text: sunspots.

text: Furthermore,

text: we

text: have

text: determined

text: separately

text: the

text: evolution

text: of

text: negative

text: and

text: positive

text: polarity

text: displacement,

text: i.e.

text: as

text: a

text: function

text: of

text: time

text: of

text: the

text: two

text: ARs

text: (AR

text: and

text: AR

text: We

text: have

text: found,

text: where

text: there

text: is

text: a

text: fast

text: CME

text: the

text: negative

text: polarity

text: area-weighted

text: barycenter

text: has

text: moved

text: before

text: the

text: fast

text: CME

text: and

text: the

text: positive

text: polarity

text: “stayed”

text: at

text: the

text: same

text: coordinates.

text: Otherwise,

text: when

text: the

text: AR

text: produced

text: ﬂares

text: but

text: no

text: CME,

text: then

text: the

text: barycenters

text: of

text: both

text: the

text: negative

text: and

text: the

text: positive

text: polarity

text: sunspots

text: have

text: moved

text: around.

text: This

text: latter

text: empirical

text: relation

text: may

text: mean

text: that

text: the

text: highly

text: stressed

text: region

text: would

text: relax

text: itself

text: via

text: these

text: unwinding

text: motions,

text: not

text: leaving

text: enough

text: free

text: energy

text: there

text: for

text: a

text: major

text: mass

text: uplift.

text: The

text: results

text: are

text: encour-

text: aging

text: but

text: we

text: need

text: to

text: conﬁrm

text: statistically

text: this

text: latter

text: statement

text: by

text: carrying

text: out

text: the

text: study

text: on

text: much

text: larger

text: samples.

text: Acknowledgements

text: MBK

text: is

text: grateful

text: to

text: the

text: University

text: of

text: Sheﬃeld

text: for

text: the

text: support

text: received

text: while

text: carrying

text: out

text: research

text: for

text: some

text: time

text: there.

text: RE

text: and

text: MSR

text: are

text: grateful

text: to

text: Science

text: and

text: Technology

text: Facilities

text: Council

text: (STFC)

text: UK

text: and

text: the

text: Royal

text: Society

text: (UK).

text: The

text: authors

text: also

text: acknowledge

text: the

text: support

text: received

text: from

text: the

text: CAS

text: Key

text: Laboratory

text: of

text: Solar

text: Activity,

text: National

text: Astronomical

text: Observato-

text: ries

text: Commission

text: for

text: Collaborating

text: Research

text: Program.

text: RE

text: acknowledges

text: the

text: support

text: received

text: from

text: the

text: CAS

text: Presidents

text: International

text: Fellowship

text: Ini-

text: tiative,

text: Grant

text: No.

text: References

text: Alicia

text: N.

text: Aarnio,

text: Keivan

text: G.

text: Stassun,

text: W.

text: Jeﬀrey

text: Hughes,

text: Sarah

text: L.

text: McGregor,

text: Solar

text: Flares

text: and

text: Coronal

text: Mass

text: Ejections:

text: A

text: Statistically

text: Determined

text: Flare

text: Flux-CME

text: Mass

text: Correlation,

text: Solar

text: Phys.,

text: Horace

text: W

text: Babcock,

text: D.

text: Harold

text: Babcock,

text: The

text: Sun’s

text: Magnetic

text: Field,

text: The

text: Astrophys.

text: J.,

text: Baranyi,

text: T.,

text: Gy˝ori,

text: L.,

text: Ludm´any,

text: A.,

text: On-line

text: Tools

text: for

text: Solar

text: Data

text: Compiled

text: at

text: the

text: Debrecen

text: Observatory

text: and

text: Their

text: Extensions

text: with

text: the

text: Greenwich

text: Sunspot

text: Data,

text: Solar

text: Phys.,

text: Chandra,

text: R.,

text: Schmieder,

text: B.,

text: Mandrini,

text: C.

text: H.,

text: Dmoulin,

text: P.,

text: Pariat,

text: E.,

text: T¨or¨ok,

text: T,

text: Uddin,

text: W,

text: Homologous

text: Flares

text: and

text: Magnetic

text: Field

text: Topology

text: in

text: Active

text: Region

text: NOAA

text: on

text: November

text: Solar

text: Phys.,


text: ﬂare watch alert tools. 3. Analysis We have selected two ARs that may demonstrate well typical behaviours of pre-ﬂare phase, ﬂaring with fast CME and ﬂaring without CME at all. For the analysis we employed the SDO/HMI-Debrecen Data sunspot cata- logue (Baranyi et al., 2016). HMIDD provides accurate and detailed posi- tion, area, and mean estimated magnetic ﬁeld information for all observable sunspots and sunspot groups at an hourly basis from 2010 to the end of 2014. Figure 1 shows AR 12158 and Figure 2 depicts AR 12192 in their white- light appearance (upper panel) and the corresponding magnetogram (bot- tom panel). The areas encircled by the red ellipses in the upper panel of Figures 1 and 2 are the study areas containing spots of opposite polarities. These study areas are where the most intense ﬂares are in connection with the location of the strongest magnetic gradient. Figure 1: AR 12158. The X1.6 energetic class ﬂare occurred with fast “halo” CME − (v = 1267kms 1). Top panel: Intensity at 13:07 on 9 September 2014. Bottom linear panel: Magnetogram at 13:07 on 9 September 2014. The resulting diagrams of W G analysis of AR 12158 are shown in Fig. M 3. AR 12158 is a typical example for the case of ﬂare occurring with a fast CME (Vemareddy et al., 2016; Zhang et al., 2017). Fig. 3 shows the variation of the W G value (top panel), distance (in the middle panel) and M net magnetic ﬂux (bottom panel). Preceding the X1.6-class ﬂare, the W G · M has increased to a maximum (W Gmax = 2.19 106 Wb/m), after that, it is M followed by a less steep decrease which ends with an X1.6-class energetic 6 ##LTFigure## ##LTFigure##

text: ﬂare

text: watch

text: alert

text: tools.

text: Analysis

text: We

text: have

text: selected

text: two

text: ARs

text: that

text: may

text: demonstrate

text: well

text: typical

text: behaviours

text: of

text: pre-ﬂare

text: phase,

text: ﬂaring

text: with

text: fast

text: CME

text: and

text: ﬂaring

text: without

text: CME

text: at

text: all.

text: For

text: the

text: analysis

text: we

text: employed

text: the

text: SDO/HMI-Debrecen

text: Data

text: sunspot

text: cata-

text: logue

text: (Baranyi

text: et

text: al.,

text: HMIDD

text: provides

text: accurate

text: and

text: detailed

text: posi-

text: tion,

text: area,

text: and

text: mean

text: estimated

text: magnetic

text: ﬁeld

text: information

text: for

text: all

text: observable

text: sunspots

text: and

text: sunspot

text: groups

text: at

text: an

text: hourly

text: basis

text: from

text: to

text: the

text: end

text: of

text: Figure

text: shows

text: AR

text: and

text: Figure

text: depicts

text: AR

text: in

text: their

text: white-

text: light

text: appearance

text: (upper

text: panel)

text: and

text: the

text: corresponding

text: magnetogram

text: (bot-

text: tom

text: panel).

text: The

text: areas

text: encircled

text: by

text: the

text: red

text: ellipses

text: in

text: the

text: upper

text: panel

text: of

text: Figures

text: and

text: are

text: the

text: study

text: areas

text: containing

text: spots

text: of

text: opposite

text: polarities.

text: These

text: study

text: areas

text: are

text: where

text: the

text: most

text: intense

text: ﬂares

text: are

text: in

text: connection

text: with

text: the

text: location

text: of

text: the

text: strongest

text: magnetic

text: gradient.

text: Figure

text: AR

text: The

text: energetic

text: class

text: ﬂare

text: occurred

text: with

text: fast

text: “halo”

text: CME

text: (v

text: Top

text: panel:

text: Intensity

text: at

text: on

text: September

text: Bottom

text: linear

text: panel:

text: Magnetogram

text: at

text: on

text: September

text: The

text: resulting

text: diagrams

text: of

text: W

text: G

text: analysis

text: of

text: AR

text: are

text: shown

text: in

text: Fig.

text: M

text: AR

text: is

text: a

text: typical

text: example

text: for

text: the

text: case

text: of

text: ﬂare

text: occurring

text: with

text: a

text: fast

text: CME

text: (Vemareddy

text: et

text: al.,

text: Zhang

text: et

text: al.,

text: Fig.

text: shows

text: the

text: variation

text: of

text: the

text: W

text: G

text: value

text: (top

text: panel),

text: distance

text: (in

text: the

text: middle

text: panel)

text: and

text: M

text: net

text: magnetic

text: ﬂux

text: (bottom

text: panel).

text: Preceding

text: the

text: ﬂare,

text: the

text: W

text: G

text: M

text: has

text: increased

text: to

text: a

text: maximum

text: (W

text: Gmax

text: Wb/m),

text: after

text: that,

text: it

text: is

text: M

text: followed

text: by

text: a

text: less

text: steep

text: decrease

text: which

text: ends

text: with

text: an

text: energetic

text: ##LTFigure##

text: ##LTFigure##