-
1
-
-
84912554060
-
-
N. A. M. Araújo, P. Grassberger, B. Kahng, K. J. Schrenk, and R. M. Ziff, Eur. Phys. J. 223, 2307 (2014).
-
(2014)
Eur. Phys. J.
, vol.223
, pp. 2307
-
-
Araújo, N.A.M.1
Grassberger, P.2
Kahng, B.3
Schrenk, K.J.4
Ziff, R.M.5
-
2
-
-
0035474697
-
-
D. S. Callaway, J. E. Hopcroft, J. M. Kleinberg, M. E. J. Newman, and S. H. Strogatz, Phys. Rev. E 64, 041902 (2001). 1063-651X 10.1103/PhysRevE.64.041902
-
(2001)
Phys. Rev. e
, vol.64
, pp. 041902
-
-
Callaway, D.S.1
Hopcroft, J.E.2
Kleinberg, J.M.3
Newman, M.E.J.4
Strogatz, S.H.5
-
7
-
-
77951126500
-
-
S. V. Buldyrev, R. Parshani, G. Paul, H. E. Stanley, and S. Havlin, Nature 464, 1025 (2010). NATUAS 0028-0836 10.1038/nature08932
-
(2010)
Nature
, vol.464
, pp. 1025
-
-
Buldyrev, S.V.1
Parshani, R.2
Paul, G.3
Stanley, H.E.4
Havlin, S.5
-
11
-
-
84892662283
-
-
L. Chen, F. Ghanbarnejad, W. Cai, and P. Grassberger, Europhys. Lett. 104, 50001 (2013). EULEEJ 0295-5075 10.1209/0295-5075/104/50001
-
(2013)
Europhys. Lett.
, vol.104
, pp. 50001
-
-
Chen, L.1
Ghanbarnejad, F.2
Cai, W.3
Grassberger, P.4
-
16
-
-
0001475585
-
-
J. Adler, Physica A 171, 453 (1991). PHYADX 0378-4371 10.1016/0378-4371(91)90295-N
-
(1991)
Physica A
, vol.171
, pp. 453
-
-
Adler, J.1
-
18
-
-
84936975340
-
-
A forerunner of bootstrap percolation was the threshold model of Granovetter [64]
-
A forerunner of bootstrap percolation was the threshold model of Granovetter [64].
-
-
-
-
19
-
-
79961078843
-
-
G. J. Baxter, S. N. Dorogovtsev, A. V. Goltsev, and J. F. F. Mendes, Phys. Rev. E 83, 051134 (2011). PLEEE8 1539-3755 10.1103/PhysRevE.83.051134
-
(2011)
Phys. Rev. e
, vol.83
, pp. 051134
-
-
Baxter, G.J.1
Dorogovtsev, S.N.2
Goltsev, A.V.3
Mendes, J.F.F.4
-
20
-
-
79960625377
-
-
P. Grassberger, C. Christensen, G. Bizhani, S.-W. Son, and M. Paczuski, Phys. Rev. Lett. 106, 225701 (2011). PRLTAO 0031-9007 10.1103/PhysRevLett.106.225701
-
(2011)
Phys. Rev. Lett.
, vol.106
, pp. 225701
-
-
Grassberger, P.1
Christensen, C.2
Bizhani, G.3
Son, S.-W.4
Paczuski, M.5
-
22
-
-
41349106348
-
-
M. E. J. Newman, Phys. Rev. E 66, 016128 (2002). 1063-651X 10.1103/PhysRevE.66.016128
-
(2002)
Phys. Rev. e
, vol.66
, pp. 016128
-
-
Newman, M.E.J.1
-
24
-
-
84855560656
-
-
S.-W. Son, G. Bizhani, C. Christensen, P. Grassberger, and M. Paczuski, Europhys. Lett. 97, 16006 (2012). EULEEJ 0295-5075 10.1209/0295-5075/97/16006
-
(2012)
Europhys. Lett.
, vol.97
, pp. 16006
-
-
Son, S.-W.1
Bizhani, G.2
Christensen, C.3
Grassberger, P.4
Paczuski, M.5
-
26
-
-
84255194232
-
-
J. Gao, S. V. Buldyrev, H. E. Stanley, and S. Havlin, Nat. Phys. 8, 40 (2011). 1745-2473 10.1038/nphys2180
-
(2011)
Nat. Phys.
, vol.8
, pp. 40
-
-
Gao, J.1
Buldyrev, S.V.2
Stanley, H.E.3
Havlin, S.4
-
35
-
-
84861803957
-
-
W. Li, A. Bashan, S. V. Buldyrev, H. E. Stanley, and S. Havlin, Phys. Rev. Lett. 108, 228702 (2012). PRLTAO 0031-9007 10.1103/PhysRevLett.108.228702
-
(2012)
Phys. Rev. Lett.
, vol.108
, pp. 228702
-
-
Li, W.1
Bashan, A.2
Buldyrev, S.V.3
Stanley, H.E.4
Havlin, S.5
-
36
-
-
84885431092
-
-
A. Bashan, Y. Berezin, S. V. Buldyrev, and S. Havlin, Nat. Phys. 9, 667 (2013). 1745-2473 10.1038/nphys2727
-
(2013)
Nat. Phys.
, vol.9
, pp. 667
-
-
Bashan, A.1
Berezin, Y.2
Buldyrev, S.V.3
Havlin, S.4
-
37
-
-
84924785670
-
-
Y. Berezin, A. Bashan, M. M. Danziger, D. Li, and S. Havlin, Scientific Reports 5, 8934 (2015) 10.1038/srep08934.
-
(2015)
Scientific Reports
, vol.5
, pp. 8934
-
-
Berezin, Y.1
Bashan, A.2
Danziger, M.M.3
Li, D.4
Havlin, S.5
-
38
-
-
84870877026
-
-
G. J. Baxter, S. N. Dorogovtsev, A. V. Goltsev, and J. F. F. Mendes, Phys. Rev. Lett. 109, 248701 (2012). PRLTAO 0031-9007 10.1103/PhysRevLett.109.248701
-
(2012)
Phys. Rev. Lett.
, vol.109
, pp. 248701
-
-
Baxter, G.J.1
Dorogovtsev, S.N.2
Goltsev, A.V.3
Mendes, J.F.F.4
-
39
-
-
84889259893
-
-
L. D. Valdez, P. A. Macri, H. E. Stanley, and L. A. Braunstein, Phys. Rev. E 88, 050803 (2013). PLEEE8 1539-3755 10.1103/PhysRevE.88.050803
-
(2013)
Phys. Rev. e
, vol.88
, pp. 050803
-
-
Valdez, L.D.1
Macri, P.A.2
Stanley, H.E.3
Braunstein, L.A.4
-
40
-
-
84889248544
-
-
D. Cellai, E. López, J. Zhou, J. P. Gleeson, and G. Bianconi, Phys. Rev. E 88, 052811 (2013) 10.1103/PhysRevE.88.052811.
-
(2013)
Phys. Rev. e
, vol.88
, pp. 052811
-
-
Cellai, D.1
López, E.2
Zhou, J.3
Gleeson, J.P.4
Bianconi, G.5
-
43
-
-
84904202315
-
-
D. Zhou, A. Bashan, R. Cohen, Y. Berezin, N. Shnerb, and S. Havlin, Phys. Rev. E 90, 012803 (2014) 10.1103/PhysRevE.90.012803.
-
(2014)
Phys. Rev. e
, vol.90
, pp. 012803
-
-
Zhou, D.1
Bashan, A.2
Cohen, R.3
Berezin, Y.4
Shnerb, N.5
Havlin, S.6
-
44
-
-
84923830816
-
-
S. Hwang, S. Choi, Deokjae Lee, and B. Kahng, Phys. Rev. E 91, 022814 (2015) 10.1103/PhysRevE.91.022814.
-
(2015)
Phys. Rev. e
, vol.91
, pp. 022814
-
-
Hwang, S.1
Choi, S.2
Lee, D.3
Kahng, B.4
-
45
-
-
84936975343
-
-
There exists also a fast algorithm to find the largest viable cluster [51], but since only the largest cluster is followed during the cascade, it might give wrong results in cases where an initially large cluster is taken over during the cascade by a cluster that had started smaller. This does not happen on random treelike graphs, but it might happen on more general graphs
-
There exists also a fast algorithm to find the largest viable cluster [51], but since only the largest cluster is followed during the cascade, it might give wrong results in cases where an initially large cluster is taken over during the cascade by a cluster that had started smaller. This does not happen on random treelike graphs, but it might happen on more general graphs.
-
-
-
-
47
-
-
84899716186
-
-
(R)
-
B. Min and K.-I. Goh, Phys. Rev. E 89, 040802 (R) (2014) 10.1103/PhysRevE.89.040802.
-
(2014)
Phys. Rev. e
, vol.89
, pp. 040802
-
-
Min, B.1
Goh, K.-I.2
-
48
-
-
23544451028
-
-
P. L. Leath, Phys. Rev. B 14, 5046 (1976). 1098-0121 10.1103/PhysRevB.14.5046
-
(1976)
Phys. Rev. B
, vol.14
, pp. 5046
-
-
Leath, P.L.1
-
49
-
-
84936975344
-
-
Notice that our families of waves are similar but yet differ from the "cascades" discussed in Ref. [7]. The latter are nested sequences of clusters which all contain the maximal viable cluster, while in our algorithm the nested clusters all contain the same seed (Equation presented)
-
Notice that our families of waves are similar but yet differ from the "cascades" discussed in Ref. [7]. The latter are nested sequences of clusters which all contain the maximal viable cluster, while in our algorithm the nested clusters all contain the same seed (Equation presented).
-
-
-
-
50
-
-
24844442721
-
-
D. Dhar, Phys. Rev. Lett. 64, 1613 (1990). PRLTAO 0031-9007 10.1103/PhysRevLett.64.1613
-
(1990)
Phys. Rev. Lett.
, vol.64
, pp. 1613
-
-
Dhar, D.1
-
52
-
-
84936975345
-
-
Because sites are indexed for helical b.c. by single indices, this leads to slightly simpler and faster codes. For the sizes used in this paper, periodic and helical b.c. lead to numerically indistinguishable results
-
Because sites are indexed for helical b.c. by single indices, this leads to slightly simpler and faster codes. For the sizes used in this paper, periodic and helical b.c. lead to numerically indistinguishable results.
-
-
-
-
56
-
-
27244450624
-
-
Y. J. Deng and H. W. J. Blote, Phys. Rev. E 72, 016126 (2005). PLEEE8 1539-3755 10.1103/PhysRevE.72.016126
-
(2005)
Phys. Rev. e
, vol.72
, pp. 016126
-
-
Deng, Y.J.1
Blote, H.W.J.2
-
57
-
-
84884126903
-
-
P. Grassberger, J. Stat. Phys. 153, 289 (2013). JSTPBS 0022-4715 10.1007/s10955-013-0824-7
-
(2013)
J. Stat. Phys.
, vol.153
, pp. 289
-
-
Grassberger, P.1
-
58
-
-
21144468989
-
-
P. Grassberger, J. Phys. A 25, 5867 (1992). JPHAC5 0305-4470 10.1088/0305-4470/25/22/015
-
(1992)
J. Phys. A
, vol.25
, pp. 5867
-
-
Grassberger, P.1
-
59
-
-
0000898051
-
-
J. L. Cardy, J. Phys. A 25, L201 (1992). JPHAC5 0305-4470 10.1088/0305-4470/25/4/009
-
(1992)
J. Phys. A
, vol.25
, pp. L201
-
-
Cardy, J.L.1
-
63
-
-
84936975348
-
-
Notice that interfaces in 1+1-dimensional systems are smooth, as long as they are not pinned but moving, as in the KPZ problem or Eden growth
-
Notice that interfaces in 1+1-dimensional systems are smooth, as long as they are not pinned but moving, as in the KPZ problem or Eden growth.
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