-
1
-
-
0003672584
-
-
edited by A. McKane et al., Plenum, New York
-
[1] G. Grinstein, in Scale Invariance, Interfaces and Nonequilibrium Dynamics, NATO Advanced Study Institute, Series B: Physics, vol. 344, edited by A. McKane et al., (Plenum, New York, 1995).
-
(1995)
Scale Invariance, Interfaces and Nonequilibrium Dynamics, NATO Advanced Study Institute, Series B: Physics
, vol.344
-
-
Grinstein, G.1
-
3
-
-
11944274853
-
-
World Scientific, Singapore
-
[3] T. Vicsek, Fractal Growth Phenomena (World Scientific, Singapore, 1992); A. Erzan, L. Pietronero and A. Vespignani, Rev. Mod. Phys. 67, 545 (1995).
-
(1992)
Fractal Growth Phenomena
-
-
Vicsek, T.1
-
4
-
-
11944274853
-
-
[3] T. Vicsek, Fractal Growth Phenomena (World Scientific, Singapore, 1992); A. Erzan, L. Pietronero and A. Vespignani, Rev. Mod. Phys. 67, 545 (1995).
-
(1995)
Rev. Mod. Phys.
, vol.67
, pp. 545
-
-
Erzan, A.1
Pietronero, L.2
Vespignani, A.3
-
7
-
-
15744401041
-
-
[5] P. Bak, C. Tang and K. Wiesenfeld, Phys. Rev. Lett. 59, 381 (1987); Phys. Rev. A 38, 364 (1988).
-
(1988)
Phys. Rev. A
, vol.38
, pp. 364
-
-
-
12
-
-
4243736448
-
-
[9] A. Vespignani and S. Zapperi, Phys. Rev. Lett. 78, 4793 (1997); Phys. Rev. E 57, 6345 (1998).
-
(1998)
Phys. Rev. E
, vol.57
, pp. 6345
-
-
-
14
-
-
85037801759
-
-
e-print condmat/9909009
-
[11] See the excellent review by D. Dhar, e-print condmat/9909009.
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-
-
Dhar, D.1
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15
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0025449061
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[12] Avalanche exponents: P. Grassberger and S. S. Manna, J. Phys. (France) 51, 1077 (1990); S. S. Manna, J. Stat. Phys. 59, 509 (1990); S. Lübeck and K.D. Usadel, Phys. Rev. E 55, 4095 (1997); ibid. 56, 5138 (1997). Upper critical dimension: A. Chessa, E. Marinari, A. Vespignani and S. Zapperi, Phys. Rev. E 57, R6241 (1998); S. Lübeck, ibid 56, 1590 (1997). Universality classes: A. Ben-Hur and O. Biham, Phys. Rev. E 53, R1317 (1996); A. Chessa, H. E. Stanley, A. Vespignani and S. Zapperi, Phys. Rev. E 59, R12 (1999). Multifractal properties: L. P. Kadanoff, S. R. Nagel, L. Wu and S. Zhou, Phys. Rev. A 39, 6524 (1989); M. De Menech, A. L. Stella and C. Tebaldi, Phys. Rev. E 58, R2677 (1998).
-
(1990)
J. Phys. (France)
, vol.51
, pp. 1077
-
-
Grassberger, P.1
Manna, S.S.2
-
16
-
-
33646989508
-
-
[12] Avalanche exponents: P. Grassberger and S. S. Manna, J. Phys. (France) 51, 1077 (1990); S. S. Manna, J. Stat. Phys. 59, 509 (1990); S. Lübeck and K.D. Usadel, Phys. Rev. E 55, 4095 (1997); ibid. 56, 5138 (1997). Upper critical dimension: A. Chessa, E. Marinari, A. Vespignani and S. Zapperi, Phys. Rev. E 57, R6241 (1998); S. Lübeck, ibid 56, 1590 (1997). Universality classes: A. Ben-Hur and O. Biham, Phys. Rev. E 53, R1317 (1996); A. Chessa, H. E. Stanley, A. Vespignani and S. Zapperi, Phys. Rev. E 59, R12 (1999). Multifractal properties: L. P. Kadanoff, S. R. Nagel, L. Wu and S. Zhou, Phys. Rev. A 39, 6524 (1989); M. De Menech, A. L. Stella and C. Tebaldi, Phys. Rev. E 58, R2677 (1998).
-
(1990)
J. Stat. Phys.
, vol.59
, pp. 509
-
-
Manna, S.S.1
-
17
-
-
0040646893
-
-
[12] Avalanche exponents: P. Grassberger and S. S. Manna, J. Phys. (France) 51, 1077 (1990); S. S. Manna, J. Stat. Phys. 59, 509 (1990); S. Lübeck and K.D. Usadel, Phys. Rev. E 55, 4095 (1997); ibid. 56, 5138 (1997). Upper critical dimension: A. Chessa, E. Marinari, A. Vespignani and S. Zapperi, Phys. Rev. E 57, R6241 (1998); S. Lübeck, ibid 56, 1590 (1997). Universality classes: A. Ben-Hur and O. Biham, Phys. Rev. E 53, R1317 (1996); A. Chessa, H. E. Stanley, A. Vespignani and S. Zapperi, Phys. Rev. E 59, R12 (1999). Multifractal properties: L. P. Kadanoff, S. R. Nagel, L. Wu and S. Zhou, Phys. Rev. A 39, 6524 (1989); M. De Menech, A. L. Stella and C. Tebaldi, Phys. Rev. E 58, R2677 (1998).
-
(1997)
Phys. Rev. E
, vol.55
, pp. 4095
-
-
Lübeck, S.1
Usadel, K.D.2
-
18
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0031274846
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[12] Avalanche exponents: P. Grassberger and S. S. Manna, J. Phys. (France) 51, 1077 (1990); S. S. Manna, J. Stat. Phys. 59, 509 (1990); S. Lübeck and K.D. Usadel, Phys. Rev. E 55, 4095 (1997); ibid. 56, 5138 (1997). Upper critical dimension: A. Chessa, E. Marinari, A. Vespignani and S. Zapperi, Phys. Rev. E 57, R6241 (1998); S. Lübeck, ibid 56, 1590 (1997). Universality classes: A. Ben-Hur and O. Biham, Phys. Rev. E 53, R1317 (1996); A. Chessa, H. E. Stanley, A. Vespignani and S. Zapperi, Phys. Rev. E 59, R12 (1999). Multifractal properties: L. P. Kadanoff, S. R. Nagel, L. Wu and S. Zhou, Phys. Rev. A 39, 6524 (1989); M. De Menech, A. L. Stella and C. Tebaldi, Phys. Rev. E 58, R2677 (1998).
-
(1997)
Phys. Rev. E
, vol.56
, pp. 5138
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19
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0001636995
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[12] Avalanche exponents: P. Grassberger and S. S. Manna, J. Phys. (France) 51, 1077 (1990); S. S. Manna, J. Stat. Phys. 59, 509 (1990); S. Lübeck and K.D. Usadel, Phys. Rev. E 55, 4095 (1997); ibid. 56, 5138 (1997). Upper critical dimension: A. Chessa, E. Marinari, A. Vespignani and S. Zapperi, Phys. Rev. E 57, R6241 (1998); S. Lübeck, ibid 56, 1590 (1997). Universality classes: A. Ben-Hur and O. Biham, Phys. Rev. E 53, R1317 (1996); A. Chessa, H. E. Stanley, A. Vespignani and S. Zapperi, Phys. Rev. E 59, R12 (1999). Multifractal properties: L. P. Kadanoff, S. R. Nagel, L. Wu and S. Zhou, Phys. Rev. A 39, 6524 (1989); M. De Menech, A. L. Stella and C. Tebaldi, Phys. Rev. E 58, R2677 (1998).
-
(1998)
Phys. Rev. E
, vol.57
-
-
Chessa, A.1
Marinari, E.2
Vespignani, A.3
Zapperi, S.4
-
20
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4244205069
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[12] Avalanche exponents: P. Grassberger and S. S. Manna, J. Phys. (France) 51, 1077 (1990); S. S. Manna, J. Stat. Phys. 59, 509 (1990); S. Lübeck and K.D. Usadel, Phys. Rev. E 55, 4095 (1997); ibid. 56, 5138 (1997). Upper critical dimension: A. Chessa, E. Marinari, A. Vespignani and S. Zapperi, Phys. Rev. E 57, R6241 (1998); S. Lübeck, ibid 56, 1590 (1997). Universality classes: A. Ben-Hur and O. Biham, Phys. Rev. E 53, R1317 (1996); A. Chessa, H. E. Stanley, A. Vespignani and S. Zapperi, Phys. Rev. E 59, R12 (1999). Multifractal properties: L. P. Kadanoff, S. R. Nagel, L. Wu and S. Zhou, Phys. Rev. A 39, 6524 (1989); M. De Menech, A. L. Stella and C. Tebaldi, Phys. Rev. E 58, R2677 (1998).
-
(1997)
Phys. Rev. E
, vol.56
, pp. 1590
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Lübeck, S.1
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21
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0000063883
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[12] Avalanche exponents: P. Grassberger and S. S. Manna, J. Phys. (France) 51, 1077 (1990); S. S. Manna, J. Stat. Phys. 59, 509 (1990); S. Lübeck and K.D. Usadel, Phys. Rev. E 55, 4095 (1997); ibid. 56, 5138 (1997). Upper critical dimension: A. Chessa, E. Marinari, A. Vespignani and S. Zapperi, Phys. Rev. E 57, R6241 (1998); S. Lübeck, ibid 56, 1590 (1997). Universality classes: A. Ben-Hur and O. Biham, Phys. Rev. E 53, R1317 (1996); A. Chessa, H. E. Stanley, A. Vespignani and S. Zapperi, Phys. Rev. E 59, R12 (1999). Multifractal properties: L. P. Kadanoff, S. R. Nagel, L. Wu and S. Zhou, Phys. Rev. A 39, 6524 (1989); M. De Menech, A. L. Stella and C. Tebaldi, Phys. Rev. E 58, R2677 (1998).
-
(1996)
Phys. Rev. E
, vol.53
-
-
Ben-Hur, A.1
Biham, O.2
-
22
-
-
0002674992
-
-
[12] Avalanche exponents: P. Grassberger and S. S. Manna, J. Phys. (France) 51, 1077 (1990); S. S. Manna, J. Stat. Phys. 59, 509 (1990); S. Lübeck and K.D. Usadel, Phys. Rev. E 55, 4095 (1997); ibid. 56, 5138 (1997). Upper critical dimension: A. Chessa, E. Marinari, A. Vespignani and S. Zapperi, Phys. Rev. E 57, R6241 (1998); S. Lübeck, ibid 56, 1590 (1997). Universality classes: A. Ben-Hur and O. Biham, Phys. Rev. E 53, R1317 (1996); A. Chessa, H. E. Stanley, A. Vespignani and S. Zapperi, Phys. Rev. E 59, R12 (1999). Multifractal properties: L. P. Kadanoff, S. R. Nagel, L. Wu and S. Zhou, Phys. Rev. A 39, 6524 (1989); M. De Menech, A. L. Stella and C. Tebaldi, Phys. Rev. E 58, R2677 (1998).
-
(1999)
Phys. Rev. E
, vol.59
-
-
Chessa, A.1
Stanley, H.E.2
Vespignani, A.3
Zapperi, S.4
-
23
-
-
0000563105
-
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[12] Avalanche exponents: P. Grassberger and S. S. Manna, J. Phys. (France) 51, 1077 (1990); S. S. Manna, J. Stat. Phys. 59, 509 (1990); S. Lübeck and K.D. Usadel, Phys. Rev. E 55, 4095 (1997); ibid. 56, 5138 (1997). Upper critical dimension: A. Chessa, E. Marinari, A. Vespignani and S. Zapperi, Phys. Rev. E 57, R6241 (1998); S. Lübeck, ibid 56, 1590 (1997). Universality classes: A. Ben-Hur and O. Biham, Phys. Rev. E 53, R1317 (1996); A. Chessa, H. E. Stanley, A. Vespignani and S. Zapperi, Phys. Rev. E 59, R12 (1999). Multifractal properties: L. P. Kadanoff, S. R. Nagel, L. Wu and S. Zhou, Phys. Rev. A 39, 6524 (1989); M. De Menech, A. L. Stella and C. Tebaldi, Phys. Rev. E 58, R2677 (1998).
-
(1989)
Phys. Rev. A
, vol.39
, pp. 6524
-
-
Kadanoff, L.P.1
Nagel, S.R.2
Wu, L.3
Zhou, S.4
-
24
-
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0000131814
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[12] Avalanche exponents: P. Grassberger and S. S. Manna, J. Phys. (France) 51, 1077 (1990); S. S. Manna, J. Stat. Phys. 59, 509 (1990); S. Lübeck and K.D. Usadel, Phys. Rev. E 55, 4095 (1997); ibid. 56, 5138 (1997). Upper critical dimension: A. Chessa, E. Marinari, A. Vespignani and S. Zapperi, Phys. Rev. E 57, R6241 (1998); S. Lübeck, ibid 56, 1590 (1997). Universality classes: A. Ben-Hur and O. Biham, Phys. Rev. E 53, R1317 (1996); A. Chessa, H. E. Stanley, A. Vespignani and S. Zapperi, Phys. Rev. E 59, R12 (1999). Multifractal properties: L. P. Kadanoff, S. R. Nagel, L. Wu and S. Zhou, Phys. Rev. A 39, 6524 (1989); M. De Menech, A. L. Stella and C. Tebaldi, Phys. Rev. E 58, R2677 (1998).
-
(1998)
Phys. Rev. E
, vol.58
-
-
De Menech, M.1
Stella, A.L.2
Tebaldi, C.3
-
25
-
-
84957320021
-
-
[13] A. Díaz-Guilera, Europhys. Lett. 26, 177 (1994); L. Pietronero, A. Vespignani and S. Zapperi, Phys. Rev. Lett. 72, 1690 (1994); J. Hasty and K. Wiesenfeld, J. Stat. Phys. 86, 1179 (1997).
-
(1994)
Europhys. Lett.
, vol.26
, pp. 177
-
-
Díaz-Guilera, A.1
-
26
-
-
5344266869
-
-
[13] A. Díaz-Guilera, Europhys. Lett. 26, 177 (1994); L. Pietronero, A. Vespignani and S. Zapperi, Phys. Rev. Lett. 72, 1690 (1994); J. Hasty and K. Wiesenfeld, J. Stat. Phys. 86, 1179 (1997).
-
(1994)
Phys. Rev. Lett.
, vol.72
, pp. 1690
-
-
Pietronero, L.1
Vespignani, A.2
Zapperi, S.3
-
27
-
-
0031093405
-
-
[13] A. Díaz-Guilera, Europhys. Lett. 26, 177 (1994); L. Pietronero, A. Vespignani and S. Zapperi, Phys. Rev. Lett. 72, 1690 (1994); J. Hasty and K. Wiesenfeld, J. Stat. Phys. 86, 1179 (1997).
-
(1997)
J. Stat. Phys.
, vol.86
, pp. 1179
-
-
Hasty, J.1
Wiesenfeld, K.2
-
31
-
-
85037792374
-
-
note
-
[17] The expert reader will have noticed that activated random walks follow the same local dynamics as the Manna sandpile [7].
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-
-
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32
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85037799227
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in preparation
-
[18] Details of simulations of activated random walkers are given in R. Dickman, A. Vespignani, S. Zapperi, M. A. Muñoz, and M. Alava, in preparation.
-
-
-
Dickman, R.1
Vespignani, A.2
Zapperi, S.3
Muñoz, M.A.4
Alava, M.5
-
33
-
-
0003491331
-
-
edited by V. Privman, Cambridge University Press, Cambridge
-
[19] R. Dickman, in Nonequilibrium Statistical Mechanics in One Dimension, edited by V. Privman, (Cambridge University Press, Cambridge 1996); G. Grinstein and M. A. Muñoz, in Fourth Granada Lectures in Computational Physics, edited by P. Garrido and J. Marro, Lecture Notes in Physics, 493, 223 (Springer-Verlag, Berlin, 1997). J. Marro and R. Dickman, Nonequilibrium Phase Transitions in Lattice Models (Cambridge University Press, Cambridge, 1999).
-
(1996)
Nonequilibrium Statistical Mechanics in One Dimension
-
-
Dickman, R.1
-
34
-
-
0001697794
-
-
in Fourth Granada Lectures in Computational Physics, edited by P. Garrido and J. Marro, Springer-Verlag, Berlin
-
[19] R. Dickman, in Nonequilibrium Statistical Mechanics in One Dimension, edited by V. Privman, (Cambridge University Press, Cambridge 1996); G. Grinstein and M. A. Muñoz, in Fourth Granada Lectures in Computational Physics, edited by P. Garrido and J. Marro, Lecture Notes in Physics, 493, 223 (Springer-Verlag, Berlin, 1997). J. Marro and R. Dickman, Nonequilibrium Phase Transitions in Lattice Models (Cambridge University Press, Cambridge, 1999).
-
(1997)
Lecture Notes in Physics
, vol.493
, pp. 223
-
-
Grinstein, G.1
Muñoz, M.A.2
-
35
-
-
0003827467
-
-
Cambridge University Press, Cambridge
-
[19] R. Dickman, in Nonequilibrium Statistical Mechanics in One Dimension, edited by V. Privman, (Cambridge University Press, Cambridge 1996); G. Grinstein and M. A. Muñoz, in Fourth Granada Lectures in Computational Physics, edited by P. Garrido and J. Marro, Lecture Notes in Physics, 493, 223 (Springer-Verlag, Berlin, 1997). J. Marro and R. Dickman, Nonequilibrium Phase Transitions in Lattice Models (Cambridge University Press, Cambridge, 1999).
-
(1999)
Nonequilibrium Phase Transitions in Lattice Models
-
-
Marro, J.1
Dickman, R.2
-
39
-
-
0001606645
-
-
[23] H. K. Janssen, Z. Phys. 42, 141 (1981); ibid. 58, 311 (1985).
-
(1981)
Z. Phys.
, vol.42
, pp. 141
-
-
Janssen, H.K.1
-
40
-
-
0002471868
-
-
[23] H. K. Janssen, Z. Phys. 42, 141 (1981); ibid. 58, 311 (1985).
-
(1985)
Z. Phys.
, vol.58
, pp. 311
-
-
-
43
-
-
0001387229
-
-
[26] This is the case of branching, annihilating random walks with even numbers of offspring, also known as the "directed Ising" universality class. See: P. Grassberger, F. Krause, and T. von der Twer, J. Phys. A 17, L105 (1984); P. Grassberger, ibid. 22, L1103 (1989); H. Takayasu and A. Yu. Tretyakov, Phys. Rev. Lett. 68, 3060 (1992); I. Jensen, Phys. Rev. E 50, 3623 (1994); N. Menyhard and G. Ódor, J. Phys. A 29, 7739 (1996); J. Cardy and U. C. Täuber, Phys. Rev. Lett. 77, 4780 (1996). H. Hinrichsen, Phys. Rev. E 55, 219 (1997); W. Hwang, S. Kwon, H. Park, and H. Park, Phys. Rev. E 57, 6438 (1998).
-
(1984)
J. Phys. A
, vol.17
-
-
Grassberger, P.1
Krause, F.2
Von Der Twer, T.3
-
44
-
-
0001062457
-
-
[26] This is the case of branching, annihilating random walks with even numbers of offspring, also known as the "directed Ising" universality class. See: P. Grassberger, F. Krause, and T. von der Twer, J. Phys. A 17, L105 (1984); P. Grassberger, ibid. 22, L1103 (1989); H. Takayasu and A. Yu. Tretyakov, Phys. Rev. Lett. 68, 3060 (1992); I. Jensen, Phys. Rev. E 50, 3623 (1994); N. Menyhard and G. Ódor, J. Phys. A 29, 7739 (1996); J. Cardy and U. C. Täuber, Phys. Rev. Lett. 77, 4780 (1996). H. Hinrichsen, Phys. Rev. E 55, 219 (1997); W. Hwang, S. Kwon, H. Park, and H. Park, Phys. Rev. E 57, 6438 (1998).
-
(1989)
J. Phys. A
, vol.22
-
-
Grassberger, P.1
-
45
-
-
3442896393
-
-
[26] This is the case of branching, annihilating random walks with even numbers of offspring, also known as the "directed Ising" universality class. See: P. Grassberger, F. Krause, and T. von der Twer, J. Phys. A 17, L105 (1984); P. Grassberger, ibid. 22, L1103 (1989); H. Takayasu and A. Yu. Tretyakov, Phys. Rev. Lett. 68, 3060 (1992); I. Jensen, Phys. Rev. E 50, 3623 (1994); N. Menyhard and G. Ódor, J. Phys. A 29, 7739 (1996); J. Cardy and U. C. Täuber, Phys. Rev. Lett. 77, 4780 (1996). H. Hinrichsen, Phys. Rev. E 55, 219 (1997); W. Hwang, S. Kwon, H. Park, and H. Park, Phys. Rev. E 57, 6438 (1998).
-
(1992)
Phys. Rev. Lett.
, vol.68
, pp. 3060
-
-
Takayasu, H.1
Tretyakov, A.Yu.2
-
46
-
-
11544348027
-
-
[26] This is the case of branching, annihilating random walks with even numbers of offspring, also known as the "directed Ising" universality class. See: P. Grassberger, F. Krause, and T. von der Twer, J. Phys. A 17, L105 (1984); P. Grassberger, ibid. 22, L1103 (1989); H. Takayasu and A. Yu. Tretyakov, Phys. Rev. Lett. 68, 3060 (1992); I. Jensen, Phys. Rev. E 50, 3623 (1994); N. Menyhard and G. Ódor, J. Phys. A 29, 7739 (1996); J. Cardy and U. C. Täuber, Phys. Rev. Lett. 77, 4780 (1996). H. Hinrichsen, Phys. Rev. E 55, 219 (1997); W. Hwang, S. Kwon, H. Park, and H. Park, Phys. Rev. E 57, 6438 (1998).
-
(1994)
Phys. Rev. E
, vol.50
, pp. 3623
-
-
Jensen, I.1
-
47
-
-
0030574401
-
-
[26] This is the case of branching, annihilating random walks with even numbers of offspring, also known as the "directed Ising" universality class. See: P. Grassberger, F. Krause, and T. von der Twer, J. Phys. A 17, L105 (1984); P. Grassberger, ibid. 22, L1103 (1989); H. Takayasu and A. Yu. Tretyakov, Phys. Rev. Lett. 68, 3060 (1992); I. Jensen, Phys. Rev. E 50, 3623 (1994); N. Menyhard and G. Ódor, J. Phys. A 29, 7739 (1996); J. Cardy and U. C. Täuber, Phys. Rev. Lett. 77, 4780 (1996). H. Hinrichsen, Phys. Rev. E 55, 219 (1997); W. Hwang, S. Kwon, H. Park, and H. Park, Phys. Rev. E 57, 6438 (1998).
-
(1996)
J. Phys. A
, vol.29
, pp. 7739
-
-
Menyhard, N.1
Ódor, G.2
-
48
-
-
3342997262
-
-
[26] This is the case of branching, annihilating random walks with even numbers of offspring, also known as the "directed Ising" universality class. See: P. Grassberger, F. Krause, and T. von der Twer, J. Phys. A 17, L105 (1984); P. Grassberger, ibid. 22, L1103 (1989); H. Takayasu and A. Yu. Tretyakov, Phys. Rev. Lett. 68, 3060 (1992); I. Jensen, Phys. Rev. E 50, 3623 (1994); N. Menyhard and G. Ódor, J. Phys. A 29, 7739 (1996); J. Cardy and U. C. Täuber, Phys. Rev. Lett. 77, 4780 (1996). H. Hinrichsen, Phys. Rev. E 55, 219 (1997); W. Hwang, S. Kwon, H. Park, and H. Park, Phys. Rev. E 57, 6438 (1998).
-
(1996)
Phys. Rev. Lett.
, vol.77
, pp. 4780
-
-
Cardy, J.1
Täuber, U.C.2
-
49
-
-
0001707101
-
-
[26] This is the case of branching, annihilating random walks with even numbers of offspring, also known as the "directed Ising" universality class. See: P. Grassberger, F. Krause, and T. von der Twer, J. Phys. A 17, L105 (1984); P. Grassberger, ibid. 22, L1103 (1989); H. Takayasu and A. Yu. Tretyakov, Phys. Rev. Lett. 68, 3060 (1992); I. Jensen, Phys. Rev. E 50, 3623 (1994); N. Menyhard and G. Ódor, J. Phys. A 29, 7739 (1996); J. Cardy and U. C. Täuber, Phys. Rev. Lett. 77, 4780 (1996). H. Hinrichsen, Phys. Rev. E 55, 219 (1997); W. Hwang, S. Kwon, H. Park, and H. Park, Phys. Rev. E 57, 6438 (1998).
-
(1997)
Phys. Rev. E
, vol.55
, pp. 219
-
-
Hinrichsen, H.1
-
50
-
-
0001366270
-
-
[26] This is the case of branching, annihilating random walks with even numbers of offspring, also known as the "directed Ising" universality class. See: P. Grassberger, F. Krause, and T. von der Twer, J. Phys. A 17, L105 (1984); P. Grassberger, ibid. 22, L1103 (1989); H. Takayasu and A. Yu. Tretyakov, Phys. Rev. Lett. 68, 3060 (1992); I. Jensen, Phys. Rev. E 50, 3623 (1994); N. Menyhard and G. Ódor, J. Phys. A 29, 7739 (1996); J. Cardy and U. C. Täuber, Phys. Rev. Lett. 77, 4780 (1996). H. Hinrichsen, Phys. Rev. E 55, 219 (1997); W. Hwang, S. Kwon, H. Park, and H. Park, Phys. Rev. E 57, 6438 (1998).
-
(1998)
Phys. Rev. E
, vol.57
, pp. 6438
-
-
Hwang, W.1
Kwon, S.2
Park, H.3
Park, H.4
-
55
-
-
0041469272
-
-
[30] A. A. Ali and D. Dhar, Phys. Rev. E 51, R2705 (1995); Phys. Rev. E 52, 4804 (1995).
-
(1995)
Phys. Rev. E
, vol.52
, pp. 4804
-
-
-
56
-
-
85037792745
-
-
Ref [12]
-
[31] See L. P. Kadanoff et al in Ref [12]
-
-
-
Kadanoff, L.P.1
-
57
-
-
0000943599
-
-
[32] The question of open versus closed models for SOC is also discussed in A. Montakhab and J. M. Carlson, Phys. Rev. E 58, 5608 (1998).
-
(1998)
Phys. Rev. E
, vol.58
, pp. 5608
-
-
Montakhab, A.1
Carlson, J.M.2
-
58
-
-
85037784731
-
-
e-print: cond-mat/9902195
-
[33] Sometimes the supervisor holds the job description "gardener"; see H. M. Broeker and P. Grassberger, e-print: cond-mat/9902195.
-
-
-
Broeker, H.M.1
Grassberger, P.2
-
65
-
-
36149039879
-
-
[40] Epidemics with immunity fall in the universality class of dynamic percolation. See J. L. Cardy and P. Grassberger, J. Phys. A 18, L267 (1985); H. K. Janssen, Z. Phys. B 58, 311 (1985).
-
(1985)
J. Phys. A
, vol.18
-
-
Cardy, J.L.1
Grassberger, P.2
-
66
-
-
0000940180
-
-
[40] Epidemics with immunity fall in the universality class of dynamic percolation. See J. L. Cardy and P. Grassberger, J. Phys. A 18, L267 (1985); H. K. Janssen, Z. Phys. B 58, 311 (1985).
-
(1985)
Z. Phys. B
, vol.58
, pp. 311
-
-
Janssen, H.K.1
-
67
-
-
3843080724
-
-
[41] A. Vespignani, R. Dickman, M. A. Muñoz, and Stefano Zapperi, Phys. Rev. Lett. 81, 5676 (1998).
-
(1998)
Phys. Rev. Lett.
, vol.81
, pp. 5676
-
-
Vespignani, A.1
Dickman, R.2
Muñoz, M.A.3
Zapperi, S.4
-
68
-
-
4243410993
-
-
[42] M. A. Muñoz, R. Dickman, A. Vespignani, and Stefano Zapperi, Phys. Rev. E 59, 6175 (1999).
-
(1999)
Phys. Rev. E
, vol.59
, pp. 6175
-
-
Muñoz, M.A.1
Dickman, R.2
Vespignani, A.3
Zapperi, S.4
-
70
-
-
0030705043
-
-
and references therein
-
[44] See H. Leschhorn, T. Nattermann, S. Stepanow and L-H. Tang, Ann. Phys. 6, 1 (1997), and references therein.
-
(1997)
Ann. Phys.
, vol.6
, pp. 1
-
-
Leschhorn, H.1
Nattermann, T.2
Stepanow, S.3
Tang, L.-H.4
-
73
-
-
44049111126
-
-
[47] Extremal dynamics has been introduced in invasion percolation [46], applied to linear interface models in S. I. Zaitsev, Physica A 189, 411, (1992), and S. Roux and A. Hansen, J. Phys. (France) I, 4, 515 (1994); and to quenched KPZ in : K. Sneppen, Phys. Rev. Lett. 69, 3539 (1992); S. Havlin, A.-L. Barabási, S. V. Buldyrev, C. K. Peng, M. Schwartz, H. E. Stanley, and T. Vicsek, in Growth Patterns in Physical Sciences and Biology [Proc. 1991 NATO Advanced Research Workshop, Granada], edited by J. M. Garcia-Ruiz, E. Louis, P. Meakin, and L. M. Sander (Plenum Press, New York, 1993).
-
(1992)
Physica A
, vol.189
, pp. 411
-
-
Zaitsev, S.I.1
-
74
-
-
0002391619
-
-
[47] Extremal dynamics has been introduced in invasion percolation [46], applied to linear interface models in S. I. Zaitsev, Physica A 189, 411, (1992), and S. Roux and A. Hansen, J. Phys. (France) I, 4, 515 (1994); and to quenched KPZ in : K. Sneppen, Phys. Rev. Lett. 69, 3539 (1992); S. Havlin, A.-L. Barabási, S. V. Buldyrev, C. K. Peng, M. Schwartz, H. E. Stanley, and T. Vicsek, in Growth Patterns in Physical Sciences and Biology [Proc. 1991 NATO Advanced Research Workshop, Granada], edited by J. M. Garcia-Ruiz, E. Louis, P. Meakin, and L. M. Sander (Plenum Press, New York, 1993).
-
(1994)
J. Phys. (France) I
, vol.4
, pp. 515
-
-
Roux, S.1
Hansen, A.2
-
75
-
-
0000757572
-
-
[47] Extremal dynamics has been introduced in invasion percolation [46], applied to linear interface models in S. I. Zaitsev, Physica A 189, 411, (1992), and S. Roux and A. Hansen, J. Phys. (France) I, 4, 515 (1994); and to quenched KPZ in : K. Sneppen, Phys. Rev. Lett. 69, 3539 (1992); S. Havlin, A.-L. Barabási, S. V. Buldyrev, C. K. Peng, M. Schwartz, H. E. Stanley, and T. Vicsek, in Growth Patterns in Physical Sciences and Biology [Proc. 1991 NATO Advanced Research Workshop, Granada], edited by J. M. Garcia-Ruiz, E. Louis, P. Meakin, and L. M. Sander (Plenum Press, New York, 1993).
-
(1992)
Phys. Rev. Lett.
, vol.69
, pp. 3539
-
-
Sneppen, K.1
-
76
-
-
85037797893
-
-
Proc. 1991 NATO Advanced Research Workshop, Granada, edited by J. M. Garcia-Ruiz, E. Louis, P. Meakin, and L. M. Sander Plenum Press, New York
-
[47] Extremal dynamics has been introduced in invasion percolation [46], applied to linear interface models in S. I. Zaitsev, Physica A 189, 411, (1992), and S. Roux and A. Hansen, J. Phys. (France) I, 4, 515 (1994); and to quenched KPZ in : K. Sneppen, Phys. Rev. Lett. 69, 3539 (1992); S. Havlin, A.-L. Barabási, S. V. Buldyrev, C. K. Peng, M. Schwartz, H. E. Stanley, and T. Vicsek, in Growth Patterns in Physical Sciences and Biology [Proc. 1991 NATO Advanced Research Workshop, Granada], edited by J. M. Garcia-Ruiz, E. Louis, P. Meakin, and L. M. Sander (Plenum Press, New York, 1993).
-
(1993)
Growth Patterns in Physical Sciences and Biology
-
-
Havlin, S.1
Barabási, A.-L.2
Buldyrev, S.V.3
Peng, C.K.4
Schwartz, M.5
Stanley, H.E.6
Vicsek, T.7
-
82
-
-
84914594352
-
-
[52] G. Parisi and L. Pietronero, Europhys. Lett. 16, 321 (1991); Physica A 179, 16 (1991).
-
(1991)
Physica A
, vol.179
, pp. 16
-
-
-
87
-
-
0000575664
-
-
[57] Similar paths have been followed by K. Sneppen, Physica A 221, 168 (1995); M. Vergeles, Phys. Rev. Lett. 75, 1969 (1995); A. Gabrielle, G Calderelli, and L. Pietronero, e-print: cond-mat/9910425.
-
(1995)
Physica A
, vol.221
, pp. 168
-
-
Sneppen, K.1
-
88
-
-
0000181566
-
-
[57] Similar paths have been followed by K. Sneppen, Physica A 221, 168 (1995); M. Vergeles, Phys. Rev. Lett. 75, 1969 (1995); A. Gabrielle, G Calderelli, and L. Pietronero, e-print: cond-mat/9910425.
-
(1995)
Phys. Rev. Lett.
, vol.75
, pp. 1969
-
-
Vergeles, M.1
-
89
-
-
0000575664
-
-
e-print: cond-mat/9910425
-
[57] Similar paths have been followed by K. Sneppen, Physica A 221, 168 (1995); M. Vergeles, Phys. Rev. Lett. 75, 1969 (1995); A. Gabrielle, G Calderelli, and L. Pietronero, e-print: cond-mat/9910425.
-
-
-
Gabrielle, A.1
Calderelli, G.2
Pietronero, L.3
-
93
-
-
0002619760
-
-
[61] B. Jovanović, S. V. Buldyrev, S. Havlin, and H. E. Stanley, Phys. Rev. E 50, R2403 (1994).
-
(1994)
Phys. Rev. E
, vol.50
-
-
Jovanović, B.1
Buldyrev, S.V.2
Havlin, S.3
Stanley, H.E.4
-
95
-
-
0000098514
-
-
e-print: cond-mat/9910029
-
[62] A. Lipowski and M. /Lopata, Phys. Rev. E 60, 1516 (1999); A. Lipowski, e-print: cond-mat/9910029.
-
-
-
Lipowski, A.1
-
96
-
-
0001550945
-
-
[63] It is sometimes argued that Takayasu's aggregation model (H. Takayasu, Phys. Rev. Lett. 63, 2563 (1989)) is an example of SOC without slow driving. The model has a scale-invariant scaling limit, rather than a stationary state as such. More significantly, Dhar has shown that Takayasu's model is equivalent to a sandpile model, which does exhibit scale invariance under slow driving.
-
(1989)
Phys. Rev. Lett.
, vol.63
, pp. 2563
-
-
Takayasu, H.1
-
97
-
-
85037803095
-
-
note
-
[64] See Ref. [11], which also includes a discussion of directed sandpiles [35], for which the avalanche exponents have been determined.
-
-
-
-
98
-
-
0003432181
-
-
Copernicus, New York
-
[65] P. Bak, How Nature works (Copernicus, New York, 1996).
-
(1996)
How Nature Works
-
-
Bak, P.1
-
103
-
-
0029657037
-
-
[70] V. Frette, K. Christensen, A.M. Malthe-Sørenssen, J. Feder, T. Jøssang and P. Meakin, Nature 397, 49 (1996).
-
(1996)
Nature
, vol.397
, pp. 49
-
-
Frette, V.1
Christensen, K.2
Malthe-Sørenssen, A.M.3
Feder, J.4
Jøssang, T.5
Meakin, P.6
-
107
-
-
0000054421
-
-
[74] D. Spasojević, S. Bukvić, S. Milosević, and H. E. Stanley, Phys. Rev. E 54, 2531 (1996).
-
(1996)
Phys. Rev. E
, vol.54
, pp. 2531
-
-
Spasojević, D.1
Bukvić, S.2
Milosević, S.3
Stanley, H.E.4
-
109
-
-
0000658964
-
-
[76] S. Zapperi, P. Cizeau, G. Durin, and H. E. Stanley, Phys. Rev. B 58, 6353 (1998).
-
(1998)
Phys. Rev. B
, vol.58
, pp. 6353
-
-
Zapperi, S.1
Cizeau, P.2
Durin, G.3
Stanley, H.E.4
-
112
-
-
0001413916
-
-
[79] S. Field, J. Witt, F. Nori, and X. Ling, Phys. Rev. Lett. 74, 1206 (1995).
-
(1995)
Phys. Rev. Lett.
, vol.74
, pp. 1206
-
-
Field, S.1
Witt, J.2
Nori, F.3
Ling, X.4
-
113
-
-
0001415983
-
-
[80] C. J. Olson, C. Reichhard and F. Nori, Phys. Rev. B 56, 6175 (1997); K. E. Bassler and M. Paczuski, Phys. Rev. Lett. 81, 3761 (1998).
-
(1997)
Phys. Rev. B
, vol.56
, pp. 6175
-
-
Olson, C.J.1
Reichhard, C.2
Nori, F.3
-
114
-
-
0032569546
-
-
[80] C. J. Olson, C. Reichhard and F. Nori, Phys. Rev. B 56, 6175 (1997); K. E. Bassler and M. Paczuski, Phys. Rev. Lett. 81, 3761 (1998).
-
(1998)
Phys. Rev. Lett.
, vol.81
, pp. 3761
-
-
Bassler, K.E.1
Paczuski, M.2
-
115
-
-
0000089235
-
-
[81] A. Garcimartín, A. Guarino, L. Bellon and S. Ciliberto, Phys. Rev. Lett. 79, 3202 (1997); A. Guarino, A. Garcimartín and S. Ciliberto, Eur. Phys. J. B 6, 13 (1998).
-
(1997)
Phys. Rev. Lett.
, vol.79
, pp. 3202
-
-
Garcimartín, A.1
Guarino, A.2
Bellon, L.3
Ciliberto, S.4
-
116
-
-
0032303154
-
-
[81] A. Garcimartín, A. Guarino, L. Bellon and S. Ciliberto, Phys. Rev. Lett. 79, 3202 (1997); A. Guarino, A. Garcimartín and S. Ciliberto, Eur. Phys. J. B 6, 13 (1998).
-
(1998)
Eur. Phys. J. B
, vol.6
, pp. 13
-
-
Guarino, A.1
Garcimartín, A.2
Ciliberto, S.3
-
117
-
-
0000128806
-
-
[82] C. Maes, A. Van Moffaert, H. Frederix and H. Strauven, Phys. Rev. B 57, 4987 (1998).
-
(1998)
Phys. Rev. B
, vol.57
, pp. 4987
-
-
Maes, C.1
Van Moffaert, A.2
Frederix, H.3
Strauven, H.4
-
118
-
-
0000165398
-
-
[83] A. Petri, G. Paparo, A. Vespignani, A. Alippi and M. Costantini, Phys. Rev. Lett. 73, 3423 (1994).
-
(1994)
Phys. Rev. Lett.
, vol.73
, pp. 3423
-
-
Petri, A.1
Paparo, G.2
Vespignani, A.3
Alippi, A.4
Costantini, M.5
-
122
-
-
18044365129
-
-
[87] S. Zapperi, P. Ray, H. E. Stanley and A. Vespignani, Phys. Rev. E 59, 5049 (1999).
-
(1999)
Phys. Rev. E
, vol.59
, pp. 5049
-
-
Zapperi, S.1
Ray, P.2
Stanley, H.E.3
Vespignani, A.4
-
124
-
-
4243894272
-
-
[89] L. Carrillo, L. Mañosa, J. Ortín, A. Planes and E. Vives, Phys. Rev. Lett. 81, 1889 (1998).
-
(1998)
Phys. Rev. Lett.
, vol.81
, pp. 1889
-
-
Carrillo, L.1
Mañosa, L.2
Ortín, J.3
Planes, A.4
Vives, E.5
-
128
-
-
0030805295
-
-
[93] Conflicting conclusions have been drawn from the same paleontologic data: R. V. Solé S. C. Manrubia, M. Benton and P. Bak, Nature 388, 764 (1997); J. W. Kirchner and A. Weil, Nature 395, 337 (1998).
-
(1997)
Nature
, vol.388
, pp. 764
-
-
Solé, R.V.1
Manrubia, S.C.2
Benton, M.3
Bak, P.4
-
129
-
-
0032563869
-
-
[93] Conflicting conclusions have been drawn from the same paleontologic data: R. V. Solé S. C. Manrubia, M. Benton and P. Bak, Nature 388, 764 (1997); J. W. Kirchner and A. Weil, Nature 395, 337 (1998).
-
(1998)
Nature
, vol.395
, pp. 337
-
-
Kirchner, J.W.1
Weil, A.2
-
130
-
-
0001349398
-
-
[94] See for example: K. Chen, P. Bak and S. P. Obukhov, Phys. Rev. A 43, 625 (1991); J. M. Carlson, J. S. Langer and B. E. Shaw, Rev. Mod. Phys. 66, 657 (1994); J. B. Rundle, W. Klein and S. Gross, Phys. Rev. Lett. 76, 4285 (1996); J. B. Rundle, D. L. Turcotte and W. Klein (eds.) Proceedings of the Santa Fe Institute Workshop on Reduction and Predictability of Natural Disasters, Santa Fe, NM, 1994 (Addison-Welsley, Reading, MA, 1995), and references therein.
-
(1991)
Phys. Rev. A
, vol.43
, pp. 625
-
-
Chen, K.1
Bak, P.2
Obukhov, S.P.3
-
131
-
-
12044257283
-
-
[94] See for example: K. Chen, P. Bak and S. P. Obukhov, Phys. Rev. A 43, 625 (1991); J. M. Carlson, J. S. Langer and B. E. Shaw, Rev. Mod. Phys. 66, 657 (1994); J. B. Rundle, W. Klein and S. Gross, Phys. Rev. Lett. 76, 4285 (1996); J. B. Rundle, D. L. Turcotte and W. Klein (eds.) Proceedings of the Santa Fe Institute Workshop on Reduction and Predictability of Natural Disasters, Santa Fe, NM, 1994 (Addison-Welsley, Reading, MA, 1995), and references therein.
-
(1994)
Rev. Mod. Phys.
, vol.66
, pp. 657
-
-
Carlson, J.M.1
Langer, J.S.2
Shaw, B.E.3
-
132
-
-
0000764651
-
-
[94] See for example: K. Chen, P. Bak and S. P. Obukhov, Phys. Rev. A 43, 625 (1991); J. M. Carlson, J. S. Langer and B. E. Shaw, Rev. Mod. Phys. 66, 657 (1994); J. B. Rundle, W. Klein and S. Gross, Phys. Rev. Lett. 76, 4285 (1996); J. B. Rundle, D. L. Turcotte and W. Klein (eds.) Proceedings of the Santa Fe Institute Workshop on Reduction and Predictability of Natural Disasters, Santa Fe, NM, 1994 (Addison-Welsley, Reading, MA, 1995), and references therein.
-
(1996)
Phys. Rev. Lett.
, vol.76
, pp. 4285
-
-
Rundle, J.B.1
Klein, W.2
Gross, S.3
-
133
-
-
0001349398
-
-
Addison-Welsley, Reading, MA, and references therein
-
[94] See for example: K. Chen, P. Bak and S. P. Obukhov, Phys. Rev. A 43, 625 (1991); J. M. Carlson, J. S. Langer and B. E. Shaw, Rev. Mod. Phys. 66, 657 (1994); J. B. Rundle, W. Klein and S. Gross, Phys. Rev. Lett. 76, 4285 (1996); J. B. Rundle, D. L. Turcotte and W. Klein (eds.) Proceedings of the Santa Fe Institute Workshop on Reduction and Predictability of Natural Disasters, Santa Fe, NM, 1994 (Addison-Welsley, Reading, MA, 1995), and references therein.
-
(1995)
Proceedings of the Santa Fe Institute Workshop on Reduction and Predictability of Natural Disasters, Santa Fe, NM, 1994
-
-
Rundle, J.B.1
Turcotte, D.L.2
Klein, W.3
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