Lyapunov exponents and transport in the Zhang model of self-organized criticality

Cessac B, Blanchard P, Krüger T (2001)
PHYSICAL REVIEW E 64(1).

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Zeitschriftenaufsatz | Veröffentlicht | Englisch
Abstract / Bemerkung
We discuss the role played by Lyapunov exponents in the dynamics of Zhang's model of self-organized criticality. We show that a Large part of the spectrum (the slowest modes) is associated with energy transport in the lattice. In particular, we give bounds on the first negative Lyapunov exponent in terms of the energy flux dissipated at the boundaries per unit of time. We then establish an explicit formula for the transport modes that appear as diffusion modes in a landscape where the metric is given by the density of active sites. We use a finite size scaling ansatz for the Lyapunov spectrum, and relate the scaling exponent to the scaling of quantities such as avalanche size, duration, density of active sites, etc.
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PHYSICAL REVIEW E
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64
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1
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Cessac B, Blanchard P, Krüger T. Lyapunov exponents and transport in the Zhang model of self-organized criticality. PHYSICAL REVIEW E. 2001;64(1).
Cessac, B., Blanchard, P., & Krüger, T. (2001). Lyapunov exponents and transport in the Zhang model of self-organized criticality. PHYSICAL REVIEW E, 64(1). doi:10.1103/PhysRevE.64.016133
Cessac, B., Blanchard, P., and Krüger, T. (2001). Lyapunov exponents and transport in the Zhang model of self-organized criticality. PHYSICAL REVIEW E 64.
Cessac, B., Blanchard, P., & Krüger, T., 2001. Lyapunov exponents and transport in the Zhang model of self-organized criticality. PHYSICAL REVIEW E, 64(1).
B. Cessac, P. Blanchard, and T. Krüger, “Lyapunov exponents and transport in the Zhang model of self-organized criticality”, PHYSICAL REVIEW E, vol. 64, 2001.
Cessac, B., Blanchard, P., Krüger, T.: Lyapunov exponents and transport in the Zhang model of self-organized criticality. PHYSICAL REVIEW E. 64, (2001).
Cessac, B, Blanchard, Philippe, and Krüger, Tyll. “Lyapunov exponents and transport in the Zhang model of self-organized criticality”. PHYSICAL REVIEW E 64.1 (2001).

5 Zitationen in Europe PMC

Daten bereitgestellt von Europe PubMed Central.

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29 References

Daten bereitgestellt von Europe PubMed Central.

Self-organized criticality: An explanation of the 1/f noise.
Bak P, Tang C, Wiesenfeld K., Phys. Rev. Lett. 59(4), 1987
PMID: 10035754
Self-organized criticality.
Bak P, Tang C, Wiesenfeld K., Phys. Rev., A 38(1), 1988
PMID: 9900174

Bak, 1996
Self-organized critical state of sandpile automaton models.
Dhar D., Phys. Rev. Lett. 64(14), 1990
PMID: 10041442

Dhar, J. Phys. A 23(), 1990

Majumdar, Physica A 185(), 1992
Exactly solved model of self-organized critical phenomena.
Dhar D, Ramaswamy R., Phys. Rev. Lett. 63(16), 1989
PMID: 10040637
Scaling theory of self-organized criticality.
Zhang YC., Phys. Rev. Lett. 63(5), 1989
PMID: 10041083

Sornette, J. Phys. (France) 5(), 1995
Scaling and universality in avalanches.
Kadanoff LP, Nagel SR, Wu L, Zhou Sm., Phys. Rev., A 39(12), 1989
PMID: 9901255

Blanchard, J. Stat. Phys. 88(), 1997

Cessac, 1998

Blanchard, J. Stat. Phys. 98(), 2000

Dickman, Phys. Rev. E 57(), 1998

Giacometti, Phys. Rev. E 58(), 1998

Vespignani, Phys. Rev. E 57(), 1998

Oseledec, Trans. Moscow Math. Soc. 19(), 1968

Eckmann, Rev. Mod. Phys. 57(), 1985
Liapunov exponents from time series.
Eckmann J, Kamphorst SO, Ruelle D, Ciliberto S., Phys. Rev., A 34(6), 1986
PMID: 9897880

Ledrappier, Ann. Math. 122(), 1985
Spatiotemporal intermittency on the sandpile.
Erzan A, Sinha S., Phys. Rev. Lett. 66(21), 1991
PMID: 10043607

Newmann, Commun. Math. Phys. 103(), 1986

Von, Physica D 101(), 1997

Pietronero, Physica A 173(), 1991

Grassberger, J. Phys. (France) 51(), 1990
Lyapunov instability of dense Lennard-Jones fluids.
Posch HA, Hoover WG., Phys. Rev., A 38(1), 1988
PMID: 9900186
Self-organized critical state of sandpile automaton models.
Dhar D., Phys. Rev. Lett. 64(14), 1990
PMID: 10041442

Luebeck, Phys. Rev. E 56(), 1997

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