---
_id: '1616785'
abstract:
- lang: eng
text: 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.
article_type: original
author:
- first_name: B
full_name: Cessac, B
last_name: Cessac
- first_name: Philippe
full_name: Blanchard, Philippe
id: '40322'
last_name: Blanchard
- first_name: Tyll
full_name: Krüger, Tyll
id: '87692'
last_name: Krüger
citation:
ama: Cessac B, Blanchard P, Krüger T. Lyapunov exponents and transport in the Zhang
model of self-organized criticality. *PHYSICAL REVIEW E*. 2001;64(1).
angewandte-chemie: B. Cessac, P. Blanchard, and T. Krüger, “Lyapunov exponents
and transport in the Zhang model of self-organized criticality”, *PHYSICAL
REVIEW E*, **2001**, *64*.
apa: 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
apa_indent: 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

aps: ' B. Cessac, P. Blanchard, and T. Krüger, Lyapunov exponents and transport
in the Zhang model of self-organized criticality, PHYSICAL REVIEW E **64**,
(2001).'
bio1: Cessac B, Blanchard P, Krüger T (2001)

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

PHYSICAL REVIEW E 64(1).
chicago: Cessac,
B, Blanchard, Philippe, and Krüger, Tyll. 2001. “Lyapunov exponents and transport
in the Zhang model of self-organized criticality”. *PHYSICAL REVIEW E*
64 (1).

default: Cessac B, Blanchard P, Krüger T (2001)

*PHYSICAL REVIEW E*
64(1).
dgps: Cessac,
B., Blanchard, P. & Krüger, T. (2001). Lyapunov exponents and transport in
the Zhang model of self-organized criticality. *PHYSICAL REVIEW E*, *64*(1).
AMERICAN PHYSICAL SOC. doi:10.1103/PhysRevE.64.016133.

frontiers: Cessac, B., Blanchard, P., and Krüger, T. (2001). Lyapunov exponents
and transport in the Zhang model of self-organized criticality. *PHYSICAL REVIEW
E* 64.
harvard1: Cessac, B., Blanchard, P., & Krüger, T., 2001. Lyapunov exponents
and transport in the Zhang model of self-organized criticality. *PHYSICAL REVIEW
E*, 64(1).
ieee: ' 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.'
lncs: ' Cessac, B., Blanchard, P., Krüger, T.: Lyapunov exponents and transport
in the Zhang model of self-organized criticality. PHYSICAL REVIEW E. 64, (2001).'
mla: 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).
wels: 'Cessac, B.; Blanchard, P.; Krüger, T. (2001): Lyapunov exponents and transport
in the Zhang model of self-organized criticality *PHYSICAL REVIEW E*,64:(1)'
date_created: 2010-04-28T13:02:37Z
date_updated: 2018-07-24T12:59:42Z
department:
- _id: '29104678'
document_type: journalArticle
doi: 10.1103/PhysRevE.64.016133
edit_mode: expert
external_id:
isi:
- '000169907300043'
pmid:
- '11461357'
first_author: Cessac, B
intvolume: ' 64'
isi: '1'
issue: '1'
language:
- iso: eng
pmid: '1'
publication: PHYSICAL REVIEW E
publication_identifier:
eissn:
- 1095-3787
issn:
- 1063-651X
publication_status: published
publisher: AMERICAN PHYSICAL SOC
quality_controlled: '1'
status: public
title: Lyapunov exponents and transport in the Zhang model of self-organized criticality
type: journal_article
volume: '64'
year: '2001'
...