THE AVERAGE AVALANCHE SIZE IN THE MANNA MODEL AND OTHER MODELS OF SELF-ORGANIZED CRITICALITY

2013 ◽  
Vol 27 (05) ◽  
pp. 1350009 ◽  
Author(s):  
GUNNAR PRUESSNER
Keyword(s):  
Field Theory ◽  
Boundary Conditions ◽  
Higher Dimensions ◽  
One Dimension ◽  
Leading Order ◽  
Numerical Work ◽  
Avalanche Size ◽  
Self Organized ◽  
Self Organized Criticality ◽  
External Driving

The average avalanche size can be calculated exactly in a number of models of self-organized criticality (SOC). While the calculation is straight-forward in one dimension, it is more involved in higher dimensions and further complicated by the presence of different boundary conditions and different forms of external driving. Amplitudes of the leading order are determined analytically and evaluated to obtain analytical references for numerical work. A subtle link exists between the procedure to calculate the average avalanche size and the field theory of SOC.

A SIMPLE NEURON NETWORK BASED ON HEBB'S RULE

2011 ◽  
Vol 22 (07) ◽  
pp. 755-763
Author(s):  
GUI-QING ZHANG ◽  
ZI YU ◽  
QIU-YING YANG ◽  
TIAN-LUN CHEN
Keyword(s):  
Finite Size ◽  
Neural Model ◽  
Fat Tails ◽  
Neuron Network ◽  
Finite Size Effects ◽  
Gaussian Shape ◽  
Avalanche Size ◽  
Self Organized ◽  
Self Organized Criticality ◽  
The Stability

A weighted mechanism in neural networks is studied. This paper focuses on the neuron's behaviors in an area of brain. Our model could regenerate the power-law behaviors and finite size effects of neural avalanche. The probability density functions (PDFs) for the neural avalanche size differing at different times (lattice size) have fat tails with a q-Gaussian shape and the same parameter value of q in the thermodynamical limit. Above two kinds of behaviors show that our neural model can well present self-organized critical behavior. The robustness of PDFs shows the stability of self-organized criticality. Meanwhile, the avalanche scaling relation of the waiting time has been found.

Field Theory for a Model of Self-Organized Criticality

1994 ◽  
Vol 27 (2) ◽  
pp. 97-102 ◽  
Author(s):  
M Paczuski ◽  
S Maslov ◽  
P Bak
Keyword(s):  
Field Theory ◽  
Self Organized ◽  
Self Organized Criticality

SELF-ORGANIZED CRITICALITY IN AN EARTHQUAKE MODEL BASED ON ASSORTATIVE SCALE-FREE NETWORKS

2011 ◽  
Vol 22 (05) ◽  
pp. 483-493 ◽  
Author(s):  
MIN LIN ◽  
GANG WANG
Keyword(s):  
Stress Evolution ◽  
Scale Invariant ◽  
Avalanche Size ◽  
Scale Free ◽  
Self Organized ◽  
Dynamical Behaviors ◽  
Period Distribution ◽  
Scale Free Networks ◽  
Earthquake Model ◽  
Self Organized Criticality

A modified Olami–Feder–Christensen (OFC) earthquake model on scale-free networks with assortative mixing is introduced. In this model, the distributions of avalanche sizes and areas display power-law behaviors. It is found that the period distribution of avalanches displays a scale-invariant law with the increment of range parameter d. More importantly, different assortative topologies lead to different dynamical behaviors, such as the distribution of avalanche size, the stress evolution process, and period distribution.

scholarly journals Emergence of Lagrangian Field Theory from Self-Organized Criticality

2020 ◽  
Author(s):  
Ervin Goldfain
Keyword(s):  
Field Theory ◽  
Critical Behavior ◽  
Large Scale ◽  
Complex Dynamics ◽  
Large Scale Systems ◽  
Self Organized ◽  
Lagrangian Field Theory ◽  
Self Organized Criticality ◽  
Universal Mechanism

Self-organized criticality (SOC) is a universal mechanism for self-sustained critical behavior in large-scale systems evolving outside equilibrium. Our report explores a tentative link between SOC and Lagrangian field theory, with the long-term goal of bridging the gap between complex dynamics and the non-perturbative behavior of quantum fields.

scholarly journals Disentangling the thermofield-double state

2022 ◽  
Vol 2022 (1) ◽  
Author(s):  
Pouria Dadras
Keyword(s):  
Field Theory ◽  
Black Hole ◽  
Strong Coupling ◽  
Entanglement Entropy ◽  
Coarse Grained ◽  
One Dimension ◽  
Leading Order ◽  
Point Function ◽  
Replica Trick ◽  
Large N

Abstract In this paper, we consider the evolution of the thermofield-double state under the double-traced operator that connects its both sides. We will compute the entanglement entropy of the resulting state using the replica trick for the large N field theory. To leading order, it can be computed from the two-point function of the theory, where, in CFTs, it is fixed by the symmetries. Due to the exponential decay of the interaction, the entanglement entropy saturates about the thermal time after the interaction is on. Next, we restrict ourselves to one dimension and assume that the theory at strong coupling is effectively described by the Schwarzian action. We then compute the coarse-grained entropy of the resulting state using the four-point function. The equality of the two entropies implies that the double-traced operators in our theory act coherently. In AdS/CFT correspondence where the thermofield-double state corresponds to a two-sided black hole, the action of a double-traced operator corresponds to shrinking or expanding the black hole in the bulk.

THE EVIDENCE FOR SELF-ORGANIZED CRITICALITY IN SANDPILE DYNAMICS

Fractals ◽  
1995 ◽  
Vol 03 (03) ◽  
pp. 431-443 ◽  
Author(s):  
J. FEDER
Keyword(s):  
Characteristic Size ◽  
Size Distributions ◽  
Exponential Distributions ◽  
Avalanche Size ◽  
Stretched Exponential ◽  
Self Organized ◽  
Self Organized Criticality ◽  
Stretched Exponential Distribution ◽  
Rotating Drums ◽  
Low Rate

Self-organized criticality (SOC) is thought to describe avalanche dynamics in sandpiles. Experiments on the dynamics of “sandpiles” fall in two broad categories. Sandpiles in rotating drums exhibit periodic large avalanches, which is inconsistent with SOC. Other experiments study sandpiles on a circular support driven by the addition of grains of sand at a low rate from above and centered with respect to the support. The mass of avalanches that drop sand off the support is typically measured by a balance. It has been claimed that the observed avalanche statistics is consistent with SOC. However, I find that experiments described in the literature all have avalanche-size distributions that can be very well described by stretched-exponential distributions. Since the stretched-exponential distribution has a characteristic size, I conclude that the experiments described in the literature are inconsistent with SOC.

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