AVALANCHES IN THE DIRECTED PERCOLATION DEPINNING AND SELF-ORGANIZED DEPINNING MODELS OF INTERFACE ROUGHENING

Fractals ◽  
1996 ◽  
Vol 04 (03) ◽  
pp. 307-319 ◽  
Author(s):  
S. V. BULDYREV ◽  
L. A. N. AMARAL ◽  
A. -L. BARABÁSI ◽  
S. T. HARRINGTON ◽  
S. HAVLIN ◽  
...  
Keyword(s):  
Size Distribution ◽  
Quenched Disorder ◽  
Directed Percolation ◽  
Invasion Process ◽  
Avalanche Size ◽  
Scaling Properties ◽  
Self Organized ◽  
Interface Roughening

We review the recently introduced Directed Percolation Depinning (DPD) and Self-Organized Depinning (SOD) models for interface roughening with quenched disorder. The differences in the dynamics of the invasion process in these two models are discussed and different avalanche definitions are presented. The scaling properties of the avalanche size distribution and the properties of active cells are discussed.

A DIMENSION FORMULA FOR SELF-SIMILAR AND SELF-AFFINE FRACTALS

Fractals ◽  
1995 ◽  
Vol 03 (03) ◽  
pp. 525-531 ◽  
Author(s):  
GREG HUBER ◽  
MOGENS H. JENSEN ◽  
KIM SNEPPEN
Keyword(s):  
Time Series ◽  
Size Distribution ◽  
Fragment Size ◽  
General Relation ◽  
Fractal Dimensions ◽  
Directed Percolation ◽  
Fragment Size Distribution ◽  
Scaling Properties ◽  
Dimension Formula ◽  
Self Similar

A geometric and very general relation between the size distribution and the fractal dimensions of a set of objects is presented. The applications are numerous, ranging from fragmentation experiments to time series. For example, it may be used to understand the fragment-size distribution of fragmenting gypsum. The formalism also generalizes to self-affine fractals, and here it is applied to the scaling properties of self-interactions in (1+1)-d directed percolation.

FRACTALS, SCALING AND THE QUESTION OF SELF-ORGANIZED CRITICALITY IN MAGNETIZATION PROCESSES

Fractals ◽  
1995 ◽  
Vol 03 (02) ◽  
pp. 351-370 ◽  
Author(s):  
GIANFRANCO DURIN ◽  
GIORGIO BERTOTTI ◽  
ALESSANDRO MAGNI
Keyword(s):  
Fractal Dimension ◽  
Domain Wall ◽  
Power Spectra ◽  
Domain Wall Motion ◽  
Soft Magnetic Materials ◽  
Barkhausen Effect ◽  
Scaling Properties ◽  
Domain Wall Dynamics ◽  
Self Organized ◽  
Self Organized Criticality

The main physical aspects and the theoretical description of stochastic domain wall dynamics in soft magnetic materials are reviewed. The intrinsically random nature of domain wall motion results in the Barkhausen effect, which exibits scaling properties at low magnetization rates and 1/f power spectra. It is shown that the Barkhausen signal ν, as well as the size Δx and the duration Δu of jumps follow distributions of the form ν−α, Δx−β, Δu−γ, with α=1−c, β=3/2−c/2, γ=2–c, where c is a dimensionless parameter proportional to the applied field rate. These results are analytically calculated by means of a stochastic differential equation for the domain wall dynamics in a random perturbed medium with brownian properties and then compared to experiments. The Barkhausen signal is found to be related to a random Cantor dust with fractal dimension D=1−c, from which the scaling exponents are calculated using simple properties of fractal geometry. Fractal dimension Δ of the signal v is also studied using four different methods of calculation, giving Δ≈1.5, independent of the method used and of the parameter c. The stochastic model is analyzed in detail in order to clarify if the shown properties can be interpreted as manifestations of self-organized criticality in magnetic systems.

scholarly journals Universality in the One-Dimensional Self-Organized Critical Forest-Fire Model

1994 ◽  
Vol 49 (9) ◽  
pp. 856-860
Author(s):  
Barbara Drossel ◽  
Siegfried Clar ◽  
Franz Schwabl
Keyword(s):  
Size Distribution ◽  
Forest Fire ◽  
Nearest Neighbor ◽  
The Self ◽  
One Dimension ◽  
Fire Model ◽  
One Dimensional ◽  
Self Organized ◽  
Forest Fire Model ◽  
The One

Abstract We modify the rules of the self-organized critical forest-fire model in one dimension by allowing the fire to jum p over holes of ≤ k sites. An analytic calculation shows that not only the size distribution of forest clusters but also the size distribution of fires is characterized by the same critical exponent as in the nearest-neighbor model, i.e. the critical behavior of the model is universal. Computer simulations confirm the analytic results.

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.

scholarly journals Analysis of the one-dimensional Yut-Nori game: Winning strategy and avalanche-size distribution

2013 ◽  
Vol 63 (8) ◽  
pp. 1497-1502
Author(s):  
Hye Jin Park ◽  
Hasung Sim ◽  
Hang-Hyun Jo ◽  
Beom Jun Kim
Keyword(s):  
Size Distribution ◽  
Winning Strategy ◽  
Avalanche Size ◽  
One Dimensional ◽  
The One

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.

ANOMALOUS INTERFACE ROUGHENING: THE ROLE OF A GRADIENT IN THE DENSITY OF PINNING SITES

Fractals ◽  
1993 ◽  
Vol 01 (04) ◽  
pp. 818-826 ◽  
Author(s):  
L.A.N. AMARAL ◽  
A.-L. BARABÁSI ◽  
S.V. BULDYREV ◽  
S. HAVLIN ◽  
H.E. STANLEY
Keyword(s):  
Correlation Length ◽  
Qualitative Agreement ◽  
Critical Concentration ◽  
Scaling Properties ◽  
Correlation Lengths ◽  
Longitudinal Correlation ◽  
New Correlation ◽  
Roughness Exponent ◽  
Interface Roughening

We study the effect on interface roughening of a gradient ∇p in the density of pinning sites p. We identify a new correlation length, ξ, which is a function of ∇p: ξ~(∇p)−γ/α, where α=ν⊥/ν|| is the roughness exponent, and γ=ν⊥/(1+ν⊥). The exponents ν⊥ and ν|| characterize the transverse and longitudinal correlation lengths. To investigate the effect of ∇p on the scaling properties of the interface in (1+1) and (2+1) dimensions, we calculate the critical concentration, pc, and the exponents γ and α from which ν⊥ and ν|| can be determined. Our results are in qualitative agreement with some of the features of imbibition experiments.

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