Sandpiles

2017 ◽  
Author(s):  
Paul Charbonneau
Keyword(s):  
Power Law ◽  
Slope Angle ◽  
The Self ◽  
Numerical Implementation ◽  
Sandpile Model ◽  
Self Organized ◽  
Self Organized Criticality

This chapter describes a simple computational idealization of a sandpile. When sand trickles slowly through your fingers, a small conical pile of sand forms below your hand. Sand avalanches of various sizes intermittently slide down the slope of the pile, which is growing both in width and in height but maintains the same slope angle. The pile of sand is a classic example of self-organized criticality. The chapter first provides an overview of the sandpile model before discussing its numerical implementation and a representative simulation involving a small 100-node lattice. It then examines the invariant power-law behavior of avalanches and the self-organized criticality of a sandpile. The chapter includes exercises and further computational explorations, along with a suggested list of materials for further reading.

scholarly journals Transition from Self-Organized Criticality into Self-Organization during Sliding Si3N4 Balls against Nanocrystalline Diamond Films

Entropy ◽  
2019 ◽  
Vol 21 (11) ◽  
pp. 1055
Author(s):  
Bogatov ◽  
Podgursky ◽  
Vagiström ◽  
Yashin ◽  
Shaikh ◽  
...  
Keyword(s):  
Friction Force ◽  
Power Law ◽  
Early Stage ◽  
Nanocrystalline Diamond ◽  
The Self ◽  
Self Organization ◽  
Power Law Distribution ◽  
Reciprocating Sliding ◽  
Self Organized ◽  
Self Organized Criticality

The paper investigates the variation of friction force (Fx) during reciprocating sliding tests on nanocrystalline diamond (NCD) films. The analysis of the friction behavior during the run-in period is the focus of the study. The NCD films were grown using microwave plasma-enhanced chemical vapor deposition (MW-PECVD) on single-crystalline diamond SCD(110) substrates. Reciprocating sliding tests were conducted under 500 and 2000 g of normal load using Si3N4 balls as a counter body. The friction force permanently varies during the test, namely Fx value can locally increase or decrease in each cycle of sliding. The distribution of friction force drops (dFx) was extracted from the experimental data using a specially developed program. The analysis revealed a power-law distribution f-µ of dFx for the early stage of the run-in with the exponent value (µ) in the range from 0.6 to 2.9. In addition, the frequency power spectrum of Fx time series follows power-law distribution f-α with α value in the range of 1.0–2.0, with the highest values (1.6–2.0) for the initial stage of the run-in. No power-law distribution of dFx was found for the later stage of the run-in and the steady-state periods of sliding with the exception for periods where a relatively extended decrease of coefficient of friction (COF) was observed. The asperity interlocking leads to the stick-slip like sliding at the early stage of the run-in. This tribological behavior can be related to the self-organized criticality (SOC). The emergence of dissipative structures at the later stages of the run-in, namely the formation of ripples, carbonaceous tribolayer, etc., can be associated with the self-organization (SO).

Traffic Jams

2017 ◽  
Author(s):  
Paul Charbonneau
Keyword(s):  
Collective Behavior ◽  
The Self ◽  
Traffic Model ◽  
Numerical Implementation ◽  
Basic Design ◽  
Traffic Jam ◽  
Traffic Jams ◽  
Self Organized ◽  
Car Traffic ◽  
Self Organized Criticality

This chapter considers the occurrence of traffic jams in the flow of moving automobiles as an example of complex collective behavior emerging from the interactions of system elements. It begins with a discussion of the basic design principle of an automobile traffic model and the numerical implementation of the model using the Python code. It then describes a representative simulation involving an ensemble of 300 cars initially at rest and distributed randomly, with a mean spacing of 10 units. It also examines how the traffic jam model behaves, traffic jams as avalanches, and the self-organized criticality of car traffic. The chapter includes exercises and further computational explorations, along with a suggested list of materials for further reading.

Problem behavior in autism spectrum disorders: A paradigmatic self-organized perspective of network structures

2019 ◽  
Vol 42 ◽  
Author(s):  
Lucio Tonello ◽  
Luca Giacobbi ◽  
Alberto Pettenon ◽  
Alessandro Scuotto ◽  
Massimo Cocchi ◽  
...  
Keyword(s):  
Autism Spectrum Disorder ◽  
Problem Behaviors ◽  
Autism Spectrum ◽  
The Self ◽  
Network Structures ◽  
Self Organized ◽  
Critical Equilibrium ◽  
Self Organized Criticality ◽  
Acute Agitation ◽  
Spectrum Disorders

AbstractAutism spectrum disorder (ASD) subjects can present temporary behaviors of acute agitation and aggressiveness, named problem behaviors. They have been shown to be consistent with the self-organized criticality (SOC), a model wherein occasionally occurring “catastrophic events” are necessary in order to maintain a self-organized “critical equilibrium.” The SOC can represent the psychopathology network structures and additionally suggests that they can be considered as self-organized systems.

scholarly journals Observational evidence in favor of scale-free evolution of sunspot groups

2018 ◽  
Vol 618 ◽  
pp. A183
Author(s):  
A. Shapoval ◽  
J.-L. Le Mouël ◽  
M. Shnirman ◽  
V. Courtillot
Keyword(s):  
Weibull Distribution ◽  
Power Law ◽  
Large Range ◽  
Scale Free ◽  
Self Organized ◽  
Self Organized Criticality ◽  
Spatio Temporal ◽  
Computational Procedures ◽  
Definition Of ◽  
Sunspot Groups

Context. The hypothesis stating that the distribution of sunspot groups versus their size (φ) follows a power law in the domain of small groups was recently highlighted but rejected in favor of a Weibull distribution. Aims. In this paper we reconsider this question, and are led to the opposite conclusion. Methods. We have suggested a new definition of group size, namely the spatio-temporal “volume” (V) obtained as the sum of the observed daily areas instead of a single area associated with each group. Results. With this new definition of “size”, the width of the power-law part of the distribution φ ∼ 1/Vβ increases from 1.5 to 2.5 orders of magnitude. The exponent β is close to 1. The width of the power-law part and its exponent are stable with respect to the different catalogs and computational procedures used to reduce errors in the data. The observed distribution is not fit adequately by a Weibull distribution. Conclusions. The existence of a wide 1/V part of the distribution φ suggests that self-organized criticality underlies the generation and evolution of sunspot groups and that the mechanism responsible for it is scale-free over a large range of sizes.

scholarly journals Extra investigation of the self-organized critical Manna model at higher critical dimension

2021 ◽  
pp. 1-12
Author(s):  
Andrey Viktorovich Podlazov
Keyword(s):  
Power Law ◽  
Critical Dimension ◽  
The Self ◽  
Two Dimensional ◽  
Upper Critical Dimension ◽  
Self Organized ◽  
Logarithmic Corrections ◽  
Universal Indicator ◽  
Sandpile Models ◽  
Power Law Distributions

I investigate the nature of the upper critical dimension for isotropic conservative sandpile models and calculate the emerging logarithmic corrections to power-law distributions. I check the results experimentally using the case of Manna model with the theoretical solution known for all statement starting from the two-dimensional one. In addition, based on this solution, I construct a non-trivial super-universal indicator for this model. It characterizes the distribution of avalanches by time the border of their region needs to pass its width.

"SPIRAL WAVE–TRAVELING CLUSTERING" INTERMITTENCY AND 1/f-NOISE IN A 2D COUPLED MAP LATTICE

1999 ◽  
Vol 09 (05) ◽  
pp. 929-937 ◽  
Author(s):  
MARK A. PUSTOVOIT ◽  
VALERY I. SBITNEV
Keyword(s):  
Probability Density ◽  
Exponential Decay ◽  
Power Law ◽  
Strange Attractor ◽  
Spiral Wave ◽  
Spiral Waves ◽  
Coupled Map Lattice ◽  
The Self ◽  
Saddle Node Bifurcation ◽  
Self Organized

Intermittency of checkerboard spiral waves and traveling clusterings originating from sudden shrinking of the strange attractor of the 2D CML in the neighborhood of the saddle-node bifurcation boundary is found. A power-law probability density for lifetimes in the spiral wave (laminar) phase is observed, while in the checkerboard clusterings (bursting) phase the above quantity exhibits an exponential decay. This difference can be interpreted through the self-organized behavior of the spiral waves, and the passive relaxation of the disordered checkerboard clusterings.

Self-Organized Criticality and Dynamic Instability of Microtubule Growth

1995 ◽  
Vol 50 (9-10) ◽  
pp. 739-740 ◽  
Author(s):  
Peter Babinec ◽  
Melánia Babincová
Keyword(s):  
Power Law ◽  
Dynamic Instability ◽  
Relative Number ◽  
Self Organized ◽  
Self Organized Criticality ◽  
Microtubule Growth

Abstract We have shown that the distribution of lengths of site nucleated microtubules obey an algebraic power law relationship D(s) = As-τ, where D(s) is relative number of microtubules with length 5, A and τ are constants. This relationship indicates the possibility of a self-organized criticality in the dynamic instability of microtubule growth

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