scholarly journals Self-Organized Criticality of Traffic Flow: There is Nothing Sweet about the Sweet Spot

2021 ◽  
Author(s):  
Jorge Laval
Keyword(s):  
Traffic Flow ◽  
Initial Conditions ◽  
Critical Density ◽  
Basic Unit ◽  
Power Law Distribution ◽  
Fundamental Diagram ◽  
Brownian Excursion ◽  
Self Organized ◽  
Time Space ◽  
Self Organized Criticality

This paper shows that the kinematic wave model exhibits self-organized criticality when initialized with random initial conditions around the critical density. A direct consequence is that conventional traffic management strategies seeking to maximize the flow may be detrimental as they make the system more unpredictable and more prone to collapse. Other implications for traffic flow in the capacity state are discussed, such as: \item jam sizes obey a power-law distribution with exponents 1/2, implying that both its mean and variance diverge to infinity, and therefore traditional statistical methods fail for prediction and control, \item the tendency to be at the critical state is an intrinsic property of traffic flow driven by our desire to travel at the maximum possible speed, \item traffic flow in the critical region is chaotic in that it is highly sensitive to initial conditions, \item aggregate measures of performance are proportional to the area under a Brownian excursion, and therefore are given by different scalings of the Airy distribution, \item traffic in the time-space diagram forms self-affine fractals where the basic unit is a triangle, in the shape of the fundamental diagram, containing 3 traffic states: voids, capacity and jams. This fractal nature of traffic flow calls for analysis methods currently not used in our field.

scholarly journals Self-Organized Criticality of Traffic Flow

2021 ◽  
Author(s):  
Jorge Laval
Keyword(s):  
Traffic Flow ◽  
Initial Conditions ◽  
Critical Density ◽  
Basic Unit ◽  
Brownian Excursion ◽  
Flow Models ◽  
Self Organized ◽  
Time Space ◽  
Traffic Flow Models ◽  
Self Organized Criticality

This paper shows that the kinematic wave model exhibits self-organized criticality when initialized with random initial conditions around the critical density. This has several important implications for traffic flow in the capacity state, such as: \item jam sizes obey a power law distribution with exponents 1/2, implying that both the mean and variance diverge to infinity, \item self-organization is an intrinsic property of traffic flow models in general, independently of other random perturbations, \item this critical behavior is a consequence of the flow maximization objective of traffic flow models, which can be observed on a density range around the critical density that depends on the length of the segment, \item typical measures of performance are proportional to the area under a Brownian excursion, and therefore are given by different scalings of the Airy distribution, \item traffic in the time-space diagram forms self-affine fractals where the basic unit is a triangle, in the shape of the fundamental diagram, containing 3 traffic states: voids, capacity and jams.

Modeling Research on Spatiotemporal Dynamics of the Hippocampus

1997 ◽  
Vol 07 (01) ◽  
pp. 187-198 ◽  
Author(s):  
Haijian Sun ◽  
Lin Liu ◽  
Chunhua Feng ◽  
Aike Guo
Keyword(s):  
Pyramidal Cells ◽  
Behavioral Pattern ◽  
Spatiotemporal Dynamics ◽  
Epileptic Focus ◽  
Power Law Distribution ◽  
Ca1 Pyramidal Cells ◽  
Self Organized ◽  
Hippocampal Ca1 ◽  
Self Organized Criticality ◽  
Neurological Insult

The spatiotemporal dynamics of the hippocampus is studied. We first propose a fractal algorithm to model the growth of hippocampal CA1 pyramidal cells, together with an avalanche model for information transmission. Then the optical records of an epileptic focus in the hippocampus are analyzed and simulated. These processes indicate that the hippocampus normally stays in self-organized criticality with a harmonious spatiotemporal behavioral pattern, that is, showing 1/f fluctuation and power law distribution. In case of a neurological insult, the hippocampal system may step into supercriticality and initiate epilepsy.

Boundedness and Other Theories for Complex Systems

2013 ◽  
pp. 108-125
Keyword(s):  
Initial Conditions ◽  
Traditional Approach ◽  
Deterministic Chaos ◽  
Mathematical Object ◽  
Self Organized ◽  
Self Organized Criticality ◽  
Universal Properties ◽  
The One ◽  
Global Invariant ◽  
Sensitivity To Initial Conditions

A comparison between the concept of boundedness on the one hand, and the theory of self-organized criticality (SOC) and the deterministic chaos on the other hand, is made. The focus is put on the methodological importance of the general frame through which an enormous class of empirical observations is viewed. The major difference between the concept of boundedness and the theory of self organized criticality is that under boundedness, the response comprises both specific and universal part, and thus a system has well defined “identity,” while SOC assumes response as a global invariant which has only universal properties. Unlike the deterministic chaos, the boundedness is free to explain the sensitivity to initial conditions independently from the mathematical object that generates them. Alongside, it turns out that the traditional approach to the deterministic chaos has its ample understanding under the concept of boundedness.

SELF-ORGANIZED CRITICALITY MODEL FOR EARTHQUAKES: QUIESCENCE, FORESHOCKS AND AFTERSHOCKS

1999 ◽  
Vol 09 (12) ◽  
pp. 2249-2255 ◽  
Author(s):  
S. HAINZL ◽  
G. ZÖLLER ◽  
J. KURTHS
Keyword(s):  
Power Law ◽  
B Value ◽  
Power Law Distribution ◽  
Aftershock Activity ◽  
Omori Law ◽  
Self Organized ◽  
Spatiotemporal Clustering ◽  
Self Organized Criticality ◽  
Clustering Of Events ◽  
Foreshock Activity

We introduce a crust relaxation process in a continuous cellular automaton version of the Burridge–Knopoff model. Analogously to the original model, our model displays a robust power law distribution of event sizes (Gutenberg–Richter law). The principal new result obtained with our model is the spatiotemporal clustering of events exhibiting several characteristics of earthquakes in nature. Large events are accompanied by a precursory quiescence and by localized fore- and aftershocks. The increase of foreshock activity as well as the decrease of aftershock activity follows a power law (Omori law) with similar exponents p and q. All empirically observed power law exponents, the Richter B-value, p and q and their variability can be reproduced simultaneously by our model, which depends mainly on the level of conservation and the relaxation time.

Self-organized criticality in 1D stochastic traffic flow model

1997 ◽  
Vol 40 (3) ◽  
pp. 509-520 ◽  
Author(s):  
N.C. Pesheva ◽  
D.P. Daneva ◽  
J.G. Brankov
Keyword(s):  
Traffic Flow ◽  
Flow Model ◽  
Traffic Flow Model ◽  
Self Organized ◽  
Self Organized Criticality

SELF-ORGANIZED CRITICALITY IN 1D TRAFFIC FLOW

Fractals ◽  
1996 ◽  
Vol 04 (03) ◽  
pp. 279-283 ◽  
Author(s):  
TAKASHI NAGATANI
Keyword(s):  
Traffic Flow ◽  
Transition Probability ◽  
Annihilation Process ◽  
One Dimensional ◽  
Traffic Jams ◽  
Self Organized ◽  
Stochastic Transition ◽  
Self Organized Criticality ◽  
The One ◽  
Empty Wave

Annihilation process of traffic jams is investigated in a one-dimensional traffic flow on a highway. The one-dimensional fully asymmetric exclusion model with open boundaries for parallel update is extended to take into account stochastic transition of cars, where a car moves ahead with transition probability pt. Near pt=1, the system is driven asymptotically into a steady state exhibiting a self-organized criticality. Traffic jams with various lifetimes (or sizes) appear and disappear by colliding with an empty wave. The typical lifetime <m> of traffic jams scales as [Formula: see text], where ∆pt=1−pt. It is shown that the cumulative lifetime distribution Nm(∆pt) satisfies the scaling form [Formula: see text].

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).

Self-Organized Critical Models

2003 ◽  
Author(s):  
M. E. J. Newman ◽  
R. G. Palmer
Keyword(s):  
Computer Simulations ◽  
Power Law ◽  
Large Scale ◽  
Fitness Landscape ◽  
Fitness Landscapes ◽  
Power Law Distribution ◽  
Edge Of Chaos ◽  
Self Organized ◽  
Self Organized Criticality ◽  
Phenotype Space

The models discussed in the last chapter are intriguing, but present a number of problems. In particular, most of the results about them come from computer simulations, and little is known analytically about their properties. Results such as the power-law distribution of extinction sizes and the system's evolution to the "edge of chaos" are only as accurate as the simulations in which they are observed. Moreover, it is not even clear what the mechanisms responsible for these results are, beyond the rather general arguments that we have already given. In order to address these shortcomings, Bak and Sneppen (1993; Sneppen et al. 1995; Sneppen 1995; Bak 1996) have taken Kauffman's ideas, with some modification, and used them to create a considerably simpler model of large-scale coevolution which also shows a power-law distribution of avalanche sizes and which is simple enough that its properties can, to some extent, be understood analytically. Although the model does not directly address the question of extinction, a number of authors have interpreted it, using arguments similar to those of section 1.2.2.5, as a possible model for extinction by biotic causes. The Bak-Sneppen model is one of a class of models that show "self-organized criticality," which means that regardless of the state in which they start, they always tune themselves to a critical point of the type discussed in section 2.4, where power-law behavior is seen. We describe self-organized criticality in more detail in section 3.2. First, however, we describe the Bak-Sneppen model itself. In the model of Bak and Sneppen there are no explicit fitness landscapes, as there are in NK models. Instead the model attempts to mimic the effects of landscapes in terms of "fitness barriers." Consider figure 3.1, which is a toy representation of a fitness landscape in which there is only one dimension in the genotype (or phenotype) space. If the mutation rate is low compared with the time scale on which selection takes place (as Kauffman assumed), then a population will spend most of its time localized around a peak in the landscape (labeled P in the figure).

scholarly journals Global Bifurcation Diagram for the Kerner–Konhäuser Traffic Flow Model

2015 ◽  
Vol 25 (05) ◽  
pp. 1550064 ◽  
Author(s):  
Joaquín Delgado ◽  
Patricia Saavedra
Keyword(s):  
Dynamical System ◽  
Traffic Flow ◽  
Flow Model ◽  
Initial Conditions ◽  
Global Bifurcation ◽  
Traveling Wave Solutions ◽  
Stable Limit ◽  
Fundamental Diagram ◽  
Change Of Variables ◽  
Stable Limit Cycles

We study traveling wave solutions of the Kerner–Konhäuser PDE for traffic flow. By a standard change of variables, the problem is reduced to a dynamical system in the plane with three parameters. In a previous paper [Carrillo et al., 2010] it was shown that under general hypotheses on the fundamental diagram, the dynamical system has a surface of critical points showing either a fold or cusp catastrophe when projected under a two-dimensional plane of parameters named qg–vg. In either case, a one parameter family of Takens–Bogdanov (TB) bifurcation takes place, and therefore local families of Hopf and homoclinic bifurcation arising from each TB point exist. Here, we prove the existence of a degenerate Takens–Bogdanov bifurcation (DTB) which in turn implies the existence of Generalized Hopf or Bautin bifurcations (GH). We describe numerically the global lines of bifurcations continued from the local ones, inside a cuspidal region of the parameter space. In particular, we compute the first Lyapunov exponent, and compare with the GH bifurcation curve. We present some families of stable limit cycles which are taken as initial conditions in the PDE leading to stable traveling waves.

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