scholarly journals Criticality or Supersymmetry Breaking?

Symmetry ◽  
2020 ◽  
Vol 12 (5) ◽  
pp. 805
Author(s):  
Igor V. Ovchinnikov ◽  
Wenyuan Li ◽  
Yuquan Sun ◽  
Andrew E. Hudson ◽  
Karlheinz Meier ◽  
...  
Keyword(s):  
Dynamical Systems ◽  
Chaotic Behavior ◽  
Power Spectra ◽  
Stochastic Dynamical Systems ◽  
Scale Free ◽  
Self Organized ◽  
Neuromorphic Hardware ◽  
1D Chain ◽  
Self Organized Criticality ◽  
Type Power

In many stochastic dynamical systems, ordinary chaotic behavior is preceded by a full-dimensional phase that exhibits 1/f-type power spectra and/or scale-free statistics of (anti)instantons such as neuroavalanches, earthquakes, etc. In contrast with the phenomenological concept of self-organized criticality, the recently found approximation-free supersymmetric theory of stochastics (STS) identifies this phase as the noise-induced chaos (N-phase), i.e., the phase where the topological supersymmetry pertaining to all stochastic dynamical systems is broken spontaneously by the condensation of the noise-induced (anti)instantons. Here, we support this picture in the context of neurodynamics. We study a 1D chain of neuron-like elements and find that the dynamics in the N-phase is indeed featured by positive stochastic Lyapunov exponents and dominated by (anti)instantonic processes of (creation) annihilation of kinks and antikinks, which can be viewed as predecessors of boundaries of neuroavalanches. We also construct the phase diagram of emulated stochastic neurodynamics on Spikey neuromorphic hardware and demonstrate that the width of the N-phase vanishes in the deterministic limit in accordance with STS. As a first result of the application of STS to neurodynamics comes the conclusion that a conscious brain can reside only in the N-phase.

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.

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.

Complexity and Criticality

2020 ◽  
pp. 42-50
Author(s):  
Helmut Satz
Keyword(s):  
Complex System ◽  
Complex Systems ◽  
Critical Point ◽  
Correlation Length ◽  
Critical Behavior ◽  
Scale Free ◽  
Self Organized ◽  
Self Organized Criticality ◽  
Free Behavior

Complex systems and critical behavior in complex system are defined in terms of correlation between constituents in the medium, subject to screening by intermediate constituents. At a critical point, the correlation length diverges—as a result, one finds the scale-free behavior also observed for bird flocks. This behavior is therefore possibly a form of 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.

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