Detection of self-organized criticality behavior in an electronic circuit designed to solve a third order non-linear ODE (NL-ODE) for a damped KdV equation

2019 ◽  
Vol 29 (8) ◽  
pp. 083116
Author(s):  
Amit Kumar Jha ◽  
Debasmita Banerjee ◽  
A. N. Sekar Iyengar ◽  
M. S. Janaki
Keyword(s):  
Electronic Circuit ◽  
Kdv Equation ◽  
Third Order ◽  
Self Organized ◽  
Non Linear ◽  
Linear Ode ◽  
Self Organized Criticality

Self-Organized Criticality: A New Theory of Political Behaviour and Some of Its Implications

2001 ◽  
Vol 31 (2) ◽  
pp. 427-445 ◽  
Author(s):  
GREGORY G. BRUNK
Keyword(s):  
Linear Perspective ◽  
Political Behaviour ◽  
Self Organized ◽  
Or Groups ◽  
Non Linear ◽  
Self Organized Criticality

Adopting a particular non-linear perspective resolves numerous paradoxes about collective political behaviour. Self-organized criticality occurs if the sensitivity of individuals or groups to each other's actions increases with the passage of time, and, therefore, sudden changes may occur as cascades. In this way scandals, betrayals, miscalculations and other seemingly insignificant actions can sometimes cause cabinet dissolutions, strikes, riots, electoral landslides, wars and a multitude of other phenomena that, until now, have seemed to have had nothing in common.

scholarly journals Harmonic dynamics of the abelian sandpile

2019 ◽  
Vol 116 (8) ◽  
pp. 2821-2830 ◽  
Author(s):  
Moritz Lang ◽  
Mikhail Shkolnikov
Keyword(s):  
Abelian Group ◽  
Stochastic Dynamics ◽  
Third Order ◽  
Infinite Domains ◽  
Self Organized ◽  
Abelian Sandpile ◽  
Self Organized Criticality ◽  
Self Similar ◽  
Smooth Transformation ◽  
Sandpile Group

The abelian sandpile is a cellular automaton which serves as the archetypical model to study self-organized criticality, a phenomenon occurring in various biological, physical, and social processes. Its recurrent configurations form an abelian group, whose identity is a fractal composed of self-similar patches. Here, we analyze the evolution of the sandpile identity under harmonic fields of different orders. We show that this evolution corresponds to periodic cycles through the abelian group characterized by the smooth transformation and apparent conservation of the patches constituting the identity. The dynamics induced by second- and third-order harmonics resemble smooth stretchings and translations, respectively, while the ones induced by fourth-order harmonics resemble magnifications and rotations. Based on an extensive analysis of these sandpile dynamics on domains of different size, we conjecture the existence of several scaling limits for infinite domains. Furthermore, we show that the space of harmonic functions provides a set of universal coordinates identifying configurations between different domains, which directly implies that the sandpile group admits a natural renormalization. Finally, we show that the harmonic fields can be induced by simple Markov processes and that the corresponding stochastic dynamics show remarkable robustness. Our results suggest that harmonic fields might split the sandpile group into subsets showing different critical coefficients and that it might be possible to extend the fractal structure of the identity beyond the boundaries of its domain.

Friction-Induced Vibrations: From Linear Stability Criteria to Non-Linear Analysis of Limiting Cycles

2010 ◽  
Author(s):  
Michael Nosonovsky
Keyword(s):  
Elastic Waves ◽  
Linear Analysis ◽  
Stability Criteria ◽  
Self Organized ◽  
Elastic Bodies ◽  
Limiting Cycle ◽  
Non Linear ◽  
Self Organized Criticality ◽  
Frictional Interface ◽  
Unstable Vibration

The contact of two elastic bodies with a frictional interface can lead to friction-induced instabilities. The instabilities are either due to the velocity-dependence of friction, or due to the coupling of friction with the thermal expansion or wear, or due to the destabilization of the interface elastic waves. The instabilities lead to friction-induced vibrations. The linear elasticity usually provides a criterion for the onset of the instability and predicts that the amplitude of the unstable vibration grows exponentially with time. However, it does not provide any information about the amplitudes of vibrations. It is expected that the amplitudes of vibrations grow exponentially until they leave the range of applicability of the linear theory and reach a certain limiting cycle. We discuss how various non-linear methods of pattern-formation analysis can be applied to this problem, including the Turing systems, self-organized criticality, etc.

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.

Self-Organized Criticality in the Autowave Model of Speciation

2020 ◽  
Vol 75 (5) ◽  
pp. 398-408
Author(s):  
A. Y. Garaeva ◽  
A. E. Sidorova ◽  
N. T. Levashova ◽  
V. A. Tverdislov
Keyword(s):  
Self Organized ◽  
Self Organized Criticality

Modeling Extinction

2003 ◽  
Author(s):  
M. E. J. Newman ◽  
R. G. Palmer
Keyword(s):  
Evolutionary Biology ◽  
Large Scale ◽  
Competitive Exclusion ◽  
Applied Mathematics ◽  
Santa Fe ◽  
New Approach ◽  
Self Organized ◽  
Self Organized Criticality ◽  
Extinction Events ◽  
Mass Extinction Events

Developed after a meeting at the Santa Fe Institute on extinction modeling, this book comments critically on the various modeling approaches. In the last decade or so, scientists have started to examine a new approach to the patterns of evolution and extinction in the fossil record. This approach may be called "statistical paleontology," since it looks at large-scale patterns in the record and attempts to understand and model their average statistical features, rather than their detailed structure. Examples of the patterns these studies examine are the distribution of the sizes of mass extinction events over time, the distribution of species lifetimes, or the apparent increase in the number of species alive over the last half a billion years. In attempting to model these patterns, researchers have drawn on ideas not only from paleontology, but from evolutionary biology, ecology, physics, and applied mathematics, including fitness landscapes, competitive exclusion, interaction matrices, and self-organized criticality. A self-contained review of work in this field.

scholarly journals Perturbative linearization of super-Yang-Mills theories in general gauges

2021 ◽  
Vol 2021 (6) ◽  
Author(s):  
Hannes Malcha ◽  
Hermann Nicolai
Keyword(s):  
Large Class ◽  
Fourth Order ◽  
Landau Gauge ◽  
Third Order ◽  
Yang Mills ◽  
Free Theory ◽  
Non Linear ◽  
Functional Measure ◽  
Non Local ◽  
Jacobi Determinant

Abstract Supersymmetric Yang-Mills theories can be characterized by a non-local and non-linear transformation of the bosonic fields (Nicolai map) mapping the interacting functional measure to that of a free theory, such that the Jacobi determinant of the transformation equals the product of the fermionic determinants obtained by integrating out the gauginos and ghosts at least on the gauge hypersurface. While this transformation has been known so far only for the Landau gauge and to third order in the Yang-Mills coupling, we here extend the construction to a large class of (possibly non-linear and non-local) gauges, and exhibit the conditions for all statements to remain valid off the gauge hypersurface. Finally, we present explicit results to second order in the axial gauge and to fourth order in the Landau gauge.

Mitigating the Effects of Non-Linear Distortion Using Polarizers in Microwave Photonic Link

2019 ◽  
Vol 0 (0) ◽  
Author(s):  
Sarika Singh ◽  
Sandeep K. Arya ◽  
Shelly Singla
Keyword(s):  
Dynamic Range ◽  
Extinction Ratio ◽  
Polarization Angle ◽  
Third Order ◽  
Microwave Photonic ◽  
Linear Behavior ◽  
Spurious Free Dynamic Range ◽  
Non Linear ◽  
Intermodulation Distortions ◽  
Insertion Losses

AbstractA scheme to suppress nonlinear intermodulation distortion in microwave photonic (MWP) link is proposed by using polarizers to compensate inherent non-linear behavior of dual-electrode Mach-Zehnder modulator (DE-MZM). Insertion losses and extinction ratio have also been considered. Simulation results depict that spurious free dynamic range (SFDR) of proposed link reaches to 130.743 dB.Hz2/3. A suppression of 41 dB in third order intermodulation distortions and an improvement of 15.3 dB is reported when compared with the conventional link. In addition, an electrical spectrum at different polarization angles is extracted and 79^\circ is found to be optimum value of polarization angle.

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