scholarly journals Persistent dynamic correlations in self-organized critical systems away from their critical point

2007 ◽  
Vol 373 ◽  
pp. 215-230 ◽  
Author(s):  
Ryan Woodard ◽  
David E. Newman ◽  
Raúl Sánchez ◽  
Benjamin A. Carreras
Keyword(s):  
Critical Point ◽  
Critical Systems ◽  
Dynamic Correlations ◽  
Self Organized

scholarly journals The emergence of integrated information, complexity, and consciousness at criticality

2019 ◽  
Author(s):  
Sina Khajehabdollahi ◽  
Pubuditha M. Abeyasinghe ◽  
Adrian M. Owen ◽  
Andrea Soddu
Keyword(s):  
Phase Transition ◽  
Ising Model ◽  
Critical Point ◽  
Critical Systems ◽  
Dynamical Phase ◽  
Self Organized ◽  
Self Organized Criticality ◽  
Ancient Problem ◽  
Emergence Of Complexity ◽  
Integrated Information

AbstractUsing the critical Ising model of the brain, integrated information as a measure of consciousness is measured in toy models of generic neural networks. Monte Carlo simulations are run on 159 random weighted networks analogous to small 5-node neural network motifs. The integrated information generated by this sample of small Ising models is measured across the model parameter space. It is observed that integrated information, as a type of order parameter not unlike a concept like magnetism, undergoes a phase transition at the critical point in the model. This critical point is demarcated by the peaks of the generalized susceptibility of integrated information, a point where the ‘consciousness’ of the system is maximally susceptible to perturbations and on the boundary between an ordered and disordered form. This study adds further evidence to support that the emergence of consciousness coincides with the more universal patterns of self-organized criticality, evolution, the emergence of complexity, and the integration of complex systems.Author summaryUnderstanding consciousness through a scientific and mathematical language is slowly coming into reach and so testing and grounding these emerging ideas onto empirical observations and known systems is a first step to properly framing this ancient problem. This paper in particular explores the Integrated Information Theory of Consciousness framed within the physics of the Ising model to understand how and when consciousness, or integrated information, can arise in simple dynamical systems. The emergence of consciousness is treated like the emergence of other classical macroscopic observables in physics such as magnetism and understood as a dynamical phase of matter. Our findings show that the sensitivity of consciousness in a complex system is maximized when the system is undergoing a phase transition, also known as a critical point. This result, combined with a body of evidence highlighting the privelaged state of critical systems suggests that, like many other complex phenomenon, consciousness may simply follow from/emerge out of the tendency of a system to self-organize to criticality.

scholarly journals THE SELF-ORGANIZED MULTI-LATTICE MONTE CARLO SIMULATION

2004 ◽  
Vol 15 (09) ◽  
pp. 1249-1268 ◽  
Author(s):  
DENIS HORVÁTH ◽  
MARTIN GMITRA
Keyword(s):  
Monte Carlo ◽  
Finite Size ◽  
Simulation Method ◽  
Monte Carlo Step ◽  
The Self ◽  
Square Lattice ◽  
Critical Systems ◽  
Lattice Systems ◽  
Steady Regime ◽  
Self Organized

Self-organized Monte Carlo simulations of 2D Ising ferromagnet on the square lattice are performed. The essence of the suggested simulation method is an artificial dynamics consisting of the well-known single-spin-flip Metropolis algorithm supplemented by a random walk on the temperature axis. The walk is biased towards the critical region through a feedback based on instantaneous energy and magnetization cumulants, which are updated at every Monte Carlo step and filtered through a special recursion algorithm. The simulations revealed the invariance of the temperature probability distribution function, once some self-organized critical steady regime is reached, which is called here noncanonical equilibrium. The mean value of this distribution approximates the pseudocritical temperature of canonical equilibrium. In order to suppress finite-size effects, the self-organized approach is extended to multi-lattice systems, where the feedback basis on pairs of instantaneous estimates of the fourth-order magnetization cumulant on two systems of different size. These replica-based simulations resemble, in Monte Carlo lattice systems, some of the invariant statistical distributions of standard self-organized critical systems.

Supercritical Adsorption

2005 ◽  
Author(s):  
Eldred H. Chimowitz
Keyword(s):  
Stationary Phase ◽  
Critical Point ◽  
Dynamic Models ◽  
Molecular Diffusion ◽  
Plug Flow ◽  
Fluid Phase ◽  
Commercial Application ◽  
Critical Systems ◽  
Mobile Phases ◽  
Column Dynamics

In this chapter, we discuss adsorption phenomena in supercritical systems, a situation that occurs in many application areas in chemical-process and materials engineering. An example of a commercial application in this area, which has achieved wide acceptance as a tool in analytical chemistry, is supercritical fluid chromatography (SFC). Not only is SFC a powerful technique for chemical analysis, but it also is a useful method for measuring transportive and thermodynamic properties in the near-critical systems. In the next section, we analyze adsorption-column dynamics using simple dynamic models, and describe how data from a chromatographic column can be used to estimate various thermodynamic and transport properties.We then proceed to discuss the effects of proximity to the critical point on adsorption behavior in these systems. The closer the system is to its critical point, the more interesting is its behavior. For very dilute solute systems, like those considered here, the energy balance is often ignored to a first approximation; this leads to a simple set of mass-balance equations defining transport for each species. These equations can be developed to various levels of complexity, depending upon the treatment of the adsorbent (stationary phase). The conceptual view of these phases can span a wide range of possibilities ranging from completely nonporous solids (fused structures) to porous materials with complicated ill-defined pore structures. Given these considerations, it is customary to make the following assumptions in the development of a simple model of adsorber-bed dynamics: . . .1. The stationary and mobile phases are continuous in the direction of the flow, with the fluid phase possessing a flat velocity profile (“plug” flow).. . . . . . 2. The porosity of the stationary phase is considered constant irrespective of pressure and temperature conditions (i.e., it is incompressible). . . . . . .3. The column is considered to be radially homogeneous, leading to a set of equations with one spatially independent variable, representing distance along the column axis. . . . . . . 4. The dispersion term in the model equation represents the combined effects of molecular diffusion and dispersion due to convective stirring in the bed. These effects are combined into an effective phenomenological dispersion coefficient, considered to be constant throughout the column. . . .

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.

scholarly journals Stochastic oscillations and dragon king avalanches in self-organized quasi-critical systems

2019 ◽  
Vol 9 (1) ◽  
Author(s):  
Osame Kinouchi ◽  
Ludmila Brochini ◽  
Ariadne A. Costa ◽  
João Guilherme Ferreira Campos ◽  
Mauro Copelli
Keyword(s):  
Critical Systems ◽  
Self Organized ◽  
Stochastic Oscillations

scholarly journals RELAXING NEAR THE CRITICAL POINT

2001 ◽  
Vol 16 (supp01c) ◽  
pp. 1274-1276
Author(s):  
M. SIMIONATO
Keyword(s):  
Critical Point ◽  
Heavy Ions ◽  
Distribution Functions ◽  
Critical Systems ◽  
Chiral Phase ◽  
Long Wavelength ◽  
Equilibrium Dynamics ◽  
Slowing Down ◽  
Large N ◽  
Early Universe Cosmology

I present an analysis of the relaxation rate for long-wavelength fluctuations of the order parameter in an O(N) scalar theory near the critical point. Our motivation is to model the non-equilibrium dynamics of critical fluctuations near the chiral phase transition in QCD. In the next-to-leading order in the large N expansion we find a critical slowing down regime, i.e. an increasing of the relaxation time of long wavelengths fluctuations. This result suggests, for near critical systems, relevant deviations from thermal equilibrium for the distribution functions of low-energy particles and could have important phenomenological consequences in Heavy Ions Collision and in the Early Universe Cosmology.

scholarly journals Some properties of sandpile models as prototype of self-organized critical systems

2021 ◽  
Vol 96 (11) ◽  
pp. 112001
Author(s):  
M N Najafi ◽  
S Tizdast ◽  
J Cheraghalizadeh
Keyword(s):  
Critical Systems ◽  
Self Organized ◽  
Sandpile Models

scholarly journals Engineering Self-Organized Criticality in Living Cells

2020 ◽  
Author(s):  
Blai Vidiella ◽  
Antoni Guillamon ◽  
Josep Sardanyes ◽  
Victor Maull ◽  
Nuria Conde ◽  
...  
Keyword(s):  
Critical Point ◽  
Gene Networks ◽  
Collective Intelligence ◽  
Living Cells ◽  
Intracellular Traffic ◽  
E Coli ◽  
Order And Disorder ◽  
Self Organized ◽  
Molecular Noise ◽  
Self Organized Criticality

Complex dynamical fluctuations, from molecular noise within cells, collective intelligence, brain dynamics or computer traffic have been shown to display noisy behaviour consistent with a critical state between order and disorder. Living close to the critical point can have a number of adaptive advantages and it has been conjectured that evolution could select (and even tend to) these critical states. One way of approaching such state is by means of so-called self-organized criticality (SOC) where the system poises itself close to the critical point. Is this the case of living cells? It is difficult to test this idea given the enormous dimensionality associated with gene and metabolic webs. In this paper, we present an alternative approach: to engineer synthetic gene networks displaying SOC behaviour. This is achieved by exploiting the presence of a saturation (congestion) phenomenon of the ClpXP protein degradation machinery in E. coli cells. Using a feedback design that detects and then reduces ClpXP congestion, a {\em critical motif} is built from a two-gene network system, where SOC can be successfully implemented. Both deterministic and stochastic models are used, consistently supporting the presence of criticality in intracellular traffic. The potential implications for both cellular dynamics and designed intracellular noise are discussed.

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