We present an empirical study of the long-term evolution of several social indicators (e.g. human population growth, statistics of deadly quarrels, diffusion of democratic systems, etc.). We assume that the human species emerge, develop and become extinct with similar evolutionary patterns that other terrestrial species. We propose that the long-term indicators are showing some sort of macro-transition in their long-term behavior that we defined as “Technological Adolescent Age.” We present an estimation of this period. Assuming the “Principle of Mediocrity” and using the Drake Equation we calculate a lower threshold for the number of technological civilizations in the galaxy.

http://link.springer.com/content/pdf/10.1007/978-1-4020-4968-2_51.pdf

Self-Organized Criticality

A Description of the Terrestrial Technological Adolescence Case

The possible paralelism existing between phase transitions and fracture in disordered materials, is discussed using the well-known Fiber Bundle Models and a probabilistic approach suited to smooth fluctuations near the critical point. Two limiting cases of load redistribution are analyzed: the global transfer scheme, and the local transfer rule. The models are then studied and contrasted by defining the branching ratio as an order parameter indicative of the distance of the system to the critical point. In the case of long range interactions, i.e., the global rule, the results indicate that fracture can be seen as a second-order phase transition, whereas for the case of short range interactions (the local transfer rule) the bundle fails suddenly with no prior significant precursory activity signaling the imminent collapse of the system, this case being a first-order like phase transition.

Phase Transitions in Load Transfer Models of Fracture

Extreme fluctuations have been modeled based on point nonpotential and potential systems of stochastic equations, in which white noise induces random processes with a power-law frequency dependence of the power spectra. The distribution of extreme fluctuations corresponds to the maximum of statistical entropy, which indicates their stability. The stability of fluctuation processes with 1/f  α power spectra has been analyzed based on the principle of maximum information entropy.

Stability of Random Processes with the 1/f α Spectrum

Since Self-Organised Criticality (SOC) was introduced in the 1987 both the nature of the self-organisation and of the criticality remains controversial. Recent observations on rain precipitation and on brain activity suggest that real systems may dynamically wander about in the vicinity of criticality rather than tune to a critical point. We use computer simulations to study the Drossel-Schwable forest-fire model of SOC and find that it exhibits behaviour similar to that found for rain and brain activity. In particular we analyse the residence time for different densities of trees and perform finite size scaling analysis of the with of the distribution of residence times. We conclude that despite of the long known fact that this model does not exhibit exact scaling and power laws its behaviour may exactly for that be very relevant to real physical systems.

The Forest Fire Model Revisited

Dieses Kapitel knupft unmittelbar an die Ergebnisse der beiden vorhergehenden uber den ferromagnetischen Phasenubergang und den Gas-Flussigkeits-ubergang an. Zunachst werden einige allgemeine Betrachtungen uber Symmetriebrechung und Phasenubergange vorangestellt. Dann werden verschiedene Phasenubergange und kritische Punkte besprochen und Analogien aufgezeigt. Anschliesend befassen wir uns eingehend mit dem kritischen Verhalten und werden durch die statische Skalentheorie eine phanomenologische Beschreibung derartiger Erscheinungen geben. Im darauf folgenden Abschnitt werden die wesentlichen Gedanken der Renormierungsgruppentheorie in einem einfachen Modell besprochen und dabei die Skalengesetze abgeleitet. Schlieslich fuhren wir die Ginzburg-Landau-Theorie1 ein, die einen wichtigen Grundstein fur die verschiedenen Naherungsmethoden in der Theorie kritischer Phanomene bildet.

Self-Organized Criticality

Citations

A Description of the Terrestrial Technological Adolescence Case

Phase Transitions in Load Transfer Models of Fracture

Stability of Random Processes with the 1/f α Spectrum

The Forest Fire Model Revisited

Phasenübergänge, Skaleninvarianz, Renormierungsgruppentheorie und Perkolation

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