Self-organized criticality (SOC) is a property of dynamical systems that have a critical point as an attractor. Their macroscopic behavior thus displays the spatial or temporal scale-invariance characteristic of the critical point of a phase transition, but without the need to tune control parameters to a precise value, because the system, effectively, tunes itself as it evolves towards criticality.
The concept was put forward by Per Bak, Chao Tang and Kurt Wiesenfeld ("BTW") in a paper
published in 1987 in Physical Review Letters, and is considered to be one of the mechanisms by which complexity arises in nature. Its concepts have been applied across fields as diverse as geophysics, physical cosmology, evolutionary biology and ecology, bio-inspired computing and optimization (mathematics), economics, quantum gravity, sociology, solar physics, plasma physics, neurobiology and others.
SOC is typically observed in slowly driven non-equilibrium systems with many degrees of freedom and strongly nonlinear dynamics. Many individual examples have been identified since BTW's original paper, but to date there is no known set of general characteristics that guarantee a system will display SOC.
Self-organized criticality is one of a number of important discoveries made in statistical physics and related fields over the latter half of the 20th century, discoveries which relate particularly to the study of complexity in nature. For example, the study of cellular automata, from the early discoveries of Stanislaw Ulam and John von Neumann through to John Conway's Game of Life and the extensive work of Stephen Wolfram, made it clear that complexity could be generated as an emergent feature of extended systems with simple local interactions. Over a similar period of time, Benoît Mandelbrot's large body of work on fractals showed that much complexity in nature could be described by certain ubiquitous mathematical laws, while the extensive study of phase transitions carried out in the 1960s and 1970s showed how scale invariant phenomena such as fractals and power laws emerged at the critical point between phases.
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In probability and statistics, the Tweedie distributions are a family of probability distributions which include the purely continuous normal, gamma and inverse Gaussian distributions, the purely discrete scaled Poisson distribution, and the class of compound Poisson–gamma distributions which have positive mass at zero, but are otherwise continuous. Tweedie distributions are a special case of exponential dispersion models and are often used as distributions for generalized linear models.
Complexity economics is the application of complexity science to the problems of economics. It relaxes several common assumptions in economics, including general equilibrium theory. While it does not reject the existence of an equilibrium, it sees such equilibria as "a special case of nonequilibrium", and as an emergent property resulting from complex interactions between economic agents. The complexity science approach has also been applied to computational economics.
Self-organized criticality (SOC) is a property of dynamical systems that have a critical point as an attractor. Their macroscopic behavior thus displays the spatial or temporal scale-invariance characteristic of the critical point of a phase transition, but without the need to tune control parameters to a precise value, because the system, effectively, tunes itself as it evolves towards criticality. The concept was put forward by Per Bak, Chao Tang and Kurt Wiesenfeld ("BTW") in a paper published in 1987 in Physical Review Letters, and is considered to be one of the mechanisms by which complexity arises in nature.
This course is an introduction to the non-perturbative bootstrap approach to Conformal Field Theory and to the Gauge/Gravity duality, emphasizing the fruitful interplay between these two ideas.
The lectures will provide an introduction to magnetism in materials, covering fundamentals of spin and orbital degrees of freedom, interactions between moments and some typical ordering patterns. Sele
Introduction to the physics of random processes and disordered systems, providing an overview over phenomena, concepts and theoretical approachesTopics include:
Random walks; Roughening/pinning; Lo
On propose dans ce MOOC de se former à et avec Thymio :
apprendre à programmer le robot Thymio et ce faisant, s’initier
à l'informatique et la robotique.
In diesem Kurs handelt es sich um das Verständnis der grundlegenden Mechanismen eines Roboters wie Thymio, seiner Programmierung mit verschiedenen Sprachen und seiner Verwendung im Unterricht mit den
In diesem Kurs handelt es sich um das Verständnis der grundlegenden Mechanismen eines Roboters wie Thymio, seiner Programmierung mit verschiedenen Sprachen und seiner Verwendung im Unterricht mit den
The structuring of mid-IR materials, such as chalcogenide glass (ChG), at the micro and nano scales, is of high interest for the fabrication of photonic devices in general, and for spectroscopy applic
We report on a self-organized process initiated on a potassium-tungsten-tellurite glass surface under repetitive femtosecond laser irradiation in a regime where cumulative effects lead to a localized