A complexity view of rainfall.
TLDR
It is shown that rain events are analogous to a variety of nonequilibrium relaxation processes in Nature such as earthquakes and avalanches and that power laws describe the number of rain events versus size and number of droughts versus duration.Abstract:
We show that rain events are analogous to a variety of nonequilibrium relaxation processes in Nature such as earthquakes and avalanches. Analysis of high-resolution rain data reveals that power laws describe the number of rain events versus size and number of droughts versus duration. In addition, the accumulated water column displays scale-less fluctuations. These statistical properties are the fingerprints of a self-organized critical process and may serve as a benchmark for models of precipitation and atmospheric processes.read more
Citations
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The restaurant at the end of the random walk: recent developments in the description of anomalous transport by fractional dynamics
Ralf Metzler,Joseph Klafter +1 more
TL;DR: Fractional dynamics has experienced a firm upswing during the past few years, having been forged into a mature framework in the theory of stochastic processes as mentioned in this paper, and a large number of research papers developing fractional dynamics further, or applying it to various systems have appeared since our first review article on the fractional Fokker-Planck equation.
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Emergent complex neural dynamics
TL;DR: Viewing the brain in terms of collective dynamics is one approach now yielding some insight.
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Long-term persistence and multifractality of precipitation and river runoff records
Jan W. Kantelhardt,Jan W. Kantelhardt,Eva Koscielny-Bunde,Diego Rybski,Peter Braun,Armin Bunde,Shlomo Havlin,Shlomo Havlin +7 more
TL;DR: In this paper, the authors compare the multifractal temporal scaling properties of precipitation and river discharge records on large timescales and find that daily runoffs are characterized by an asymptotic scaling exponent that indicates a slow power law decay of the runoff autocorrelation function and varies from river to river in a wide range.
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Theoretical studies of self-organized criticality
TL;DR: In this article, the authors provide a pedagogical introduction to the abelian sandpile model of self-organized criticality, and its related models, including the ABELIAN group, the algebra of particle addition operators, the burning test for recurrent states, equivalence to the spanning trees problem, and the exact solution of the directed version of the model in any dimension.
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Critical phenomena in atmospheric precipitation
TL;DR: In this paper, the authors argue that a critical value of water vapour (the tuning parameter) marks a non-equilibrium continuous phase transition to a regime of strong atmospheric convection and precipitation, with correlated regions on scales of tens to hundreds of kilometres.
References
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Book
How Nature Works: The Science of Self-Organized Criticality
TL;DR: This chapter discusses the Sandpile Paradigm, Earthquakes, Starquakes, and Solar Flares, and the "Game of Life": Complexity Is Criticality, and Is Life a Self-Organized Critical Phenomenon?
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Self‐Organized Criticality: Emergent Complex Behavior in Physical and Biological Systems
TL;DR: This chapter discusses the characterization of the SOC state and the search for a formalism in systems exhibiting SOC.