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Full-Text Articles in Physical Sciences and Mathematics
The Poissonian Origin Of Power Laws In Solar Flare Waiting Time Distributions, Markus J. Aschwanden, Jay R. Johnson
The Poissonian Origin Of Power Laws In Solar Flare Waiting Time Distributions, Markus J. Aschwanden, Jay R. Johnson
Faculty Publications
In this study we aim for a deeper understanding of the power-law slope, α, of waiting time distributions. Statistically independent events with linear behavior can be characterized by binomial, Gaussian, exponential, or Poissonian size distribution functions. In contrast, physical processes with nonlinear behavior exhibit spatiotemporal coherence (or memory) and "fat tails" in their size distributions that fit power-law-like functions, as a consequence of the time variability of the mean event rate, as demonstrated by means of Bayesian block decomposition in the work of Wheatland et al. In this study we conduct numerical simulations of waiting time distributions N( …
The Solar Memory From Hours To Decades, Markus J. Aschwanden, Jay R. Johnson
The Solar Memory From Hours To Decades, Markus J. Aschwanden, Jay R. Johnson
Faculty Publications
Waiting-time distributions allow us to distinguish at least three different types of dynamical systems, including (i) linear random processes (with no memory); (ii) nonlinear, avalanche-type, nonstationary Poisson processes (with memory during the exponential growth of the avalanche rise time); and (iii) chaotic systems in the state of a nonlinear limit cycle (with memory during the oscillatory phase). We describe the temporal evolution of the flare rate λ(t) ∝ t p with a polynomial function, which allows us to distinguish linear (p ≈ 1) from nonlinear (p 2) events. The power-law slopes α of the observed waiting times (with full …