Physics – Geophysics
Scientific paper
Dec 2009
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2009agufmsm42b..08w&link_type=abstract
American Geophysical Union, Fall Meeting 2009, abstract #SM42B-08
Physics
Geophysics
[3200] Mathematical Geophysics
Scientific paper
The Earth's magnetosphere is quite clearly “complex" in the everyday sense of the word. However, in the last 15 to 20 years there has been a growing thread in space physics (e.g. Freeman & Watkins [Science, 2002] , Chapman & Watkins [Space Science Reviews, 2001]) using and developing some of the emerging science of complex systems (e.g. Sornette, 2nd Edition, 2004). A particularly well-studied set of system properties has been derived from those used in the study of critical phenomena, notably correlation functions, power spectra, distributions of bursts above a threshold, and so on (e.g. Watkins [Nonlinear Processes in Geophysics, 2002]). These have revealed behaviours familiar from many other complex systems, such as burstiness, long range dependence, heavy tailed probability distributions and so forth. The results of these studies are typically interpreted within existing paradigms, most notably self-organised criticality. However, just as in other developing areas of complexity science (Sornette, op. cit.; Watkins & Freeman [Science, 2008]), it is increasingly being realised that the diagnostics in use have not been extensively studied outside the context in which they were originally proposed. This means that, for example, it is not well established what the expected distribution of bursts above a fixed threshold will be for time series other than Brownian (or fractional Brownian) motion. We will describe some preliminary investigations (Watkins et al [Physical Review E, 2009]) into the burst distribution problem, using Linear Fractional Stable Motion as a controllable toy model of a process exhibiting both long-range dependence and heavy tails. A by product of the work was a differential equation for LFSM (Watkins et al, op cit), which we also briefly discuss. Current and future work will also focus on the thorny problem of distinguishing turbulence from SOC in natural datasets (Watkins et al; Uritsky et al [Physical Review Letters, 2009]) with limited dynamic range, an area which will also be briefly discussed.
Chapman Sandra C.
Credgington Dan
Rosenberg S. J.
Sánchez Rafael
Watkins Nicholas Wynn
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