HR: 16:20h
AN: NG44A-01 INVITED     [Abstracts]
TI: Linear Fractional Stable Motion: can we use it to Model the Noah and Joseph Effects in Space Physics and Elsewhere ?
AU: * Watkins, N W
EM: nww@bas.ac.uk
AF: British Antarctic Survey, High Cross, Madingley Road, Cambridge, CB3 0ET, United Kingdom
AB: There is by now abundant evidence for scaling in many fluctuating quantities in the coupled solar-terrestrial system (solar wind, magnetosphere and ionosphere). Physical explanations have thus naturally been sought (see e.g. the surveys of Chapman and Watkins [2001]; Freeman and Watkins [2002] and Vassiliadis [2006]) in descriptions such as low dimensional chaos, turbulence and SOC. These latter two models differ, in that SOC was directly inspired by a wish to unify spatial (fractal) and temporal (1/f) scaling, while the study of turbulence has over time placed increasing emphasis on scaling and multiscaling phenomenology since the seminal work of Kolmogorov [1941]. I here discuss a complementary approach (Watkins [2002]; Watkins et al. [2005]) - the use of deliberately oversimplified mathematical testbeds that may capture relevant phenomenology and/or give insight. The model I will discuss is Linear Fractional Stable Motion (LFSM), which unites long range dependence-the Joseph effect-exemplified by fractional Brownian motion with the heavy tailed jumps-the Noah effect-of Levy flights. LFSM is in fact not purely a toy model but has known links to extremal dynamics. Intriguingly, LFSM exhibits the appearance of multiaffinity while giving (at least in 1D) avalanche phenomenology in the sense of power law-tailed pdfs for burst sizes and durations. I will discuss numerical simulations, some analytical scaling arguments and a diffusion-like equation for LFSM.
DE: 4425 Critical phenomena
DE: 4440 Fractals and multifractals
DE: 4468 Probability distributions, heavy and fat-tailed (3265)
DE: 4475 Scaling: spatial and temporal (1872, 3270, 4277)
SC: Nonlinear Geophysics [NG]
MN: 2007 Joint Assembly