HR: 1340h
AN: NG23A-1181    [Abstracts]
TI: Fluctuations in Total Quantities as a Probe of Complex Behaviour
AU: McRobie, F
EM: fiona.mcrobie@oxford.ac.uk
AF: British Antarctic Survey, High Cross, Madingley Road, Cambridge, CB3 0ET United Kingdom
AU: McRobie, F
EM: fiona.mcrobie@oxford.ac.uk
AF: Now Brasenose College, University of Oxford, Oxford, OX1 4AJ United Kingdom
AU: * Watkins, N W
EM: nww@bas.ac.uk
AF: British Antarctic Survey, High Cross, Madingley Road, Cambridge, CB3 0ET United Kingdom
AU: Chapman, S C
EM: sandrac@astro.warwick.ac.uk
AF: Space and Astrophysics, University of Warwick, Coventry, CV4 7AL
AU: Rowlands, G
EM: G.Rowlands@warwick.ac.uk
AF: Space and Astrophysics, University of Warwick, Coventry, CV4 7AL
AB: Very frequently in physics one studies a macroscopic variable which averages the effect of N microscopic degrees of freedom (dof). In equilibrium systems, where the dof are uncorrelated, the fluctuations are forced to a Gaussian form quite rapidly with increasing N by the central limit theorem. Increasingly, however, attention is focused on the non-Gaussian fluctuations seen in long-range correlated, critical systems. Recent progress was made by Bramwell ${\it et \ al}$ [Nature, 1998; PRL, 2000] who observed a particular non-Gaussian fluctuation probability density (pdf) in both confined laboratory turbulence and the XY model of critical phenomena, subsequently reporting it in many other critical models such as sandpiles. Chapman ${\em et \ al }$ [2000] proposed that the similar functional form of this pdf to the Gumbel distribution of extreme statistics might be due to the fluctuations in patches of activity in a complex system being dominated by the largest event. This is counter-intuitive, because of the behaviour of the short-ranged distributions with which we are more familiar, but similar questions been the subject of recent interest in solid state physics [Romeo ${\em et \ al}$, Eur. Phys. J. B, 2003]. We here examine this idea using a lognormal random process, showing under which circumstances the sums and maxima are similarly distributed. We also examine the effect of breaking statistical independence by means of a Hurst exponent not equal to 0.5. We also discuss applications to burst pdfs of the type first calculated for the auroral indices by Takalo [1993] and Consolini [1997].
DE: 3200 MATHEMATICAL GEOPHYSICS (New field)
DE: 3250 Fractals and multifractals
SC: Nonlinear Geophysics [NG]
MN: 2004 AGU Fall Meeting