Physics
Scientific paper
May 1994
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1994natur.369..129e&link_type=abstract
Nature, Volume 369, Issue 6476, pp. 129-131 (1994).
Physics
43
Scientific paper
SUSTAINED nonequiibrium systems can be characterized by a fractal dimension D>=0, which can be considered to be a measure of the number of independent degrees of freedom1. The dimension D is usually estimated from time series2 but the available algorithms are unreliable and difficult to apply when D is larger than about 5 (refs 3,4). Recent advances in experimental technique5-8 and in parallel computing have now made possible the study of big systems with large fractal dimensions, raising new questions about what physical properties determine D and whether these physical properties can be used in place of time-series to estimate large fractal dimensions. Numerical simulations9-11 suggest that sufficiently large homogeneous systems will generally be extensively chaotic12, which means that D increases linearly with the system volume V. Here we test an hypothesis that follows from this observation: that the fractal dimension of extensive chaos is determined by the average spatial disorder as measured by the spatial correlation length ɛ associated with the equal-time two-point correlation function -a measure of the correlations between different regions of the system. We find that the hypothesis fails for a representative spatiotemporal chaotic system. Thus, if there is a length scale that characterizes homogeneous extensive chaos, it is not the characteristic length scale of spatial disorder.
Egolf David A.
Greenside Henry S.
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