Citation

Chen YJ, Papanikolaou S, Sethna JP, Zapperi S, Durin G. Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 2011; 84(6-1): 061103.

Affiliation

Laboratory of Atomic and Solid State Physics (LASSP), Clark Hall, Cornell University, Ithaca, New York 14853-2501, USA.

Copyright

(Copyright © 2011, American Physical Society, Publisher American Institute of Physics)

DOI

unavailable

PMID

22304036

Abstract

We introduce a systematic method for extracting multivariable universal scaling functions and critical exponents from data. We exemplify our insights by analyzing simulations of avalanches in an interface using simulations from a driven quenched Kardar-Parisi-Zhang (qKPZ) equation. We fully characterize the spatial structure of these avalanches-we report universal scaling functions for size, height, and width distributions, and also local front heights. Furthermore, we resolve a problem that arises in many imaging experiments of crackling noise and avalanche dynamics, where the observed distributions are strongly distorted by a limited field of view. Through artificially windowed data, we show these distributions and their multivariable scaling functions may be written in terms of two control parameters: the window size and the characteristic length scale of the dynamics. For the entire system and the windowed distributions we develop accurate parametrizations for the universal scaling functions, including corrections to scaling and systematic error bars, facilitated by a novel software environment SloppyScaling.

Language: en