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Sci Rep. 2011;1:34. doi: 10.1038/srep00034. Epub 2011 Jul 11.

Growing interfaces uncover universal fluctuations behind scale invariance.

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  • 1Department of Physics, The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo, 113-0033, Japan. kazumasa@daisy.phys.s.u-tokyo.ac.jp

Abstract

Stochastic motion of a point - known as Brownian motion - has many successful applications in science, thanks to its scale invariance and consequent universal features such as Gaussian fluctuations. In contrast, the stochastic motion of a line, though it is also scale-invariant and arises in nature as various types of interface growth, is far less understood. The two major missing ingredients are: an experiment that allows a quantitative comparison with theory and an analytic solution of the Kardar-Parisi-Zhang (KPZ) equation, a prototypical equation for describing growing interfaces. Here we solve both problems, showing unprecedented universality beyond the scaling laws. We investigate growing interfaces of liquid-crystal turbulence and find not only universal scaling, but universal distributions of interface positions. They obey the largest-eigenvalue distributions of random matrices and depend on whether the interface is curved or flat, albeit universal in each case. Our exact solution of the KPZ equation provides theoretical explanations.

PMID:
22355553
[PubMed - indexed for MEDLINE]
PMCID:
PMC3216521
Free PMC Article
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