2011年7月
Growing interfaces uncover universal fluctuations behind scale invariance
SCIENTIFIC REPORTS
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- 巻
- 1
- 号
- 開始ページ
- 34
- 終了ページ
- 記述言語
- 英語
- 掲載種別
- 研究論文(学術雑誌)
- DOI
- 10.1038/srep00034
- 出版者・発行元
- NATURE PUBLISHING GROUP
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.
- リンク情報
- ID情報
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- DOI : 10.1038/srep00034
- ISSN : 2045-2322
- Web of Science ID : WOS:000296048900001