Universal Fluctuations of Growing Interfaces: Evidence in Turbulent Liquid Crystals

Abstract

We investigate growing interfaces of topological-defect turbulence in the electroconvection of nematic liquid crystals. The interfaces exhibit self-affine roughening characterized by both spatial and temporal scaling laws of the Kardar-Parisi-Zhang theory in 1+1 dimensions. Moreover, we reveal that the distribution and the two-point correlation of the interface fluctuations are universal ones governed by the largest eigenvalue of random matrices. This provides quantitative experimental evidence of the universality prescribing detailed information of scale-invariant fluctuations.

4 pages, 5 figures; minor changes made; note added

References in corpus (4)

• The one-dimensional KPZ equation: an exact solution and its universality
• Directed percolation criticality in turbulent liquid crystals
• Dynamic Scaling of Non-Euclidean Interfaces
• Comment on "Dynamic Scaling of Non-Euclidean Interfaces" [arXiv:0804.1898]

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