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Universal fluctuations of growing interfaces : Evidence in liquid-crystal turbulences
Stochastic growth of interfaces – a common phenomenon in our daily lives as we experience, for instance, in a coffee stain on a shirt – provides an intriguing situation where the scale invariance leads to universal scaling laws even out of equilibrium. This universality of growing
interfaces is theoretically well understood on the basis of the Kardar-Parisi-Zhang (KPZ) equation, but it has been quite elusive in experiments despite substantial efforts. Here, we fill this gap and go further, showing an experimental evidence of the universality beyond the scaling laws. We investigate interfaces of growing topological-defect turbulence in electrically
driven nematic liquid crystals. Characterizing detailed statistical properties of the interface fluctuations, we find not only the KPZ scaling laws, but also "universal distributions" found formerly in solvable models, which are exactly – and surprisingly – the largest eigenvalue distributions of random matrices. In the seminar I also show evidence for geometry-dependent
"sub-universality classes" in the KPZ class and possible reasons why our system shows such clear universal fluctuations.
References : K. A. Takeuchi and M. Sano, Phys. Rev. Lett. 104, 230601 (2010) ; and forthcoming papers.
Contact : mathilde.reyssat[at]espci.fr