Growing interfaces uncover universal fluctuations behind scale invariance.

Scientific Reports
Kazumasa A TakeuchiHerbert Spohn

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.

References

Mar 3, 1986·Physical Review Letters·M KardarY C Zhang
Oct 16, 1989·Physical Review Letters·M A RubioJ P Gollub
Aug 8, 1994·Physical Review Letters·T EngoyS Roux
Sep 16, 2000·Physical Review Letters·M Prahofer, H Spohn
Oct 10, 2006·Physical Review Letters·M DegawaE D Williams
Dec 7, 2007·Proceedings of the National Academy of Sciences of the United States of America·Oskar HallatschekDavid R Nelson
Apr 7, 2010·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Kazumasa A TakeuchiMasaki Sano
Sep 28, 2010·Physical Review Letters·Kazumasa A Takeuchi, Masaki Sano
Sep 28, 2010·Physical Review Letters·Tomohiro Sasamoto, Herbert Spohn

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Citations

Oct 2, 2015·Proceedings of the National Academy of Sciences of the United States of America·Vladislav PopkovGunter M Schütz
Nov 1, 2017·Scientific Reports·L BöttcherH J Herrmann
Oct 3, 2018·Reports on Progress in Physics·Rosalind J Allen, Bartlomiej Waclaw
Mar 10, 2012·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·T J OliveiraS G Alves
May 18, 2013·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·T J OliveiraS C Ferreira
Aug 5, 2017·Physical Review Letters·Yohsuke T Fukai, Kazumasa A Takeuchi
Jun 28, 2013·Journal of Physics. Condensed Matter : an Institute of Physics Journal·T A de AssisF Borondo
Jan 14, 2017·Physical Review. E·Hui XiaYueheng Lan
Jun 21, 2017·Scientific Reports·Renan A L AlmeidaTiago J Oliveira
Jan 20, 2018·Physical Review. E·A P SolonM Kardar
May 20, 2018·Physical Review. E·Sidiney G Alves
Aug 17, 2018·Physical Review. E·I S S Carrasco, T J Oliveira
Aug 18, 2018·Physical Review Letters·J WhitehouseD Mukamel
Oct 24, 2019·Physical Review. E·Alexander P Kartun-GilesCarl P Dettmann
Jun 13, 2020·Physical Review Letters·Kazuya FujimotoYuki Kawaguchi
Jul 9, 2020·Physical Review Letters·Takayasu IwatsukaKazumasa A Takeuchi
Aug 29, 2020·Physical Review Letters·Jacopo De NardisRomain Vasseur
Jan 24, 2015·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Tapas Singha, Malay K Nandy
May 17, 2017·Physical Review. E·Hyungjoon SohHawoong Jeong
May 6, 2017·Physical Review Letters·Takashi ImamuraTomohiro Sasamoto
Feb 29, 2020·Physical Review Letters·Yohsuke T Fukai, Kazumasa A Takeuchi
Jul 22, 2020·Physical Review. E·Daniel VillarrubiaPedro Córdoba-Torres
Jun 25, 2020·Physical Review. E·Enrique Rodríguez-Fernández, Rodolfo Cuerno
Sep 5, 2015·Physical Review Letters·Masahiko Ueda, Shin-ichi Sasa
Sep 28, 2017·Physical Review Letters·Abhishek DharGrégory Schehr
Apr 8, 2017·Physical Review Letters·Jacopo De NardisKazumasa A Takeuchi
Aug 8, 2018·Physical Review Letters·Pierre Le DoussalGrégory Schehr
Sep 27, 2018·Physical Review. E·Silvia N Santalla, Silvio C Ferreira
Feb 16, 2019·Physical Review Letters·Abbas Ali SaberiJoachim Krug
Aug 17, 2020·Physical Review. E·Alexander VladimirovSergei Nechaev
Jun 15, 2016·Physical Review. E·Sidiney G Alves, Silvio C Ferreira
Jan 20, 2018·Physical Review. E·Fredric LamAndrew J Higgins
Aug 8, 2018·Physical Review Letters·Fernando CaballeroMichael E Cates
Jun 30, 2018·Physical Review Letters·Zeying ChenTomohiro Sasamoto
Aug 25, 2018·Physical Review Letters·Ivan CorwinLi-Cheng Tsai
Apr 20, 2019·Physical Review. E·I S S Carrasco, T J Oliveira
Oct 8, 2014·Journal of Physics. Condensed Matter : an Institute of Physics Journal·C P de CastroR F S Andrade

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