Growing interfaces uncover universal fluctuations behind scale invariance

Scientific Reports

Volumn 1, Issue , 2011, Pages

  Takeuchi, Kazumasa A ^a   Sano, Masaki ^a   Sasamoto, Tomohiro ^b   Spohn, Herbert ^c  

^a UNIVERSITY OF TOKYO   (Japan)

^b CHIBA UNIVERSITY   (Japan)

^c TECHNICAL UNIVERSITY OF MUNICH   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

ARTICLE; CHEMICAL MODEL; CHEMISTRY; COMPUTER SIMULATION; CRYSTALLIZATION; DIFFUSION; LIQUID CRYSTAL; METHODOLOGY; STATISTICAL MODEL;

COMPUTER SIMULATION; CRYSTALLIZATION; DIFFUSION; LIQUID CRYSTALS; MODELS, CHEMICAL; MODELS, STATISTICAL;

EID: 81155130410     PISSN: None     EISSN: 20452322     Source Type: Journal    
DOI: 10.1038/srep00034     Document Type: Article

References (34)

1. Stanley, H. E. Introduction to Phase Transitions and Critical Phenomena (Oxford Univ. Press, Oxford, 1987).
2. Henkel, M. Conformal Invariance and Critical Phenomena (Springer, Berlin, 1999).
3. Frisch, U. Turbulence: The Legacy of A. N. Kolmogorov (Cambridge Univ. Press, Cambridge, 1996).
4. Barabai, A.-L. & Stanley, H. E. Fractal Concepts in Surface Growth (Cambridge Univ. Press, Cambridge, 1995).
5. Meakin, P. The growth of rough surfaces and interfaces. Phys. Rep. 235, 189-289 (1993).
6. Halpin-Healy, T. & Zhang, Y.-C. Kinetic roughening phenomena, stochastic growth, directed polymers and all that. Aspects of multidisciplinary statistical mechanics. Phys. Rep. 254, 215-414 (1995).
7. Family, F. & Vicsek, T. Scaling of the active zone in the Eden process on percolation networks and the ballistic deposition model. J. Phys. A 18, L75-L81 (1985).
8. Rubio, M. A., Edwards, C. A., Dougherty, A. & Gollub, J. P. Self-affine fractal interfaces from immiscible displacement in porous media. Phys. Rev. Lett. 63, 1685-1688 (1989).
9. Wakita, J., Itoh, H., Matsuyama, T. & Matsushita, M. Self-affinity for the growing interface of bacterial colonies. J. Phys. Soc. Jpn. 66, 67-72 (1997).
10. Kardar, M., Parisi, G. & Zhang, Y.-C. Dynamic scaling of growing interfaces. Phys. Rev. Lett. 56, 889-892 (1986).
11. Forster, D., Nelson, D. R. & Stephen, M. J. Large-distance and long-time properties of a randomly stirred fluid. Phys. Rev. A 16, 732-749 (1977).
12. Maunuksela, J. et al. Kinetic roughening in slow combustion of paper. Phys. Rev. Lett. 79, 1515-1518 (1997). (Pubitemid 127655561)
13. Kertez, J., Horvah, V. K. & Weber, F. Self-affine rupture lines in paper sheets. Fractals 1, 67-74 (1993).
14. Eng, T., Mal, K. J., Hansen, A. & Roux, S. Roughness of two-dimensional cracks in wood. Phys. Rev. Lett. 73, 834-837 (1994). (Pubitemid 24976335)
15. Degawa, M., et al. Distinctive fluctuations in a confined geometry. Phys. Rev. Lett. 97, 080601 (2006).
16. Hallatschek, O., Hersen, P., Ramanathan, S. & Nelson, D. R. Genetic drift at expanding frontiers promotes gene segregation. Proc. Natl. Acad. Sci. USA 104, 19926-19930 (2007).
17. Csaho?, Z., Honda, K. & Vicsek, T. Dynamics of suface roughening in disordered media. J. Phys. A 26, L171-L178 (1993).
18. Takeuchi, K. A. & Sano, M. Universal fluctuations of growing interfaces: evidence in turbulent liquid crystals. Phys. Rev. Lett. 104, 230601 (2010).
19. de Gennes, P. G. & Prost, J. The Physics of Liquid Crystals, 2nd ed (Oxford Univ. Press, Oxford, 1993).
20. Kai, S. & Zimmermann, W. Pattern dynamics in the electrohydrodynamics of nematic liquid crystals. Prog. Theor. Phys. Suppl. 99, 458-492 (1989).
21. Takeuchi, K. A., Kuroda, M., Chate? H. & Sano, M. Experimental rezlization of directed percolation criticality in turbulent kiquid crystals. Phys. Rev. E 80, 051116 (2009).
22. Mehta, M. L. Random Matrices, 3rd ed (Elsevier, Amsterdam, 2004).
23. Trach, C. & Widom, H. Level-spacing distributions and the Airy kenel. Commun. Math. Phys. 159, 151-174 (1994).
24. Tracy, C. & Widom, H. On orthogonal and symplectic matrix ensembles. Commun. Math. Phys. 1777, 727-754 (1996).
25. Kriecherbauer, T. & Krug, J. A pedestrian's view on interacting particle systems, KPZ universality and random matrices. J. Phys. A 43, 403001 (2010).
26. Sasamoto, T. & Spohn, H. The 1 1 1-dimensional Kardar-Parisi-Zhang equation and its universality class. J. Stat. Mech. (2010) P11013.
27. Tracy, C. & Widom, H. Asymptotics in ASEP with step initial condition. Commun. Math. Phys. 290, 129-154 (2009).
28. Sasamoto, T. & Spohn, H. One-dimensional Kardar-Parisi-Zhang equation: an exact solution and its universality. Phys. Rev. Lett. 104, 230602 (2010).
29. Amir, G., Corwin, I. & Quastel, J. Probability distribution of the free energy of the continuum directed random polymer in 111 dimensions. Commun. Pure Appl. Math. 64, 466-537 (2011).
30. Johansson, K. Shape fluctuations and random matrices. Commun. Math. Phys. 209, 437-476 (2000).
31. Praofer, M. & Spohn, H. Universal distributions for growth processes in 111 dimensions and random matrices. Phys. Rev. Lett. 84, 4882-4885 (2000).
32. Baik, J. & Rains, E. M. in Random Matrix Models and Their Applications (eds Bleher, P. M. & Its, A. R. ) vol. 40, 1-19 (Cambridge Univ. Press, Cambridge, 2001).
33. Borodin, A., Ferrari, P. L., Praofer, M. & Sasamoto, T. Fluctuation properties of the TASEP with periodic initial configuration. J. Stat. Phys. 129, 1055-1080 (2007).
34. After submission of ourmanuscript, an exact solution of the KPZ equation for the flat case was reported in Calabrese, P. & Le Doussal, P. An exact solution for the KPZ equation with flat initial conditions, arXiv:1104. 1993v1 (2011).