Physics Letters A 339 (2005) 23–32 www.elsevier.com/locate/pla Anomalous roughness of turbulent interfaces with system size dependent local roughness exponent Alexander S. Balankin a,b,c,∗ , Daniel Morales Matamoros b,c a SEPI, ESIME, Instituto Politécnico Nacional, México D.F. 07738, Mexico b Grupo “Mecánica Fractal”, Mexico 1 c Instituto Mexicano de Petróleo, México D.F. 07730, Mexico Received 12 November 2004; received in revised form 9 February 2005; accepted 11 February 2005 Available online 14 March 2005 Communicated by C.R. Doering Abstract In a system far from equilibrium the system size can play the role of control parameter that governs the spatiotemporal dynamics of the system. Accordingly, the kinetic roughness of interfaces in systems far from equilibrium may depend on the system size. To get an insight into this problem, we performed a detailed study of rough interfaces formed in paper combustion experiments. Using paper sheets of different width λ, we found that the turbulent flame fronts display anomalous multi-scaling characterized by non-universal global roughness exponent α and by the system size dependent spectrum of local roughness exponents, ζ q (λ) = ζ 1 (1)q −ω λ φ <α, whereas the burning fronts possess conventional multi-affine scaling characterized by the universal spectrum of roughness exponent ζ q = 0.93q −0.15 . The structure factor of turbulent flame fronts also exhibits unconventional scaling dependence on λ. These results are expected to apply to a broad range of far from equilibrium systems when the kinetic energy fluctuations exceed a certain critical value.  2005 Elsevier B.V. All rights reserved. PACS: 68.35.Fx; 05.40.-a; 05.70.Ln; 61.43.Hv Keywords: Roughness; Scaling; Far from equilibrium systems 1. Introduction Kinetic roughening of interfaces occurs in a wide variety of physical situations, ranging from the crys- * Corresponding author. E-mail address: abalankin@ipn.mx (A.S. Balankin). 1 http://www.mfractal.esimez.ipn.mx. tal growth [1,2], fluid invasion in porous media [1,3] and motion of flux lines in superconductors [4], to the meandering fire front propagation in a forest [5] and fracture phenomena [6,7]. In many cases of interest, a growing interface can be represented by a single- valued function z(x,t) giving the interface location at position x at time t [1–7]. Extensive theoretical and experimental studies of the last decade have led to a 0375-9601/$ – see front matter  2005 Elsevier B.V. All rights reserved. doi:10.1016/j.physleta.2005.02.064