Anomalous roughness with system-size-dependent local roughness exponent

We note that in a system far from equilibrium the interface roughening may depend on the system size which plays the role of control parameter. To detect the size effect on the interface roughness, we study the scaling properties of rough interfaces formed in paper combustion experiments. Using paper sheets of different width λL₀, we found that the turbulent flame fronts display anomalous multiscaling characterized by nonuniversal global roughness exponent α and the system-size-dependent spectrum of local roughness exponents ζq(λ)=ζ₁(1)q^-ωλ^φ<α, whereas the burning fronts possess conventional multiaffine scaling. The structure factor of turbulent flame fronts also exhibit 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.