Unconventional anomalous roughening in the slow combustion of paper

The height fluctuations in the flame front during slow combustion of paper display an unconventional anomalous scaling behaviour, whereas the burning front roughness is statistically self-affine. The anomalous roughness is characterized by different scaling exponents in the local (zeta (1)) and the global (alpha > zeta (1)) length scales. Furthermore, we find that the local roughness exponent, as well as the power spectrum S (structure factor of flame front), decrease as the sheet width W increases as zeta (1) proportional to S proportional to W-nu, where nu > 0, despite the fact that the global roughness exponent alpha does not depend on W. This distinguishes the unconventional anomalous roughening from the scaling behaviour expected in the cases of super-roughening and intrinsic anomalous roughening. The physical implications of these points are discussed.