SCALING PROPERTIES OF THE KURAMOTO-SIVASHINSKY EQUATION

The Kuramoto-Sivishinsky model describes the dynamics of a cellular fl ame front. It has been known for some time that on scales large compar ed with the size of a cell the front appears to be a self-affine fract al which has noisy dynamics in 1+1 dimensions. We use the inverse meth od of Lam and Sander (Phys. Rev. Lett. 71, 561 (1993)) to show explici tly how the scaling occurs and how deterministic chaos at small scales develops into noisy dynamics at large scales, and how a small scale p attern becomes a large scale disordered fractal via an intermediate sc aling regime.