We present robust scaling laws for the Euler characteristic and curvatures applicable to any symmetric system undergoing phase separating or ordering kinetics. We apply it to the phase ordering in a system of the nonconserved scalar order parameter and find three scaling regimes. The appearance of the preferred nonzero curvature of an interface separating +/- domains marks the crossover to the ...

The theory of growth kinetics developed previously is extended to the asym-metric case of oo-critical quenches for systems with a conserved scalar order parameter. In this instance the new parameter M, the average global value of the order parameter, enters the theory. For M = 0 one has critical quenches, while for suuciently large M one approaches the coexistence curve. For all M the theory su...

The scaling function of Lyapunov exponents for intermittent systems is full of particularities if compared with hyperbolic cases or the usual, nonhyperbolic, parabola. One particularity arises when this function is calculated from finite-time Lyapunov exponents: Different scaling properties with respect to the length of the finite-time chains emerge. As expected from random walk models, the sca...

The off-diagonal profile φ od (v) associated with a local operator φ̂(v) (order parameter or energy density) close to the boundary of a semi-infinite strip with width L is obtained at criticality using conformal methods. It involves the surface exponent x φ and displays a simple universal behaviour which crosses over from surface finite-size scaling when v/L is held constant to corner finite-siz...