Scaling behavior of cyclical roughness and maximal height of growing surfaces

Two new problems in kinetic surface roughening, namely, the scaling behavior of cyclical growth and that of the maximal height, are investigated using a variety of analytical approaches as well as extensive numerical simulations.; The scaling behavior of roughness is studied for surfaces grown by two alternating primary processes, typically deposition and desorption. To characterize the roughness in such cyclical processes, we have generalized the dynamic scaling hypothesis by replacing the time by the number of cycles n. In the early-time regime, the roughness is predicted to grow as $nb$. The roughness saturates to its maximal value in the late-time regime, which scales with the system size L as L α. The relations between the cyclical exponents and the corresponding exponents of the primary processes are explored. Exact results are obtained for linear primary processes, whereas an approximate renormalization scheme is employed to analyze nonlinear effects in the primary processes. Numerical simulations of atomistic growth models support the analytical results. When the distribution of the application times of the primary processes has a power law tail and a diverging mean, the dynamic and growth exponents change continuously with that power.; In many realistic situations the maximal (or minimal) height of a growing surface is the most relevant characteristic of the surface. Scaling arguments are combined with the extremal value theory of independent random variables to infer that the maximal height relative to the average grows as $tblnL-balnt+C1/a$ in the early-time regime. Thus it increases logarithmically slower than the roughness. In the late-time regime of saturated roughness, the maximal height relative to the average increases as Lα , as does the roughness. Exact results for the maximal height of some specific models with a 1D Brownian curve behavior are derived. Numerical simulations of various surface growth models are consistent with our analytical predictions.; Potential applications of these results include accelerated testing of rechargeable batteries, breakdown predictions and improved cancer treatment.