Asymptotic function for multi-growth surfaces using power-law noise

Abstract

Numerical simulations are used to investigate the multiaffine exponent ${\alpha }_q$ and multi-growth exponent ${\beta }_q$ of ballistic deposition growth for noise obeying a power-law distribution. The simulated values of ${\beta }_q$ are compared with the asymptotic function ${\beta }_q=\frac{1}{q}$ that is approximated from the power-law behavior of the distribution of height differences over time. They are in good agreement for large $q$. The simulated ${\alpha }_q$ is found in the range $\frac{1}{q}\le {\alpha }_q\le \frac{2}{q+1}$. This implies that large rare events tend to break the KPZ universality scaling-law at higher order $q$.

5 pages, 4 figures, to be published in Phys. Rev. E

Cited by in corpus (1)

• Classification of KPZQ and BDP models by multiaffine analysis