Abstract
The self-affinity of growing systems with radial symmetry, from tumours to grain–grain displacement, has attracted increasing interest in the last decade. In this work, we analyse features of the interface scaling of these clusters through large scale simulations (up to 3 × 107 particles) of two-dimensional growth processes with special emphasis on the off-lattice Eden model. The central objective is a discussion about an important pitfall associated with the evaluation of the growth exponent β of these systems. We show that the β value depends on the choice of the origin used to determine the interface width. We considered two strategies frequently used. When the width was evaluated in relation to the centre of mass (CM) of the border, the exponent obtained for the Eden model was βCM = 0.404 ± 0.013, in very good agreement with previous reported values. However, if the border CM was replaced by the initial seed position (a static origin), the exponent β0 = 0.333 ± 0.010, in complete agreement with the Kardar–Parisi–Zhang (KPZ) value βKPZ = 1/3, was found. The difference between βCM and β0 was explained through the border CM fluctuations that grow faster than the overall interface fluctuations. Indeed, we show that the exponents β0 and βCM characterize large and small wavelength fluctuations of the interface, respectively. These finds were also observed in three distinct lattice models, in which the lattice-imposed anisotropy is absent.