Consider the one-parameter generalizations of the logarithmic and exponential functions which are obtained from the integration of non-symmetrical hyperboles. These generalizations coincide to the one obtained in the context of non-extensive thermostatistics. We show that these functions are...

Considering some deposition models with limited mobility, we show that the typical decay of the interface width to its saturation value is exponential, which defines the crossover or saturation time τ. We present a method to calculate a characteristic time τ0 proportional to τ and estimate...

We study the statistical properties of the star-shaped approximation of in vitro tumor profiles. The emphasis is on the two-point correlation structure of the radii of the tumor as a function of time and angle. In particular, we show that spatial two-point correlators follow a cosine law....

In this work, we studied the role played by the inactive sites present on the substrate of a growing surface. In our model, one particle sticks at the surface if the site where it falls is an active site. However, we allow the deposited particle to diffuse along the surface in accordance with...

We introduce a new class of growth models, with a surface restructuring mechanism in which impinging particles may dislodge suspended particles, previously aggregated on the same column in the deposit. The flux of these particles is controlled through a probability p. These systems present a...

In order to estimate roughness exponents of interface growth models, we propose the calculation of effective exponents from the roughness fluctuation σ in the steady state. We compare the finite-size behavior of these exponents and the ones calculated from the average roughness 〈w2〉 for two...

We consider a generalized two-species population dynamic model and analytically solve it for the amensalism and commensalism ecological interactions. These two-species models can be simplified to a one-species model with a time dependent extrinsic growth factor. With a one-species model with an...

We present a ballistic deposition model for the surface growth of a binary species A and C. Numerical simulations of the growth kinetics show a deviation from the Kardar–Parisi–Zhang universality class, model valid for only one kind of deposited particles. The study also shows that when the...