Dynamic properties in a family of competitive growing models

Abstract

The properties of a wide variety of growing models, generically called $X/RD$, are studied by means of numerical simulations and analytic developments. The study comprises the following $X$ models: Ballistic Deposition, Random Deposition with Surface Relaxation, Das Sarma-Tamboronea, Kim-Kosterlitz, Lai-Das Sarma, Wolf-Villain, Large Curvature, and three additional models that are variants of the Ballistic Deposition model. It is shown that after a growing regime, the interface width becomes saturated at a crossover time ($t_{x2}$) that, by fixing the sample size, scales with $p$ according to $t_{x2}(p)\propto p^{-y},(p>0)$, where $y$ is an exponent. Also, the interface width at saturation ($W_{sat}$) scales as $W_{sat}(p)\propto p^{-\delta },(p>0)$, where $\delta$ is another exponent. It is proved that, in any dimension, the exponents $\delta$ and $y$ obey the following relationship: $\delta =y{\beta }_{RD}$, where ${\beta }_{RD}=1/2$ is the growing exponent for $RD$. Furthermore, both exponents exhibit universality in the $p\to 0$ limit. By mapping the behaviour of the average height difference of two neighbouring sites in discrete models of type $X/RD$ and two kinds of random walks, we have determined the exact value of the exponent $\delta$. Finally, by linking four well-established universality classes (namely Edwards-Wilkinson, Kardar-Parisi-Zhang, Linear-MBE and Non-linear-MBE) with the properties of both random walks, eight different stochastic equations for all the competitive models studied are derived.

arXiv comment23 pages, 6 figures, Submitted to Phys. Rev. E

References in corpus (7)

• Forest fires and other examples of self-organized criticality
• Phase ordering and roughening on growing films
• Noise Reduction and Universality in Limited Mobility Models of Nonequilibrium Growth
• Scaling Behavior of Cyclical Surface Growth
• Exact scalings in competitive growth models
• Scaling in the two-component surface growth
• Kinetic roughening and phase ordering in the two-component growth model

Cited by in corpus (13)

• Surface and Bulk Properties of Deposits Grown with a Bidisperse Ballistic Deposition Model
• Thin film growth models with long surface diffusion lengths
• Parameter free scaling relation for nonequilibrium growth processes
• Characterisation of non-equilibrium growth through global two-time quantities
• Nonuniversal effects in mixing correlated-growth processes with randomness: Interplay between bulk morphology and surface roughening
• Surface properties and scaling behavior of a generalized ballistic deposition model in (1+1)-dimension
• Simulating the initial growth of a deposit from colloidal suspensions
• Surface and bulk properties of ballistic deposition models with bond breaking
• Langevin equations for competitive growth models
• Thin film deposition with time varying temperature
• Anomalous roughening in competitive growth models with time-decreasing rates of correlated dynamics
• Competition between surface relaxation and ballistic deposition models in scale free networks
• Comment on "Dynamic properties in a family of competitive growing models"