Properties of the interfaces generated by the competition between stable and unstable growth models
| Autor: | Isabel M Irurzun, Ezequiel V. Albano, C. M. Horowitz |
|---|---|
| Rok vydání: | 2005 |
| Předmět: |
Competitive Behavior
Models Statistical Surface Properties Population Dynamics Monte Carlo method Growth State (functional analysis) Models Biological Biopolymers Fractal Models Chemical Lattice size Neoplasms Saturation (graph theory) Animals Humans Computer Simulation Statistical physics Crystallization Scaling Cell Proliferation Mathematical physics Mathematics |
| Zdroj: | Physical Review E. 72 |
| ISSN: | 1550-2376 1539-3755 |
| DOI: | 10.1103/physreve.72.036116 |
| Popis: | Two different growing mechanisms, given by the Eden model (EM) and the unstable Eden model (UEM), are used to numerically explore the properties of the interface generated by a competitive dynamic process in which particles are aggregated according to the rules of the EM with probability $(1\ensuremath{-}p)$ and following the UEM with probability $p$. Based on extensive numerical simulations, it is shown that the interface width exhibits a growing regime that at time ${t}_{x2}$ crosses over to a saturation state such that the width $({W}_{\mathit{sat}})$ remains stationary. It is shown that ${W}_{\mathit{sat}}$ and ${t}_{x2}$ depend on both the lattice size $L$ and the probability $p$. This behavior can be rationalized by proposing new scaling relationships, which are tested numerically. Furthermore, the relevant exponents are determined showing that the instabilities of the UEM dominate the dynamics of the growing process. |
| Databáze: | OpenAIRE |
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