Coarsening with non-trivial in-domain dynamics: correlations and interface fluctuations

Abstract

Using numerical simulations we investigate the space-time properties of a system in which spirals emerge within coarsening domains, thus giving rise to non-trivial internal dynamics. Initially proposed in the context of population dynamics, the studied six-species model exhibits growing domains composed of three species in a rock-paper-scissors relationship. Through the investigation of different quantities, such as space-time correlations and the derived characteristic length, autocorrelation, density of empty sites, and interface width, we demonstrate that the non-trivial dynamics inside the domains affects the coarsening process as well as the properties of the interfaces separating different domains. Domain growth, aging, and interface fluctuations are shown to be governed by exponents whose values differ from those expected in systems with curvature driven coarsening.

21 pages, 8 figures, accepted for publication in Physical Review E

References in corpus (18)

• Statistical physics of social dynamics
• Evolutionary games on graphs
• Cyclic dominance in evolutionary games: A review
• Junctions and spiral patterns in Rock-Paper-Scissors type models
• Coexistence and Survival in Conservative Lotka-Volterra Networks
• Crossover in Growth Law and Violation of Superuniversality in the Random Field Ising Model
• Self-organizing patterns maintained by competing associations in a six-species predator-prey model
• Segregation process and phase transition in cyclic predator-prey models with even number of species
• Non-equilibrium relaxation of an elastic string in a random potential
• Phase transitions induced by variation of invasion rates in spatial cyclic predator-prey models with four or six species
• Interplay between partnership formation and competition in generalized May-Leonard games
• Growing correlations and aging of an elastic line in a random potential
• Aging in coarsening diluted ferromagnets
• Cyclic competition of four species: mean field theory and stochastic evolution
• Stochastic evolution of four species in cyclic competition
• Spirals and coarsening patterns in the competition of many species: A complex Ginzburg-Landau approach
• Rock-paper-scissors played within competing domains in predator-prey games
• Relaxation processes in a system with logarithmic growth

Cited by in corpus (8)

• Stochastic population dynamics in spatially extended predator-prey systems
• The effect of habitats and fitness on species coexistence in systems with cyclic dominance
• Dynamically generated hierarchies in games of competition
• Invasion controlled pattern formation in a generalized multi-species predator-prey system
• Performance of weak species in the simplest generalization of the rock-paper-scissors model to four species
• Effects of a pestilent species on the stability of cyclically dominant species
• Death by starvation in May-Leonard models
• Impact of parity in rock-paper-scissors type models