Superdiffusion, large-scale synchronization and topological defects

Abstract

We study an ensemble of random walkers carrying internal noisy phase oscillators which are synchronized among the walkers by local interactions. Due to individual mobility, the interaction partners of every walker change randomly, hereby introducing an additional, independent source of fluctuations, thus constituting the intrinsic nonequilibrium nature of the temporal dynamics. We employ this paradigmatic model system to discuss how the emergence of order is affected by motion of individual entities. In particular, we consider both, normal diffusive motion and superdiffusion. A non-Hamiltonian field theory including multiplicative noise terms is derived which describes the nonequilibrium dynamics at the macroscale. This theory reveals a defect-mediated transition from incoherence to quasi long-range order for normal diffusion of oscillators in two dimensions, implying a power-law dependence of all synchronization properties on system size. In contrast, superdiffusive transport suppresses the emergence of topological defects, thereby inducing a continuous synchronization transition to long-range order in two dimensions. These results are consistent with particle-based simulations.

7 pages, 5 figures, submitted to Phys. Rev. E

References in corpus (10)

• Tuned, driven, and active soft matter
• Applications of Field-Theoretic Renormalization Group Methods to Reaction-Diffusion Problems
• The acceleration of evolutionary spread by long-range dispersal
• Pattern formation mechanisms in motility mutants of Myxococcus xanthus
• Dynamics and Steady States in excitable mobile agent systems
• Mobility induces global synchronization of oscillators in periodic extended systems
• Optimal cellular mobility for synchronization arising from the gradual recovery of intercellular interactions
• Synchronisation and liquid crystalline order in soft active fluids
• The Phase Synchronized State of Oriented Active Fluids
• Motion-induced synchronization in metapopulations of mobile agents

Cited by in corpus (24)

• Self-Propelled Rods: Insights and Perspectives for Active Matter
• The synchronized dynamics of time-varying networks
• Activity induced synchronization: From Mutual Flocking to Chiral Self-Sorting
• Derivation of a hydrodynamic theory for mesoscale dynamics in microswimmer suspensions
• Pattern Formation in Chemically Interacting Active Rotors with Self-Propulsion
• Emergence of synchronization in multiplex networks of mobile Rössler oscillators
• Describing synchronization and topological excitations in arrays of magnetic spin torque oscillators through the Kuramoto model
• Mesoscale pattern formation of self-propelled rods with velocity reversal
• Flocking of two unfriendly species: The two-species Vicsek model
• Synchronization in dynamical networks of locally coupled self-propelled oscillators
• Synchronization of moving oscillators in three dimensional space
• Active Brownian Rods
• Diversity of phase transitions and phase separations in active fluids
• Reaction processes among self-propelled particles
• Active hydrodynamics of synchronization and ordering in moving oscillators
• A Finite Volume Method for Continuum Limit Equations of Nonlocally Interacting Active Chiral Particles
• Hydrodynamic Equations for Flocking Models without Velocity Alignment
• Uncovering novel phase transitions in dense dry polar active fluids using a lattice Boltzmann method
• Dynamics of dissipative topological defects in coupled phase oscillators
• Gaussian theory for spatially distributed self-propelled particles
• Anomalous Behaviour of Mutual Information in Finite Flocks
• Hydrodynamics of Active Lévy Matter
• Active Lévy Matter: Anomalous Diffusion, Hydrodynamics and Linear Stability
• Polar flocks with discretized directions: the active clock model approaching the Vicsek model