Diffusive persistence on disordered lattices and random networks.

Area of Science:

• Statistical Physics
• Network Science
• Complex Systems

Background:

• Stochastic processes in networks exhibit complex temporal dynamics.
• Understanding fluctuations and their lifetimes is crucial for network behavior.
• Diffusive persistence quantifies the temporal stability of fields within network nodes.

Purpose of the Study:

• Investigate diffusive persistence in various disordered and random networks.
• Determine how network topology influences temporal characteristics of fluctuations.
• Analyze scaling behavior and finite-size effects at and above the percolation threshold.

Main Methods:

• Analysis of diffusive persistence in 2D disordered networks and random networks (e.g., Erdős-Rényi).
• Calculation of scaling exponents for diffusive persistence as a function of time and system size.
• Examination of finite-size effects at the percolation threshold.

Main Results:

• In 2D disordered networks above percolation, diffusive persistence scales as P(t,L)∼t^{-θ} with θ≃0.186.
• At the percolation threshold, the scaling exponent shifts to θ≃0.141 due to structural transitions.
• Finite-size effects at the percolation threshold show a power law P(t,L)∼L^{-zθ} with z≃2.86.
• Random networks lack simple power-law scaling above the percolation threshold.

Conclusions:

• Network topology critically impacts diffusive persistence and fluctuation lifetimes.
• Percolation transitions significantly alter scaling behaviors in disordered networks.
• Disordered and random networks exhibit fundamentally different persistence dynamics.