Double transition in a model of oscillating percolation

Area of Science:

• Statistical Physics
• Complex Systems

Background:

• Lattice percolation models are fundamental to understanding connectivity in various systems.
• Pulsating disks introduce a dynamic element to traditional static percolation problems.

Purpose of the Study:

• To investigate the distinct transition points in a lattice percolation model using pulsating disks.
• To analyze the impact of disk dynamics on connectivity and information propagation.

Main Methods:

• Simulating a lattice where sites are occupied by sinusoidally pulsating disks.
• Defining bond connectivity based on disk overlap and phase angles.
• Identifying transition points based on the emergence of spanning clusters.

Main Results:

• Observed two critical transition points: R0c=0.908(5) for spanning connected bonds (instant information propagation) and R0*=0.5907(3) for spanning live bonds (finite-time propagation).
• Both transitions exhibit critical behavior characteristic of ordinary percolation.
• Information propagation speed differs significantly between the two transition points.

Conclusions:

• The pulsating disk model exhibits robust critical phenomena relevant to percolation theory.
• The findings offer insights into information transfer dynamics in complex networks, particularly wireless sensor networks.