Self-organized criticality driven by droplet influx and random fusion

• DOI: 10.48550/arxiv.2502.06236
• Publication Date: 2025-02-10
• Authors: Bo Lyu; Jie Lin
• Keywords: Self-organized Criticality

The droplet size distribution typically decays exponentially in solutions formed by liquid-liquid phase separation. Nevertheless, a power-law of nucleoli volumes has been observed amphibian oocytes, which appears similar to the cluster reaction-limited aggregation. In this work, we study mechanism distributed sizes and unveil self-organized criticality driven influx random fusion between droplets. Surprisingly, dynamics is governed Smoluchowski equation as aggregation systems. system reaches critical state area fraction approaches value at with $1.5$ exponent. Furthermore, also spatially scale-free divergent correlation length state, marked giant droplet-density fluctuations decay pair function.