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| Main Authors: | , |
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| Format: | Preprint |
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2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2502.06236 |
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| _version_ | 1866913695233212416 |
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| author | Lyu, Bohan Lin, Jie |
| author_facet | Lyu, Bohan Lin, Jie |
| contents | The droplet size distribution typically decays exponentially in solutions formed by liquid-liquid phase separation. Nevertheless, a power-law distribution of nucleoli volumes has been observed in amphibian oocytes, which appears similar to the cluster size distribution in reaction-limited aggregation. In this work, we study the mechanism of power-law distributed droplet sizes and unveil a self-organized criticality driven by droplet influx and random fusion between droplets. Surprisingly, the droplet size dynamics is governed by a similar Smoluchowski equation as the cluster size in aggregation systems. The system reaches a critical state as the area fraction approaches the critical value at which the droplet size has a power-law distribution with a $1.5$ exponent. Furthermore, the system is also spatially scale-free with a divergent correlation length at the critical state, marked by giant droplet-density fluctuations and power-law decay of the pair correlation function. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_06236 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Self-organized criticality driven by droplet influx and random fusion Lyu, Bohan Lin, Jie Soft Condensed Matter Biological Physics The droplet size distribution typically decays exponentially in solutions formed by liquid-liquid phase separation. Nevertheless, a power-law distribution of nucleoli volumes has been observed in amphibian oocytes, which appears similar to the cluster size distribution in reaction-limited aggregation. In this work, we study the mechanism of power-law distributed droplet sizes and unveil a self-organized criticality driven by droplet influx and random fusion between droplets. Surprisingly, the droplet size dynamics is governed by a similar Smoluchowski equation as the cluster size in aggregation systems. The system reaches a critical state as the area fraction approaches the critical value at which the droplet size has a power-law distribution with a $1.5$ exponent. Furthermore, the system is also spatially scale-free with a divergent correlation length at the critical state, marked by giant droplet-density fluctuations and power-law decay of the pair correlation function. |
| title | Self-organized criticality driven by droplet influx and random fusion |
| topic | Soft Condensed Matter Biological Physics |
| url | https://arxiv.org/abs/2502.06236 |