在Bethe格子上的随机多米诺自动机和权力法集群大小分布
Mariusz Białecki1, Arpan Bagchi1, Yohei Tutiya2
1Institute of Geophysics Polish Academy of Sciences, Ks. Janusza 64, 01-452 Warszawa, Poland.
Entropy (Basel, Switzerland)
|December 24, 2025
概括
随机多米诺自动机,森林火灾模型,通过调整参数,显示集群大小分布从指数向逆功率的过渡. 组合集群是扩展逆功率定律的关键.
科学领域:
- 统计物理 统计物理
- 复杂系统建模 复杂系统建模
背景情况:
- 随机细胞自动机被用来模拟森林火灾等现象.
- 贝特格子几何学为分析复杂系统提供了一个框架.
研究的目的:
- 在Bethe格子上制定和分析随机多米诺自动机 (RDA).
- 在RDA模型中调查静态状态和集群大小分布.
主要方法:
- 随机多米诺自动机 (RDA) 作为一个随机细胞自动机的制定.
- 使用组合分析推导静态方程.
- 在集群大小分布中的参数依赖过渡的分析.
主要成果:
- 在Bethe格子上的RDA模型显示可调节的集群大小分布.
- 通过改变集群移除参数,可以观察到从指数式到反向功率分布的平稳过渡.
- 组合两个以上的集群显著延长了逆功率定律的尾巴.
结论:
- RDA模型提供了对集群大小分布中的阶段过渡的见解.
- 在RDA模型中的参数调整控制系统的稳定性和逆功率定律的范围.
- 该模型显示了与加泰罗尼亚语类似的整数序列的连接.
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