莱维扩散在权力法下 随机重置 随机重置
Jianli Liu1, Yunyun Li1, Fabio Marchesoni1,2
1MOE Key Laboratory of Advanced Micro-Structured Materials, School of Physics Science and Engineering, Tongji University, Shanghai 200092, China.
Entropy (Basel, Switzerland)
|January 28, 2026
概括
列维走路的随机重置揭示了不同的扩散行为. 权力-法律重置创建了三个制度,包括超级扩散和本地化,影响搜索策略.
科学领域:
- 统计物理 统计物理
- 复杂的系统复杂的系统.
- 非平衡的动力学.
背景情况:
- 莱维步行表现出异常扩散,这对于从金融到生物学建模现象至关重要.
- 随机重置引入了一个限制随机进程的机制,改变它们的长期行为.
研究的目的:
- 为了研究不同重置策略对莱维步行扩散动态的影响.
- 在指数和功率定律重置协议下描述平均平方位移 (MSD).
主要方法:
- 结合数值模拟和使用更新理论的理论分析.
- 对各种重置指数的平均平方位移 (MSD) 缩放规律的推导.
主要成果:
- 指数式重置导致从超扩散到和稳定状态的急剧过渡.
- 电力规律重置 (指数β) 会导致三种不同的MSD模式:自由超扩散 (β<1),可调节超扩散 (1<β<γ0+1) 和局部化 (β>γ0+1).
- 理论MSD缩放规律与模拟数据显示出极好的一致性.
结论:
- 这项研究提供了一个全面的理解,即随机重置如何塑造莱维步行扩散.
- 结果为优化搜索策略和控制复杂,不平衡系统中的运输提供了洞察力.
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