在格子上使用随机重置的扩散
Alexander K Hartmann1, Satya N Majumdar2
1Universität Oldenburg, Institut für Physik, D-26111 Oldenburg, Germany.
Physical review. E
|October 21, 2025
概括
我们得出了一种精确的公式,用于在有重置的格子上进行粒子扩散. 平均首次通道时间显示了格子上的独特行为,与连续模型不同,特别是在目标附近.
科学领域:
- 统计物理 统计物理
- 凝聚物质物理学 凝聚物质物理学
- 数学物理学的数学物理.
背景情况:
- 在各种科学领域中,粒子扩散是基本的.
- 连续模型经常简化基于格子的扩散现象.
- 了解重置的扩散对于优化搜索策略至关重要.
研究的目的:
- 在一个具有重置的d维超立方格上推导一个扩散粒子的平均首次通道时间 (MFPT) 的准确公式.
- 探索格子对扩散和重置动态的特异性影响.
- 将格子结果与现有的连续理论进行比较.
主要方法:
- 准确的分析公式推导为MFPT.
- 对缩放极限的分析,以恢复连续空间的结果.
- 参数空间的调查,包括格子尺寸和重置率.
- 数字模拟用于验证.
主要成果:
- 获得了重置格子上的MFPT的准确公式,适用于所有参数.
- 观察到格子特定的MFPT行为,在低和高的重置速率之间有分歧,其中的最小值.
- 发现了MFPT的独特的力量法分歧,其指数取决于起始位置.
- 对于目标的最近邻居,MFPT随着重置速度单调地减少,接近一个通用极限.
结论:
- 带有重置的格子扩散展示了连续理论无法捕捉到的独特现象.
- 起始位置显著影响MFPT,特别是其差异指数.
- 重置策略可以根据格子几何和目标近距离优化.
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