在异质环境中随机搜索与重置
Luiz Menon1, Celia Anteneodo1,2
1Department of Physics, <a href="https://ror.org/01dg47b60">PUC-Rio</a>, Rua Marquês de São Vicente 225, 22451-900, Rio de Janeiro, RJ, Brazil.
Physical review. E
|December 18, 2024
概括
这项研究分析了随机搜索与位置重置在不同的扩散度的环境中. 我们获得了平均首次通道时间的分析表达式,显示异质性如何影响搜索效率.
科学领域:
- 统计物理 统计物理
- 随机过程 随机过程
- 物理化学 物理化学
背景情况:
- 随机搜索是各种自然和人工过程的基础.
- 位置重置可以提高搜索效率,但对环境条件敏感.
- 空间依赖的扩散性为随机动态引入了复杂性.
研究的目的:
- 在有界的1D环境中,以空间依赖的扩散率和随机重置来导出平均首次通道时间的分析表达式.
- 调查不同扩散性配置和随机过程处方对搜索效率的影响.
- 探索在扩散异质性下重置策略的有效性.
主要方法:
- 分析表达式的推导为平均第一次通道时间 (T).
- 使用随机模拟进行验证.
- 分析斯特拉托诺维奇,伊托和反伊托的随机微积分的处方.
- 为不同的重置速率 (r) 开发非对称近似方法.
主要成果:
- 在斯特拉托诺维奇情景下,对于任意的扩散性概况D (x) 得到了平均第一次通道时间 (T) 的确切封闭式表达式.
- 对于T的非对称近似得到了小和大重置速率 (r) 的Itô和anti-Itô处方.
- 准确的线性扩散度D (x) 的结果允许详细讨论异质效应.
结论:
- 扩散异质性显著影响随机搜索与重置的有效性.
- 随机微积分的选择影响得出的分析结果.
- 重置策略可以通过考虑异质环境的特定特征来优化.
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