具有招募与死亡的异质扩散

中文摘要 AI 辅助

我们研究了一种在存在独立招募和死亡情况下的具有位置相关扩散系数的异质扩散过程。该框架推广了随机重置下的异质扩散，后者作为招募率和死亡率相等的特殊情况被恢复。在长时间极限下，系统趋近于一个非平衡稳态，其均方位移饱和到一个与招募率无关的值。至关重要的是，该饱和极限通过应用于扩散系数的有效指数直接编码了潜在的输运机制，并且我们刻画了向该稳态的非平凡转变。我们进一步推导了到达目标的平均首次通过时间，并表明对于固定的招募-死亡比，存在一个最优死亡率使搜索时间最小化。这种“死亡辅助搜索”效应通过数值评估得到证实。将招募和死亡重新解释为感染和移除过程，我们将该模型应用于流行病传播，并表明适度的移除率可以反直觉地加速而非延迟感染到达新的空间区域。在流行病学之外，我们的框架对具有并发粒子产生和毁灭的系统具有广泛相关性，例如细菌生长、反应性流体中的示踪剂扩散或拥挤环境中的细胞群体动力学。

英文摘要

We study a heterogeneous diffusion process with a position-dependent diffusion coefficient in the presence of independent recruitment and mortality. This framework generalises heterogeneous diffusion under stochastic resetting, which is recovered as the special case of equal recruitment and mortality rates. At long times, the system approaches a non-equilibrium stationary state with a mean squared displacement that saturates to a value independent of the recruitment rate. Crucially, this saturation limit directly encodes the underlying transport regime via an effective exponent applied to the diffusion coefficient, and we characterise the non-trivial transition to this stationary regime. We further derive the mean first-passage time to a target and show that, for a fixed recruitment-to-mortality ratio, an optimal mortality rate minimises the search time. This "mortality-assisted search" effect is confirmed by numerical evaluation. Reinterpreting recruitment and mortality as infection and removal processes, we apply the model to epidemic spreading and show that a moderate removal rate can counter-intuitively accelerate, rather than delay, the arrival of infection at a new spatial region. Beyond epidemiology, our framework offers broad relevance to systems featuring concurrent particle creation and destruction, such as bacterial growth, tracer diffusion in reactive fluids, or cellular population dynamics in crowded environments.

发表机构

• Escuela Superior Politécnica del Litoral, ESPOL（厄瓜多尔高等理工学院）
• Banaras Hindu University（贝拿勒斯印度教大学）
• Laboratoire de Physique et Chimie Théoriques (CNRS UMR 7019), Université de Lorraine Nancy（洛林大学南锡校区理论物理与化学实验室）
• Centro de Física Teórica e Computacional, Universidade de Lisboa（里斯本大学理论与计算物理中心）
• Research Center for Computer Science and Information Technologies, Macedonian Academy of Sciences and Arts（马其顿科学院计算机科学与信息技术研究中心）
• Institute of Physics, Faculty of Natural Sciences and Mathematics, Ss. Cyril and Methodius University（西里尔和梅托迪乌斯大学自然科学与数学学院物理研究所）
• Department of Physics, Korea University（韩国大学物理系）

机构由 AI 辅助整理，请以论文原文为准。

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Latex 2e, 26 pages, 5 figures