论文标题
随机搜索的效率与空间相关的扩散率
Efficiency of random search with space-dependent diffusivity
论文作者
论文摘要
我们解决了在具有空间相关扩散系数$ d（x）$的环境中随机搜索目标的问题。从包括Itô，Stratonovich和Hänggi-Klimontovich对相关随机过程的散布差分运算符的一般形式，我们获得了第一通道时间分布以及搜索效率$ \ MATHCAL {E} = \ langle 1/T \ rangle $。对于范式幂律扩散系数$ d（x）= d_0 | x |^α$，带有$α<2 $，它控制着迁移率是否随着距离目标的距离而增加还是减小，我们显示了不同解释的影响。对于Stratonovich框架，我们获得了搜索效率的封闭表达式，对任意扩散系数$ d（x）$有效。我们表明，异质扩散率的效率高于均匀平均水平，并且该效率仅取决于扩散率值的分布而不取决于其空间组织的分布，这些特征在其他解释下分解。
We address the problem of random search for a target in an environment with space-dependent diffusion coefficient $D(x)$. From a general form of the diffusion differential operator that includes Itô, Stratonovich, and Hänggi-Klimontovich interpretations of the associated stochastic process, we obtain the first-passage time distribution and the search efficiency $\mathcal{E}=\langle 1/t \rangle$. For the paradigmatic power-law diffusion coefficient $D(x) = D_0|x|^α$, with $α<2$, which controls whether the mobility increases or decreases with the distance from a target at the origin, we show the impact of the different interpretations. For the Stratonovich framework, we obtain a closed expression of the search efficiency, valid for arbitrary diffusion coefficient $D(x)$. We show that a heterogeneous diffusivity profile leads to lower efficiency than the homogeneous average level, and the efficiency depends only on the distribution of diffusivity values and not on its spatial organization, features that breakdown under other interpretations.
