标题： 矩形网络中的色散：有效扩散系数和大偏差率函数 显示英文标题

标题： Dispersion in rectangular networks: effective diffusivity and large-deviation rate function

摘要： 在流体通过网络流动时，扩散标量的分散有许多应用，包括生物流动、多孔介质、供水和城市污染。 受此启发，我们发展了一种大偏差理论，该理论预测了在长时间极限下，在矩形网络中释放的标量浓度的演化$t \gg 1$。 该理论提供了一个近似浓度，对于质心的大距离仍然有效，特别是对于距离高达$O(t)$的情况，因此远超标准高斯近似成立的$O(t^{1/2})$范围。 该方法的一个副产品是用于描述这个高斯近似的有效扩散张量的显式表达式。 布朗粒子的蒙特卡洛模拟验证了大偏差结果，并展示了当$t$仅稍微较大时，它们在描述标量分布方面的有效性。 显示英文摘要

摘要： The dispersion of a diffusive scalar in a fluid flowing through a network has many applications including to biological flows, porous media, water supply and urban pollution. Motivated by this, we develop a large-deviation theory that predicts the evolution of the concentration of a scalar released in a rectangular network in the limit of large time $t \gg 1$. This theory provides an approximation for the concentration that remains valid for large distances from the centre of mass, specifically for distances up to $O(t)$ and thus much beyond the $O(t^{1/2})$ range where a standard Gaussian approximation holds. A byproduct of the approach is a closed-form expression for the effective diffusivity tensor that governs this Gaussian approximation. Monte Carlo simulations of Brownian particles confirm the large-deviation results and demonstrate their effectiveness in describing the scalar distribution when $t$ is only moderately large.