具有幂律和混合等待时间分布的移动-不移动模型的速率方程、空间矩和浓度分布
Rate equations, spatial moments, and concentration profiles for mobile-immobile models with power-law and mixed waiting time distributions
摘要：
我们提出了一个框架的系统中，在一个移动区的示踪物质的扩散平流运输中断捕获在一个不动区。我们的模型统一了不同的模型方法的基础上分布阶扩散方程，激子扩散速率模型，和随机游走模型的多速率移动-不动的质量传输。我们研究了捕获时间动态的各种形式及其对可动带示踪剂质量的影响。此外，我们发现相关的突破曲线，示踪剂密度在空间中的一个固定点作为时间的函数，以及移动和固定的浓度分布和各自的时刻的运输。具体来说，我们推导出明确的形式的异常运输动力学和渐近幂律衰减的移动质量的米塔格-莱弗勒捕获时间分布。在我们的分析中，我们指出，即使是指数捕获时间密度瞬态反常输运观察。我们的研究结果不仅在地球物理学领域有直接的应用，而且在生物学、软物质和固态系统中也有直接的应用。
英文摘要：
We present a framework for systems in which diffusion-advection transport of a tracer substance in a mobile zone is interrupted by trapping in an immobile zone. Our model unifies different model approaches based on distributed-order diffusion equations, exciton diffusion rate models, and random walk models for multi-rate mobile-immobile mass transport. We study various forms for the trapping time dynamics and their effects on the tracer mass in the mobile zone. Moreover we find the associated breakthrough curves, the tracer density at a fixed point in space as function of time, as well as the mobile and immobile concentration profiles and the respective moments of the transport. Specifically we derive explicit forms for the anomalous transport dynamics and an asymptotic power-law decay of the mobile mass for a Mittag-Leffler trapping time distribution. In our analysis we point out that even for exponential trapping time densities transient anomalous transport is observed. Our results have direct applications in geophysical contexts but also in biological, soft matter, and solid state systems.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
