论文标题
部分可观测时空混沌系统的无模型预测
Rate equations, spatial moments, and concentration profiles for mobile-immobile models with power-law and mixed waiting time distributions
论文作者
论文摘要
我们提出了一个用于系统的框架，其中示踪剂物质在移动区域中的扩散 - 添加传输被诱捕在不动区域中中断。我们的模型基于分布式扩散方程，激子扩散率模型和多率移动移动IMMOBILE质量传输的随机步行模型统一了不同的模型方法。我们研究了各种形式的捕获时间动态及其对移动区域示踪剂质量的影响。此外，我们发现相关的突破曲线，示踪剂密度作为时间的函数在空间的固定点，以及移动和固定的浓度曲线以及运输的各个矩。具体而言，我们为Mittag-Leffler捕获时间分布提供了异常运输动力学和移动质量的渐近幂律衰减的明确形式。在我们的分析中，我们指出，即使对于指数捕获时间密度，也观察到了瞬态异常转运。我们的结果在地球物理环境中以及生物学，软物质和固态系统中都有直接应用。
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.
