Phenomenological modelling of anomalous dynamical systems and flows

传输过程在自然界中是基本的，从宏观的，作为流体表面上的波，通过地质相中的中间尺度的颗粒，到微观尺度的DNA转录。在历史上，均方位移随时间线性增长（菲克扩散定律，1855年）的色散过程被指定为规则的。任何其他依赖都被视为异常。由于建模方程的极端困难，异常输运的分析被回避，因为建模方程是如此强大，以至于任何偏离时间线性色散的实验证据都被认为是测量限制。在过去的50年中，测量技术的合理性和越来越多的应用程序中异常过程的文献积累，从而创建了一个跨学科的领域，需要使用高等数学。异常过程的普遍性要求分析现象学模型，即足够普遍的系统，以重现常见的事件，而无需模拟任何特定的过程。这项研究方案是对这种一般性质的系统进行研究。

Transport processes are fundamental in nature, from macroscopic, as a wave on the surface of a fluid, through an intermediate scale of particles percolating in geologic facies, and to the miscroscopic scale of DNA transcription. Historically dispersion processes, wherein the mean square displacement grew linearly in time (Fick's diffusion law, 1855) were designated as regular. Any other dependence was deemed an anomaly. Analysis of anomalous transport was eschewed due to extreme difficulty of the modelling equations, so formidable that any experimental evidence of deviation from time-linear dispersion was excused as a measurement limitation. In the last 50 years soundness of measuring techniques and accrual of documentation on anomalous processes in ever growing number of applications thus created an inter-disciplinary field, requiring use of advanced mathematics. The ubiquity of anomalous processes calls for analysis of phenomenological models, i.e. systems general enough to reproduce common occurrences without modelling any particular process. This research programme is to undertake studies of systems of such generic nature.