Phenomenological modelling of anomalous dynamical systems and flows

异常动力系统和流动的现象学建模

• 批准号: RGPIN-2017-04985
• 负责人: Nec, Yana
• 金额: $ 1.38万
• 依托单位: Thompson Rivers University
• 依托单位国家: 加拿大
• 项目类别: Discovery Grants Program - Individual
• 财政年份: 2020
• 资助国家: 加拿大
• 起止时间: 2020-01-01 至 2021-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=711237
• 关键词: Phenomenological; modelling; anomalous; dynamical; systems

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. The systems of equations to be investigated are constructed based on existing regular counterparts, whose structure and properties are largely understood. Said equations are then to be modified in accord with recent experimental results evincing anomalous behaviour. The salient outcomes of such studies are identification and explication of principal differences between regular and anomalous phenomena, in support of experimental findings. Analysis of such paradigms is crucial to the classification and understanding of complex transport processes occurring in biology, geology, chemistry and other natural sciences, as well as to the advancement of completeness of mathematical tools. This research programme will seek to reveal unifying principles underpinning anomalous dispersion processes, thus forwarding the knowledge in multiple disciplines. Trainees will master a wide spectrum of analysis and visualisation techniques, and obtain experience in inter-disciplinary collaborations. Overall this will increase the Canadian mathematical community' participation in the internationally based research on these topics. As an inter-disciplinary researcher I also work on problems defying classic solutions in environmental sciences. Projects include development of novel wellhead configuration for landfill wells, modelling of flow therein; theory of gas flow in a landfill pipe network, control and optimisation of pressure distribution; analysis of river life migration due to dam operation. Trainees will be exposed to direct cooperation with industry professionals and gain valuable experience in that environment. Working with academics, industrial companies will benefit the quality of their personnel and improve engineering practices.

传输过程是自然界的基础，从宏观的流体表面的波动，到中间尺度的地质相颗粒渗透，再到微观尺度的DNA转录。历史上，均方位移随时间线性增长（菲克扩散定律，1855）的色散过程被认为是规则的。任何其他依赖都被视为异常。异常输运的分析由于建模方程的极端困难而被回避，以至于任何偏离时间线性色散的实验证据都被原谅为测量限制。在过去的50年里，测量技术的健全和异常过程的文件积累在越来越多的应用中，因此创造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对现象学模型进行分析，即系统的普遍性足以再现常见事件，而无需对任何特定过程进行建模。这一研究方案将对这种一般性质的系统进行研究。