Multi-scale methodology for complex systems
Chemical Engineering Science, 2004, 59(8-9): 1687-1700
Jinghai Li*, Jiayuan Zhang, Wei Ge, Xinhua Liu
This paper reviews the development of the multi-scale methodology in complexity science, and elucidates the importance of understanding complex systems in chemical engineering by discussing the relevance between complex systems and a few challenging problems in this field. Multi-scale structure is considered to be the focus in studying complex systems, particularly, the following four critical issues: correlation between phenomena at different scales, compromise between different dominant mechanisms, coupling between spatial and temporal structural changes and critical phenomena occurring in complex systems. It is considered that complex systems can be formulated as a multi-objective variational problem. The multi-scale methodology is promising in coping with complex systems, which can be descriptive, correlative or variational. It will be reviewed in particular by analyzing the above four critical issues and by showing its 20-year development at IPE from a rough idea to modeling approaches, softwares and finally to industrial applications as well as its extension to a number of chemical and physical systems. The strategy of “from the particular to the general” in developing the variational multi-scale methodology is emphasized, and challenges for mathematicians and physicists are identified to show the necessity of transdisciplinary cooperations. The paper will be concluded by prospects and suggestions.
Complex system, Multi-scale, Simulation, Chemical process, Nonlinear dynamics, Stability