Multi-scale compromise and multi-level correlation in complex systems

Following a brief discussion on the importance of understanding complex systems and the effectiveness of multi-scale method in analysing complex systems in chemical engineering, this presentation characterizes the hierarchical structures in complex systems by clarifying the difference between levels and scales. That is, 'level' is defined as a domain higher than 'scale', which can be described more or less by an explicit model when studied from its upper level; while 'scale' is used to describe the structural organization within a level. Using these terms, three different kinds of multi-scale methods are discussed. The descriptive method lays a basis for the other two methods, but no correlation between the scales are considered. The correlative method can describe the correlation between neighbouring scales or levels, but has faced with closure problems within a level, which can be solved by incorporating the variational method that correlates different scales through stability conditions. The variational method is more relevant to complexity science and is discussed in more detail including its physical principle and prospects in solving engineering problems in industries. Stability is critical to the variational method, which is recognized to be subject to compromise between dominant mechanisms and relationship between different scales of phenomena in systems. This strategy, mechanism compromise and scale resolution, is elucidated by studying two-phase structure in gas-solid systems. Then, its extension to different kinds of complex systems is presented. Verification of the strategy is carried out by computer-aided experiments, and its application to industries is demonstrated by three industrial cases where the method was applied. It is indicated that the local compromise between different dominant mechanisms with respect to both time and space leads to the formation of meso-scale structure which conformed to a variational criterion defined by a minimum lumped parameter. The presentation will be concluded by discussions on the possibility of generalizing the variational multi-scale method and some prospects of the method.