Multi-Scale Compromise and Multi-Level Correlation in Complex Systems

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 mesoscale 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.