Multilevel Mesoscale Complexities in Mesoregimes: Challenges in Chemical and Biochemical Engineering.

This review discusses the complex behaviors in diverse chemical and biochemical systems to elucidate their commonalities and thus help develop a mesoscience methodology to address the complexities in even broader topics. This could possibly build a new scientific paradigm for different disciplines and could meanwhile provide effective tools to tackle the big challenges in various fields, thus paving a path toward combining the paradigm shift in science with the breakthrough in technique developments. Starting with our relatively fruitful understanding of chemical systems, the discussion focuses on the relatively pristine but very intriguing biochemical systems. It is recognized that diverse complexities are multilevel in nature, with each level being multiscale and the complexity emerging always at mesoscales in mesoregimes. Relevant advances in theoretical understandings and mathematical tools are summarized as well based on case studies, and the convergence between physics and mathematics is highlighted.