Abstract
This paper explores the application of noncooperative game theory together with the concept of Nash equilibrium to the investigation of some basic problems on multi-scale structure, especially the meso-scale structure in the multi-phase complex systems in chemical engineering. The basis of this work is the energy-minimization-multi-scale (EMMS) model proposed by Li and Kwauk (1994) and Li, et al. (2013) which identifies the multi-scale structure as a result of ‘compromise-in-competition between dominant mechanisms’ and tries to solve a multi-objective optimization problem. However, the existing methods often integrate it into a problem of single objective optimization, which does not clearly reflect the ‘compromise-in-competition’ mechanism and causes heavy computation burden as well as uncertainty in choosing suitable weighting factors. This paper will formulate the compromise in competition mechanism in EMMS model as a noncooperative game with constraints, and will describe the desired stable system state as a generalized Nash equilibrium. Then the authors will investigate the game theoretical approach for two typical systems in chemical engineering, the gas-solid fluidization (GSF) system and turbulent flow in pipe. Two different cases for generalized Nash equilibrium in such systems will be well defined and distinguished. The generalize Nash equilibrium will be solved accurately for the GSF system and a feasible method will be given for turbulent flow in pipe. These results coincide with the existing computational results and show the feasibility of this approach, which overcomes the disadvantages of the existing methods and provides deep insight into the mechanisms of multi-scale structure in the multi-phase complex systems in chemical engineering.
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Acknowledgments
The authors would like to thank Prof LI Jinghai for his encouragements and valuable suggestions; and thank Prof. YANG Ning, Dr. WANG Limin and Dr. ZHANG Lin for the helpful discussions on physics motivating this paper. The authors also thank Dr. CHENG Jinsan and Ms. XIE Siyu for their kind help in solving equations theoretically or using Matlab.
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The paper was supported by the National Natural Science Foundation of China under Grant Nos. 11688101, 91634203, 61304159 and by the National Center for Mathematics and Interdisciplinary Sciences.
This paper was recommended for publication by Editor CHEN Jie.
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Li, Y., Mu, Y., Yuan, S. et al. The game theoretical approach for multi-phase complex systems in chemical engineering. J Syst Sci Complex 30, 4–19 (2017). https://doi.org/10.1007/s11424-017-6287-1
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DOI: https://doi.org/10.1007/s11424-017-6287-1