Understanding the mesoscale structure and regime transition in bubble columns is of great significance for reactor design and scaleup.Based on the energy-minimization multiscale(EMMS)model,a noncooperative game model ...Understanding the mesoscale structure and regime transition in bubble columns is of great significance for reactor design and scaleup.Based on the energy-minimization multiscale(EMMS)model,a noncooperative game model with constraints is proposed to investigate the structural properties of gas-liquid systems in which small and large bubbles are chosen as players and the energy consumption form the objective function.The conservation equations of the system can be regarded as the constraints of the game.For the formulated noncooperative game model,the concept of the generalized Nash equilibrium(GNE)is used to characterize the solution.An algorithm is developed to numerically compute the GNE and some important structural parameters in the system.The numerical results show the existence of the GNE for all values of the superficial gas velocity Ug.As Ug varies,the trends in the state variables can be observed and the critical point of Ug identified.The overall trend of the flow regime transition agrees with the original EMMS model and experimental results,although the GNE calculation also reveals different single-bubble dominant mechanisms with increasing Ug.展开更多
This paper considers optimization problems for a new kind of control systems based on non-equilibrium dynamic games.To be precise,the authors consider the infinitely repeated games between a human and a machine based ...This paper considers optimization problems for a new kind of control systems based on non-equilibrium dynamic games.To be precise,the authors consider the infinitely repeated games between a human and a machine based on the generic 2×2 game with fixed machine strategy of finite k-step memory.By introducing and analyzing the state transfer graphes(STG),it will be shown that the system state will become periodic after finite steps under the optimal strategy that maximizes the human’s averaged payoff,which helps us to ease the task of finding the optimal strategy considerably. Moreover,the question whether the optimizer will win or lose is investigated and some interesting phenomena are found,e.g.,for the standard Prisoner’s Dilemma game,the human will not lose to the machine while optimizing her own averaged payoff when k = 1;however,when k≥2,she may indeed lose if she focuses on optimizing her own payoff only The robustness of the optimal strategy and identification problem are also considered.It appears that both the framework and the results are beyond those in the classical control theory and the traditional game theory.展开更多
基金The authors would like to thank Prof.Lei Guo for his encour-agement and profound insight to realize the game hidden in the EMMS model.The authors also thank Prof.Jinghai Li for his encour-agement and valuable suggestions.The paper is supported by the National Natural Science Foundation of China under Grant 91634203,61304159,11688101,and by the National Center for Mathematics and Interdisciplinary Sciences.
文摘Understanding the mesoscale structure and regime transition in bubble columns is of great significance for reactor design and scaleup.Based on the energy-minimization multiscale(EMMS)model,a noncooperative game model with constraints is proposed to investigate the structural properties of gas-liquid systems in which small and large bubbles are chosen as players and the energy consumption form the objective function.The conservation equations of the system can be regarded as the constraints of the game.For the formulated noncooperative game model,the concept of the generalized Nash equilibrium(GNE)is used to characterize the solution.An algorithm is developed to numerically compute the GNE and some important structural parameters in the system.The numerical results show the existence of the GNE for all values of the superficial gas velocity Ug.As Ug varies,the trends in the state variables can be observed and the critical point of Ug identified.The overall trend of the flow regime transition agrees with the original EMMS model and experimental results,although the GNE calculation also reveals different single-bubble dominant mechanisms with increasing Ug.
基金supported by the National Natural Science Foundation of China under Grant No.60821091 by the Knowledge Innovation Project of Chinese Academy of Sciences under Grant No.KJCX3-SYW-S01
文摘This paper considers optimization problems for a new kind of control systems based on non-equilibrium dynamic games.To be precise,the authors consider the infinitely repeated games between a human and a machine based on the generic 2×2 game with fixed machine strategy of finite k-step memory.By introducing and analyzing the state transfer graphes(STG),it will be shown that the system state will become periodic after finite steps under the optimal strategy that maximizes the human’s averaged payoff,which helps us to ease the task of finding the optimal strategy considerably. Moreover,the question whether the optimizer will win or lose is investigated and some interesting phenomena are found,e.g.,for the standard Prisoner’s Dilemma game,the human will not lose to the machine while optimizing her own averaged payoff when k = 1;however,when k≥2,she may indeed lose if she focuses on optimizing her own payoff only The robustness of the optimal strategy and identification problem are also considered.It appears that both the framework and the results are beyond those in the classical control theory and the traditional game theory.
