中文摘要：

这纸探索 noncooperative 游戏的应用程序和到一些的调查的纳什平衡的概念的理论多尺度的结构上的基本问题，在多相的建筑群的特别中央规模结构在化学工程的系统。这的基础工作 energy-minimization-multi-scale (扩展内存管理程序) 模型被李(1994 ) 和李建议，等。(2013 ) 它由于在主导的机制之间的 compromise-in-competition 识别多尺度的结构并且试着解决多客观的优化问题。然而，存在方法经常把它集成到单个客观优化的一个问题，它做不清楚地反映 compromise-in-competition 机制和原因象在选合适的 weighting 为因素的无常一样的重计算负担。这份报纸将在竞争提出妥协在扩展内存管理程序的机制有限制的一场 noncooperative 比赛，和愿望描述的模型需要马厩系统状态作为概括纳什平衡。然后，作者将调查游戏理论在化学药品为二个典型系统来临在管子中的工程，煤气固体的使液化(GSF ) 系统和狂暴的流动。为概括纳什的二个不同案例在如此的系统的平衡将明确、区分。generalize 纳什平衡愿望精确地被解决因为 GSF 系统和一个可行方法愿望在管子中为狂暴的流动被给。这些结果与存在与计算结果一致并且显示出这条途径的可行性，它克服存在方法的劣势并且深提供卓见进在在化学工程的多相的复杂系统的多尺度的结构的机制。

英文摘要：

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 fluidiza- tion （GSF） system and turbulent flow in pipe. Two different cases for generalized Nash equilibrinm 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.