异质完全非对称简单排它过程中的非平衡相变机理研究

Totally asymmetric simple exclusion process is an important interacting particle system. Rich spatial evolution properties of order parameters and tremendous critical phenomena can be revealed in nonequilibrium phase transitions of TASEP. The study of the nonequilibrium phase transition mechanism of the heterogeneous TASEP could provide comprehensive illustrations of the formation and evolution of structures in complex systems. Besides, it would be helpful to promote the development of the theory of foundations for complex systems in the field of nonequilibrium statistical mechanics. Based on these issues, the heterogeneous system constituted by multi-lane TASEP with the effect of weak coupling will be studied in the project. Besides, phase diagram structures of the system will be investigated by the method of mean-field analyses complemented by Monte-Carlo simulations. Moreover, the topology evolution rule of phase diagrams can be summarized. In order to understand the mechanism of the formation and evolution of the bulk-induced shock in nonequilibrium phase transitions, the shock phase appeared in phase diagrams would be emphasized. Furthermore, exact solutions of the heterogeneous multi-lane TASEP with typical boundary conditions would also be studied. Complemented by Monte-Carlo simulations, exact solutions of characteristic order parameters like the density and the current of the system would be obtained by the detailed balance principle. Thus, the universal rule of the evolution of order parameters could be summarized, which would be conducive to the profound understanding of the nonequilibrium phase transition mechanism of complex systems. The research work of the project could provide a certain theoretical reference for understanding the dynamic behavior of particles in interacting particle systems. Besides, it could also provide a certain theoretical support for exploring the formation and evolution of nonequilibrium steady state in the mesoscopic multi-body particle system.

完全非对称简单排它过程（TASEP）是一种重要的一维多体粒子相互作用系统，其非平衡相变过程蕴含着丰富的序参量空间演化信息和临界现象，深入研究异质TASEP的非平衡相变机理有助于更为充分地刻画复杂系统中的结构形成及演化规律，有利于发展复杂系统的基础理论与方法。本项目拟建立弱耦合作用下N通道TASEP，利用平均场理论结合蒙特卡洛模拟得到系统的相图，总结其拓扑结构演化规律，重点分析激波相，探索非平衡相变过程中内部诱导激波的形成演化机制。在此基础上，利用细致平衡理论结合蒙特卡洛模拟分析典型边界条件下异质N通道TASEP，得到特征序参量（密度和流量）的精确解，总结出非平衡相变过程中系统序参量演化的普适性规律，深刻理解系统的非平衡相变机理，从而为深刻理解相互作用粒子系统中粒子的动力学行为提供基础理论参考，为探索介观尺度下多体粒子系统的非平衡稳态形成及演化提供理论依据。

本项目已开展了异质多通道TASEP非平衡相变机理研究，建立了具有一般性的弱耦合作用下多通道TASEP，利用平均场理论结合蒙特卡洛模拟得到了系统相图，总结得到了相图拓扑结构演化规律，重点剖析了定域激波相及离域激波相，重点研究了内部诱导激波形成演化机理，进一步建立了典型异质多通道TASEP，利用细致平衡理论结合蒙特卡洛模拟得到了特征序参量流量和密度演化的普适性规律。已在CNSNS、EPJP、Chaos Soliton. Fract.、IJMPB、MPLB、Sci. Rep.-UK、CPB等主流刊物中发表17篇学术论文（注：第一作者16篇、共同一作1篇），其中：IF3.0以上：5篇、中科院大类1区：1篇、大类2区：1篇、大类3区：4篇、大类4区：10篇、IEEE国际会议论文：1篇、并获得IEEE国际会议ICMRA最佳论文展示奖，且均将该基金作为第一标注资助项目。已与中科大、北交大、美国莱斯大学等国内外著名高校进行密切合作，多次求教于本领域国内外知名教授及其研究团队（如：中科大复杂系统研究组的汪秉宏教授、邓友金教授团队、北交大系统科学所的贾斌教授、高自友教授团队、莱斯大学Anatoly B. Kolomeisky教授等）为项目的执行及研究进展进行方向把关、技术指导等，已联合中科大、北交大等团队联合发表了十余篇国际学术论文，正联合指导研究生5人。研究成果可为深刻理解相互作用粒子系统中粒子的动力学行为提供基础理论参考及为探索介观尺度下多体粒子系统的非平衡稳态形成及演化提供理论依据，可应用于复杂系统中活性粒子的定向输运的机制理解、运用及调控和介观尺度下复杂输运体系中自驱动粒子集群输运行为调控。项目执行期内已授权两项发明专利CN107971240B和CN106500762B，且主持人分别为第七及第三发明人。研究成果已应用于实际驱动扩散系统输运效率优化及输运调控中，已参与决策生态环保部的环保部开展生态环保领域改革落实政策性文件《环办党建函[2017]598号》、省生态环境厅《皖环函件2017-492号文件数据核算说明》、《安徽省环保厅关于再次征求“十三五”挥发性有机物总量减排目标任务意见的函》、《省VOCs减排标准》等政策文件。