Real and complex Schur forms have been receiving increasing attention from the fluid mechanics community recently,especially related to vortices and turbulence.Several decompositions of the velocity gradient tensor,su...Real and complex Schur forms have been receiving increasing attention from the fluid mechanics community recently,especially related to vortices and turbulence.Several decompositions of the velocity gradient tensor,such as the triple decomposition of motion(TDM)and normal-nilpotent decomposition(NND),have been proposed to analyze the local motions of fluid elements.However,due to the existence of different types and non-uniqueness of Schur forms,as well as various possible definitions of NNDs,confusion has spread widely and is harming the research.This work aims to clean up this confusion.To this end,the complex and real Schur forms are derived constructively from the very basics,with special consideration for their non-uniqueness.Conditions of uniqueness are proposed.After a general discussion of normality and nilpotency,a complex NND and several real NNDs as well as normal-nonnormal decompositions are constructed,with a brief comparison of complex and real decompositions.Based on that,several confusing points are clarified,such as the distinction between NND and TDM,and the intrinsic gap between complex and real NNDs.Besides,the author proposes to extend the real block Schur form and its corresponding NNDs for the complex eigenvalue case to the real eigenvalue case.But their justification is left to further investigations.展开更多
冷热电联产(combined cooling, heating and power,CCHP)系统与微电网的结合有利于促进消纳可再生能源,为了提升CCHP型微电网的经济性、环保性和稳定性,提出了两阶段优化调度模型。离线优化阶段基于需求侧响应策略,建立了基于归一化法...冷热电联产(combined cooling, heating and power,CCHP)系统与微电网的结合有利于促进消纳可再生能源,为了提升CCHP型微电网的经济性、环保性和稳定性,提出了两阶段优化调度模型。离线优化阶段基于需求侧响应策略,建立了基于归一化法向约束法的多目标规划模型,并用熵权-TOPSIS法筛选最优结果。在线优化阶段建立了基于动态矩阵控制算法的有限时域优化模型,对离线优化结果进行跟踪优化和反馈校正,以降低不确定性因素的影响。最后,设计对比方案进行分析,验证了所提优化模型的有效性。展开更多
文摘Real and complex Schur forms have been receiving increasing attention from the fluid mechanics community recently,especially related to vortices and turbulence.Several decompositions of the velocity gradient tensor,such as the triple decomposition of motion(TDM)and normal-nilpotent decomposition(NND),have been proposed to analyze the local motions of fluid elements.However,due to the existence of different types and non-uniqueness of Schur forms,as well as various possible definitions of NNDs,confusion has spread widely and is harming the research.This work aims to clean up this confusion.To this end,the complex and real Schur forms are derived constructively from the very basics,with special consideration for their non-uniqueness.Conditions of uniqueness are proposed.After a general discussion of normality and nilpotency,a complex NND and several real NNDs as well as normal-nonnormal decompositions are constructed,with a brief comparison of complex and real decompositions.Based on that,several confusing points are clarified,such as the distinction between NND and TDM,and the intrinsic gap between complex and real NNDs.Besides,the author proposes to extend the real block Schur form and its corresponding NNDs for the complex eigenvalue case to the real eigenvalue case.But their justification is left to further investigations.
文摘冷热电联产(combined cooling, heating and power,CCHP)系统与微电网的结合有利于促进消纳可再生能源,为了提升CCHP型微电网的经济性、环保性和稳定性,提出了两阶段优化调度模型。离线优化阶段基于需求侧响应策略,建立了基于归一化法向约束法的多目标规划模型,并用熵权-TOPSIS法筛选最优结果。在线优化阶段建立了基于动态矩阵控制算法的有限时域优化模型,对离线优化结果进行跟踪优化和反馈校正,以降低不确定性因素的影响。最后,设计对比方案进行分析,验证了所提优化模型的有效性。
