The edges between vertices in networks take not only the common binary values, but also the ordered values in some situations(e.g., the measurement of the relationship between people from worst to best in social netwo...The edges between vertices in networks take not only the common binary values, but also the ordered values in some situations(e.g., the measurement of the relationship between people from worst to best in social networks). In this paper, the authors study the asymptotic property of the moment estimator based on the degrees of vertices in ordered networks whose edges are ordered random variables. In particular, the authors establish the uniform consistency and the asymptotic normality of the moment estimator when the number of parameters goes to infinity. Simulations and a real data example are provided to illustrate asymptotic results.展开更多
The nanometer coherent structure evolution of spinodal decomposition and ordering coexistence phase transformation in Fe-24Al alloys is investigated by the microscopic phase field kinetic model.The results show that t...The nanometer coherent structure evolution of spinodal decomposition and ordering coexistence phase transformation in Fe-24Al alloys is investigated by the microscopic phase field kinetic model.The results show that the concentration and long-range order parameters all continuously change towards to their equilibrium values during phase transformation.With the increase of elastic interaction energy,the anisotropy along [01] or [10] elastic soft direction is more obvious and the time reaching equilibrium state is also shortened.According to the results,the formation of nanometer coherent structures during phase transformation is composed of the initial decreasing stage of order degree stage,the incubation stage,the continuous increasing stage of concentration order parameter and long-range order parameter,and the later stable stage.The spinodal decomposition and ordering is interaction;the initial ordering stage is a necessary condition of the coexistence phase transformation.The nanometer coherent structures are not found to grow during the whole phase transformation.The simulation results are in accordance with the results in experiment obtained by the aging treatment in Fe-24Al alloys.展开更多
基金supported by the National Natural Science Foundation of China under Grant Nos.11271147,11471135partially supported by the National Natural Science Foundation of China under Grant No.11401239+1 种基金Funds of CCNU from the Colleges’s Basic Research and Operation of MOE(CCNU15A02032,CCNU15ZD011)a Fund from KLAS(130026507)
文摘The edges between vertices in networks take not only the common binary values, but also the ordered values in some situations(e.g., the measurement of the relationship between people from worst to best in social networks). In this paper, the authors study the asymptotic property of the moment estimator based on the degrees of vertices in ordered networks whose edges are ordered random variables. In particular, the authors establish the uniform consistency and the asymptotic normality of the moment estimator when the number of parameters goes to infinity. Simulations and a real data example are provided to illustrate asymptotic results.
文摘The nanometer coherent structure evolution of spinodal decomposition and ordering coexistence phase transformation in Fe-24Al alloys is investigated by the microscopic phase field kinetic model.The results show that the concentration and long-range order parameters all continuously change towards to their equilibrium values during phase transformation.With the increase of elastic interaction energy,the anisotropy along [01] or [10] elastic soft direction is more obvious and the time reaching equilibrium state is also shortened.According to the results,the formation of nanometer coherent structures during phase transformation is composed of the initial decreasing stage of order degree stage,the incubation stage,the continuous increasing stage of concentration order parameter and long-range order parameter,and the later stable stage.The spinodal decomposition and ordering is interaction;the initial ordering stage is a necessary condition of the coexistence phase transformation.The nanometer coherent structures are not found to grow during the whole phase transformation.The simulation results are in accordance with the results in experiment obtained by the aging treatment in Fe-24Al alloys.
