To investigate the formation mechanism of calcium hexaluminate（CaAl_（12）O_（19）, CA_6）, the analytically pure alumina and calcia used as raw materials were mixed in CaO/Al_2O_3 ratio of 12.57：137.43 by mass. The...To investigate the formation mechanism of calcium hexaluminate（CaAl_（12）O_（19）, CA_6）, the analytically pure alumina and calcia used as raw materials were mixed in CaO/Al_2O_3 ratio of 12.57：137.43 by mass. The raw materials were ball-milled and shaped into green specimens, and fired at 1300-1600°C. Then, the phase composition and microstructure evolution of the fired specimen were studied, and a first principle calculation was performed. The results show that in the reaction system of CaO and Al_2O_3, a small amount of CA_6 forms at 1300°C, and greater amounts are formed at 1400°C and higher temperatures. The reaction is as follows： CaO ·2Al_2O_3（CA_2） ＋ 4Al_2O_3 → CA_6. The diffusions of Ca^（2＋） in CA_2 towards Al_2O_3 and Al^（3＋） in Al_2O_3 towards CA_2 change the structures in different degrees of difficulty. Compared with the difficulty of structural change and the corresponding lattice energy change, it is deduced that the main formation mechanism is the diffusion of Ca^（2＋） in CA_2 towards Al_2O_3.展开更多
An optimal control problem for a controlled backward stochastic partial differential equation in the abstract evolution form with a Bolza type performance functional is considered. The control domain is not assumed to...An optimal control problem for a controlled backward stochastic partial differential equation in the abstract evolution form with a Bolza type performance functional is considered. The control domain is not assumed to be convex, and all coefficients of the system are allowed to be random. A variational formula for the functional in a given control process direction is derived, by the Hamiltonian and associated adjoint system. As an application, a global stochastic maximum principle of Pontraygins type for the optimal controls is established.展开更多
基金financially supported by the National Nature Science Foundation of China(No.51172120)
文摘To investigate the formation mechanism of calcium hexaluminate（CaAl_（12）O_（19）, CA_6）, the analytically pure alumina and calcia used as raw materials were mixed in CaO/Al_2O_3 ratio of 12.57：137.43 by mass. The raw materials were ball-milled and shaped into green specimens, and fired at 1300-1600°C. Then, the phase composition and microstructure evolution of the fired specimen were studied, and a first principle calculation was performed. The results show that in the reaction system of CaO and Al_2O_3, a small amount of CA_6 forms at 1300°C, and greater amounts are formed at 1400°C and higher temperatures. The reaction is as follows： CaO ·2Al_2O_3（CA_2） ＋ 4Al_2O_3 → CA_6. The diffusions of Ca^（2＋） in CA_2 towards Al_2O_3 and Al^（3＋） in Al_2O_3 towards CA_2 change the structures in different degrees of difficulty. Compared with the difficulty of structural change and the corresponding lattice energy change, it is deduced that the main formation mechanism is the diffusion of Ca^（2＋） in CA_2 towards Al_2O_3.
基金Supported by the National Natural Science Foundation of China(11101140,11301177)the China Postdoctoral Science Foundation(2011M500721,2012T50391)the Zhejiang Natural Science Foundation of China(Y6110775,Y6110789)
文摘An optimal control problem for a controlled backward stochastic partial differential equation in the abstract evolution form with a Bolza type performance functional is considered. The control domain is not assumed to be convex, and all coefficients of the system are allowed to be random. A variational formula for the functional in a given control process direction is derived, by the Hamiltonian and associated adjoint system. As an application, a global stochastic maximum principle of Pontraygins type for the optimal controls is established.
