The actual effective partition coefficients of Mg and Cr in a cross-section of a dendrite arm in a direct-chill(DC)-casting ingot of 7475 aluminum alloy are obtained.Meanwhile,by analyzing the microstructure,the mecha...The actual effective partition coefficients of Mg and Cr in a cross-section of a dendrite arm in a direct-chill(DC)-casting ingot of 7475 aluminum alloy are obtained.Meanwhile,by analyzing the microstructure,the mechanism of the heterogeneous distribution of E(Al_(18)Mg_(3)Cr_(2))dispersoids in this DC ingot is revealed.The results show that the actual effective partition coefficients of Mg and Cr are 0.650 and 1.392,respectively,and they describe the heterogeneous distributions of Mg and Cr along the direction of radius of the cross-section of the dendrite arm of the alloy.After homogenization treatment at 470℃ for 24 h,Mg diffuses uniformly,but Cr hardly diffuses.Both the concentrations of Mg and Cr and the sites of heterogeneous nucleation in the alloy are the determinants of the formation of E dispersoids simultaneously.The heat treatment at 250℃ for 72 h provides a large number of the sites of heterogeneous nucleation of the formation of fine E dispersoids that will be formed in the center of the cross-section during the subsequent heat treatment at higher temperature.展开更多
A competitive LotkaVolterra reactiondiffusion system with two delays subject to Neumann boundary conditions is considered. It is well known that the positive con stant steady state of the system is globally asymptotic...A competitive LotkaVolterra reactiondiffusion system with two delays subject to Neumann boundary conditions is considered. It is well known that the positive con stant steady state of the system is globally asymptotically stable if the interspecies competition is weaker than the intraspecies one and is unstable if the interspecies com petition dominates over the intraspecies one. If the latter holds, then we show that Hopf bifurcation can occur as the parameters （delays） in the system cross some critical val ues. In particular, we prove that these Hopf bifurcations are all spatially homogeneous if the diffusive rates are suitably large, which has the same properties as Hopf bifur cation of the corresponding delayed system without diffusion. However, if the diffusive rates are suitably small, then the system generates the spatially nonhomogeneous Hopf bifurcation. Furthermore, we derive conditions for determining the direction of spatially nonhomogeneous Hopf bifurcations and the stability of bifurcating periodic solutions. These results indicate that the diffusion plays an important role for deriving the complex spatiotemporal dynamics.展开更多
基金financially supported by the National Natural Science Foundation of China(No.51871043)Fundamental Research Funds for the Central Universities of China(No.N180212010)Liaoning Natural Science Foundation of China(No.2019-MS-113)。
文摘The actual effective partition coefficients of Mg and Cr in a cross-section of a dendrite arm in a direct-chill(DC)-casting ingot of 7475 aluminum alloy are obtained.Meanwhile,by analyzing the microstructure,the mechanism of the heterogeneous distribution of E(Al_(18)Mg_(3)Cr_(2))dispersoids in this DC ingot is revealed.The results show that the actual effective partition coefficients of Mg and Cr are 0.650 and 1.392,respectively,and they describe the heterogeneous distributions of Mg and Cr along the direction of radius of the cross-section of the dendrite arm of the alloy.After homogenization treatment at 470℃ for 24 h,Mg diffuses uniformly,but Cr hardly diffuses.Both the concentrations of Mg and Cr and the sites of heterogeneous nucleation in the alloy are the determinants of the formation of E dispersoids simultaneously.The heat treatment at 250℃ for 72 h provides a large number of the sites of heterogeneous nucleation of the formation of fine E dispersoids that will be formed in the center of the cross-section during the subsequent heat treatment at higher temperature.
文摘A competitive LotkaVolterra reactiondiffusion system with two delays subject to Neumann boundary conditions is considered. It is well known that the positive con stant steady state of the system is globally asymptotically stable if the interspecies competition is weaker than the intraspecies one and is unstable if the interspecies com petition dominates over the intraspecies one. If the latter holds, then we show that Hopf bifurcation can occur as the parameters （delays） in the system cross some critical val ues. In particular, we prove that these Hopf bifurcations are all spatially homogeneous if the diffusive rates are suitably large, which has the same properties as Hopf bifur cation of the corresponding delayed system without diffusion. However, if the diffusive rates are suitably small, then the system generates the spatially nonhomogeneous Hopf bifurcation. Furthermore, we derive conditions for determining the direction of spatially nonhomogeneous Hopf bifurcations and the stability of bifurcating periodic solutions. These results indicate that the diffusion plays an important role for deriving the complex spatiotemporal dynamics.
