Stationary even single bump periodic solutions of the Swift Hohenberg equation are analyzed. The coefficient k in the equation is found to be a critical parameter. It is proved if 0<k<1 , there exist pe...Stationary even single bump periodic solutions of the Swift Hohenberg equation are analyzed. The coefficient k in the equation is found to be a critical parameter. It is proved if 0<k<1 , there exist periodic solutions having the same energy as the constant solution u=0; if 1<k<32 , there exist periodic solutions having the same energy as the stable states u=±k-1. The proof of the above results is based on a shooting technique, together with a linearization method and a scaling argument.展开更多
Dual-Phase (DP) steels are made of ductile ferrite phase and hard martensite phase.Although it became crucial in progress of automotive industry to save fuel consumption and reduce total weight of vehicles,we need mor...Dual-Phase (DP) steels are made of ductile ferrite phase and hard martensite phase.Although it became crucial in progress of automotive industry to save fuel consumption and reduce total weight of vehicles,we need more accurate estimation of distribution to mechanical properties in total amounts of specimen.DP steels have considerable difference of mechanical levels in each phase including ferrite and martensite.That is why this study focuses on deconvolution of experimental tensile curve into ferrite and martensite using EBSD for calculation of phase volume fractions and Swift equation.Nanoindentation for certain parameter of each phase was conducted to produce the deconvolution curves.展开更多
基金National Natural Science Foundation of China (1 0 0 71 0 67)
文摘Stationary even single bump periodic solutions of the Swift Hohenberg equation are analyzed. The coefficient k in the equation is found to be a critical parameter. It is proved if 0<k<1 , there exist periodic solutions having the same energy as the constant solution u=0; if 1<k<32 , there exist periodic solutions having the same energy as the stable states u=±k-1. The proof of the above results is based on a shooting technique, together with a linearization method and a scaling argument.
文摘Dual-Phase (DP) steels are made of ductile ferrite phase and hard martensite phase.Although it became crucial in progress of automotive industry to save fuel consumption and reduce total weight of vehicles,we need more accurate estimation of distribution to mechanical properties in total amounts of specimen.DP steels have considerable difference of mechanical levels in each phase including ferrite and martensite.That is why this study focuses on deconvolution of experimental tensile curve into ferrite and martensite using EBSD for calculation of phase volume fractions and Swift equation.Nanoindentation for certain parameter of each phase was conducted to produce the deconvolution curves.
