In this article, we study the flows of curves in the Galilean 3-space and its equiform geometry without any constraints. We find that the Frenet equations and the intrinsic quantities of the inelastic flows of curves ...In this article, we study the flows of curves in the Galilean 3-space and its equiform geometry without any constraints. We find that the Frenet equations and the intrinsic quantities of the inelastic flows of curves are independent of time. We show that the motion of curves in the Galilean 3-space and its equiform geometry are described by the inviscid and viscous Burgers＇ equations.展开更多
In this paper based on [1]we go further into the study of chaotic behaviour of theforced oscillator containing a square nonlinear term by the methods of multiple scalesand numerical simulation. Relation between the c...In this paper based on [1]we go further into the study of chaotic behaviour of theforced oscillator containing a square nonlinear term by the methods of multiple scalesand numerical simulation. Relation between the chaotic domain and principal resonance curve is discussed. By analyzing the stability of principal resonance curve weinfer that chaotic motion would occur near the frequency at which the principalresonance curve has vertical tangent.Results of numerical simulation confirm thisinference.Thus we offer an effective way to seek the chaotic motion of the systems which are hard to he investigated by Melnikoy method.展开更多
Grain refinement of Al alloys inoculated by rare earth elements,such as Sc,has been extensively acknowledged,while the practical behavior of how inoculant Al_(3)Sc particles affect the refinement in solidification has...Grain refinement of Al alloys inoculated by rare earth elements,such as Sc,has been extensively acknowledged,while the practical behavior of how inoculant Al_(3)Sc particles affect the refinement in solidification has not been clarified due to the non-transparency of the solidification process.Here,the microstructural evolution of primary Al_(3)Sc particles andα-Al grains in Al-10 wt.%Cu alloy solidifications with 0.2 wt.%,0.6 wt.%,and 1.0 wt.%Sc additions was investigated by in situ synchrotron X-ray radiography.The detailed mechanisms of curve motion of grains(CMG)and melt convection were revealed.The efficient grains nucleation,uniformly scattered small initial grains,and long duration of melt convection contributed to the best refinement in the 0.6 wt.%Sc addition sample.This work provides a deep insight into grain refinement in solidification with Sc addition,which will enlighten the composition design and casting process of Al alloys inoculated by rare earth elements.展开更多
文摘In this article, we study the flows of curves in the Galilean 3-space and its equiform geometry without any constraints. We find that the Frenet equations and the intrinsic quantities of the inelastic flows of curves are independent of time. We show that the motion of curves in the Galilean 3-space and its equiform geometry are described by the inviscid and viscous Burgers＇ equations.
文摘In this paper based on [1]we go further into the study of chaotic behaviour of theforced oscillator containing a square nonlinear term by the methods of multiple scalesand numerical simulation. Relation between the chaotic domain and principal resonance curve is discussed. By analyzing the stability of principal resonance curve weinfer that chaotic motion would occur near the frequency at which the principalresonance curve has vertical tangent.Results of numerical simulation confirm thisinference.Thus we offer an effective way to seek the chaotic motion of the systems which are hard to he investigated by Melnikoy method.
基金supported by the National Natural Science Foundation of China(Nos.51627802,51871152 and 51971237)the Shanghai Pujiang Program(No.21PJD030)the National Key Research and Development Program of China(No.2020YFB0311200)。
文摘Grain refinement of Al alloys inoculated by rare earth elements,such as Sc,has been extensively acknowledged,while the practical behavior of how inoculant Al_(3)Sc particles affect the refinement in solidification has not been clarified due to the non-transparency of the solidification process.Here,the microstructural evolution of primary Al_(3)Sc particles andα-Al grains in Al-10 wt.%Cu alloy solidifications with 0.2 wt.%,0.6 wt.%,and 1.0 wt.%Sc additions was investigated by in situ synchrotron X-ray radiography.The detailed mechanisms of curve motion of grains(CMG)and melt convection were revealed.The efficient grains nucleation,uniformly scattered small initial grains,and long duration of melt convection contributed to the best refinement in the 0.6 wt.%Sc addition sample.This work provides a deep insight into grain refinement in solidification with Sc addition,which will enlighten the composition design and casting process of Al alloys inoculated by rare earth elements.
