We show that higher-dimensional integrable systems including the (2+1)-dimensional generalized sine-Gordon equation and the (2+1)-dimensional complex mKdV equation are associated with motions of surfaces inducedby end...We show that higher-dimensional integrable systems including the (2+1)-dimensional generalized sine-Gordon equation and the (2+1)-dimensional complex mKdV equation are associated with motions of surfaces inducedby endowing with an extra space variable to the motions of curves on S^2(R) and S^3(R).展开更多
Based on the natural frame in the projective geometry, motions of curves in projective geometry are studied. It is shown that several integrable equations including Sawada-Kotera and KK equations arise from motion of ...Based on the natural frame in the projective geometry, motions of curves in projective geometry are studied. It is shown that several integrable equations including Sawada-Kotera and KK equations arise from motion of plane curves in projective geometries. Motion of space curves described by acceleratlon field and governed by endowing an extra space variable in similarity geometry P^3 is also studied.展开更多
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
It is shown that the Pinney equation, Ermakov systems, and their higher-order generalizations describeself-similar solutions of plane curve motions in centro-affine and affine geometries.
Group-invariant solutions to certain plane curve motions in Euclidean and centro-affine geometries areobtained. The behavior of some solutions is also presented.
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
基金National Natural Science Foundation of China under Grant No.10671156the Program for New Century Excellent Talents in Universities under Grant No.NCET-04-0968
文摘We show that higher-dimensional integrable systems including the (2+1)-dimensional generalized sine-Gordon equation and the (2+1)-dimensional complex mKdV equation are associated with motions of surfaces inducedby endowing with an extra space variable to the motions of curves on S^2(R) and S^3(R).
基金The project supported in part by National Natural Science Foundation of China under Grant No. 10371098 and the Natural Science Foundation of Shaanxi Province of ChinaIt is my pleasure to thank Prof. Qu Chang-Zheng for his helpful discussion
文摘Based on the natural frame in the projective geometry, motions of curves in projective geometry are studied. It is shown that several integrable equations including Sawada-Kotera and KK equations arise from motion of plane curves in projective geometries. Motion of space curves described by acceleratlon field and governed by endowing an extra space variable in similarity geometry P^3 is also studied.
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It is shown that the Pinney equation, Ermakov systems, and their higher-order generalizations describeself-similar solutions of plane curve motions in centro-affine and affine geometries.
文摘Group-invariant solutions to certain plane curve motions in Euclidean and centro-affine geometries areobtained. The behavior of some solutions is also presented.
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.
