Using a combination of analytical and numerical methods, the paper studies bifurcations and chaotic motions of a two-dimensional airfoil with cubic nonlinearity in incompressible flow. One type of critical points (cha...Using a combination of analytical and numerical methods, the paper studies bifurcations and chaotic motions of a two-dimensional airfoil with cubic nonlinearity in incompressible flow. One type of critical points (characterized by a negative eigenvalue, a simple zero eigenvalue and a pair of purely imaginary eigenvalues) for the bifurcation response equations is considered. With the aid of the normal form theory, the explicit expressions of the critical bifurcation lines leading to incipient and secondary bifurcations are obtained. The stability of the bifurcation solutions is also investigated. By using the undetermined coefficient method, the homoclinic orbit is found, and the uniform convergence of the homoclinic orbit series expansion is proved. It analytically demonstrates that there exists a homoclinic orbit joining the initial equilibrium point to itself, therefore Smale horseshoe chaos occurs for this system via Si'lnikov criterion. The system evolves into chaotic motion through period-doubling bifurcation, and is periodic again as the dimensionless airflow speed increases. Numerical simulations are also given, which confirm the analytical results.展开更多
Deformed odd-mass nuclei are ideal examples where the interplay between single-particle and collective degrees of freedom can be studied. Inspired by the recent experimental high-spin data in the odd-proton nuclide 17...Deformed odd-mass nuclei are ideal examples where the interplay between single-particle and collective degrees of freedom can be studied. Inspired by the recent experimental high-spin data in the odd-proton nuclide 171 Tm, we perform projected shell model(PSM) calculations to investigate structure of the ground band and other bands based on isomeric states. In addi- tion to the usual quadrupole-quadrupole force in the Hamiltonian, we employ the hexadecapole-hexadecapole(HH) interac- tion, in a self-consistent way with the hexadecapole deformation of the deformed basis. It is found that the known experi- mental data can be well described by the PSM calculation. The effect of the HH force on the quasiparticle isomeric states is discussed.展开更多
基金supported by the National Natural Science Foundation of China (Grant Nos. 10972099, 10632040)China Postdoctoral Science Foundation (Grant No. 20090450765)the Natural Science Foundation of Tianjin, China (Grant No. 09JCZDJC26800)
文摘Using a combination of analytical and numerical methods, the paper studies bifurcations and chaotic motions of a two-dimensional airfoil with cubic nonlinearity in incompressible flow. One type of critical points (characterized by a negative eigenvalue, a simple zero eigenvalue and a pair of purely imaginary eigenvalues) for the bifurcation response equations is considered. With the aid of the normal form theory, the explicit expressions of the critical bifurcation lines leading to incipient and secondary bifurcations are obtained. The stability of the bifurcation solutions is also investigated. By using the undetermined coefficient method, the homoclinic orbit is found, and the uniform convergence of the homoclinic orbit series expansion is proved. It analytically demonstrates that there exists a homoclinic orbit joining the initial equilibrium point to itself, therefore Smale horseshoe chaos occurs for this system via Si'lnikov criterion. The system evolves into chaotic motion through period-doubling bifurcation, and is periodic again as the dimensionless airflow speed increases. Numerical simulations are also given, which confirm the analytical results.
基金supported by the National Natural Science Foundation of China(Grant Nos.11305059,11275067,11135005 and 11275068)the National Basic Research Program of China(Grant No.2013CB834401)the C3S2 Computing Center of School of Science for their calculation support
文摘Deformed odd-mass nuclei are ideal examples where the interplay between single-particle and collective degrees of freedom can be studied. Inspired by the recent experimental high-spin data in the odd-proton nuclide 171 Tm, we perform projected shell model(PSM) calculations to investigate structure of the ground band and other bands based on isomeric states. In addi- tion to the usual quadrupole-quadrupole force in the Hamiltonian, we employ the hexadecapole-hexadecapole(HH) interac- tion, in a self-consistent way with the hexadecapole deformation of the deformed basis. It is found that the known experi- mental data can be well described by the PSM calculation. The effect of the HH force on the quasiparticle isomeric states is discussed.
