In this paper, inverse solutions are obtained for the class of 2D steady incompressible couple stress fluid flows. This class consists of flows for which the vorticity distribution is given by ▽2ψ=ψ+f(x,y). The so...In this paper, inverse solutions are obtained for the class of 2D steady incompressible couple stress fluid flows. This class consists of flows for which the vorticity distribution is given by ▽2ψ=ψ+f(x,y). The solutions are obtained by applying the inverse method, which makes certain hypotheses regarding the form of the velocity field and pressure but without making any regarding the boundaries of the domain occupied by the fluid. Inverse solutions are derived for three different forms of f(x,y).展开更多
We study fermionic zero modes in the self-dual vortex background on an extra two-dimensional Riemann surface in (5+1) dimensions. Using the generalized Abelian-Higgs model, we obtain the inner topological structure...We study fermionic zero modes in the self-dual vortex background on an extra two-dimensional Riemann surface in (5+1) dimensions. Using the generalized Abelian-Higgs model, we obtain the inner topological structure of the self-dual vortex and establish the exact self-duality equation with topological term. Then we analyze the Dirac operator on an extra torus and the effective Lagrangian of four-dimensional fermions with the self-dual vortex background. Solving the Dirac equation, the fermionic zero modes on a torus with the self-dual vortex background in two simple cases are obtained.展开更多
We study the properties of the Ginzburg-Landau model at the dual point for the superconductors. By making use of the U(1) gauge potential decomposition and the φ-mapping theory, we investigate the topological inner...We study the properties of the Ginzburg-Landau model at the dual point for the superconductors. By making use of the U(1) gauge potential decomposition and the φ-mapping theory, we investigate the topological inner structure of the Bogomol'nyi equations and deduce a modified decoupled Bogomol'nyi equation with a nontrivial topological term, which is ignored in conventional model. We find that the nontrivial topological term is closely related to the N-vortex, which arises from the zero points of the complex scalar field, Furthermore, we establish a relationship between Ginzburg Landau free energy and the winding number.展开更多
文摘In this paper, inverse solutions are obtained for the class of 2D steady incompressible couple stress fluid flows. This class consists of flows for which the vorticity distribution is given by ▽2ψ=ψ+f(x,y). The solutions are obtained by applying the inverse method, which makes certain hypotheses regarding the form of the velocity field and pressure but without making any regarding the boundaries of the domain occupied by the fluid. Inverse solutions are derived for three different forms of f(x,y).
基金The project supported by National Natural Science Foundation of China under Grant Nos. 10275030 and 10475034 and the Fundamental Research Fund for Physics and Mathematics of Lanzhou University (No. lzu0702)
文摘We study fermionic zero modes in the self-dual vortex background on an extra two-dimensional Riemann surface in (5+1) dimensions. Using the generalized Abelian-Higgs model, we obtain the inner topological structure of the self-dual vortex and establish the exact self-duality equation with topological term. Then we analyze the Dirac operator on an extra torus and the effective Lagrangian of four-dimensional fermions with the self-dual vortex background. Solving the Dirac equation, the fermionic zero modes on a torus with the self-dual vortex background in two simple cases are obtained.
文摘We study the properties of the Ginzburg-Landau model at the dual point for the superconductors. By making use of the U(1) gauge potential decomposition and the φ-mapping theory, we investigate the topological inner structure of the Bogomol'nyi equations and deduce a modified decoupled Bogomol'nyi equation with a nontrivial topological term, which is ignored in conventional model. We find that the nontrivial topological term is closely related to the N-vortex, which arises from the zero points of the complex scalar field, Furthermore, we establish a relationship between Ginzburg Landau free energy and the winding number.