This paper shows that the experimental results of quantum well energy transitions can be found numerically. The cases of several ZnO-ZnMgO wells are considered and their excitonic transition energies were calculated u...This paper shows that the experimental results of quantum well energy transitions can be found numerically. The cases of several ZnO-ZnMgO wells are considered and their excitonic transition energies were calculated using the finite difference method. In that way, the one-dimensional Schrödinger equation has been solved by using the BLAS and LAPACK libraries. The numerical results are in good agreement with the experimental ones.展开更多
The Ginzbury-Landau theory for bainitic transformation was devised, which contains two first-order phase transformations, one being reconstructive represented by the diffusional proeutectoidal precipitation of ferrite...The Ginzbury-Landau theory for bainitic transformation was devised, which contains two first-order phase transformations, one being reconstructive represented by the diffusional proeutectoidal precipitation of ferrite, and the other the displacive transformation. It provides a coupled mechanism for the formation of bainite. With the numerical simulation results, a diffusion-induced nucleation and a diffusion-accompanied growth of displacive transformation were suggested. This theory can be helpful to over- throw the thermodynamic difficulty of displacive transformation above the Ms temperature, and also helpful to understand the Bs temperature, the partial supersaturation, the single variation of bainitic carbides, and the incomplete-reaction phenomenon of bainitic transformation, etc..展开更多
A third-order ordinary differential equation （ODE） for thin film flow with both Neumann and Dirichlet bound- ary conditions is transformed into a second-order nonlinear ODE with Dirichlet boundary conditions. Numeri...A third-order ordinary differential equation （ODE） for thin film flow with both Neumann and Dirichlet bound- ary conditions is transformed into a second-order nonlinear ODE with Dirichlet boundary conditions. Numerical solu- tions of the nonlinear second-order ODE are investigated us- ing finite difference schemes. A finite difference formulation to an Emden-Fowler representation of the second-order non- linear ODE is shown to converge faster than a finite differ- ence formulation of the standard form of the second-order nonlinear ODE. Both finite difference schemes satisfy the von Neumann stability criteria. When mapping the numeri- cal solution of the second-order ODE back to the variables of the original third-order ODE we recover the position of the contact line. A nonlinear relationship between the position of the contact line and physical parameters is obtained.展开更多
文摘This paper shows that the experimental results of quantum well energy transitions can be found numerically. The cases of several ZnO-ZnMgO wells are considered and their excitonic transition energies were calculated using the finite difference method. In that way, the one-dimensional Schrödinger equation has been solved by using the BLAS and LAPACK libraries. The numerical results are in good agreement with the experimental ones.
文摘The Ginzbury-Landau theory for bainitic transformation was devised, which contains two first-order phase transformations, one being reconstructive represented by the diffusional proeutectoidal precipitation of ferrite, and the other the displacive transformation. It provides a coupled mechanism for the formation of bainite. With the numerical simulation results, a diffusion-induced nucleation and a diffusion-accompanied growth of displacive transformation were suggested. This theory can be helpful to over- throw the thermodynamic difficulty of displacive transformation above the Ms temperature, and also helpful to understand the Bs temperature, the partial supersaturation, the single variation of bainitic carbides, and the incomplete-reaction phenomenon of bainitic transformation, etc..
文摘A third-order ordinary differential equation （ODE） for thin film flow with both Neumann and Dirichlet bound- ary conditions is transformed into a second-order nonlinear ODE with Dirichlet boundary conditions. Numerical solu- tions of the nonlinear second-order ODE are investigated us- ing finite difference schemes. A finite difference formulation to an Emden-Fowler representation of the second-order non- linear ODE is shown to converge faster than a finite differ- ence formulation of the standard form of the second-order nonlinear ODE. Both finite difference schemes satisfy the von Neumann stability criteria. When mapping the numeri- cal solution of the second-order ODE back to the variables of the original third-order ODE we recover the position of the contact line. A nonlinear relationship between the position of the contact line and physical parameters is obtained.
