In terms of numerical method of Smoluchowski equation the behavior of fission process in diffusion model has been described and analyzed, including the reliance upon time, as well as the deformation parameters at seve...In terms of numerical method of Smoluchowski equation the behavior of fission process in diffusion model has been described and analyzed, including the reliance upon time, as well as the deformation parameters at several nuclear temperatures in this paper. The fission rates and the residual probabilities inside the saddle point are calculated for fissile nucleus n＋^238U reaction and un-fissile nucleus p＋^208Pb reaction. The results indicate that there really exists a transient fission process, which means that the pre-equillbrium fission should be taken into account for the fissile nucleus at the high temperature. Oppositely, the pre-equilibrlum fission could be neglected for the un-fissile nucleus. In the certain case the overshooting phenomenon of the fission rates will occur, which is mainly determined by the diffusive current at the saddle point. The higher the temperature is, the more obvious the overshooting phenomenon is. However, the emissions of the light particles accompanying the diffusion process may weaken or vanish the overshooting phenomenon.展开更多
The exact solution of fractional diffusion model with a location-independent source term used in the study of the concentration of fission product in spherical uranium dioxide （U02） particle is built. The adsorption...The exact solution of fractional diffusion model with a location-independent source term used in the study of the concentration of fission product in spherical uranium dioxide （U02） particle is built. The adsorption effect of the fission product on the surface of the U02 particle and the delayed decay effect are also considered. The solution is given in terms of Mittag-Leffler function with finite Hankel integral transformation and Laplace transformation. At last, the reduced forms of the solution under some special physical conditions, which is used in nuclear engineering, are obtained and corresponding remarks are given to provide significant exact results to the concentration analysis of nuclear fission products in nuclear reactor.展开更多
Non-equilibrium fission has been described by diffusion model. In order to describe the diffusion process analytically, the analytical solution of Smoluchowski equation in harmonic oscillator potential is obtained. Th...Non-equilibrium fission has been described by diffusion model. In order to describe the diffusion process analytically, the analytical solution of Smoluchowski equation in harmonic oscillator potential is obtained. This analytical solution is able to describe the probability distribution and the diffusive current with the variable x and t. The results indicate that the probability distribution and the diffusive current are relevant to the initial distribution shape, initial position, and the nuclear temperature T; the time to reach the quasi-stationary state is proportional to friction coefficient beta, but is independent of the initial distribution status and the nuclear temperature T. The prerequisites of negative diffusive current are justified. This method provides an approach to describe the diffusion process for fissile process in complicated potentials analytically.展开更多
Fracture analysis of a plane crack problem under chemo-mechanical loading is presented based on a linear chemo-elasticity model.The flux conductivity is introduced to characterize the influence of the crack defect on ...Fracture analysis of a plane crack problem under chemo-mechanical loading is presented based on a linear chemo-elasticity model.The flux conductivity is introduced to characterize the influence of the crack defect on the diffusion process.Using Fourier transform and the dislocation density functions,the crack problem is reduced to a set of singular integral equations,which are solved numerically by the Lobatto-Chebyshev method.Parametric studies are conducted to reveal the effects of flux conductivity,geometric configuration,chemical and mechanical loads on the crack tip field.The numerical results show that the stress singularity at the crack tip is usually a mixture of mode Ⅰ and mode Ⅱ types.展开更多
基金The project supported by National Natural Science Foundation of China under Grant No. 10547005
文摘In terms of numerical method of Smoluchowski equation the behavior of fission process in diffusion model has been described and analyzed, including the reliance upon time, as well as the deformation parameters at several nuclear temperatures in this paper. The fission rates and the residual probabilities inside the saddle point are calculated for fissile nucleus n＋^238U reaction and un-fissile nucleus p＋^208Pb reaction. The results indicate that there really exists a transient fission process, which means that the pre-equillbrium fission should be taken into account for the fissile nucleus at the high temperature. Oppositely, the pre-equilibrlum fission could be neglected for the un-fissile nucleus. In the certain case the overshooting phenomenon of the fission rates will occur, which is mainly determined by the diffusive current at the saddle point. The higher the temperature is, the more obvious the overshooting phenomenon is. However, the emissions of the light particles accompanying the diffusion process may weaken or vanish the overshooting phenomenon.
基金Supported by the National S&T Major Project under Grant No.ZX06901
文摘The exact solution of fractional diffusion model with a location-independent source term used in the study of the concentration of fission product in spherical uranium dioxide （U02） particle is built. The adsorption effect of the fission product on the surface of the U02 particle and the delayed decay effect are also considered. The solution is given in terms of Mittag-Leffler function with finite Hankel integral transformation and Laplace transformation. At last, the reduced forms of the solution under some special physical conditions, which is used in nuclear engineering, are obtained and corresponding remarks are given to provide significant exact results to the concentration analysis of nuclear fission products in nuclear reactor.
文摘Non-equilibrium fission has been described by diffusion model. In order to describe the diffusion process analytically, the analytical solution of Smoluchowski equation in harmonic oscillator potential is obtained. This analytical solution is able to describe the probability distribution and the diffusive current with the variable x and t. The results indicate that the probability distribution and the diffusive current are relevant to the initial distribution shape, initial position, and the nuclear temperature T; the time to reach the quasi-stationary state is proportional to friction coefficient beta, but is independent of the initial distribution status and the nuclear temperature T. The prerequisites of negative diffusive current are justified. This method provides an approach to describe the diffusion process for fissile process in complicated potentials analytically.
基金supported by the National Natural Science Foundation of China(Grant Nos.11932005 and 11772106).
文摘Fracture analysis of a plane crack problem under chemo-mechanical loading is presented based on a linear chemo-elasticity model.The flux conductivity is introduced to characterize the influence of the crack defect on the diffusion process.Using Fourier transform and the dislocation density functions,the crack problem is reduced to a set of singular integral equations,which are solved numerically by the Lobatto-Chebyshev method.Parametric studies are conducted to reveal the effects of flux conductivity,geometric configuration,chemical and mechanical loads on the crack tip field.The numerical results show that the stress singularity at the crack tip is usually a mixture of mode Ⅰ and mode Ⅱ types.
