The dislocation equations of a simple cubic lattice have been obtained by using Green＇s function method based on the discrete lattice theory with the coefficients of the secondorder differential terms and the integra...The dislocation equations of a simple cubic lattice have been obtained by using Green＇s function method based on the discrete lattice theory with the coefficients of the secondorder differential terms and the integral terms have been given explicitly in advance. The simple cubic lattice we have discussed is a solvable model, which is obtained according to the lattice statics and the symmetry principle and can verify and validate the dislocation lattice theory. It can present unified dislocation equations which are suitable for most of metals with arbitral lattice structures. Through comparing the results of the present solvable model with the dislocation lattice theory, it can be seen that, the coefficients of integral terms of the edge and screw components we obtain are in accordance with the results of the dislocation lattice theory, however, the coefficient of the second-order differential term of the screw component is not in agreement with the result of the dislocation lattice theory. This is mainly caused by the reduced dynamical matrix of the surface term, which is the essence to obtain the dislocation equation. According to the simple cubic solvable model, not only the straight dislocations but also the curved dislocations, such as the kink, can be investigated further.展开更多
The DFT transform us extended to DFTξη transform and the relationship between FT and DFTξη is given by the Fourier transform discretization theorem. Based on the theorem, the DFTξη algorithm-error equation (DFT...The DFT transform us extended to DFTξη transform and the relationship between FT and DFTξη is given by the Fourier transform discretization theorem. Based on the theorem, the DFTξη algorithm-error equation (DFTξη A-E equation) is established, and the minimization property of discrete effect and the oscillation property of truncation effect are demonstrated. All these construct the shift sampling theory——a new theory about Fourier transform computation.展开更多
基金supported by the National Natural Science Foundation of China (No. 11074313)
文摘The dislocation equations of a simple cubic lattice have been obtained by using Green＇s function method based on the discrete lattice theory with the coefficients of the secondorder differential terms and the integral terms have been given explicitly in advance. The simple cubic lattice we have discussed is a solvable model, which is obtained according to the lattice statics and the symmetry principle and can verify and validate the dislocation lattice theory. It can present unified dislocation equations which are suitable for most of metals with arbitral lattice structures. Through comparing the results of the present solvable model with the dislocation lattice theory, it can be seen that, the coefficients of integral terms of the edge and screw components we obtain are in accordance with the results of the dislocation lattice theory, however, the coefficient of the second-order differential term of the screw component is not in agreement with the result of the dislocation lattice theory. This is mainly caused by the reduced dynamical matrix of the surface term, which is the essence to obtain the dislocation equation. According to the simple cubic solvable model, not only the straight dislocations but also the curved dislocations, such as the kink, can be investigated further.
文摘The DFT transform us extended to DFTξη transform and the relationship between FT and DFTξη is given by the Fourier transform discretization theorem. Based on the theorem, the DFTξη algorithm-error equation (DFTξη A-E equation) is established, and the minimization property of discrete effect and the oscillation property of truncation effect are demonstrated. All these construct the shift sampling theory——a new theory about Fourier transform computation.
