Reflections of a Korteweg-de Vries （KdV） solitary wave and an envelope solitary wave are studied by using the particle-in-cell simulation method. Defining the phase shift of the reflected solitary wave, we notice th...Reflections of a Korteweg-de Vries （KdV） solitary wave and an envelope solitary wave are studied by using the particle-in-cell simulation method. Defining the phase shift of the reflected solitary wave, we notice that there is a phase shift of the reflected KdV solitary wave, while there is no phase shift for an envelope solitary wave. It is also noted that the reflection of a KdV solitary wave at a solid boundary is equivalent to the head-on collision between two identical amplitude solitary waves.展开更多
We calculate the first obstruction to regular homotopy of an immersion f: M(n) --> R(n + k) into r-degrees-f for a reflection r of R(n + k). In the case of k = n - 1 we give necessary and sufficient conditions for ...We calculate the first obstruction to regular homotopy of an immersion f: M(n) --> R(n + k) into r-degrees-f for a reflection r of R(n + k). In the case of k = n - 1 we give necessary and sufficient conditions for f to be regularly homotopic to r-degrees-f in terms of obstructions to the existence of a normal vectorfield of f.展开更多
The Lamb wave technique is used in the detection of internal defects in plates. The reflection of the Lamb wave at the free edge of the plate has been shown to be rather complicated. The reflected wave is usually comp...The Lamb wave technique is used in the detection of internal defects in plates. The reflection of the Lamb wave at the free edge of the plate has been shown to be rather complicated. The reflected wave is usually composed of infinite number of Lamb wave modes even in the case of incidence of one pure mode. The analysis of the reflection problem is complicated in nature as the orthogonality relations of the eigen modes of the Lamb wave concern both the stresses and displacements. We adopt the principle of the least squares as a new approach to simplify the analysis, in which the eigen-modes are taken as the trial function. It seems to be simple and effective. In most cases a good enough result can be obtained on using an 8- bit microcomputer. Here the coefficients of the various reflected modes are calculated, some interesting phenomena on the mode conversion are indicated and the conditions on the pure mode reflection are given.展开更多
基金Supported by the National Natural Science Foundation of China under Grant Nos 11275156,11547304 and 11505261
文摘Reflections of a Korteweg-de Vries （KdV） solitary wave and an envelope solitary wave are studied by using the particle-in-cell simulation method. Defining the phase shift of the reflected solitary wave, we notice that there is a phase shift of the reflected KdV solitary wave, while there is no phase shift for an envelope solitary wave. It is also noted that the reflection of a KdV solitary wave at a solid boundary is equivalent to the head-on collision between two identical amplitude solitary waves.
基金Supported partly by the National Science of China.
文摘We calculate the first obstruction to regular homotopy of an immersion f: M(n) --> R(n + k) into r-degrees-f for a reflection r of R(n + k). In the case of k = n - 1 we give necessary and sufficient conditions for f to be regularly homotopic to r-degrees-f in terms of obstructions to the existence of a normal vectorfield of f.
文摘The Lamb wave technique is used in the detection of internal defects in plates. The reflection of the Lamb wave at the free edge of the plate has been shown to be rather complicated. The reflected wave is usually composed of infinite number of Lamb wave modes even in the case of incidence of one pure mode. The analysis of the reflection problem is complicated in nature as the orthogonality relations of the eigen modes of the Lamb wave concern both the stresses and displacements. We adopt the principle of the least squares as a new approach to simplify the analysis, in which the eigen-modes are taken as the trial function. It seems to be simple and effective. In most cases a good enough result can be obtained on using an 8- bit microcomputer. Here the coefficients of the various reflected modes are calculated, some interesting phenomena on the mode conversion are indicated and the conditions on the pure mode reflection are given.
