1968年,P.Barto（?）引进了 n 维单形顶点角的概念:设Ω是 E<sup>n</sup> 中的 n 维单形,（?）<sub>0</sub>,（?）<sub>i</sub>…（?）<sub>n</sub>,依次是Ω的 n+1个界面上的单位法向...1968年,P.Barto（?）引进了 n 维单形顶点角的概念:设Ω是 E<sup>n</sup> 中的 n 维单形,（?）<sub>0</sub>,（?）<sub>i</sub>…（?）<sub>n</sub>,依次是Ω的 n+1个界面上的单位法向量,令则把θ<sub>?</sub>=arcsin|D<sub>?</sub>|定义为此单形的第 i 个界面对应的顶点角.从这个定义出发,Barto（?）建立了 n 维单形的正弦定理:展开更多
In this paper,we study two-dimensional Riemann boundary value problems of Euler system for the isentropic and irrotational Chaplygin gas with initial data being two constant states given in two sectors respectively,wh...In this paper,we study two-dimensional Riemann boundary value problems of Euler system for the isentropic and irrotational Chaplygin gas with initial data being two constant states given in two sectors respectively,where one sector is a quadrant and the other one has an acute vertex angle.We prove that the Riemann boundary value problem admits a global self-similar solution,if either the initial states are close,or the smaller sector is also near a quadrant.Our result can be applied to solving the problem of shock reflection by a ramp.展开更多
This research focuses on measuring the mode transformation and energy attenuation of wedge waves for different apex angle wedges by using laser ultrasound techniques.Pulsed laser excitation and optical deflection beam...This research focuses on measuring the mode transformation and energy attenuation of wedge waves for different apex angle wedges by using laser ultrasound techniques.Pulsed laser excitation and optical deflection beam methods for detection were used to measure the wedge waves.In experiment,various wedge waves at different locations were recorded by scanning the excitation laser along the wedge tip,and different orders of wedge waves were observed.By fixing the distance between the excitation and detection positions and scanning the samples along the direction normal to the wedge tip,the modes transformation process was obtained.It was found that the energy of the acoustic waves for 20°,25° and 30° wedges decreased exponentially to a steady energy of Rayleigh wave within the main wavelength range of the acoustic modes,while the energy of acoustic waves of 45° and 60° wedge remained stable as the propagation line was scanned away from the wedge tip.展开更多
文摘1968年,P.Barto（?）引进了 n 维单形顶点角的概念:设Ω是 E<sup>n</sup> 中的 n 维单形,（?）<sub>0</sub>,（?）<sub>i</sub>…（?）<sub>n</sub>,依次是Ω的 n+1个界面上的单位法向量,令则把θ<sub>?</sub>=arcsin|D<sub>?</sub>|定义为此单形的第 i 个界面对应的顶点角.从这个定义出发,Barto（?）建立了 n 维单形的正弦定理:
基金supported in part by National Natural Science Foundation of China(Grant No. 11031001)the Doctorial Foundation of National Educational Ministry (Grant No. 20090071110002)Tianyuan Fund of Mathematics (Grant No. 11126181)
文摘In this paper,we study two-dimensional Riemann boundary value problems of Euler system for the isentropic and irrotational Chaplygin gas with initial data being two constant states given in two sectors respectively,where one sector is a quadrant and the other one has an acute vertex angle.We prove that the Riemann boundary value problem admits a global self-similar solution,if either the initial states are close,or the smaller sector is also near a quadrant.Our result can be applied to solving the problem of shock reflection by a ramp.
基金supported by the National Natural Science Foundation of China (Grant Nos. 60878023 and 61108013)the program for New Century Excellent Talents in University (NCET)the Priority Academic Program Development of Jiangsu Higher Education Institutions
文摘This research focuses on measuring the mode transformation and energy attenuation of wedge waves for different apex angle wedges by using laser ultrasound techniques.Pulsed laser excitation and optical deflection beam methods for detection were used to measure the wedge waves.In experiment,various wedge waves at different locations were recorded by scanning the excitation laser along the wedge tip,and different orders of wedge waves were observed.By fixing the distance between the excitation and detection positions and scanning the samples along the direction normal to the wedge tip,the modes transformation process was obtained.It was found that the energy of the acoustic waves for 20°,25° and 30° wedges decreased exponentially to a steady energy of Rayleigh wave within the main wavelength range of the acoustic modes,while the energy of acoustic waves of 45° and 60° wedge remained stable as the propagation line was scanned away from the wedge tip.
