In this study, the null-field boundary integral equation method （BIEM） and the image method are used to solve the SH wave scattering problem containing semi-circular canyons and circular tunnels. To fully utilize th...In this study, the null-field boundary integral equation method （BIEM） and the image method are used to solve the SH wave scattering problem containing semi-circular canyons and circular tunnels. To fully utilize the analytical property of Circular geometry, the polar coordinates are used to expand the closed-form fundamental solution to the degenerate kernel, and the Fourier series is also introduced to represent the boundary density. By collocating boundary points to match boundary condition on the boundary, a linear algebraic system is constructed. The unknown coefficients in the algebraic system can be easily determined. In this way, a semi-analytical approach is developed. Following the experience of near-trapped modes in water wave problems of the full plane, the focusing phenomenon and near-trapped modes for the SH wave problem of the half-plane are solved, since the two problems obey the same mathematical model. In this study, it is found that the SH wave problem containing two semi-circular canyons and a circular tunnel has the near-trapped mode and the focusing phenomenon for a special incident angle and wavenumber. In this situation, the amplification factor for the amplitude of displacement is over 300.展开更多
Transcranial focused ultrasound is a booming noninvasive therapy for brain stimuli. The Kelvin–Voigt equations are employed to calculate the sound field created by focusing a 256-element planar phased array through a...Transcranial focused ultrasound is a booming noninvasive therapy for brain stimuli. The Kelvin–Voigt equations are employed to calculate the sound field created by focusing a 256-element planar phased array through a monkey skull with the time-reversal method. Mode conversions between compressional and shear waves exist in the skull. Therefore, the wave field separation method is introduced to calculate the contributions of the two waves to the acoustic intensity and the heat source, respectively. The Pennes equation is used to depict the temperature field induced by ultrasound. Five computational models with the same incident angle of 0？and different distances from the focus for the skull and three computational models at different incident angles and the same distance from the focus for the skull are studied. Numerical results indicate that for all computational models, the acoustic intensity at the focus with mode conversions is 12.05%less than that without mode conversions on average. For the temperature rise, this percentage is 12.02%. Besides, an underestimation of both the acoustic intensity and the temperature rise in the skull tends to occur if mode conversions are ignored. However, if the incident angle exceeds 30？, the rules of the over-and under-estimation may be reversed. Moreover,shear waves contribute 20.54% of the acoustic intensity and 20.74% of the temperature rise in the skull on average for all computational models. The percentage of the temperature rise in the skull from shear waves declines with the increase of the duration of the ultrasound.展开更多
According to the Interim Regulationsof Foreign Investment Orientationand the List of Foreign-FundedIndustries set by the State, Shanxi’s foreignutilization focuses on: 1.Infrastructure construction,including basic in...According to the Interim Regulationsof Foreign Investment Orientationand the List of Foreign-FundedIndustries set by the State, Shanxi’s foreignutilization focuses on: 1.Infrastructure construction,including basic industry, roads, bridges,railways, power plants, water conservancy,urban gas supply, heating, water supply,sewage treatment and environmentalprotection. 2.Resources development,including coal, petroleum, natural gas, metals,non-metal mines, fine-processing projectsand raw materials production. 3.Agricultural resourcesdevelopment and agricultural by-productsfine-processing for export.展开更多
基金Ministry of Science and Technology under Grant No.MOST 103-2815-C-019-003-E to the undergraduate studentthe NSC under Grant No.100-2221-E-019-040-MY3
文摘In this study, the null-field boundary integral equation method （BIEM） and the image method are used to solve the SH wave scattering problem containing semi-circular canyons and circular tunnels. To fully utilize the analytical property of Circular geometry, the polar coordinates are used to expand the closed-form fundamental solution to the degenerate kernel, and the Fourier series is also introduced to represent the boundary density. By collocating boundary points to match boundary condition on the boundary, a linear algebraic system is constructed. The unknown coefficients in the algebraic system can be easily determined. In this way, a semi-analytical approach is developed. Following the experience of near-trapped modes in water wave problems of the full plane, the focusing phenomenon and near-trapped modes for the SH wave problem of the half-plane are solved, since the two problems obey the same mathematical model. In this study, it is found that the SH wave problem containing two semi-circular canyons and a circular tunnel has the near-trapped mode and the focusing phenomenon for a special incident angle and wavenumber. In this situation, the amplification factor for the amplitude of displacement is over 300.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.81527901,11604361,and 91630309)
文摘Transcranial focused ultrasound is a booming noninvasive therapy for brain stimuli. The Kelvin–Voigt equations are employed to calculate the sound field created by focusing a 256-element planar phased array through a monkey skull with the time-reversal method. Mode conversions between compressional and shear waves exist in the skull. Therefore, the wave field separation method is introduced to calculate the contributions of the two waves to the acoustic intensity and the heat source, respectively. The Pennes equation is used to depict the temperature field induced by ultrasound. Five computational models with the same incident angle of 0？and different distances from the focus for the skull and three computational models at different incident angles and the same distance from the focus for the skull are studied. Numerical results indicate that for all computational models, the acoustic intensity at the focus with mode conversions is 12.05%less than that without mode conversions on average. For the temperature rise, this percentage is 12.02%. Besides, an underestimation of both the acoustic intensity and the temperature rise in the skull tends to occur if mode conversions are ignored. However, if the incident angle exceeds 30？, the rules of the over-and under-estimation may be reversed. Moreover,shear waves contribute 20.54% of the acoustic intensity and 20.74% of the temperature rise in the skull on average for all computational models. The percentage of the temperature rise in the skull from shear waves declines with the increase of the duration of the ultrasound.
文摘According to the Interim Regulationsof Foreign Investment Orientationand the List of Foreign-FundedIndustries set by the State, Shanxi’s foreignutilization focuses on: 1.Infrastructure construction,including basic industry, roads, bridges,railways, power plants, water conservancy,urban gas supply, heating, water supply,sewage treatment and environmentalprotection. 2.Resources development,including coal, petroleum, natural gas, metals,non-metal mines, fine-processing projectsand raw materials production. 3.Agricultural resourcesdevelopment and agricultural by-productsfine-processing for export.
