For the (2 + 1)-dimensional Broer-Kaup system, we study the corresponding Lie symmetry groups, and obtain the symmetry group theorem and the Backlund transformation formula of solutions finding. At the same time, we find some new exact solutions of the (2 + 1)-dimensional Broer-Kaup system and extend the results in the papers [1-4].
The modeling technique of hydrodynamic torque converter flow passage was investigated. The semi-automatic modeling technique of torque converter flow passage was proposed. The flow passage model of each converter wheel is considered as a revolution entity sliced by two curved surfaces. In order to generate the revolution entity, a new approximation method, condition optimum arc approximation, was proposed. The method was used to approximate the meridional streamlines of the inner and outer wall. As a result, the three-dimensional revolution entity can be conveniently generated. In order to create slice surfaces, the central stream surface of flow passage was approximated with a quadric surface. The normal vector of the quadric surface and the thickness/thickness-function of bade were used to calculate the discrete point coordinates of blade surfaces. Via the rotation transformation to the coordinates, the discrete point coordinates of slice surfaces were obtained. A parameterized program code used for the hydrodynamic torque converter design and semi-automatic modeling was developed. Modeling errors were calculated and analyzed. The flow passage model was generated in several minutes with the help of the program code, Auto CAD and Solidworks software. Finally, the model was inputted into Gambit, and the pre-processing task used for the numerical simulation of torque converter flow field was successfully completed. The investigation results show that the semi-automatic modeling not only can ensure the accuracy of modeling, but also librates the research and design workers of torque converter from the time-consuming modeling work, which paves the way for the numerical simulation of the complex flow field of the hydrodynamic torque converter.
The aim of this study is to examine morphology of intracranial aneurysm with neck indistinguishable from surrounding artery branches by cerebral angiography and discuss whether such aneurysms can be treated by interventional embolization. 6 patients who had not been treated by embolization due to irregular wide-necked aneurysms indistinguishable from surrounding artery branches by cerebral angiography received craniotomy for aneurysm clipping. The operations succeeded. Morphologically, neck width and location of the aneurysms were carefully observed and photographed from different directions and multi-angles during operation. The intraoperative findings were compared with the preoperative CTA and DSA images. Walls of the 6 patients’ aneurysms tightly clung to or adhered to surrounding branches and oppressed the branches into arcs, similar to the aneurysm walls in shape, and arterial branches and aneurysm walls suffered from segmental adhesion. In addition, abnormalities of communicating arteries to vary degrees were observed in 4 patients. However, after successful surgical clipping, it was revealed that the aneurysms would have been better treated by embolization since they are basically saccular aneurysms with regular sizes. Deformations in preoperative angiography may be due to anatomical variations of surrounding vessels near the aneurysms, aneurysm wall oppression or incomplete adhesion of surrounding arterial branches. Such deformations can be recognized by careful observation in preoperative angiography from different directions and multi-angles.