In order to support the functional design and simulation and the final fabrication processes for functional surfaces,it is necessary to obtain a multi-scale modelling approach representing both macro geometry and micr...In order to support the functional design and simulation and the final fabrication processes for functional surfaces,it is necessary to obtain a multi-scale modelling approach representing both macro geometry and micro details of the surface in one unified model.Based on the fractal geometry theory,a synthesized model is proposed by mathematically combining Weierstrass-Mandelbrot fractal function in micro space and freeform CAGD model in macro space.Key issues of the synthesis,such as algorithms for fractal interpolation of freeform profiles,and visualization optimization for fractal details,are addressed.A prototype of the integration solution is developed based on the platform of AutoCAD's Object ARX,and a few multi-scale modelling examples are used as case studies.With the consistent mathematic model,multi-scale surface geometries can be represented precisely.Moreover,the visualization result of the functional surfaces shows that the visualization optimization strategies developed are efficient.展开更多
A novel quantitative structure-property relationship （QSPR） model for estimating the solution surface tension of 92 organic compounds at 20℃ was developed based on newly introduced atom-type topological indices. Th...A novel quantitative structure-property relationship （QSPR） model for estimating the solution surface tension of 92 organic compounds at 20℃ was developed based on newly introduced atom-type topological indices. The data set contained non-polar and polar liquids, and saturated and unsaturated compounds. The regression analysis shows that excellent result is obtained with multiple linear regression. The predictive power of the proposed model was discussed using the leave-one-out （LOO） cross-validated （CV） method. The correlation coefficient （R） and the leave-one-out cross-validation correlation coefficient （Rcv） of multiple linear regression model are 0.991 4 and 0.991 3, respectively. The new model gives the average absolute relative deviation of 1.81% for 92 substances. The result demonstrates that novel topological indices based on the equilibrium electro-negativity of atom and the relative bond length are useful model parameters for QSPR analysis of compounds.展开更多
基金Projects(50975092,50805052,U0834002) supported by the National Natural Science Foundation of ChinaProject(9151030101000007) supported by the Natural Science Foundation of Guangdong Province,ChinaProject(2009ZZ0041) supported by the Fundamental Research Funds for the Central Universities in China
文摘In order to support the functional design and simulation and the final fabrication processes for functional surfaces,it is necessary to obtain a multi-scale modelling approach representing both macro geometry and micro details of the surface in one unified model.Based on the fractal geometry theory,a synthesized model is proposed by mathematically combining Weierstrass-Mandelbrot fractal function in micro space and freeform CAGD model in macro space.Key issues of the synthesis,such as algorithms for fractal interpolation of freeform profiles,and visualization optimization for fractal details,are addressed.A prototype of the integration solution is developed based on the platform of AutoCAD's Object ARX,and a few multi-scale modelling examples are used as case studies.With the consistent mathematic model,multi-scale surface geometries can be represented precisely.Moreover,the visualization result of the functional surfaces shows that the visualization optimization strategies developed are efficient.
基金Projects(20775010,21075011) supported by the National Natural Science Foundation of ChinaProject(2008AA05Z405) supported by the National High Technology Research and Development Program of China+2 种基金Project(09JJ3016) supported by Hunan Provincial Natural Science Foundation,ChinaProject(09C066) supported by Scientific Research Fund of Hunan Provincial Education Department,ChinaProject(2010CL01) supported by the Foundation of Hunan Provincial Key Laboratory of Materials Protection for Electric Power and Transportation,China
文摘A novel quantitative structure-property relationship （QSPR） model for estimating the solution surface tension of 92 organic compounds at 20℃ was developed based on newly introduced atom-type topological indices. The data set contained non-polar and polar liquids, and saturated and unsaturated compounds. The regression analysis shows that excellent result is obtained with multiple linear regression. The predictive power of the proposed model was discussed using the leave-one-out （LOO） cross-validated （CV） method. The correlation coefficient （R） and the leave-one-out cross-validation correlation coefficient （Rcv） of multiple linear regression model are 0.991 4 and 0.991 3, respectively. The new model gives the average absolute relative deviation of 1.81% for 92 substances. The result demonstrates that novel topological indices based on the equilibrium electro-negativity of atom and the relative bond length are useful model parameters for QSPR analysis of compounds.
