In this paper we have investigated the reflection and the transmission of a system of two symmetric circular-arc-shaped thin porous plates submerged in deep water within the context of linear theory. The hypersingular...In this paper we have investigated the reflection and the transmission of a system of two symmetric circular-arc-shaped thin porous plates submerged in deep water within the context of linear theory. The hypersingular integral equation technique has been used to analyze the problem mathematically. The integral equations are formulated by applying Green＇s integral theorem to the fundamental potential function and the scattered potential function into a suitable fluid region, and then using the boundary condition on the porous plate surface. These are solved approximately using an expansion-cure-collocation method where the behaviour of the potential functions at the tips of the plates have been used. This method ultimately produces a very good numerical approximation for the reflection and the transmission coefficients and hydrodynamic force components. The numerical results are depicted graphically against the wave number for a variety of layouts of the arc. Some results are compared with known results for similar configurations of dual rigid plate systems available in the literature with good agreement.展开更多
There are various analytical, empirical and numerical methods to calculate groundwater inflow into tun- nels excavated in rocky media. Analytical methods have been widely applied in prediction of groundwa- ter inflow ...There are various analytical, empirical and numerical methods to calculate groundwater inflow into tun- nels excavated in rocky media. Analytical methods have been widely applied in prediction of groundwa- ter inflow to tunnels due to their simplicity and practical base theory. Investigations show that the real amount of water infiltrating into jointed tunnels is much less than calculated amount using analytical methods and obtained results are very dependent on tunnel＇s geometry and environmental situations. In this study, using multiple regression analysis, a new empirical model for estimation of groundwater seepage into circular tunnels was introduced. Our data was acquired from field surveys and laboratory analysis of core samples. New regression variables were defined after perusing single and two variables relationship between groundwater seepage and other variables. Finally, an appropriate model for estima- tion of leakage was obtained using the stepwise algorithm. Statistics like R, R2, R2e and the histogram of residual values in the model represent a good reputation and fitness for this model to estimate the groundwater seepage into tunnels. The new experimental model was used for the test data and results were satisfactory. Therefore, multiple regression analysis is an effective and efficient way to estimate the groundwater seeoage into tunnels.展开更多
In order to obtain a new-type short cylindrical cup-shaped flexspline that can be applied to space mechanisms,the APDL language of ANSYS software was employed to develop a parameterized equivalent contact model betwee...In order to obtain a new-type short cylindrical cup-shaped flexspline that can be applied to space mechanisms,the APDL language of ANSYS software was employed to develop a parameterized equivalent contact model between a flexspline and a wave generator. The validity of the parameterized equivalent contact model was verified by comparing the results of the analytic value of the contact model and the value calculated by the theoretical formula. The curvilinear trend of stress was obtained by changing the structural parameter of the flexspline. Based on the curvilinear trend of stress,multi-objective optimizations of key structural parameters were achieved. Flexspline,wave generator,and circular spline of a new 32-type short cylindrical cup-shaped harmonic reducer were designed and manufactured. A performance test bench to carry out tests on the harmonic reducer was designed. Contrast experiments were implemented to determine the efficiency of the new 32-type short cylindrical cup-shaped harmonic reducer and the conventional 32-type harmonic reducer under different conditions. The experimental results reveal that there is approximately equality in terms of efficiency between the new 32-type short cylindrical cup-shaped harmonic reducer and the conventional 32-type harmonic reducer. The volume of the flexspline of the new 32-type short cylindrical cup-shaped harmonic reducer is reduced by approximately 30% through multi-objective optimization. When the new 32-type short cylindrical cup-shaped harmonic reducer is used on the wheel of a rover prototype,the mass of the wheel hub is decreased by 0.42 kg. Test analysis of wheel motion verifies that the new 32-type short cylindrical cup-shaped harmonic reducer can meet the requirements regarding bearing capacity and efficiency.展开更多
Using polar equations for conic sections, we research conic circumscribed n-sided polygons（n ≥ 4） deeply on the basis of papers[1-3]. We obtain a general fixed value theorem for directed areas of some triangles in ...Using polar equations for conic sections, we research conic circumscribed n-sided polygons（n ≥ 4） deeply on the basis of papers[1-3]. We obtain a general fixed value theorem for directed areas of some triangles in conic circumscribed n-sided polygons and derive as many as n（n - 3） concurrent points of three lines and some other collinear, equiareal results in conic circumscribed n-sided polygons（n ≥ 4）. So the results of papers[1-3] are unified.展开更多
A numerical study has been carried out to investigate the effect of aspect ratio on heat transfer by natural convection of nanofluid taking Cu nano particles and the water as based fluid. The flow is laminar, steady s...A numerical study has been carried out to investigate the effect of aspect ratio on heat transfer by natural convection of nanofluid taking Cu nano particles and the water as based fluid. The flow is laminar, steady state, axisymmetric two-dimensional in a vertical cylindrical channel filled with porous media. Heat is generated uniformly along the center of the channel with its vertical surface remain with cooled constant wall temperature and insulated horizontal top and bottom surfaces. The governing equations which used are continuity, momentum and energy equations using Darcy law and Boussinesq＇s approximation which are transformed to dimensionless equations. The finite difference approach is used to obtain all the computational results using the MATLAB-7 program. The parameters affected on the system are Rayleigh number ranging within （10≤ Ra ≤ 103）, aspect ratio （1 ≤ As 〈 5） and the volume fraction （0 ≤0 〈 0.2）. The results obtained are presented graphically in the form of streamline and isotherm contour plots and the results show that as ~ increase from 0.01 to 0.2 the value of the mean Nusselt number increase 50.4% for Ra = 1,000.展开更多
Given any (2,4)-elliptic surface with nine smooth rational curves,eight (2)-curves and one (3)-curve,forming a Dynkin diagram of type [2,2][2,2][2,2][2,2,3],we show that a fake projective plane can be constructed from...Given any (2,4)-elliptic surface with nine smooth rational curves,eight (2)-curves and one (3)-curve,forming a Dynkin diagram of type [2,2][2,2][2,2][2,2,3],we show that a fake projective plane can be constructed from it by taking a degree 3 cover and then a degree 7 cover.We also determine the types of singular fibres of such a (2,4)-elliptic surface.展开更多
Diffusion-limited aggregation （DLA） assumes that particles perform pure random walk at a finite tem- perature and aggregate when they come close enough and stick together. Although it is well known that DLA in two d...Diffusion-limited aggregation （DLA） assumes that particles perform pure random walk at a finite tem- perature and aggregate when they come close enough and stick together. Although it is well known that DLA in two dimensions results in a ramified fractal structure, how the particle shape influences the formed morphology is still un- clear. In this work, we perform the off-lattice two-dimensional DLA simulations with different particle shapes of triangle, quadrangle, pentagon, hexagon, and octagon, respectively, and compare with the results for circular particles. Our results indicate that different particle shapes only change the local structure, but have no effects on the global structure of the formed fractal duster. The local compactness decreases as the number of polygon edges increases.展开更多
基金Partially Supported by the Department of Science and Technology Through a Research Grant to RG(No.SR/FTP/MS-020/2010)
文摘In this paper we have investigated the reflection and the transmission of a system of two symmetric circular-arc-shaped thin porous plates submerged in deep water within the context of linear theory. The hypersingular integral equation technique has been used to analyze the problem mathematically. The integral equations are formulated by applying Green＇s integral theorem to the fundamental potential function and the scattered potential function into a suitable fluid region, and then using the boundary condition on the porous plate surface. These are solved approximately using an expansion-cure-collocation method where the behaviour of the potential functions at the tips of the plates have been used. This method ultimately produces a very good numerical approximation for the reflection and the transmission coefficients and hydrodynamic force components. The numerical results are depicted graphically against the wave number for a variety of layouts of the arc. Some results are compared with known results for similar configurations of dual rigid plate systems available in the literature with good agreement.
文摘There are various analytical, empirical and numerical methods to calculate groundwater inflow into tun- nels excavated in rocky media. Analytical methods have been widely applied in prediction of groundwa- ter inflow to tunnels due to their simplicity and practical base theory. Investigations show that the real amount of water infiltrating into jointed tunnels is much less than calculated amount using analytical methods and obtained results are very dependent on tunnel＇s geometry and environmental situations. In this study, using multiple regression analysis, a new empirical model for estimation of groundwater seepage into circular tunnels was introduced. Our data was acquired from field surveys and laboratory analysis of core samples. New regression variables were defined after perusing single and two variables relationship between groundwater seepage and other variables. Finally, an appropriate model for estima- tion of leakage was obtained using the stepwise algorithm. Statistics like R, R2, R2e and the histogram of residual values in the model represent a good reputation and fitness for this model to estimate the groundwater seepage into tunnels. The new experimental model was used for the test data and results were satisfactory. Therefore, multiple regression analysis is an effective and efficient way to estimate the groundwater seeoage into tunnels.
基金Project(2010DFR70270) supported by the International Science and Technology Cooperation Project with RussiaProjects(50975059,61005080) supported by the National Natural Science Foundation of China+2 种基金Project(B07018) supported by "111" Program of ChinaProject(SKLRS200801A02) supported by the Foundation of State Key Laboratory of Robotics and System (Harbin Institute of Technology),ChinaProject(HIT2009061) supported by the Key Subject Laboratory Open Fund of China
文摘In order to obtain a new-type short cylindrical cup-shaped flexspline that can be applied to space mechanisms,the APDL language of ANSYS software was employed to develop a parameterized equivalent contact model between a flexspline and a wave generator. The validity of the parameterized equivalent contact model was verified by comparing the results of the analytic value of the contact model and the value calculated by the theoretical formula. The curvilinear trend of stress was obtained by changing the structural parameter of the flexspline. Based on the curvilinear trend of stress,multi-objective optimizations of key structural parameters were achieved. Flexspline,wave generator,and circular spline of a new 32-type short cylindrical cup-shaped harmonic reducer were designed and manufactured. A performance test bench to carry out tests on the harmonic reducer was designed. Contrast experiments were implemented to determine the efficiency of the new 32-type short cylindrical cup-shaped harmonic reducer and the conventional 32-type harmonic reducer under different conditions. The experimental results reveal that there is approximately equality in terms of efficiency between the new 32-type short cylindrical cup-shaped harmonic reducer and the conventional 32-type harmonic reducer. The volume of the flexspline of the new 32-type short cylindrical cup-shaped harmonic reducer is reduced by approximately 30% through multi-objective optimization. When the new 32-type short cylindrical cup-shaped harmonic reducer is used on the wheel of a rover prototype,the mass of the wheel hub is decreased by 0.42 kg. Test analysis of wheel motion verifies that the new 32-type short cylindrical cup-shaped harmonic reducer can meet the requirements regarding bearing capacity and efficiency.
基金Foundation item： Supported by Natural Science Foundation of China（60675022）
文摘Using polar equations for conic sections, we research conic circumscribed n-sided polygons（n ≥ 4） deeply on the basis of papers[1-3]. We obtain a general fixed value theorem for directed areas of some triangles in conic circumscribed n-sided polygons and derive as many as n（n - 3） concurrent points of three lines and some other collinear, equiareal results in conic circumscribed n-sided polygons（n ≥ 4）. So the results of papers[1-3] are unified.
文摘A numerical study has been carried out to investigate the effect of aspect ratio on heat transfer by natural convection of nanofluid taking Cu nano particles and the water as based fluid. The flow is laminar, steady state, axisymmetric two-dimensional in a vertical cylindrical channel filled with porous media. Heat is generated uniformly along the center of the channel with its vertical surface remain with cooled constant wall temperature and insulated horizontal top and bottom surfaces. The governing equations which used are continuity, momentum and energy equations using Darcy law and Boussinesq＇s approximation which are transformed to dimensionless equations. The finite difference approach is used to obtain all the computational results using the MATLAB-7 program. The parameters affected on the system are Rayleigh number ranging within （10≤ Ra ≤ 103）, aspect ratio （1 ≤ As 〈 5） and the volume fraction （0 ≤0 〈 0.2）. The results obtained are presented graphically in the form of streamline and isotherm contour plots and the results show that as ~ increase from 0.01 to 0.2 the value of the mean Nusselt number increase 50.4% for Ra = 1,000.
基金supported by the National Research Foundation of Korea funded by the Ministry of Education,Science and Technology (Grant No. NRF-2007-2-C00002)
文摘Given any (2,4)-elliptic surface with nine smooth rational curves,eight (2)-curves and one (3)-curve,forming a Dynkin diagram of type [2,2][2,2][2,2][2,2,3],we show that a fake projective plane can be constructed from it by taking a degree 3 cover and then a degree 7 cover.We also determine the types of singular fibres of such a (2,4)-elliptic surface.
基金Supported by the Hundred Talent Program of the Chinese Academy of Sciences (CAS)the National Natural Science Foundation of China under Grant Nos. 10974208, 11121403, 1083401401, and 91027045
文摘Diffusion-limited aggregation （DLA） assumes that particles perform pure random walk at a finite tem- perature and aggregate when they come close enough and stick together. Although it is well known that DLA in two dimensions results in a ramified fractal structure, how the particle shape influences the formed morphology is still un- clear. In this work, we perform the off-lattice two-dimensional DLA simulations with different particle shapes of triangle, quadrangle, pentagon, hexagon, and octagon, respectively, and compare with the results for circular particles. Our results indicate that different particle shapes only change the local structure, but have no effects on the global structure of the formed fractal duster. The local compactness decreases as the number of polygon edges increases.
