Prandtl’s lifting line theory was generalized to the lifting problem of a three-dimensional hydrofoil in the presence of a free surface. Similar to the classical lifting theory, the singularity distribution method wa...Prandtl’s lifting line theory was generalized to the lifting problem of a three-dimensional hydrofoil in the presence of a free surface. Similar to the classical lifting theory, the singularity distribution method was utilized to solve two-dimensional lifting problems for the hydrofoil beneath the free surface at the air-water interface, and a lifting line theory was developed to correct three-dimensional effects of the hydrofoil with a large aspect ratio. Differing from the classical lifting theory, the main focus was on finding the three-dimensional Green function of the free surface induced by the steady motion of a system of horseshoe vortices under the free surface. Finally, numerical examples were given to show the relationship between the lift coefficient and submergence Froude numbers for 2-D and 3-D hydrofoils. If the submergence Froude number is small free surface effect will be significant registered as the increase of lift coefficient. The validity of these approaches was examined in comparison with the results calculated by other methods.展开更多
Applying 3-dimension finite difference method, the distribution characteristics of horizontal field transfer functions for rectangular conductor have been computed, and the law of distribution for Re-part and Im-part ...Applying 3-dimension finite difference method, the distribution characteristics of horizontal field transfer functions for rectangular conductor have been computed, and the law of distribution for Re-part and Im-part has been given. The influences of source field period, the conductivity, the buried depth and the length of the conductor on the transfer functions were studied. The extrema of transfer functions appear at the center, the four corners and around the edges of conductor, and move with the edges. This feature demonstrates that around the edges are best places for transfer functions' observation.展开更多
In this work,di erent kinds of traveling wave solutions and uncategorized soliton wave solutions are obtained in a three dimensional(3-D)nonlinear evolution equations(NEEs)through the implementation of the modi ed ext...In this work,di erent kinds of traveling wave solutions and uncategorized soliton wave solutions are obtained in a three dimensional(3-D)nonlinear evolution equations(NEEs)through the implementation of the modi ed extended direct algebraic method.Bright-singular and dark-singular combo solitons,Jacobi's elliptic functions,Weierstrass elliptic functions,constant wave solutions and so on are attained beside their existing conditions.Physical interpretation of the solutions to the 3-D modi ed KdV-Zakharov-Kuznetsov equation are also given.展开更多
The vector method (VM) of quantitative texture analysis has been entirely reconstructedin the Euler space using Roe’s notation. The reconstructed VM, called the generalized vectormethod (GVM), has got rid of the limi...The vector method (VM) of quantitative texture analysis has been entirely reconstructedin the Euler space using Roe’s notation. The reconstructed VM, called the generalized vectormethod (GVM), has got rid of the limitations arising from the original form of orientationrepresentation of the VM, such as the inconvenience in searching the relation between tex-tures and physical properties of materials, and conserves all the advantages of VM. The investigation on a cubic crystal system indicates that the texture vector of a samplemay be quantitatively determined with the GVM, using a complete or even an incompletepole figure. Also, the series expansion coefficients of the crystallite orientation distributionfunction (ODF) needed in calculating macroscopic anisotropies of the sample can be easilyevaluated.展开更多
基金Supported by the National Natural Science Foundation of China under Grant No.50921001973 Program under Grant No. 2010CB83270
文摘Prandtl’s lifting line theory was generalized to the lifting problem of a three-dimensional hydrofoil in the presence of a free surface. Similar to the classical lifting theory, the singularity distribution method was utilized to solve two-dimensional lifting problems for the hydrofoil beneath the free surface at the air-water interface, and a lifting line theory was developed to correct three-dimensional effects of the hydrofoil with a large aspect ratio. Differing from the classical lifting theory, the main focus was on finding the three-dimensional Green function of the free surface induced by the steady motion of a system of horseshoe vortices under the free surface. Finally, numerical examples were given to show the relationship between the lift coefficient and submergence Froude numbers for 2-D and 3-D hydrofoils. If the submergence Froude number is small free surface effect will be significant registered as the increase of lift coefficient. The validity of these approaches was examined in comparison with the results calculated by other methods.
文摘Applying 3-dimension finite difference method, the distribution characteristics of horizontal field transfer functions for rectangular conductor have been computed, and the law of distribution for Re-part and Im-part has been given. The influences of source field period, the conductivity, the buried depth and the length of the conductor on the transfer functions were studied. The extrema of transfer functions appear at the center, the four corners and around the edges of conductor, and move with the edges. This feature demonstrates that around the edges are best places for transfer functions' observation.
文摘In this work,di erent kinds of traveling wave solutions and uncategorized soliton wave solutions are obtained in a three dimensional(3-D)nonlinear evolution equations(NEEs)through the implementation of the modi ed extended direct algebraic method.Bright-singular and dark-singular combo solitons,Jacobi's elliptic functions,Weierstrass elliptic functions,constant wave solutions and so on are attained beside their existing conditions.Physical interpretation of the solutions to the 3-D modi ed KdV-Zakharov-Kuznetsov equation are also given.
基金Project supported by the National Natural Science Foundation of China.
文摘The vector method (VM) of quantitative texture analysis has been entirely reconstructedin the Euler space using Roe’s notation. The reconstructed VM, called the generalized vectormethod (GVM), has got rid of the limitations arising from the original form of orientationrepresentation of the VM, such as the inconvenience in searching the relation between tex-tures and physical properties of materials, and conserves all the advantages of VM. The investigation on a cubic crystal system indicates that the texture vector of a samplemay be quantitatively determined with the GVM, using a complete or even an incompletepole figure. Also, the series expansion coefficients of the crystallite orientation distributionfunction (ODF) needed in calculating macroscopic anisotropies of the sample can be easilyevaluated.
