Using a field equation with a phase factor, a universal analytic potential-energy function applied to the interactions between diatoms or molecules is derived, and five kinds of potential curves of common shapes are o...Using a field equation with a phase factor, a universal analytic potential-energy function applied to the interactions between diatoms or molecules is derived, and five kinds of potential curves of common shapes are obtained adjusting the phase factors. The linear thermal expansion coefficients and Young's moduli of eleven kinds of face-centered cubic (fcc) metals - Al, Cu, Ag, etc. are calculated using the potential-energy function; the computational results are quite consistent with experimental values. Moreover, an analytic relation between the linear thermal expansion coefficients and Young's moduli of fcc metals is given using the potential-energy function. Finally, the force constants of fifty-five kinds of diatomic moleculars with low excitation state are computed using this theory, and they are quite consistent with RKR (Rydberg-Klein-Rees) experimental values.展开更多
Based on the equation of momentum conservation, an improved equation for the quisi-steady penetration of a long rod into homogeneous semi-infinite targets has been derived, assuming that the flow interface between the...Based on the equation of momentum conservation, an improved equation for the quisi-steady penetration of a long rod into homogeneous semi-infinite targets has been derived, assuming that the flow interface between the rod material and the target material is hemispherical and that the normal pressure on the interface is defined by the dynamic spherical cavity expansion. The equation has a form similar to the Tate equation, and the parameters in this equation have definite physical senses and practical values..展开更多
Taking the Konopelchenko-Dubrovsky system as a simple example, some familles of rational formal hyperbolic function solutions, rational formal triangular periodic solutions, and rational solutions are constructed by u...Taking the Konopelchenko-Dubrovsky system as a simple example, some familles of rational formal hyperbolic function solutions, rational formal triangular periodic solutions, and rational solutions are constructed by using the extended Riccati equation rational expansion method presented by us. The method can also be applied to solve more nonlinear partial differential equation or equations.展开更多
We develop a two-relaxation-time (TRT) Lattice Boltzmann model for hydrodynamicequations with variable source terms based on equivalent equilibriumfunctions. A special parametrization of the free relaxation parameter ...We develop a two-relaxation-time (TRT) Lattice Boltzmann model for hydrodynamicequations with variable source terms based on equivalent equilibriumfunctions. A special parametrization of the free relaxation parameter is derived. Itcontrols, in addition to the non-dimensional hydrodynamic numbers, any TRT macroscopicsteady solution and governs the spatial discretization of transient flows. Inthis framework, the multi-reflection approach [16, 18] is generalized and extended forDirichlet velocity, pressure and mixed (pressure/tangential velocity) boundary conditions.We propose second and third-order accurate boundary schemes and adapt themfor corners. The boundary schemes are analyzed for exactness of the parametrization,uniqueness of their steady solutions, support of staggered invariants and for the effectiveaccuracy in case of time dependent boundary conditions and transient flow.When the boundary scheme obeys the parametrization properly, the derived permeabilityvalues become independent of the selected viscosity for any porous structureand can be computed efficiently. The linear interpolations [5, 46] are improved withrespect to this property.展开更多
This paper introduces higher-order solutions of the quadratic nonlinear stochastic oscillatory equation. Solutions with different orders and different number of corrections are obtained with the WHEP technique which u...This paper introduces higher-order solutions of the quadratic nonlinear stochastic oscillatory equation. Solutions with different orders and different number of corrections are obtained with the WHEP technique which uses the WienerHermite expansion and perturbation technique. The equivalent deterministic equations are derived for each order and correction. The solution ensemble average and variance are estimated and compared for different orders, different number of corrections and different strengths of the nonlinearity. The solutions are simulated using symbolic computation software such as Mathematica. The comparisons between different orders and different number of corrections show the importance of higher-order and higher corrected WHEP solutions for the nonlinear stochastic differential equations.展开更多
A novel method for obtaining the approximate symmetry of a partial differential equation with a small parameter is introduced. By expanding the independent variable and the dependent variable in the small parameter se...A novel method for obtaining the approximate symmetry of a partial differential equation with a small parameter is introduced. By expanding the independent variable and the dependent variable in the small parameter series, we obtain more affluent approximate symmetries. The method is applied to two perturbed nonlinear partial differential equations and new approximate solutions are derived.展开更多
Conical cam mechanism has been widely used in modern machinery and equipment.However,the commonly used planar expansion methods for the design of spatial cam contour produce significant errors,because these methods in...Conical cam mechanism has been widely used in modern machinery and equipment.However,the commonly used planar expansion methods for the design of spatial cam contour produce significant errors,because these methods incorrectly use the distance from the axis of the follower to the main conical cam to replace the corresponding arc length on the conical cam.HSIEH,et al,used analytical methods to achieve higher accuracy,but these analytical methods have their own drawbacks since they are too complicated for practical use.Through the analysis of the errors created during the generation of conical cam contour using the existing expansion methods,this paper proposes to include diverge angle in the calculation of conical cam rotation angle in the equation of conical cam contour expansion.This correction eliminates the error generated by the commonly used methods.Based on the expression of the follower＇s 3D trajectory and the spatial geometry of conical cam,this paper has deduced the planar polar curve equation for determining polar coordinates for the curve of planar expansion outline.Furthermore,this paper provides an example of conical cam contour design based on sinusoidal acceleration variation.According to polar coordinates and the movement of curve equation function expression,this paper applies MATLAB software to solve coordinates for the cam expansion curve and uses AutoCAD software to generate conical cam expansion contour that meets the requirement of the law of motion.The proposed method provides a design process that is simple,intuitive and easy to master and implement.It also avoids the design error in the traditional methods for generating contour of conical cam with oscillating follower that requires high precision.展开更多
In this work, by means of a new more general ansatz and the symbolic computation system Maple, we extend the Riccati equation rational expansion method [Chaos, Solitons ＆ Fractals 25 （2005） 1019] to uniformly const...In this work, by means of a new more general ansatz and the symbolic computation system Maple, we extend the Riccati equation rational expansion method [Chaos, Solitons ＆ Fractals 25 （2005） 1019] to uniformly construct a series of stochastic nontravelling wave solutions for nonlinear stochastic evolution equation. To illustrate the effectiveness of our method, we take the stochastic mKdV equation as an example, and successfully construct some new and more general solutions including a series of rational formal nontraveling wave and coefficient functions＇ soliton-like solution.s and trigonometric-like function solutions. The method can also be applied to solve other nonlinear stochastic evolution equation or equations.展开更多
By combining Chapman-Enskog expansion with the BGK approximation to Baltzmann equation and Navier-Stokes equation was obtained. And an expression of (Darcy's) law was obtained through taking variable average over ...By combining Chapman-Enskog expansion with the BGK approximation to Baltzmann equation and Navier-Stokes equation was obtained. And an expression of (Darcy's) law was obtained through taking variable average over Navier-Stokes equation on some representative space in porous media,and finally an example was taken to prove its reliability.展开更多
In this paper, we evaluate the integrals that are solutions of the heat and Stokes’ equations obtained by Fokas’ transform method by deriving exact formulas. Our method is more accurate and efficient than the contou...In this paper, we evaluate the integrals that are solutions of the heat and Stokes’ equations obtained by Fokas’ transform method by deriving exact formulas. Our method is more accurate and efficient than the contour deformation and parametrization used by Fokas to compute these integrals. In fact, for the heat equation, our solution is exact up to the imaginary error function and for the Stokes equation, our solution is exact up to the incomplete Airy function. In addition, our solutions extend to the lateral boundary without convergence issues, allow for asymptotic expansions, and are much faster than those obtained by other methods.展开更多
基金Supported in part by the Natural Science Foundation of Henan Province of China(0111050200) the Natural Science Foundation of Education Department of Henan Province of China(2003110003) the Science Foundation of Henan University of Science and Technology(2003QN13)
基金This work was supported by the National Natural Science Foundation of China (No. 40274044).
文摘Using a field equation with a phase factor, a universal analytic potential-energy function applied to the interactions between diatoms or molecules is derived, and five kinds of potential curves of common shapes are obtained adjusting the phase factors. The linear thermal expansion coefficients and Young's moduli of eleven kinds of face-centered cubic (fcc) metals - Al, Cu, Ag, etc. are calculated using the potential-energy function; the computational results are quite consistent with experimental values. Moreover, an analytic relation between the linear thermal expansion coefficients and Young's moduli of fcc metals is given using the potential-energy function. Finally, the force constants of fifty-five kinds of diatomic moleculars with low excitation state are computed using this theory, and they are quite consistent with RKR (Rydberg-Klein-Rees) experimental values.
文摘Based on the equation of momentum conservation, an improved equation for the quisi-steady penetration of a long rod into homogeneous semi-infinite targets has been derived, assuming that the flow interface between the rod material and the target material is hemispherical and that the normal pressure on the interface is defined by the dynamic spherical cavity expansion. The equation has a form similar to the Tate equation, and the parameters in this equation have definite physical senses and practical values..
基金The project partially supported by the State Key Basic Research Program of China under Grant No. 2004CB318000
文摘Taking the Konopelchenko-Dubrovsky system as a simple example, some familles of rational formal hyperbolic function solutions, rational formal triangular periodic solutions, and rational solutions are constructed by using the extended Riccati equation rational expansion method presented by us. The method can also be applied to solve more nonlinear partial differential equation or equations.
文摘We develop a two-relaxation-time (TRT) Lattice Boltzmann model for hydrodynamicequations with variable source terms based on equivalent equilibriumfunctions. A special parametrization of the free relaxation parameter is derived. Itcontrols, in addition to the non-dimensional hydrodynamic numbers, any TRT macroscopicsteady solution and governs the spatial discretization of transient flows. Inthis framework, the multi-reflection approach [16, 18] is generalized and extended forDirichlet velocity, pressure and mixed (pressure/tangential velocity) boundary conditions.We propose second and third-order accurate boundary schemes and adapt themfor corners. The boundary schemes are analyzed for exactness of the parametrization,uniqueness of their steady solutions, support of staggered invariants and for the effectiveaccuracy in case of time dependent boundary conditions and transient flow.When the boundary scheme obeys the parametrization properly, the derived permeabilityvalues become independent of the selected viscosity for any porous structureand can be computed efficiently. The linear interpolations [5, 46] are improved withrespect to this property.
文摘This paper introduces higher-order solutions of the quadratic nonlinear stochastic oscillatory equation. Solutions with different orders and different number of corrections are obtained with the WHEP technique which uses the WienerHermite expansion and perturbation technique. The equivalent deterministic equations are derived for each order and correction. The solution ensemble average and variance are estimated and compared for different orders, different number of corrections and different strengths of the nonlinearity. The solutions are simulated using symbolic computation software such as Mathematica. The comparisons between different orders and different number of corrections show the importance of higher-order and higher corrected WHEP solutions for the nonlinear stochastic differential equations.
文摘A novel method for obtaining the approximate symmetry of a partial differential equation with a small parameter is introduced. By expanding the independent variable and the dependent variable in the small parameter series, we obtain more affluent approximate symmetries. The method is applied to two perturbed nonlinear partial differential equations and new approximate solutions are derived.
基金supported by National Natural Science Foundation of China(Grant No.50645032)Zhejiang Provincial Natural Science Foundation of China(Grant No.Y105686)Ningbo Municipal Natural Science Foundation of China(Grant No.2008A610038)
文摘Conical cam mechanism has been widely used in modern machinery and equipment.However,the commonly used planar expansion methods for the design of spatial cam contour produce significant errors,because these methods incorrectly use the distance from the axis of the follower to the main conical cam to replace the corresponding arc length on the conical cam.HSIEH,et al,used analytical methods to achieve higher accuracy,but these analytical methods have their own drawbacks since they are too complicated for practical use.Through the analysis of the errors created during the generation of conical cam contour using the existing expansion methods,this paper proposes to include diverge angle in the calculation of conical cam rotation angle in the equation of conical cam contour expansion.This correction eliminates the error generated by the commonly used methods.Based on the expression of the follower＇s 3D trajectory and the spatial geometry of conical cam,this paper has deduced the planar polar curve equation for determining polar coordinates for the curve of planar expansion outline.Furthermore,this paper provides an example of conical cam contour design based on sinusoidal acceleration variation.According to polar coordinates and the movement of curve equation function expression,this paper applies MATLAB software to solve coordinates for the cam expansion curve and uses AutoCAD software to generate conical cam expansion contour that meets the requirement of the law of motion.The proposed method provides a design process that is simple,intuitive and easy to master and implement.It also avoids the design error in the traditional methods for generating contour of conical cam with oscillating follower that requires high precision.
基金The author would like to thank the referees very much for their careful reading of the manuscript and many valuable suggestions.
文摘In this work, by means of a new more general ansatz and the symbolic computation system Maple, we extend the Riccati equation rational expansion method [Chaos, Solitons ＆ Fractals 25 （2005） 1019] to uniformly construct a series of stochastic nontravelling wave solutions for nonlinear stochastic evolution equation. To illustrate the effectiveness of our method, we take the stochastic mKdV equation as an example, and successfully construct some new and more general solutions including a series of rational formal nontraveling wave and coefficient functions＇ soliton-like solution.s and trigonometric-like function solutions. The method can also be applied to solve other nonlinear stochastic evolution equation or equations.
文摘By combining Chapman-Enskog expansion with the BGK approximation to Baltzmann equation and Navier-Stokes equation was obtained. And an expression of (Darcy's) law was obtained through taking variable average over Navier-Stokes equation on some representative space in porous media,and finally an example was taken to prove its reliability.
文摘In this paper, we evaluate the integrals that are solutions of the heat and Stokes’ equations obtained by Fokas’ transform method by deriving exact formulas. Our method is more accurate and efficient than the contour deformation and parametrization used by Fokas to compute these integrals. In fact, for the heat equation, our solution is exact up to the imaginary error function and for the Stokes equation, our solution is exact up to the incomplete Airy function. In addition, our solutions extend to the lateral boundary without convergence issues, allow for asymptotic expansions, and are much faster than those obtained by other methods.
