In this paper, we obtain a properly posed set of nodes for interpolation on a sphere. Moreover it is applied to construct properly posed set of nodes for Lagrange interpolation on the trivariate polynomial space of to...In this paper, we obtain a properly posed set of nodes for interpolation on a sphere. Moreover it is applied to construct properly posed set of nodes for Lagrange interpolation on the trivariate polynomial space of total degree n.展开更多
In this paper, we have investigated large scale disturbance in barotropic atmosphere on a sphere. It demonstrates that: considering nonlinear effects of interaction between waves in barotropic vorticity equation, the ...In this paper, we have investigated large scale disturbance in barotropic atmosphere on a sphere. It demonstrates that: considering nonlinear effects of interaction between waves in barotropic vorticity equation, the wave packet of the disturbance is governed by the famous equation-nonlinear Schrodinger equation. For the solitary wave, two factors are very important: one is spherical effect of the disturbance and the other is meridional shear of blocking high. In comparison with the results of local Cartesian coordinates, the former factor is the individuality of spherical soliton.展开更多
For the motion of a sphere on a rough horizontal plane, in the previous paper[1]the author aimed at providing approximate analytical solutions while the nutation is neglected,In this paper ,the control equations for t...For the motion of a sphere on a rough horizontal plane, in the previous paper[1]the author aimed at providing approximate analytical solutions while the nutation is neglected,In this paper ,the control equations for the sphere with nutation have beendeduced on the basis of paper [1]. Through the medium of solving these equations,the conclusion for the velocity of contact point in paper [1]is still proved true for the case with nutation.What is more ,some interesting results are gained ,for example the ve-locity of centre and contact point is relative to the angular velocity of spin and nuta-tion the direction of velocity of centre and contact point is constant.Under the condi-tion which is supposed to be weak nutation,the approximate analytical solutions are obtained,so that the results of paper [1]is proved to be true.展开更多
Fiber suspensions flow through a tube containing a sphere in the dilute and concentrated regimes is simulated numerically with the Lattice Boltzmann Method （LBM）. The numerical results of fiber orientation distribut...Fiber suspensions flow through a tube containing a sphere in the dilute and concentrated regimes is simulated numerically with the Lattice Boltzmann Method （LBM）. The numerical results of fiber orientation distribution based on a statistical scheme are obtained and agree qualitatively with the experimental ones for the flow through a parallel plate channel comaining a cylinder. The results show that the sphere in the tube results in a change in the fiber orientation distribution downstream of the sphere along the flow and transverse directions. The influences of the sphere on the fiber orientation distribution are more significant for the concentrated suspensions than for the dilute one. The effect of the initial fiber orientations on the fiber orientation distribution is significant upstream of the sphere but small downstream of the sphere.展开更多
Research efforts made so far to simulate fibre suspension flows are limited to fibre suspensions in Newtonian fluids.Though short fibre composites are mostly made of polymers,lack of suitable constitutive equations fo...Research efforts made so far to simulate fibre suspension flows are limited to fibre suspensions in Newtonian fluids.Though short fibre composites are mostly made of polymers,lack of suitable constitutive equations for fibre suspensions in viscoelastic fluids frustrates attempts to simulate flows of these suspensions. A preliminary work done by the author led to a constitutive equation for semiconcentrated fibre suspensions in the Oldroyd-B fluid.This paper describes the mathematical formulation of the flow problems for such a suspension and the numerical procedure to solve them.Some numerical results of flow past a sphere in a tube are also presented.展开更多
A method that series perturbations approximate solutions to N-S equations with boundary conditions was discussed and adopted. Then the method was proved in which the asymptotic solutions of viscous fluid flow past a s...A method that series perturbations approximate solutions to N-S equations with boundary conditions was discussed and adopted. Then the method was proved in which the asymptotic solutions of viscous fluid flow past a sphere were deducted. By the ameliorative asymptotic expansion matched method, the matched functions, are determined easily and the ameliorative curve of drag coefficient is coincident well with measured data in the case that Reynolds number is less than or equal to 40 000.展开更多
Biharmonic maps are generalizations of harmonic maps. A well-known result on harmonic maps between surfaces shows that there exists no harmonic map from a torus into a sphere(whatever the metrics chosen) in the homoto...Biharmonic maps are generalizations of harmonic maps. A well-known result on harmonic maps between surfaces shows that there exists no harmonic map from a torus into a sphere(whatever the metrics chosen) in the homotopy class of maps of Brower degree±1. It would be interesting to know if there exists any biharmonic map in that homotopy class of maps. The authors obtain some classifications on biharmonic maps from a torus into a sphere, where the torus is provided with a flat or a class of non-flat metrics whilst the sphere is provided with the standard metric. The results in this paper show that there exists no proper biharmonic maps of degree±1 in a large family of maps from a torus into a sphere.展开更多
A semiclassical lattice Boltzmann method is presented for axisymmetric flows of gas of particles of arbitrary statistics.The method is first derived by directly projecting the Uehling-Uhlenbeck Boltzmann-BGK equations...A semiclassical lattice Boltzmann method is presented for axisymmetric flows of gas of particles of arbitrary statistics.The method is first derived by directly projecting the Uehling-Uhlenbeck Boltzmann-BGK equations in twodimensional rectangular coordinates onto the tensor Hermite polynomials using moment expansion method and then the forcing strategy of Halliday et al.(Phys.Rev.E.,64(2001),011208)is adopted and forcing term is added into the resulting microdynamic evolution equation.The determination of the forcing terms is dictated by yielding the emergent macroscopic equations toward a particular target form.The correct macroscopic equations of the incompressible axisymmetric viscous flows are recovered through the Chapman-Enskog expansion.Computations of uniform flow over a sphere to verify the method are included.The results also indicate distinct characteristics of the effects of quantum statistics.展开更多
文摘In this paper, we obtain a properly posed set of nodes for interpolation on a sphere. Moreover it is applied to construct properly posed set of nodes for Lagrange interpolation on the trivariate polynomial space of total degree n.
文摘In this paper, we have investigated large scale disturbance in barotropic atmosphere on a sphere. It demonstrates that: considering nonlinear effects of interaction between waves in barotropic vorticity equation, the wave packet of the disturbance is governed by the famous equation-nonlinear Schrodinger equation. For the solitary wave, two factors are very important: one is spherical effect of the disturbance and the other is meridional shear of blocking high. In comparison with the results of local Cartesian coordinates, the former factor is the individuality of spherical soliton.
文摘For the motion of a sphere on a rough horizontal plane, in the previous paper[1]the author aimed at providing approximate analytical solutions while the nutation is neglected,In this paper ,the control equations for the sphere with nutation have beendeduced on the basis of paper [1]. Through the medium of solving these equations,the conclusion for the velocity of contact point in paper [1]is still proved true for the case with nutation.What is more ,some interesting results are gained ,for example the ve-locity of centre and contact point is relative to the angular velocity of spin and nuta-tion the direction of velocity of centre and contact point is constant.Under the condi-tion which is supposed to be weak nutation,the approximate analytical solutions are obtained,so that the results of paper [1]is proved to be true.
基金supported by the Doctoral Program of Higher Education in China(Grant No.20120101110121)
文摘Fiber suspensions flow through a tube containing a sphere in the dilute and concentrated regimes is simulated numerically with the Lattice Boltzmann Method （LBM）. The numerical results of fiber orientation distribution based on a statistical scheme are obtained and agree qualitatively with the experimental ones for the flow through a parallel plate channel comaining a cylinder. The results show that the sphere in the tube results in a change in the fiber orientation distribution downstream of the sphere along the flow and transverse directions. The influences of the sphere on the fiber orientation distribution are more significant for the concentrated suspensions than for the dilute one. The effect of the initial fiber orientations on the fiber orientation distribution is significant upstream of the sphere but small downstream of the sphere.
基金This paper is supported by the University of Melbourne,the National Natural Science Foundation of China and Zhejiang Province.
文摘Research efforts made so far to simulate fibre suspension flows are limited to fibre suspensions in Newtonian fluids.Though short fibre composites are mostly made of polymers,lack of suitable constitutive equations for fibre suspensions in viscoelastic fluids frustrates attempts to simulate flows of these suspensions. A preliminary work done by the author led to a constitutive equation for semiconcentrated fibre suspensions in the Oldroyd-B fluid.This paper describes the mathematical formulation of the flow problems for such a suspension and the numerical procedure to solve them.Some numerical results of flow past a sphere in a tube are also presented.
文摘A method that series perturbations approximate solutions to N-S equations with boundary conditions was discussed and adopted. Then the method was proved in which the asymptotic solutions of viscous fluid flow past a sphere were deducted. By the ameliorative asymptotic expansion matched method, the matched functions, are determined easily and the ameliorative curve of drag coefficient is coincident well with measured data in the case that Reynolds number is less than or equal to 40 000.
基金supported by the Natural Science Foundation of China(No.11361073)supported by the Natural Science Foundation of Guangxi Province of China(No.2011GXNSFA018127)
文摘Biharmonic maps are generalizations of harmonic maps. A well-known result on harmonic maps between surfaces shows that there exists no harmonic map from a torus into a sphere(whatever the metrics chosen) in the homotopy class of maps of Brower degree±1. It would be interesting to know if there exists any biharmonic map in that homotopy class of maps. The authors obtain some classifications on biharmonic maps from a torus into a sphere, where the torus is provided with a flat or a class of non-flat metrics whilst the sphere is provided with the standard metric. The results in this paper show that there exists no proper biharmonic maps of degree±1 in a large family of maps from a torus into a sphere.
基金supported by CQSE Subproject#597R0066-69 and NSC 97-2221-E002-063-MY3They also acknowledge the support of NCHC in providing resource under the national project “Knowledge Innovation National Grid”in Taiwan are acknowledged.
文摘A semiclassical lattice Boltzmann method is presented for axisymmetric flows of gas of particles of arbitrary statistics.The method is first derived by directly projecting the Uehling-Uhlenbeck Boltzmann-BGK equations in twodimensional rectangular coordinates onto the tensor Hermite polynomials using moment expansion method and then the forcing strategy of Halliday et al.(Phys.Rev.E.,64(2001),011208)is adopted and forcing term is added into the resulting microdynamic evolution equation.The determination of the forcing terms is dictated by yielding the emergent macroscopic equations toward a particular target form.The correct macroscopic equations of the incompressible axisymmetric viscous flows are recovered through the Chapman-Enskog expansion.Computations of uniform flow over a sphere to verify the method are included.The results also indicate distinct characteristics of the effects of quantum statistics.
