On the Nonlinear Stability of Three-Dimensional Quasigeostrophic Motions in Spherical Geometry

Nonlinear stability criteria for the motions geoverned by three-dimensional quasigeostrophic model in spherical geometry are obtained by using Arnol＇d＇s variational principle and a priori estimate method. The results gained in this paper are parallel to Arnol＇d＇s second theorem and better than the known results. Especially, under the approximation of vertically integrated nondivergency, criteria corresponding to Arnol＇d＇s second theorem are first established by a detailed analysis.

Higgs Algebraic Symmetry of Screened System in a Spherical Geometry

The orbits and the dynamical symmetries for the screened Coulomb potentials and isotropic harmonic oscillators have been studied by Wu and Zeng [Z.B. Wund J.Y. Zeng, Phys. Rev. A 62 （2000） 032509]. We find similar properties in the corresponding systems in a sphericM space, whose dynamical symmetries are described by Higgs algebra. There exist extended Runge-Lenz vector for screened Coulomb potentials and extended quadruple tensor for screened harmonic oscillators. They, together with angular momentum, constitute the generators of the geometrical symmetry group. Moreover, there exist an infinite number of dosed orbits for suitable angular momentum values, and we give the equations of the classical orbits. The eigenenergy spectrum and corresponding eigenstates in these systems are derived.

Inverse Kinematics Analysis of a 6-DOF Manipulator Using Spherical Geometry Method

A 6-DOF cooperative manipulator is used for human spinal deformity detection.In order to ensure the scanning quality of spinal deformity and improve the solution rate and speed of inverse motion solution of the manipulator,an inverse kinematics analytical method based on spherical geometry is proposed in this paper.We take the AUBO-i5 collaborative manipulator as the research object,which combines the rapidity of analytical solution with the flexibility of spherical solution.In the Robot Operating System,the simulation experiment solves the inverse kinematics of 10000 sets of randomly generated postures.The success rate and time-consuming of the solution are calculated.Compared with the two commonly used inverse kinematics solving algorithms,TRAC-IK and KDL,this method has obvious advantages in terms of success rate and average time-consuming.

Rayleigh–Taylor instability at spherical interfaces of incompressible fluids

Rayleigh–Taylor instability（RTI） of three incompressible fluids with two interfaces in spherical geometry is derived analytically. The growth rate on the two interfaces and the perturbation feedthrough coefficients between two spherical interfaces are derived. For low-mode perturbation, the feedthrough effect from outer interface to inner interface is much more severe than the corresponding planar case, while the feedback from inner interface to the outer interface is smaller than that in planar geometry. The low-mode perturbations lead to the pronounced RTI growth on the inner interface of a spherical shell that are larger than the cylindrical and planar results. It is the low-mode perturbation that results in the difference between the RTI growth in spherical and cylindrical geometry. When the mode number of the perturbation is large enough, the results in cylindrical geometry are recovered.

Implementation of the Semi-Lagrangian Advection Scheme on a Quasi-Uniform Overset Grid on a Sphere

The semi-Lagrangian advection scheme is implemented on a new quasi-uniform overset （Yin-Yang） grid on the sphere. The Yin-Yang grid is a newly developed grid system in spherical geometry with two perpendicularly-oriented latitude-longitude grid components （called Yin and Yang respectively） that overlapp each other, and this effectively avoids the coordinate singularity and the grid convergence near the poles. In this overset grid, the way of transferring data between the Yin and Yang components is the key to maintaining the accuracy and robustness in numerical solutions. A numerical interpolation for boundary data exchange, which maintains the accuracy of the original advection scheme and is computationally efficient, is given in this paper. A standard test of the solid-body advection proposed by Williamson is carried out on the Yin-Yang grid. Numerical results show that the quasi-uniform Yin-Yang grid can get around the problems near the poles, and the numerical accuracy in the original semi-Lagrangian scheme is effectively maintained in the Yin-Yang grid.

Asymptotic-Preserving Discrete Schemes for Non-Equilibrium Radiation Diffusion Problem in Spherical and Cylindrical Symmetrical Geometries

We study the asymptotic-preserving fully discrete schemes for nonequilibrium radiation diffusion problem in spherical and cylindrical symmetric geometry.The research is based on two-temperature models with Larsen’s flux-limited diffusion operators.Finite volume spatially discrete schemes are developed to circumvent the singularity at the origin and the polar axis and assure local conservation.Asymmetric second order accurate spatial approximation is utilized instead of the traditional first order one for boundary flux-limiters to consummate the schemes with higher order global consistency errors.The harmonic average approach in spherical geometry is analyzed,and its second order accuracy is demonstrated.By formal analysis,we prove these schemes and their corresponding fully discrete schemes with implicitly balanced and linearly implicit time evolutions have first order asymptoticpreserving properties.By designing associated manufactured solutions and reference solutions,we verify the desired performance of the fully discrete schemes with numerical tests,which illustrates quantitatively they are first order asymptotic-preserving and basically second order accurate,hence competent for simulations of both equilibrium and non-equilibrium radiation diffusion problems.

Moving Mesh Kinetic Simulation for Sheared Rodlike Polymers with High Potential Intensities

The Doi-Hess equation that describes the evolution of an orientational dis-tribution function is capable of predicting several rheological features of nematic poly-mers.Since the orientational distribution function becomes sharply peaked as poten-tial intensity increases,powerful numerical methods become necessary in the relevant numerical simulations.In this paper,a numerical scheme based on the moving grid techniques will be designed to solve the orientational distribution functions with high potential intensities.Numerical experiments are carried out to demonstrate the effec-tiveness and robustness of the proposed scheme.