Padé approximants are used to find approximate vortex solutions of any winding number in the context of Gross-Pitaevskii equation for a uniform condensate and condensates with axisymmetric trapping potentials. Rational function and generalised rational function approximations of axisymmetric solitary waves of the Gross-Pitaevskii equation are obtained in two and three dimensions. These approxim...

A modified lattice Boltzmann model based on the two-dimensional, nine-velocity lattice-Bhatnagar-Gross-Krook fluid is presented for axisymmetric flows. A spatially and temporally varying source term is incorporated into the evolution equation for the momentum distribution function on a two-dimensional Cartesian lattice. The precise form of the source term is derived through a Chapman-Enskog ana...

We study stability of axisymmetric liquid bridges between two axisymmetric solid bodies in the absence of gravity under arbitrary asymmetric perturbations which are expanded into a set of angular Fourier modes. We determine the stability region boundary for every angular mode in case of both fixed and free contact lines. Application of this approach allows us to demonstrate existence of stable ...

In this paper, 3-dimensional linear instability analysis has been carried out for unsteady pipe flow. An inflectional velocity profile from [2] has been considered and the stability analysis of it has been carried out for (axisymmetric mode) and 0 = n 2 & 1 = n . It was revealed that the profile is unstable for both axisymmetric and non-axisymmetric modes. The mode 1 = n was observed to be most...

The generation of solar non-axisymmetric magnetic fields is studied based on a linear α −Ω dynamo model in a rotating spherical frame. The model consists of a solarlike differential rotation, a magnetic diffusivity varied with depth, and three types of α-effects with different locations, i.e. the tachocline, the whole convective zone and the sub-surface. Some comparisons of the critical α-value...

We discuss steady-state transonic outflows obtained by direct numerical solution of the hydrodynamic and magnetohydrodynamic equations. We make use of the Versatile Advection Code, a software package for solving systems of (hyperbolic) partial differential equations. We proceed stepwise from a spherically symmetric, isothermal, unmagnetized, non-rotating Parker wind to arrive at axisymmetric, p...

We investigate stability of Toomre-Hayashi model for a self-gravitating, rotating gas disk. The rotation velocity, vφ, and sound speed, cs, are spatially constant in the model. We show that the model is unstable against an axisymmetric perturbation irrespectively of the values of vφ and cs. When the ratio, vφ/cs, is large, the model disk is geometrically thin and unstable against an axisymmetri...

We classify all (−1)−homogeneous axisymmetric no swirl solutions of incompressible stationary Navier-Stokes equations in three dimension which are smooth on the unit sphere minus the south pole, parameterize them as a two dimensional surface with boundary, and analyze their pressure profiles near the north pole. Then we prove that there is a curve of (−1)−homogeneous axisymmetric solutions with...

It was shown by Weyl that the general static axisymmetric solution of the vacuum Einstein equations in four dimensions is given in terms of a single axisymmetric solution of the Laplace equation in three-dimensional flat space. Weyl’s construction is generalized here to arbitrary dimension D ≥ 4. The general solution of the D-dimensional vacuum Einstein equations that admits D− 2 orthogonal com...

A lattice Boltzmann method for axisymmetric multiphase flows is presented and validated. The method is capable of accurately modeling flows with variable density. We develop the classic Shan-Chen multiphase model [Phys. Rev. E 47, 1815 (1993)] for axisymmetric flows. The model can be used to efficiently simulate single and multiphase flows. The convergence to the axisymmetric Navier-Stokes equa...