We find the existence conditions of unduloidal and nodoidal menisci between two solid spheres and study their stability in the framework of nonspectral theory of stability of axisymmetric menisci between two axisymmetric solid bodies in the absence of gravity.

Static axisymmetric Einstein–Maxwell–Dilaton and stationary axisymmetric Einstein–Maxwell–Dilaton–Axion theories in four space–time dimensions are shown to be integrable by means of the inverse scattering transform method. PASC number(s): 97.60.Lf, 04.60.+n, 11.17.+y

We study the non-stationary Navier-Stokes equations in the entire three-dimensional space under the assumption that the data are axisymmetric. We extend the regularity criterion for axisymmetric weak solutions given in [10].

Several experiments involving two-dimensional and axisymmetric bodies have been carried out in a Trisonic wind tunnel at supersonic speeds to investigate and analyse the measured values of base pressure and to compare them with those from the theoretical methods. The objective of the experiments was to obtain an appropriate method for processing the results of wind tunnel tests on rockets or ai...

A systematic way to derive the conserved quantities for the axisymmetric liquid jet, free jet and wall jet using conservation laws is presented. The flow in axisymmetric jets is governed by Prandtl’s momentum boundary layer equation and the continuity equation. The multiplier approach is used to construct a basis of conserved vectors for the system of two partial differential equations for the ...

We investigate some simple finite element discretizations for the axisymmetric Laplace equation and the azimuthal component of the axisymmetric Maxwell equations as well as multigrid algorithms for these discretizations. Our analysis is targeted at simple model problems and our main result is that the standard V-cycle with point smoothing converges at a rate independent of the number of unknown...

We examine nonlinear oscillations of slender tori in the vicinity of black holes and compact stars. These tori represent useful probes of the complicated, nonlinear dynamics of real accretion disks and provide at least qualitative understanding of their oscillations. We demonstrate that epicyclic modes of such tori are weakly coupled due to the pressure and gravitational forces. We explore all ...

The axisymmetric flows with swirl or rotation were solved by a hybrid scheme with lattice Boltzmann method for the axial and radial velocities and finite-difference method for the azimuthal (or swirl) velocity and the temperature. An incompressible axisymmetric lattice Boltzmann D2Q9 model was proposed to solve the axial and radial velocities through inserting source terms into the two-dimensio...

We investigate the validity of Thorne’s hoop conjecture in non-axisymmetric spacetimes by examining the formation of apparent horizons numerically. If spaces have a discrete symmetry about one axis, we can specify the boundary conditions to determine an apparent horizon even in non-axisymmetric spaces. We implement, for the first time, the “hoop finder” in non-axisymmetric spaces with a discret...

Axisymmetric spacetimes with a conformal symmetry are studied and it is shown that, if there is no further conformal symmetry, the axial Killing vector and the conformal Killing vector must commute. As a direct consequence, in con-formally stationary and axisymmetric spacetimes, no restriction is made by assuming that the axial symmetry and the conformal timelike symmetry commute. Furthermore, ...