Magnetohydrodynamic Model of Equatorial Plasma Torus in Planetary Nebulae

Some basic structures in planetary nebulae are modeled as self-organized magnetohydrodynamic (MHD) plasma configurations with radial flow. These configurations are described by time self-similar dynamics, where space and time dependences of each physical variable are in separable form. Axisymmetric toroidal MHD plasma configuration is solved under the gravitational field of a central star of mass $M$. With an azimuthal magnetic field, this self-similar MHD model provides an equatorial structure in the form of an axisymmetric torus with nested and closed toroidal magnetic field lines. In the absence of an azimuthal magnetic field, this formulation models the basic features of bipolar planetary nebulae. The evolution function, which accounts for the time evolution of the system, has a bounded and an unbounded evolution track governed respectively by a negative and positive energy density constant $H$.Comment: 14 figure

Global axisymmetric stability analysis for a composite system of two gravitationally coupled scale-free discs

In a composite system of gravitationally coupled stellar and gaseous discs, we perform linear stability analysis for axisymmetric coplanar perturbations using the two-fluid formalism. The background stellar and gaseous discs are taken to be scale-free with all physical variables varying as powers of cylindrical radius $r$ with compatible exponents. The unstable modes set in as neutral modes or stationary perturbation configurations with angular frequency $\omega=0$.Comment: 7 pages using AAS styl

Stabilization of nonlinear velocity profiles in athermal systems undergoing planar shear flow

We perform molecular dynamics simulations of model granular systems undergoing boundary-driven planar shear flow in two spatial dimensions with the goal of developing a more complete understanding of how dense particulate systems respond to applied shear. In particular, we are interested in determining when these systems will possess linear velocity profiles and when they will develop highly localized velocity profiles in response to shear. In previous work on similar systems we showed that nonlinear velocity profiles form when the speed of the shearing boundary exceeds the speed of shear waves in the material. However, we find that nonlinear velocity profiles in these systems are unstable at very long times. The degree of nonlinearity slowly decreases in time; the velocity profiles become linear when the granular temperature and density profiles are uniform across the system at long times. We measure the time $t_l$ required for the velocity profiles to become linear and find that $t_l$ increases as a power-law with the speed of the shearing boundary and increases rapidly as the packing fraction approaches random close packing. We also performed simulations in which differences in the granular temperature across the system were maintained by vertically vibrating one of the boundaries during shear flow. We find that nonlinear velocity profiles form and are stable at long times if the difference in the granular temperature across the system exceeds a threshold value that is comparable to the glass transition temperature in an equilibrium system at the same average density. Finally, the sheared and vibrated systems form stable shear bands, or highly localized velocity profiles, when the applied shear stress is lowered below the yield stress of the static part of the system.Comment: 11 pages, 14 figure