Disk Stability and Turbulence Generation: Effects of the Stellar Component

Galactic disks consist of both stars and gas. The stars gravitationally influence the gas either in disks at large or within spiral arms, leading to the formation of giant clouds and turbulence driving in the gas. In featureless disks as in flocculent galaxies, swing amplification operating in a combined star-gas disk is efficient to form bound condensations and feed a significant level of random gas motions. This occurs when the gaseous Toomre parameter is less than 1.4 for the stellar parameters similar to the solar neighbourhood conditions. In disks with spiral features, on the other hand, spiral-arm spurs and associated giant clouds develop as a consequence of magneto-Jeans instability in which magnetic tension counterbalances the stabilizing Coriolis force. Spiral shocks are inherently unstable when the vertical dimension is taken into account, exhibiting flapping motions of the shock front. This naturally converts the kinetic energy in galaxy rotation into random kinetic energy of the gas. The resulting turbulent motions are supersonic and persist despite strong shock dissipation. Thermal instability occurring in gas flows across spiral arms prompts phases transitions that produce a significant fraction of thermally-unstable, intermediate-temperature gas in the postshock expansion zones.

Stiffness and Damping Response Associated with Shock Attenuation in Downhill Running

Studies on shock attenuation during running have induced alterations in impact loading by imposing kinematic constraints, e.g., stride length changes. The role of shock attenuation mechanisms has been shown using mass-spring-damper (MSD) models, with spring stiffness related to impact shock dissipation. The present study altered the magnitude of impact loading by changing downhill surface grade, thus allowing runners to choose their own preferred kinematic patterns. We hypothesized that increasing downhill grade would cause concomitant increases in both impact shock and shock attenuation, and that MSD model stiffness values would reflect these increases. Ten experienced runners ran at 4.17 m/s on a treadmill at surface grades of 0% (level) to 12% downhill. Accelerometers were placed on the tibia and head, and reflective markers were used to register segmental kinematics. An MSD model was used in conjunction with head and tibial accelerations to determine head/arm/trunk center of mass (HATCOM) stiffness (K1), and lower extremity (LEGCOM) stiffness (K2) and damping (C). Participants responded to increases in downhill grade in one of two ways. Group LowSAhad lower peak tibial accelerations but greater peak head accelerations than Group HighSA, and thus had lower shock attenuation. LowSAalso showed greater joint extension at heelstrike, higher HATCOMheelstrike velocity, reduced K1stiffness, and decreased damping than HighSA. The differences between groups were exaggerated at the steeper downhill grades. The separate responses may be due to conflicts between the requirements of controlling HATCOMkinematics and shock attenuation. LowSAneeded greater joint extension to resist their higher HATCOMheelstrike velocities, but a consequence of this strategy was the reduced ability to attenuate shock with the lower extremity joints during early stance. With lower HATCOMimpact velocities, the HighSArunners were able to adopt a strategy that gave more control of shock attenuation, especially at the steepest grades.

ADVANCED HYPERBOLIC DIVERGENCE CLEANING SCHEME FOR SHALLOW WATER MAGNETOHYDRODYNAMICS

An advanced hyperbolic divergence cleaning scheme based on "generalized Lagrange multiplier" (GLM) for the equations of "shallow water magnetohydrodynamics" (SMHD) is presented. This scheme is based on the two-step method which is comprised of the standard finite-volume updating step for the nonlinear genuine SMHD system and the divergence cleaning step for the linear GLM-based Maxwell subsystem. The divergence cleaning step can be applied several times per each computational time step, in order to accelerate the transports of the divergence error out of the computational domain. The presented two-step method is compared with the standard GLM method based on operator splitting. It is shown that the standard operator-splitting based method has the shock dissipation problem, particularly when the multiple subcycles of the divergence cleaning step is performed per each time step. On the contrary, the introduction of the multiple subcycles for the new GLM–Maxwell subsystem does not suffer from the dissipation of the shocks, and produces better shock resolution. The presented method can be further applied to the full magnetohydrodynamics equations.

Mass Loss in Stars of Moderate Mass by Stellar Winds and Effects on the Evolution

Some 30 years ago it became clear that the solar corona is a plasma with a temperature of the order of 106K. As the underlying layers have only temperatures of 5000 K a mechanism had to be discovered, capable to explain this high temperature. A solution to the problem was found when it was realized that mechanical energy losses, by shock dissipation of wave energy can heat up a plasma to such high temperatures. This mechanical energy is formed in the deeper layers of the atmosphere and transported outwards. Dissipation becomes significant in regions where the density is sufficiently low.Wave propagation in a compressible medium in the presence of gravity and magnetic fields has been treated as a general problem, among others by Ferraro and Plumpton [1958). Three basic parameters are present: compressibility of the medium, gravity and magnetic field.