It is widely believed that stars form from collapsing interstellar clouds. However, molecular clouds typically contain of the order of 103 solar masses. Thus a mechanism is required that allows a collapsing cloud to fragment into a number of collapsing stellar sized sub-condensations. The early work was based on a virial theorem approach—defining a critical mass a cloud must exceed in order for its gravitational force to overcome the resistive thermal, rotational and magnetic forces, thus allowing the cloud to collapse. This critical mass is analogous to the Jeans mass for non-rotating, non-magnetic clouds. It is thought that a cloud containing several critical masses may collapse into several sub-condensations. Further, it is thought that the galactic magnetic field will cause the critical mass to decrease as the cloud collapses, allowing the cloud to fragment into a number of sub-condensations. The critical mass decreases as the cloud flattens down the field lines (since Mcrit ∝ B3/ϱ2 and B ∝ ϱk, K < ⅔ for non-isotropic collapse).

A new method for solving heat diffusion in three dimensional particle simulations is described. The difficulties encounted by other authors is discussed, in particular the difficulty of including boundary conditions in particle simulations. One and three dimensional tests of the method are described.

Techniques in QED (quantum electrodynamics) have been developed previously (see for example Melrose and Parle 1983) allowing one to treat electron-photon and photon-photon interactions exactly in the magnetized vacuum and allowing one to include the effects of a medium. These techniques are extended to include particle-particle interactions. Exact cross-sections for electron-electron collisions are derived and compared with known expressions. Such calculations have application in studies of the formation and transfer of radiation in the atmospheres surrounding neutron stars.

Very few (if any at all) three dimensional models of the final evolutionary stages of a star’s life have appeared in the literature. Such models may be important if the stellar core maintains sufficient rotational energy during it’s lifetime so that when collapse finally occurs, the increase of rotational energy to gravitational energy, may lead to a non-axisymmetric instability.

A sequence of core collapse models with decreasing rotation rate is considered. These models were calculated using a three dimensional, post-Newtonian, hydrodynamical, numerical code. The results show that for high precollapse rotational energies the core can become unstable resulting in the formation of what resemble ‘spiral arms’. Unfortunately, because of limits on computer time, the calculations had to be discontinued shortly after this development occurred.

A new family of solutions for stationary convection (Murphy and Lopez 1984) has been established which exists within the astrophysical range of parameter values — large Rayleigh number and low Prandtl number. These single mode Type II solutions, which have a non-zero component of vertical vorticity, apparently do not exist at higher Prandtl numbers and are characterized by a lower vertical velocity and heat flux, when compared to the equivalent single mode Type I solutions for Rayleigh — Benard convection with zero vertical vorticity. In turn the vertical component of vorticity associated with Type II solutions is responsible for modifying the horizontal components of the velocity field to establish cyclonic or swirling type solutions within the hexagonal convection cell.

Expressions for the physical structure of a sequence of two zone polytropic stellar models, based on composite analytical solutions of the Lane-Emden equation with indices n = 1 and n = 5, hâve been determined. The coefficients of vibrational stability for radial oscillations of this sequence of models have also been calculated and it is found that increasing the extent of the n = 5 outer zone has a stabilizing effect.

Characteristic frequencies of some modes of radial pulsations and their relative displacements have been determined for a sequence of composite polytropic stellar models having an inner zone of index n = 1 and an envelope n = 5. It is demonstrated that vibrational stability increases with the degree of central condensation of the individual two zone models.

The time dependent multimode equations for magnetoconvection have been solved numerically for a range of parameter values and cell sizes. The solutions demonstrate the nonlinear interactions between the different scales of motion and how the induced magnetic field is concentrated into the smaller length scale. The generation of mean kinetic and magnetic helicity occurs at low Prandtl number which has significant physical interpretations in the solar situation.

A unique data set of 160 MHz solar noise storm positions and polarizations covering a complete sunspot cycle interval from the Skylab period of 1973 through the Solar Maximum intervals of 1980 and 1984 is presented in the form of 27.28-day synoptic plots.