We investigate the interaction between a singular surface and a strong shock in the self-gravitating interstellar gas clouds with the assumption of spherical symmetry. Using the method of the Lie group of transformations, a particular solution of the flow variables and the cooling–heating function for an infinitely strong shock is obtained. This paper explores an application of the singular surface theory in the evolution of an acceleration wave front propagating through an unperturbed medium. We discuss the formation of an acceleration, considering the cases of compression and expansion waves. The influence of the cooling–heating function on a shock formation is explained. The results of a collision between a strong shock and an acceleration wave are discussed using the Lax evolutionary conditions.
doi:10.1017/S1446181121000328
Abstract
We investigate the interaction between a singular surface and a strong shock in the self-gravitating interstellar gas clouds with the assumption of spherical symmetry. Using the method of the Lie group of transformations, a particular solution of the flow variables and the cooling–heating function for an infinitely strong shock is obtained. This paper explores an application of the singular surface theory in the evolution of an acceleration wave front propagating through an unperturbed medium. We discuss the formation of an acceleration, considering the cases of compression and expansion waves. The influence of the cooling–heating function on a shock formation is explained. The results of a collision between a strong shock and an acceleration wave are discussed using the Lax evolutionary conditions.
The singular surface theory has been used to determine the law of propagation of weak discontinuities and the problem of growth and decay of waves. The effect of radioactive heat transfer has been treated using a differential approximation which is valid over entire optical depth range. The effects of wave geometry and magnetic field with finite electrical conductivity on the global behavior of the wave amplitude have also been studied. The two cases of diverging and converging waves have been discussed separately.
SynopsisThe cubic surfaces in, save for the elliptic cone, are, whatever their singularities, projections of del Pezzo's non-singular surface F, of order 9 in. It is explained how, merely by specifying the geometrical relation of the vertex of projection to F, each cubic surface is obtainable “at a stroke”, without using spaces of intermediate dimensions.
ABSTRACTGrowth kinetics on non-singular surfaces were studied by Monte Carlo simulations. In contrast to the growth on singular and vicinal surfaces, the sticking coefficient on the non-singular surfaces was found to decrease with increase of the surface roughness. Simulations of annealing processes showed that surface diffusion of atoms leads to a stationary surface roughness, which is explained by multiple configurations having the lowest energy in the non-singular surface.
Weak discontinuities in electrically conducting and radiating gases
