Articles written in Proceedings – Mathematical Sciences
Volume 94 Issue 1 September 1985 pp 27-42
In this paper the kinematics of a curved shock of arbitrary strength has been discussed using the theory of generalised functions. This is the extension of Moslov’s work where he has considered isentropic flow even across the shock. The condition for a nontrivial jump in the flow variables gives the shock manifold equation (sme). An equation for the rate of change of shock strength along the shock rays (defined as the characteristics of the sme) has been obtained. This exact result is then compared with the approximate result of shock dynamics derived by Whitham. The comparison shows that the approximate equations of shock dynamics deviate considerably from the exact equations derived here. In the last section we have derived the conservation form of our shock dynamic equations. These conservation forms would be very useful in numerical computations as it would allow us to derive difference schemes for which it would not be necessary to fit the shock-shock explicitly.
Volume 110 Issue 1 February 2000 pp 35-53
This paper is a first attempt at classifying connections on small vertex models i.e., commuting squares of the form displayed in (1.2) below. More precisely, if we let