Stress in dilute suspensions

Generally, two types of theory are used to describe the field equations for suspensions. The so-called postulated equations are based on the kinetic theory of mixtures, which logically should give reasonable equations for solutions. The basis for the use of such theory for suspensions is tenuous, though it at least gives a logical path for mathematical arguments. It has the disadvantage that it leads to a system of equations which is underdetermined, in a sense that can be made precise. On the other hand, the so-called averaging theory starts with a determined system, but the very process of averaging renders the resulting system underdetermined. A third type of theory is proposed in which the kinetic theory of gases is used to motivate continuum equations for the suspended particles. This entails an interpretation of the stress in the particles that is different from the usual one. Classical theory is used to describe the motion of the suspending medium. The result is a determined system for a dilute suspension. Extension of the theory to more concentrated systems is discussed

Morphic and principal-ideal group rings

We observe that the class of left and right artinian left and right morphic rings agrees with the class of artinian principal ideal rings. For $R$ an artinian principal ideal ring and $G$ a group, we characterize when $RG$ is a principal ideal ring; for finite groups $G$, this characterizes when $RG$ is a left and right morphic ring. This extends work of Passman, Sehgal and Fisher in the case when $R$ is a field, and work of Chen, Li, and Zhou on morphic group rings.Comment: 21 page