It has been conjectured (Liu and Nagel, Nature 1998) that it should be possible to bring together several different systems with a slow dynamics into a common description, and that their behavior may be controlled by a certain critical point.
In a study in 2007 (Olsson and Teitel, PRL 2007) we confirmed the existence of critical scaling in a simple model of interacting particles that is popular in the context of jamming. The simulations were done in two dimensions, at zero temperature, and around the jamming density and for the simplest possible model of dissipation.
We are now extending this previous study in several different directions, two of these are: (1) We have found that one of our models shows clear evidence of Discontinuous shear thickening (DST) even though it lacks the two ingredients that according to an emerging consensus should be essential for DST. We therefore plan to do thorough simulations with different models to sort out the importance of various features of the models to generate this phenomenon. (2) We have also started doing shearing simulations with ellipsoidal particles. This is one way to approach more realistic systems, since few real systems consist of spherical particles. It is also an interesting modification since e.g. the basic results that the behavior is controlled by the distance to the isostatic state with a given number of contacts per particle, is not easily generalized to ellipsoidal particles. With this modification we are thus really on uncharted territory.