I am studying the jamming transition with computer simulations of idealized mathematical models. The concept of jamming - think traffic jam – is the slowing down of the dynamics as the density increases up to the jamming density, where motion is no longer possible. This transition may be thought of as a liquid to solid transition but it is unusual in the sense that the solid is as disordered as the liquid - an ordinary liquid-to-solid transition is from a disordered liquid to an ordered solid - and it is not so easy to see exactly what is going on in the transition.
To study this transition we are doing simulations in two, three, and four dimensions. For the two-dimensional case we are mostly using circular disks of two different sizes. The disks interact when they are in contact with a force that is proportional to the particle overlaps and the motion of a given particle is given by the total force on that particle due to all its contacting particles. The simulations are mostly done with 65 536 particles in long runs where the simulation cell is slowly sheared and a key quantity is the viscosity, which is the resistance against this shearing. As the solid phase is approached the viscosity increases rapidly and the value of the exponent that describes this increase, and its dependence of the dimensionality, is a highly disputed subject.
With non-circular particles there are even more phenomena since the particles will often need to rotate in order to fit in. The figure shows two configurations with ellipsoidal particles. One is a starting configuration and the second is the configuration after a ten percent shearing of the simulation cell.
Physical Review E. Statistical, Nonlinear, and Soft Matter Physics: Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics, The American Physical Society 2010, Vol. 81, (4) : 040301-
Physical Review E. Statistical, Nonlinear, and Soft Matter Physics: Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics, The American Physical Society 2010, Vol. 82, (3) : 031303-