The Jamming Transition and the Marginally Jammed Solid

When a system jams, it undergoes a transition from a flowing to a rigid state. Despite this important change in the dynamics, the internal structure of the system remains disordered in the solid as well as the fluid phase. In this way jamming is quite different from crystallization, the other common way in which a fluid solidifies. Jamming is a paradigm for thinking about how many different types of fluids-from molecular liquids to macroscopic granular matter-develop rigidity. Here we review recent work on the jamming transition. We start with perhaps the simplest model: friction-less spheres interacting via repulsive finite-range forces at zero temperature. In this highly idealized case, the transition has aspects of both first- and second-order transitions. From studies of the normal modes of vibration for the marginally jammed solid, new physics has emerged for how a material can be rigid without having the elastic properties of a normal solid. We first survey the simulation data and theoretical arguments that have been proposed to understand this behavior. We then review work that has systematically gone beyond the ideal model to see whether the scenario developed there is more generally applicable. This includes work that examines the effect of nonspherical particles, friction, and temperature on the excitations and the dynamics. We briefly touch on recent laboratory experiments that have begun to make contact with simulations and theory.