We have studied how two- and three-dimensional systems made up of particles interacting with finite range, repulsive potentials jam (i.e., develop a yield stress in a disordered state) at zero temperature and zero applied stress. At low packing fractions phi, the system is not jammed and each particle can move without impediment from its neighbors. For each configuration, there is a unique jamming threshold phi(c) at which particles can no longer avoid each other, and the bulk and shear moduli simultaneously become nonzero. The distribution of phi(c) values becomes narrower as the system size increases, so that essentially all configurations jam at the same packing fraction in the thermodynamic limit. This packing fraction corresponds to the previously measured value for random close packing. In fact, our results provide a well-defined meaning for "random close packing" in terms of the fraction of all phase space with inherent structures that jam. The jamming threshold, point J, occurring at zero temperature and applied stress and at the random-close-packing density, has properties reminiscent of an ordinary critical point. As point J is approached from higher packing fractions, power-law scaling is found for the divergence of the first peak in the pair correlation function and in the vanishing of the pressure, shear modulus, and excess number of overlapping neighbors. Moreover, near point J, certain quantities no longer self-average, suggesting the existence of a length scale that diverges at J. However, point J also differs from an ordinary critical point: the scaling exponents do not depend on dimension but do depend on the interparticle potential. Finally, as point J is approached from high packing fractions, the density of vibrational states develops a large excess of low-frequency modes. Indeed, at point J, the density of states is a constant all the way down to zero frequency. All of these results suggest that point J is a point of maximal disorder and may control behavior in its vicinity-perhaps even at the glass transition.

No abstract

We conduct numerical simulations of random packings of frictionless particles at T = 0. The packing fraction where the pressure becomes nonzero is the same as the jamming threshold, where the static shear modulus becomes nonzero. The distribution of threshold packing fractions narrows, and its peak approaches random close packing as the system size increases. For packing fractions within the peak, there is no self-averaging, leading to exponential decay of the interparticle force distribution.

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: frictionless 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.

Chemokines play a central role in regulating processes essential to the immune function of T cells1-3, such as their migration within lymphoid tissues and targeting of pathogens in sites of inflammation. Here we track T cells using multi-photon microscopy to demonstrate that the chemokine CXCL10 enhances the ability of CD8+ T cells to control the pathogen T. gondii in the brains of chronically infected mice. This chemokine boosts T cell function in two different ways: it maintains the effector T cell population in the brain and speeds up the average migration speed without changing the nature of the walk statistics. Remarkably, these statistics are not Brownian; rather, CD8+ T cell motility in the brain is well described by a generalized Lévy walk. According to our model, this surprising feature enables T cells to find rare targets with more than an order of magnitude more efficiency than Brownian random walkers. Thus, CD8+ T cell behavior is similar to Lévy strategies reported in organisms ranging from mussels to marine predators and monkeys4-10, and CXCL10 aids T cells in shortening the average time to find rare targets.