Jamming in Perspective

Jammingoccurs when objects like grains are packed tightly together (e.g. grain silos). It is highly cooperative and can lead to phenomena like earthquakes, traffic jamsetc. In this Letter we point out the paramount importance of the underlying contact network for jammedsystems; it must have both isostatic plus one contacts {\it{and}} a finite bulk modulus. Isostatic means that the number of degrees of freedom are exactly balanced by the number of constraints. This defines a large class of networks that can be constructed without the necessity of packing particles together (either in the lab or computationally). One such construction, which we explore here, involves setting up the Delaunay triangulationof a Poisson disk sampling, and then removing edges to maximize the bulk modulus, until the isostatic plus one point is reached. This construction works in any dimensions and here we give results in 2d where we also show how such networks can be transformed into a jammed disk pack.