Complex behavior from simple interactions

Recent Research Directions

Traditionally, high strength lightweight materials are created from mechanically rigid structures with a combination of compressive and tensile forces. By contrast, purely compressive materials such as sand and gravel do not typically offer a high strength to weight ratio. By considering sphere packings in which all forces are compressive, we determine the limits on creating low density rigid systems. An Apollonian sphere packing proves that a rigid packing can completely fill space, but what is the lowest density a stable packing can achieve?
Diffusion is pervasive in the natural world. Over one hundred years ago Einstein created a remarkably simple and effective theory describing the behavior of a single diffusing particle that has since been applied countless times to widely disparate physical systems. We will show that for large numbers of particles diffusing in the same environment, this theory does not correspond to reality as it neglects the effects of the common environment in which all particles live.
In critical phenomena, quantities generally obey power law relations from a critical point. In jamming, the exponents to the power laws between pressure, packing fraction, and number of excess contacts can be derived exactly in the limit of infinite dimensions by the mean field theory of glasses and jamming. While these exponents are expected to be exact above the upper critical dimension, the prefactors to these power law scalings are generally not.