Alladi Ramakrishnan Hall

Entropy, Disorder and Scaling near the Unjamming Transition

Kabir Ramola

Brandeis University

Systems composed of macroscopic particulate matter where the large size of particles renders them robust to thermal agitations have been of continued interest in statistical physics. The point at which such systems begin to exhibit global rigidity or 'jamming' with increasing density has been the focus of intense research over the last decade. Decompressing such solids to the point where mechanical equilibrium can no longer be achieved leads to ‘unjamming’. We study jammed packings of soft disks in two dimensions as they approach the unjamming transition. Using extensive numerical simulations we show that the configuration space of jammed disk packings decomposes into basins of attraction that become equal in size as the trasition is approached. We then develop a scaling theory of the unjamming transition by defining local areas uniquely assigned to the contact points between disks. This construction allows us to quantify the microscopic disorder in the system, and also serves to define a local order parameter. We show that the distribution of this local order parameter exhibits divergences as the unjamming transition is approached. Using a mean-field analysis that includes three-body correlations, we demonstrate that these divergences predict several observed power-law behaviours of global quantities near the transition.