Levich Institute Seminar Announcement, 04/17/2012
Tuesday, 04/17/2012
2:00 PM
Steinman Hall, Room #312
(Chemical Engineering Conference Room)

Professor Mark Shattuck
City College of CUNY
Levich Institute

"Granular Thermodynamics and Statistical Mechanics"


Thermodynamics is generally not applicable to systems with energy input and dissipation present, and identifying relevant tools for understanding these far-from-equilibrium systems poses a serious challenge. Excited granular materials have become a canonical system to explore such ideas since they are inherently dissipative due to inter-particle frictional contacts and inelastic collisions. Granular materials also have far reaching practical importance in a number of industries, but accumulated ad-hoc knowledge is often the only design tool.

An important feature of driven granular systems is that the energy input and dissipation mechanisms can be balanced such that a Non-Equilibrium Steady-State (NESS) is achieved. This NESS shares many properties of systems in thermodynamic equilibrium. In particular, the structure and dynamics of the NESS are almost identical to equilibrium systems. Further, we present strong experimental evidence for a NESS first-order phase transition in a vibrated two-dimensional granular fluid. The phase transition between a gas and a crystal is characterized by a discontinuous change in both density and temperature and exhibits rate dependent hysteresis. Finally, we measure a “free energy”-like function for the system, whose minimum determines the state of the system

In quaisistatic systems granular packings composed of frictionless particles with purely repulsive contact interactions are strongly anharmonic. When perturbed along an eigenmode of the static packing (in the harmonic approximation), energy leaks from the original mode of vibration to a continuum of frequencies even when the system is under significant compression due to the breaking of the weakest contact. In light of this, we perform numerical simulations to measure the displacement matrix averaged over fluctuations and the associated eigenspectrum of weakly vibrated frictionless packings, which possess well-defined equilibrium positions that are different than those of the nearest static packing. We find that there is an increase in the number of low-frequency eigenmodes of the displacement matrix in the harmonic approximation (over the number of low-frequency modes in the static case) and these modes provide a more accurate description of the system dynamics. We also investigate the extent to which these results hold for systems with continuous potentials with repulsive and attractive interactions.