Levich Institute Seminar Announcement,
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 farfromequilibrium systems poses a serious challenge. Excited granular materials have become a canonical system to explore such ideas since they are inherently dissipative due to interparticle frictional contacts and inelastic collisions. Granular materials also have far reaching practical importance in a number of industries, but accumulated adhoc 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 NonEquilibrium SteadyState (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 firstorder phase transition in a vibrated twodimensional 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
welldefined equilibrium positions that are different than those of
the nearest static packing. We find that there is an increase in the
number of lowfrequency eigenmodes of the displacement matrix in the
harmonic approximation (over the number of lowfrequency 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.
