For a decade starting in the late 90’s, we performed a series of experiments on thin vibrated layers, which provide an accessible experimental system with nominally uniform energy input, identical particles, and apparently ergodic dynamics, making it an ideal system to compare with equilibrium kinetic theory and statistical mechanics.

Our early work [1, 2] described non-equilibrium effects including dynamic clustering and a condensation into an ordered solid with a coexisting gas, and show in this figure:

Follow-on work by our group and others showed that these effects are a consequence of non-uniform energy input that arises because the driving depends on the local state of the system, despite uniform boundary conditions.

At the level of kinetic theory, we provided clear experimental measurement of non-Guassian velocity distributions [1] and early measurements of velocity correlations [3]), but more importantly showed that the nature of the energy input determines velocity correlations, and that energy input and dissipation together determine the velocity distributions [3]. We also showed, however, that in a regime where the actual energy input is uniform, the monolayer exhibits a phase transition that matches the equilibrium system in surprising detail [4].

By studying layers between one and two particle diameters deep, we discovered a rich phase diagram remarkably similar to that observed in equilibrium.  One example of a surprising phase found in both experiments and computer simulations is shown in this image:

In our initial discovery [5] we showed that there was a large difference between the ‘granular temperature’ of the two phases, and that this difference arose primarily from a difference in the rate of energy input (also [6]), and in a follow-on paper ([7]) we showed the complete phase diagram. Finally, we have shown that inelasticity does have direct effects on the phase diagram ([8]), but that they are more subtle than the changes that arise from variations in energy injection ([6]).

This work helped establish the role of energy flow in determining local statistical properties such as velocity distributions and correlations, and the critical role of feedback between local system dynamics and energy flow in determining the phase behavior. These observations have considerable implications for researchers studying active matter (as demonstrated in our technical comment, [9]), where the energy source is internal to the system, and the dependence of that source on the local state of the system is often not known.

 

[1]  Olafsen, J. S. and Urbach, J. S. (1998). Clustering, order, and collapse in a driven granular monolayer. Phys. Rev. Lett. 81, 4369–4372.

[2]  Olafsen, J. S. and Urbach, J. S. (1999). Velocity distributions and density fluctuations in a granular gas. Phys Rev E Stat Phys Plasmas Fluids Relat Interdiscip Topics 60, R2468–71.

[3]  Prevost, A., Egolf, D., and Urbach, J. (2002). Forcing and Velocity Correlations in a Vibrated Granular Monolayer. Phys. Rev. Lett. 89.

[4]  Olafsen, J. S. and Urbach, J. S. (2005). Two-Dimensional Melting Far from Equilibrium in a Granular Monolayer. Phys. Rev. Lett. 95, 098002.

[5]  Prevost, A., Melby, P., Egolf, D., and Urbach, J. (2004). Nonequilibrium two-phase coexistence in a confined granular layer. Phys. Rev. E 70.

[6]  Lobkovsky, A. E., Reyes, F. V., and Urbach, J. S. (2010). The effects of forcing and dissipation on phase transitions in thin granular layers. Eur. Phys. J. Spec. Top. 179, 113–122.

[7]  Melby, P., Reyes, F. V., Prevost, A., Robertson, R., Kumar, P., Egolf, D. A., and Urbach, J. S. (2005). The dynamics of thin vibrated granular layers. J. Phys.: Condens. Matter 17, S2689–S2704.

[8]  Reyes, F. and Urbach, J. (2008). Effect of inelasticity on the phase transitions of a thin vibrated granular layer. Phys. Rev. E 78.

9]  Aranson, I. S., Snezhko, A., Olafsen, J. S., and Urbach, J. S. (2008). Comment on ”Long-Lived Giant Number Fluctuations in a Swarming Granular Nematic”. Science 320, 612c–612c.