1. Pressure measurement in 2D granular gases. Jean-Christophe Géminard and Claude Laroche Laboratoire de Physique Ecole Normale Supérieure de Lyon FRANCE

2. Glass or steel beads Diameter 1 - 3.5 mmNumber 400-1500 PlateMetal (typ. Dural)Area S = 10  10 cm 2 Sinusoidal vibration Acceleration  < 3Frequency f = 50-80 Hz Introduction

3. At large enough acceleration, the beads form a homogeneous "2D granular gas" Introduction

4. J. S. Olafsen and J. S. Urbach, Phys. Rev. Lett. 81 4369 (1998) J. S. Olafsen and J. S. Urbach, Phys. Rev. E 60 R2468 (1999) W. Losert, D. G. Cooper, A Kudrolli, and J. P. Gollub, Chaos 9 682 (1999) W. Losert, D. G. Cooper, and J. P. Gollub, Phys. Rev. E 59 5855 (1999) Introduction Collapse from J. S. Urbach website

5. The collapse nucleates at larger acceleration when the overall density is larger. When at "equilibrium" with the collapse, the density of the gas does not depend on the overall density. Introduction "Crystal"-gas equilibrium Acceleration Number of beads

6. Introduction Bead-plate restitution coefficient Question: What is the effect of a change in the bead-plate restitution coefficient?

7. Introduction Bead-plate restitution coefficient Acceleration Percentage For the same pressure, the number density increases when the temperature is decreased. The percentage does not depend on the overall density and tends to a constant value at large accelerations.

8. The density difference at large accelerations increases when the difference in the restitution coefficients is increased. Introduction Bead-plate restitution coefficient Restitution coefficient of plate B Percentage

9. One side wall consists of a "pendulum". We measure the tilt angle of the pendulum in the steady state Pressure Pressure measurement

10. One observes a transition at  c, indenpendant of the density. Above  c, the pressure is proportional to the acceleration Pressure measurement Dimensionless acceleration Acceleration Pressure

11. Pressure measurement Number density Density Temperature T G  P/N The temperature slightly increases with the number density.

12. Pressure measurement Vibration frequency Frequency Critical acceleratrion  c  f The transition corresponds to a given ratio bouncing frequency / vibration frequency. Slope

13. Pressure measurement Bead-plate restitution coefficient Restitution coefficient Inverse temperature The temperature decreases when the restitution coefficient is decreased

14. Pressure measurement Bead diameter We measure the pressure difference between compartments A and B.

15. Pressure measurement Bead diameter Acceleration Pressure difference The pressures in compartments A and B are almost equal, at large acceleration, for the same mass density. Departure is observed for  <  C.

16. Flaws Small range of frequencies and accelerations. Lack of information about the bead-bead restitution coefficient. But… Pressure measurements provide reliable informations on the steady properties of the system. The transition at  C, which corresponds to a given ratio, bouncing frequency / vibration frequency is likely to be due to underlying attractors to periodic motion. We propose Conclusion