%0 Book Section %1 statphys23_0426 %A Lai, P. %A Chan, C. %A Hou, M. %B Abstract Book of the XXIII IUPAP International Conference on Statistical Physics %C Genova, Italy %D 2007 %E Pietronero, Luciano %E Loreto, Vittorio %E Zapperi, Stefano %K bi-dispersed gas granular materials statphys23 topic-7 %T Oscillations in a Compartmentalized Bi-disperse Granular Gas %U http://st23.statphys23.org/webservices/abstract/preview_pop.php?ID_PAPER=426 %X Recently, there have been a lot of interests in the understanding of the basic properties of granular systems under shaking. At first sight, granular gases produced by shaking share some similarities with their molecular counter parts. Both systems are characterized by random motions and collisions. However, granular systems are not in thermal equilibrium and some unusual phenomena, which are not possible in equilibrium systems, can occur in granular systems. Phenomena such as Maxwell's demon 1, clustering 2 and even granular clocks 3,4 have been reported for granular gases in two-compartment systems. Although there are some basic understandings of the properties of a granular gas of a single type of grains, the physics of a bi-disperse granular gas is still far from clear. For example, it is still not clear if there is only one single temperature for the whole system or the two types of grains have their own temperatures. In Ref3, a granular gas consisted of a mixture of two type of grains is produced in a two-compartment by shaking. Oscillations in the distribution of grains between the two compartments can be observed when the shaking of the systems is tuned to certain values. These authors have to make use of phenomenological assumptions such as the Brazil nut effects (BNE) to explain their granular clock. However, at the same time, the reverse BNE (RBNE) assumption is used to explain a similar phenomenon 4 by other authors. Here, we report the results of a new model developed to understand the mechanism of the granular clock. The model is based on the observation that the processes of evaporation and condensation are unstable for a granular gas. In our model, the granular temperatures of the two types of grains can be different since they are related not only to the shaking velocity but also to the composition of the gas. Oscillations in the system can be explained easily by the asymmetric collisions properties between the two types of grains. No BNE or RBNE assumptions are needed. Therefore, even grains of the same size in a bi-disperse system can produce granular oscillations. Predictions of our model are verified by experiments. In particular, both our experiments and model show that the transition from a homogeneous state to an oscillatory state in such a system is via a Hopf bifurcation; similar to the case of the segregation of a single type of grains in a two-compartmentalized system1. 1) J. Eggers, Phys. Rev. Lett. 83, 5322 (1999).\\ 2) R. Mikkelsen, D. van der Meer, Ko van der Weele, D. Lohse, Phys. Rev. Lett. 89, 214301 (2002); Phys. Rev. E 70, 061307 (2004).\\ 3) R. Lambiotte,J .M. Salazar, and L. Brenig, Phys. Lett. A 343, 224 (2005).\\ 4) S. Viridi, M. Schmick, and M. Markus, Phys. Rev. E 74, 041301 (2006).

@incollection{statphys23_0426, abstract = {Recently, there have been a lot of interests in the understanding of the basic properties of granular systems under shaking. At first sight, granular gases produced by shaking share some similarities with their molecular counter parts. Both systems are characterized by random motions and collisions. However, granular systems are not in thermal equilibrium and some unusual phenomena, which are not possible in equilibrium systems, can occur in granular systems. Phenomena such as Maxwell's demon [1], clustering [2] and even granular clocks [3,4] have been reported for granular gases in two-compartment systems. Although there are some basic understandings of the properties of a granular gas of a single type of grains, the physics of a bi-disperse granular gas is still far from clear. For example, it is still not clear if there is only one single temperature for the whole system or the two types of grains have their own temperatures. In Ref[3], a granular gas consisted of a mixture of two type of grains is produced in a two-compartment by shaking. Oscillations in the distribution of grains between the two compartments can be observed when the shaking of the systems is tuned to certain values. These authors have to make use of phenomenological assumptions such as the Brazil nut effects (BNE) to explain their granular clock. However, at the same time, the reverse BNE (RBNE) assumption is used to explain a similar phenomenon [4] by other authors. Here, we report the results of a new model developed to understand the mechanism of the granular clock. The model is based on the observation that the processes of evaporation and condensation are unstable for a granular gas. In our model, the granular temperatures of the two types of grains can be different since they are related not only to the shaking velocity but also to the composition of the gas. Oscillations in the system can be explained easily by the asymmetric collisions properties between the two types of grains. No BNE or RBNE assumptions are needed. Therefore, even grains of the same size in a bi-disperse system can produce granular oscillations. Predictions of our model are verified by experiments. In particular, both our experiments and model show that the transition from a homogeneous state to an oscillatory state in such a system is via a Hopf bifurcation; similar to the case of the segregation of a single type of grains in a two-compartmentalized system[1]. 1) J. Eggers, Phys. Rev. Lett. 83, 5322 (1999).\\ 2) R. Mikkelsen, D. van der Meer, Ko van der Weele, D. Lohse, Phys. Rev. Lett. 89, 214301 (2002); Phys. Rev. E 70, 061307 (2004).\\ 3) R. Lambiotte,J .M. Salazar, and L. Brenig, Phys. Lett. A 343, 224 (2005).\\ 4) S. Viridi, M. Schmick, and M. Markus, Phys. Rev. E 74, 041301 (2006).}, added-at = {2007-06-20T10:16:09.000+0200}, address = {Genova, Italy}, author = {Lai, P. and Chan, C. and Hou, M.}, biburl = {https://www.bibsonomy.org/bibtex/207c340d736caf81f29c4105d3b584a66/statphys23}, booktitle = {Abstract Book of the XXIII IUPAP International Conference on Statistical Physics}, editor = {Pietronero, Luciano and Loreto, Vittorio and Zapperi, Stefano}, interhash = {f1c40d3b31289e4a0b8f06b559db0006}, intrahash = {07c340d736caf81f29c4105d3b584a66}, keywords = {bi-dispersed gas granular materials statphys23 topic-7}, month = {9-13 July}, timestamp = {2007-06-20T10:16:20.000+0200}, title = {Oscillations in a Compartmentalized Bi-disperse Granular Gas}, url = {http://st23.statphys23.org/webservices/abstract/preview_pop.php?ID_PAPER=426}, year = 2007 }