In colloidal and granular systems, energy and temperature do not play a major role. The dynamics of such systems are dominated by the geometrical packing fraction of their constituents and may be described by various kinetically-constrained models [1]. We focus on the Kob-Andersen model [2], which is defined as a lattice gas with only on-site exclusion, for which particles can move to neighboring sites only if they have less than a certain number of occupied neighbors. Most previous research considered infinite systems, while actual experimental systems are finite. We consider finite-size and semi-infinite system in any dimension, which are infinite in several directions, but finite in the other directions [3,4].

By increasing the density of particles in the system, it becomes jammed, i.e. almost all the particles can never move according to the kinetic constraints. It has been proven [5-7] that a system which is infinite in all directions, gets jammed only at a density of 1, when all lattice sites are occupied by particles. We find, analytically and numerically, that non-infinite systems become jammed at some finite, size- and shape-dependent density which nears 1 as the size of the system is increased.

Because the jamming density depends on the shape of the system, it is possible to jam or unjam the system just by changing its shape, without altering its total volume or particle density, as seen in experiments [8]. In the protocol we give here, the jamming transition does not occur by exerting forces on the system, but by performing ensemble averages over systems with fixed shape and density.

References:

[1] F. Ritort and P. Sollich, Advances in Physics 52, 219 (2003)

[2] W. Kob and H. C. Andersen, Phys. Rev. E 48, 4364 (1993)

[3] E. Teomy and Y. Shokef, Phys. Rev. E 86, 051133 (2012)

[4] E. Teomy and Y. Shokef, Phys. Rev. E 89, 032204 (2014)

[5] A. E. Holroyd, Probability Theory and Related Fields 125, 195 (2003)

[6] C. Toninelli, G. Biroli, and D. S. Fisher, Phys. Rev. Lett. 92, 185504 (2004)

[7] J. Balogh, B. Bollobas, H. Duminil-Copin, and R. Morris, Trans. Amer. Math. Soc. 364, 2667 (2012)

[8] D. Bi, J. Zhang, B. Chakraborty, and R. P. Behringer, Nature 480, 355 (2011)