We investigate the dynamics of an ensemble of smooth elastic or inelastic hard spheres confined between two horizontal plates separated a distance of the order of the diameter of the particles, in such a way that the system is quasi-two-dimensional. A kinetic equation is formulated that accurately describes the dynamics of the system in the low density limit [1]. When the particles collides elastically, the equation is used to study the self-diffusion process. When the particles are inelastic and the walls vibrates vertically, the system reaches a stationary state that can be spatially homogeneous or not depending on the parameters. The kinetic equation is used to derive an equation of state that explains this phenomenology [2].
[1] J. J. Brey, M. I. García de Soria , and P. Maynar, ``Dynamics and
kinetic theory of hard spheres under strong confinement'',
Phys. Rev. E 110, 034127 (2024).
[2] P. Maynar, M. I. García de Soria, and J. J. Brey, ``Understanding
an instability ini vibrated granular monolayers'', Phys. Rev. E 99,
032903 (2019).
A. Puglisi