Abstract: I will briefly review the problem of random close packing (or maximally random jammed packings) of spheres, starting from the statistical physics of hard sphere systems, for which analytical results were developed in the 20th century and early 21st century by, among others, Percus, Lebowitz, Stillinger and Torquato, Edwards, Parisi and others. I will then show how an analytical closed-form solution for the random close packing volume fractions in d=2 and d=3 can be built from the Percus-Yevick solution to the many-body hard sphere hierarchy in the liquid state [1]. A robust justification to the assumptions used (i.e. 1-the use of liquid state theory at jamming, and, 2-the use of the ordered close packing FCC condition as an effective boundary condition) has been provided in [2] based on new numerical calculations with the Jiao-Torquato algorithm. I will then show how the analytical solution can be extended to make predictions of RCP volume fractions for polydisperse and bidisperse hard sphere systems [2], which capture the trends as a function of the size polydispersity, or the size asymmetry, in good agreement with numerical simulations. In the final part of the talk, I will present closed-form results for the elasticity of random sphere packings [3] and recent developments for the plasticity of amorphous solids, where unexpected topological defects have been recently discovered [4].

[1] A. Zaccone, Phys. Rev. Lett. 128, 028002 (2022)

[2] C. Anzivino et al., J. Chem. Phys. 158, 044901 (2023)

[3] A. Zaccone & E. Scossa-Romano, Phys. Rev. B 83, 184205 (2011)

[4] M. Baggioli et al., Phys. Rev. Lett. 127, 015501 (2021)