Host: 叶方富研究员

Abstract:

Predicting the densest random disc packing fraction is relevant to a range of disciplines and technologies. It was an unsolved problem for many decades. Two difficulties hindered a general solution in the past: the absence of a clear disorder criterion makes the problem ill-defined and the density depends on the packing protocol, giving rise to an infinite parameter space.

In this talk, I present an approach that made it possible to solve the problem theoretically. Theapproach consists of first bypassing the infinite parameter space difficulty by parameterising all packings by their cell order distribution (COD). Then, an a-priori disorder criterion is formulated to make sure that any solution yields a disordered packing. Finally, I identify the densest disordered COD.

I describe the application of the method to solve the problem for mono-disperse discs, for which the random close packing fraction is found to be φRCP = 0.852514….

I next use the method to determine the theoretical value of φRCP for bi-disperse systems, where it is not a number but a function of the size ratio and concentration of small discs.

The method itself is useful beyond the random close packing problem, for example to predict the highest packing fraction for specific packing protocols, as I hope to have time to illustrate. It can also be extended to determine the loose random packing.

References

1. R. Blumenfeld, Disorder Criterion and Explicit Solution for the Disc Random Packing
Problem, Phys. Rev. Lett. 127, 118002 (2021); Phys. Rev. Lett. 127, 259901 (2021)
2. R. Blumenfeld, Random close packing fraction of bidisperse discs: Theoretical derivation and
exact bounds, https://arxiv.org/pdf/2509.20132 (2026)

About the speaker:

Professor Raphael Blumenfeld is a theoretical physicist based at the University of Cambridge, a Senior Research Fellow at Imperial College London, and a distinguished Visiting Professor at Central South University, China. He got his Ph.D. in Physics at Tel Aviv University. Professor Raphael Blumenfeld’s research focuses on the physics of granular materials with particular emphasis on stress propagation, mechanical stability, and the collective behavior of granular systems. For his detailed contribution in the field please visit his Web at https://rafi.blumenfeld.co.uk.

Inviter: 厚美瑛研究员（mayhou@iphy.ac.cn）