Hyperuniformity near jamming transition over a wide range of bidispersity

Abstract

We numerically investigate hyperuniformity in two-dimensional frictionless jammed packings of bidisperse systems. Hyperuniformity is characterized by the suppression of density fluctuations at large length scales, and the structure factor asymptotically vanishes in the small-wavenumber limit as $S(q)\propto q^{\alpha }$, where $\alpha >0$. It is well known that jammed configurations exhibit hyperuniformity over a wide range of wavenumbers windows, down to $q^{\ast }\sigma \approx 0.2$, where $\sigma$ is the particle diameter. In two dimensions, we find that the exponent $\alpha$ is approximately $0.6\text{–}0.7$. This contrasts with the reported value of $\alpha =1$ for three-dimensional systems. We employ an advanced method recently introduced by Rissone \textit{et al.} \href{https://link.aps.org/doi/10.1103/PhysRevLett.127.038001}{[Phys. Rev. Lett. {\bf 127}, 038001 (2021)]}, originally developed for monodisperse and three-dimensional systems, to determine $\alpha$ with high precision. This exponent is found to be unchanged for all size ratios between small and large particles, except in the monodisperse case, where the system crystallizes.

arXiv comment11 pages, 9 figures

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