Modelling vibration patterns in granular materials

The ‘Laguerre ensemble’ statistical model can better describe the vibrational patterns of granular materials at a critical point of transition in their behaviour.

New York | Heidelberg, 24 May 2024

Granular materials are collections of solid particles which can behave in similar ways to both solids and liquids via interactions between grains. Previously, researchers have explored how the behaviours of these materials can be described in the language of statistical mechanics.

Through new research published in EPJ E , Onuttom Narayan at the University of California, together with Harsh Mathur at Case Western Reserve University, show how the characteristic vibrational patterns associated with granular materials at the point where they transition to more solid-like states can be reproduced more accurately. The work could help researchers to gain a deeper understanding of how granular materials behave.

In turn, these insights could be applied across a wide range of scenarios where granular materials can be found: from improvements to the materials used in manufacturing and construction, to better early warning systems for natural disasters, such as landslides and avalanches.

Granular materials are especially challenging to study since their properties are subject to constant fluctuations, which cause their grains to re-arrange themselves. One particularly important behaviour is called the ‘jamming transition’, beyond which a granular material will behave more like a solid.

Jamming transitions occur when their grains reach a critical density, preventing them from flowing past each other. At this point, granular materials will display acoustic vibrations at a characteristic set of frequencies, named a ‘vibrational spectrum’.

In their study, Narayan and Mathur investigated two different approaches for statistically modelling the key features of these vibrational spectra. They discovered that a type of model named a ‘Laguerre ensemble’ shows close agreement with the vibrational spectra of simulated granular materials at their jamming transitions.

By building on these results, the duo hopes that researchers in future studies could develop more accurate statistical models of granular materials.

Reference: Narayan, O., Mathur, H. Vibrational spectrum of Granular packings with random matrices. Eur. Phys. J. E 47, 19 (2024). https://doi.org/10.1140/epje/s10189-024-00414-x