Vibrations of granular materials: Theoretical physicists reveal everyday science mysteries

Coffee beans in a jar and piles of rice or sand are examples of particulate matter: materials made up of large numbers of particles on a macroscopic rather than atomic scale. Although granular matter is very common in everyday life, it represents an unexpected frontier in fundamental physics: it is poorly understood.

In a new study recently published in the journal Nature European Physical Journal ETheoretical physicists Onuttom Narayan and Harsh Mathur, UC Santa Cruz and Case Western Reserve University respectively, reveal how sound occurs in granular materials The propagation is particularly close to the so-called “interference transformation”.

Understanding the properties of particulate matter is important for many practical industrial applications. Notably, the issue of sound vibrations in particulate matter has recently become a subject of discussion in pop culture: the newly released movie Dune sparked debate about whether sound can travel through sand (it can).

Looking at a pile of meters reveals the strangeness of granular matter. If you gently push a stack of rice, it will appear solid. But if you pick up some rice and let it slip from your hands, it will pour like a liquid. Therefore, a pile of rice is neither a solid nor a liquid. It is a granular material and must be understood on its own terms.

To understand the clogging transition, imagine pouring coffee beans into a funnel with a narrow spout. If the beans are poured slowly, they will flow through the spout, but if a large amount of beans are poured into the funnel quickly, the flow of water will become clogged. When the flow rate increases, a plugging transition occurs: the material suddenly changes from a flowing state to a plugging state.

In the lab, researchers often work with bags of polystyrene beads, which are more suitable for experiments than coffee beans. This package of microbeads was found to experience acoustic vibrations at a set of characteristic frequencies. This set of characteristic frequencies is called the spectrum of the microbead set. The spectra vary from package to package of beads, so the problem is to develop a statistical understanding of the types of spectra that may occur.

Narayan and Mathur, building on previous important work by many researchers, notably Yaroslav Beltukov (Ioffe Institute, Russia) and Giorgio Parisi (Sapienza University of Rome), showed that certain statistical features of the spectrum are universal, while others No. Universal in this context refers to characteristics common to the vibrational frequencies of any sufficiently complex system; non-universal to the specific characteristics of clogging particulate matter.

Narayan and Mathur showed that universal features of the spectrum are described by stochastic matrix theory, a branch of mathematics developed by nuclear physicists in the 1950s. There are important precursors to the possibility that random matrix theory might be applicable to the vibrations of granular matter. But in new work, it has been demonstrated convincingly for the first time that the spectrum is described by a special style of stochastic matrix theory called the Laguerre ensemble.

Narayan and Mathur also developed a vibrational model of clogging granular matter that was able to explain some of the non-general features of the spectrum. The model is very similar to one Narayan developed years ago to solve another important puzzle about particulate matter: how pressure is distributed in a compressed packet of beads.

Finding unified descriptions of different phenomena is a major goal of fundamental physics. An important goal for future work is to merge the two related models into a unified description of the stress distribution and vibration spectrum.

Mathur and Narayan say particulate matter reminds us that one needs to look beyond the subatomic world, or the universe, at a cosmological scale to find important unanswered fundamental questions. The same challenging and significant issues can be found in our daily lives around us.