Granular matter is exceptionally familiar in daily life, it represents an unforeseen frontier in basic physics: Very little is comprehended about it.In a new study released just recently in the European Physical Journal E, Onuttom Narayan and Harsh Mathur, theoretical physicists at the University of California at Santa Cruz and Case Western Reserve University, respectively, shed some light on the propagation of sound through granular materials especially close to what is called “the jamming shift. The possibility that random matrix theory might be relevant to the vibrations of granular matter has important precursors. In the brand-new work, it is convincingly demonstrated for the first time that the spectra are explained by a particular flavor of random matrix theory called the Laguerre ensemble.Narayan and Mathur have actually also developed a model of the vibrations of jammed granular matter that is able to explain some of the non-universal features of the spectra. A crucial goal for future work is to combine the two associated designs into a merged description of both tension distributions and vibrational spectra.Granular matter is a tip, Mathur and Narayan stated, that one does not just have to look to the subatomic world or the universe on a cosmological scale to discover crucial unsolved essential issues: Significant and similarly difficult issues may be discovered in the daily world around us.Reference: “Vibrational spectrum of Granular packagings with random matrices” by Onuttom Narayan, and Harsh Mathur, 12 March 2024, The European Physical Journal E.DOI: 10.1140/ epje/s10189 -024 -00414- x.
Examples of granular matter: various colored plastic balls in a play area, gravel, sesame seeds and lentils (clockwise from top left). Credit: Images by Julia Kertesz, Martin Olsson, Jitender Kumar and Zyance respectively (source: Wikipedia). Coffee beans in a container and stacks of rice or sand are examples of granular matter: products composed of large numbers of macroscopic– instead of atomic scale– particles. Although granular matter is extremely familiar in daily life, it represents an unanticipated frontier in essential physics: Very little is comprehended about it.In a brand-new study released recently in the European Physical Journal E, Onuttom Narayan and Harsh Mathur, theoretical physicists at the University of California at Santa Cruz and Case Western Reserve University, respectively, shed some light on the propagation of noise through granular materials particularly near what is called “the jamming shift.” Practical Significance and Cultural RelevanceUnderstanding the homes of granular matter is very important for many practical commercial applications. Remarkably, the issue of acoustic vibrations in granular matter has just recently been a topic of conversation in pop culture: The newly released motion picture Dune has actually stimulated a debate about whether noise can propagate through sand. (The answer: it can). The strangeness of granular matter can be seen by pondering a pile of rice. If you push a stack of rice carefully, it seems strong. If you choose up some rice and let it slip through your hand, it puts like a liquid. Thus, a pile of rice is neither liquid nor solid. It is a granular material that has to be understood on its own terms.Understanding Jamming TransitionTo comprehend the jamming transition, picture pouring coffee beans through a funnel with a narrow nozzle. If the beans are poured gradually, they will stream through the nozzle, however if a lot of beans are poured into the funnel rapidly, the flow will jam. The jamming transition occurs as the flow rate is increased: The product passes abruptly from a flowing state to a jammed one.In the laboratory, researchers usually study packs of polystyrene beads which are more open to experimentation than coffee beans. It is discovered that such bead packs undergo acoustic vibrations at a set of particular frequencies. This set of particular frequencies is called the spectrum of the bead pack. The spectrum differs from bead pack to bead pack, so the problem is to establish an analytical understanding of the type of spectra that might arise.Theoretical DevelopmentsBuilding on essential prior work by lots of researchers, specifically Yaroslav Beltukov (Ioffe Institute in Russia) and Giorgio Parisi (Sapienza University of Rome), Narayan and Mathur reveal there are specific analytical functions of the spectra that are universal, while other features are non-universal. In this context, universal describes functions that would be shared by the vibrational frequencies of any sufficiently complex system; non-universal to features specific to jammed granular matter.Narayan and Mathur show that the universal features of the spectra are described by random matrix theory, a branch of mathematics established by nuclear physicists in the 1950s. The possibility that random matrix theory might be relevant to the vibrations of granular matter has essential precursors. In the new work, it is convincingly shown for the very first time that the spectra are described by a specific taste of random matrix theory called the Laguerre ensemble.Narayan and Mathur have also established a model of the vibrations of jammed granular matter that is able to explain some of the non-universal functions of the spectra. This design carefully looks like a model established by Narayan several years ago that was planned to resolve a different important puzzle about granular matter: how stress is distributed in bead loads that are compressed.Finding a merged description of different phenomena is a significant goal of essential physics. An essential goal for future work is to merge the 2 related designs into a combined description of both stress circulations and vibrational spectra.Granular matter is a tip, Mathur and Narayan said, that one does not only have to seek to the subatomic world or the universe on a cosmological scale to discover essential unsolved basic issues: Equally difficult and significant problems may be found in the daily world around us.Reference: “Vibrational spectrum of Granular packings with random matrices” by Onuttom Narayan, and Harsh Mathur, 12 March 2024, The European Physical Journal E.DOI: 10.1140/ epje/s10189 -024 -00414- x.
