Sound moving through a jammed granular material appears to change in how quickly it loses strength, a process known as attenuation, at a pressure-dependent crossover, according to a particle-based computer model. At lower frequencies, the simulations show particles moving coherently and attenuation increasing with the square of frequency. Above the crossover, the model identifies scattering modes, their decay becomes only weakly dependent on frequency, and particles no longer move in step.
The work is an arXiv preprint, version 1, dated 28 Aug 2026. It asks why attenuation in fluid-saturated granular media changes from a quadratic to a linear frequency dependence, using both damped acoustic modes, patterns of vibration that fade over time, and driven waves.
Inside the numerical experiment
The calculation varied three dimensionless, or scaled, quantities: pressure, driving frequency and grain-contact damping. Each packing contained equal numbers of small and large disks. The large disks measured 1.4 times the small-particle diameter, and starting positions and velocities were randomized subject to zero net momentum.
For wave propagation, the researchers tiled channels with units containing 100, 400 or 1,600 particles. Neighboring contacts were treated as permanent linear springs, so the simulations did not allow contacts to form or break.
To calculate the fading vibration patterns, the study used standard eigensolvers for small systems and contour-integral techniques for low-frequency large systems. Each mode was recorded with a value combining its oscillation frequency and decay rate. For driven waves, linear least-squares fits to logarithmic amplitudes and phase supplied estimates of spatial attenuation and wavenumber, a measure of how quickly the wave's phase changes in space. The calculation then used the driving frequency and fitted wavenumber to estimate phase velocity, the speed at which the wave pattern travels.
The crossover is visible in two ways
The report places the critical dimensionless frequency at the square root of dimensionless pressure. It says scattering modes occupy the intermediate band above that threshold and below normalized frequency 1, where their decay is weakly dependent on frequency. A conflicting sign in the Figure 4 caption means the exact printed pressure relation should be read cautiously.
Below the crossover, modal decay was proportional to grain-contact damping and to the square of modal frequency. At the wave level, both compression and shear waves showed the same viscous-like, quadratic frequency dependence. In that coherent regime, sideways motion was much smaller than motion along the wave direction.
Above the crossover, sideways and along-wave amplitudes became comparable, and particles no longer moved in step, meaning phase coherence was lost. The matching change in the modal and wave calculations is consistent with the authors' proposed picture that disordered contact-network modes scatter acoustic energy and produce high-frequency, near-linear attenuation.
The details depend on the wave
The detailed high-frequency fits did not produce one common rule for the two wave types. For shear waves, attenuation was reported to scale with frequency to the 4/3 power, while its effective dependence on damping was sublinear, with an exponent below 1. Large error bars and reduced fit fidelity make that estimate less secure.
For compression waves, the reported scaling was linear in frequency, included pressure raised to the one-quarter power and retained an effective sublinear dependence on damping. The damping exponent was not specified numerically, and attenuation at low damping was difficult to resolve.
Those caveats leave the exact high-frequency exponents less settled than the broad regime change. The report says a complete theory for the scattering regime and its remaining pressure dependence is still unresolved. It also leaves stronger damping incompletely characterized, because the mode structure changes and overdamped modes, where decay overwhelms oscillation, can appear.
A model-to-data check, with clear limits
When expressed in physical units, the model gave a crossover near 2.03 kHz. The authors describe that value as consistent with cited data changing from an attenuation slope of 2 to a slope of 1. That is a check that the model's estimate lines up with the data, not an independent experimental validation.
Wave-speed calculations provided a separate check. They reproduced the reported pressure scaling of the material's elastic stiffness measures and were largely insensitive to damping in the low-damping regime. A slight increase in experimental wave speed near the crossover was not reproduced by the calculation.
The model's reach is limited by its setup. It uses disk packings and permanent contacts, so it does not directly test real three-dimensional, polydisperse, frictional marine sediments or contact formation and breaking. The evidence is therefore a computational framework for granular acoustics, not quantitative validation in a real sediment.
The simulations also focus mainly on weak dimensionless damping. At stronger damping, mode structure can change and overdamped modes can appear, a transition the report does not fully characterize. Strong scattering and large error bars further limit precise estimates of high-frequency exponents.
Open questions include whether this qualitative pattern persists in three-dimensional, polydisperse and frictional packings, and how the scattering exponents and residual pressure dependence arise analytically. Until those tests and explanations exist, the preprint offers a proposed grain-scale account of acoustic attenuation in granular media rather than a complete theory or direct experimental proof.
Paper data and sources
Original title: Proximity to Jamming Governs Acoustic Attenuation in Damped Packings
Authors: Colton Kawamura, Derek R. Olson, Anthony P. Austin et al.
Journal/Repository: arXiv
Status: Preprint, not yet peer-reviewed
First online: 2026-08-28
DOI: Not available
Original paper · Full text