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arxiv: 2509.25932 · v3 · submitted 2025-09-30 · ❄️ cond-mat.soft

Quaking in Soft Granular Particles with Speed-dependent Friction: Role of Critical Volume Fraction and Inertia

Wei-Chang Lo , Jih-Chiang Tsai This is my paper

Pith reviewed 2026-05-18 12:49 UTC · model grok-4.3

classification ❄️ cond-mat.soft
keywords soft granular particlesquakingspeed-dependent frictioncritical volume fractiongrain inertiastick-slip fluctuationsStribeck-Hertz model
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The pith

Soft granular particles quake only when volume fraction exceeds a material-parameter critical value, independent of driving rate.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

This continuation of prior work uses simulations with a speed-dependent friction model across many driving speeds to study grain inertia effects on quaking. The central finding is that quaking requires the volume fraction to exceed a critical value φ_c. This φ_c depends only on material parameters and is unaffected by the driving rate. Inertia from the grains suppresses quaking, which narrows the conditions for quaking as speed rises and eliminates it at very high shear rates.

Core claim

Using the Stribeck-Hertz model in simulations over a wide range of driving speeds, we find that having the volume fraction exceeding a critical value φ_c is a necessary condition for the quaking to occur, and that the value of φ_c is determined by material parameters only, independent of the driving rate. The effect of grain inertia generally suppresses the occurrence of quaking, and state diagrams exhibit a progressive narrowing of the quaking regime as the driving speed increases and the disappearance of quaking at an extremely high shear rate.

What carries the argument

Stribeck-Hertz model that incorporates speed-dependent friction to reproduce rate-dependent stick-slip and to determine the critical volume fraction φ_c necessary for quaking.

If this is right

  • Quaking cannot occur if the volume fraction is below the critical value at any driving rate.
  • The critical volume fraction φ_c remains constant across different driving rates because it is set by material parameters.
  • Grain inertia reduces the likelihood of quaking, shrinking the parameter space where it is observed.
  • Quaking disappears entirely once the shear rate becomes extremely high due to inertial suppression.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • Controlling the volume fraction in granular systems could be used to avoid or promote quaking in applications like material handling.
  • Varying material properties in experiments could directly test the predicted independence of φ_c from rate.
  • The inertial suppression suggests a crossover to smooth flow at high speeds without stick-slip events.
  • Similar critical fractions may govern dynamics in other soft matter systems with velocity-dependent friction.

Load-bearing premise

The Stribeck-Hertz friction model and the simulation parameters accurately capture the experimental quaking dynamics for the full range of speeds studied.

What would settle it

An experiment or simulation demonstrating quaking at a volume fraction below the predicted φ_c or showing that φ_c varies with driving rate would disprove the necessity and independence claims.

Figures

Figures reproduced from arXiv: 2509.25932 by Jih-Chiang Tsai, Wei-Chang Lo.

Figure 1
Figure 1. Figure 1: FIG. 1. An example of the fluctuation of coordination num [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. The critical volume fraction [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. Time-averaged normal stresses versus the shear rates acquired from the CH model (closed symbols) and the SH model [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4. The stress ratio [PITH_FULL_IMAGE:figures/full_fig_p005_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5. Time sequences of the instantaneous stresses [PITH_FULL_IMAGE:figures/full_fig_p006_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: FIG. 6. The instantaneous stress ratios calculated from the [PITH_FULL_IMAGE:figures/full_fig_p006_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: FIG. 7. State Diagrams for granular packings governed by the SH model, at three different driving speeds: (a) [PITH_FULL_IMAGE:figures/full_fig_p007_7.png] view at source ↗
read the original abstract

Our previous numerical simulation [C.-E. Tsai et al., Physical Review Research \textbf{6}, 023065 (2024)] has shown that, for soft granular particles under quasistatic shearing, incorporating a speed-dependent friction is essential to reproduce the rate-dependent stick-slip fluctuations that have been found in the laboratory experiment [J.-C. Tsai et al., Physical Review Letters \textbf{126}, 128001 (2021)]. As a continuation, here we employ the simulation in a wide range of driving speeds to examine the role of grain inertia in the quaking dynamics. With our Stribeck-Hertz model, we find that having the volume fraction exceeding a critical value $\phi_{\text{c}}$ is a necessary condition for the quaking to occur, and that the value of $\phi_{\text{c}}$ is determined by material parameters only, independent of the driving rate. The effect of grain inertia generally suppresses the occurrence of quaking, and we conclude by presenting the state diagrams which exhibit a progressive narrowing of the quaking regime as the driving speed increases and the disappearance of quaking at an extremely high shear rate.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 3 minor

Summary. The manuscript extends prior simulations of soft granular particles under quasistatic shear with a Stribeck-Hertz speed-dependent friction model to a broad range of driving speeds. It reports that quaking requires the packing fraction to exceed a critical value φ_c fixed by material parameters alone and independent of rate; grain inertia suppresses quaking and progressively narrows the quaking regime in state diagrams until quaking vanishes at sufficiently high shear rates.

Significance. If the rate independence of φ_c is robustly demonstrated, the work supplies a material-parameter-based criterion that separates frictional from inertial contributions to stick-slip dynamics in soft granular media. The state diagrams offer a compact visualization of how inertia shrinks the quaking window, which could inform both experiments and continuum models of rate-dependent granular flow.

major comments (2)
  1. [§4] §4 (Results on volume-fraction dependence): The central claim that φ_c is independent of driving rate rests on simulations that detect quaking via stress-drop amplitude or power-spectrum thresholds. No explicit statement is given of how these detection thresholds are held fixed across rates or whether they were validated against changes in inertial number; a rate-dependent shift in the operational definition of 'quaking occurs' would undermine the reported independence even if material parameters remain constant.
  2. [§3] §3 (Simulation methods): The manuscript provides no convergence tests, time-step sensitivity analysis, or contact-stiffness checks. Because the Stribeck-Hertz transition velocity is fixed while shear rate varies, any numerical damping that masks weak events differently at high speed could artifactually move the apparent lower boundary of the quaking regime, directly affecting the claim that φ_c is determined solely by material parameters.
minor comments (3)
  1. [Abstract] Abstract: The citation to the prior PRL experiment should include the year (2021) for immediate readability.
  2. [Figures] Figure captions (state diagrams): Axes should explicitly state whether shear rate is expressed in dimensionless inertial number or dimensional units, and whether the color scale represents fluctuation amplitude or occurrence probability.
  3. [§2] Notation: The symbol φ_c is introduced without a clear operational definition (e.g., the precise fluctuation threshold) in the main text; a short sentence linking it to the detection criterion used in the figures would help.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the positive assessment of our work and for the constructive comments that help strengthen the presentation of our results on the rate independence of φ_c. We address each major comment below and will revise the manuscript to incorporate the requested clarifications and validations.

read point-by-point responses

  1. Referee: [§4] §4 (Results on volume-fraction dependence): The central claim that φ_c is independent of driving rate rests on simulations that detect quaking via stress-drop amplitude or power-spectrum thresholds. No explicit statement is given of how these detection thresholds are held fixed across rates or whether they were validated against changes in inertial number; a rate-dependent shift in the operational definition of 'quaking occurs' would undermine the reported independence even if material parameters remain constant.

    Authors: We agree that documenting the fixed thresholds is essential to substantiate the rate independence of φ_c. The stress-drop amplitude threshold (set to capture events larger than typical fluctuations in the non-quaking regime) and the power-spectrum peak criterion were deliberately held constant across all simulated shear rates, with values chosen from the well-characterized quasistatic limit. To address the concern directly, the revised manuscript will include an explicit description of these fixed thresholds together with supplementary analysis showing that the identified quaking boundaries remain unchanged when the inertial number is varied within the explored range. This addition will confirm that the operational definition does not shift artificially with rate. revision: yes

  2. Referee: [§3] §3 (Simulation methods): The manuscript provides no convergence tests, time-step sensitivity analysis, or contact-stiffness checks. Because the Stribeck-Hertz transition velocity is fixed while shear rate varies, any numerical damping that masks weak events differently at high speed could artifactually move the apparent lower boundary of the quaking regime, directly affecting the claim that φ_c is determined solely by material parameters.

    Authors: We acknowledge that the manuscript does not present explicit convergence tests. The integration time step and contact stiffness were selected following standard DEM criteria to keep particle overlaps below 1 % and to resolve the shortest contact times, with the Stribeck-Hertz parameters held fixed. In the revised version we will add a dedicated paragraph (or supplementary section) reporting time-step and stiffness convergence checks performed at both low and high shear rates. These tests will verify that the detected quaking events and the location of φ_c are insensitive to the numerical parameters, thereby excluding differential masking of weak events as a source of the observed rate independence. revision: yes

Circularity Check

0 steps flagged

No circularity in derivation of rate-independent φ_c from simulations

full rationale

The paper's central result—that φ_c is fixed by material parameters alone and independent of driving rate—is obtained by running the Stribeck-Hertz model at multiple shear rates while keeping all material parameters constant and inspecting the onset of detectable quaking fluctuations in the output time series. This threshold is an observed feature of the simulated dynamics, not a quantity defined in terms of itself or fitted to the target observable. Prior self-citations supply the friction model and experimental context but do not substitute for the new rate-variation scans; the independence claim remains directly falsifiable by repeating the protocol with altered parameters or numerics. No equation or definition reduces to its own input by construction, and the work is therefore self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

Abstract provides no explicit list of free parameters or axioms; φ_c is stated to be fixed by material parameters but the specific parameters and fitting procedure are not described.

axioms (1)
  • domain assumption The Stribeck-Hertz model captures the essential speed-dependent friction needed to produce quaking
    Invoked as the basis for all reported simulation results

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