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arxiv: 2604.13222 · v1 · submitted 2026-04-14 · ❄️ cond-mat.stat-mech · cond-mat.mtrl-sci

Global Oscillations in Depinning Models with Aging

F. V. Pereyra Aponte , E. A. Jagla This is my paper

Pith reviewed 2026-05-10 13:48 UTC · model grok-4.3

classification ❄️ cond-mat.stat-mech cond-mat.mtrl-sci
keywords depinningagingstick-slipavalanchesoscillationsmean fieldtwo dimensionspinning force
0
0 comments X

The pith

Incorporating aging into depinning models produces global oscillatory stick-slip stress that persists in two-dimensional short-range systems.

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

The paper extends the depinning model by adding an aging mechanism to each site's pinning force, causing it to strengthen while stuck and weaken while slipping. This change creates conditions for global stress oscillations in mean-field interactions through king avalanches and instabilities. The authors map out a phase diagram showing smooth flow, stick-slip, and bistable regimes. In two dimensions with local interactions the oscillations continue, but through alternating periods of high and low avalanche activity that track the stress cycles instead of requiring system-wide events. A reader might care because this links microscopic aging to macroscopic periodic behavior in driven disordered systems.

Core claim

We propose a model that extends the standard depinning paradigm by incorporating an aging mechanism into the local pinning force. This favors oscillations between a stuck state of large pinning, and a slipping state of smaller pinning. We show that for mean field interactions between sites this mechanism can lead to the appearance of king avalanches and global instabilities, producing a global oscillatory stick-slip stress regime. We construct the phase diagram for this mean field case and identify regions of smooth dynamics, pure stick-slip, and bistability. When considering two-dimensional systems with short-range interactions we find that states of global stress oscillation persist, but 2

What carries the argument

The aging mechanism added to the local pinning force, which increases pinning strength in stuck states and decreases it in slipping states to favor periodic switching.

Load-bearing premise

The aging is modeled with a chosen functional form that specifically promotes switching between high and low pinning states, without being derived from the underlying particle or defect physics.

What would settle it

A simulation or experiment in a two-dimensional depinning system with microscopically motivated aging that fails to show stress oscillations correlated with alternating high-low avalanche periods would disprove the persistence claim.

Figures

Figures reproduced from arXiv: 2604.13222 by E. A. Jagla, F. V. Pereyra Aponte.

Figure 1
Figure 1. Figure 1: FIG. 1: Normal (a) and reentrant (b) flow curves. In the first [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2: Scheme of an avalanche taking place in a one [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3: The form of [PITH_FULL_IMAGE:figures/full_fig_p005_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4: Comparison of analytical an numerically obtained [PITH_FULL_IMAGE:figures/full_fig_p005_4.png] view at source ↗
Figure 6
Figure 6. Figure 6: FIG. 6: (a) The form of [PITH_FULL_IMAGE:figures/full_fig_p006_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: FIG. 7: Phase diagram of the system in the [PITH_FULL_IMAGE:figures/full_fig_p007_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: FIG. 8: Standard deviation of the [PITH_FULL_IMAGE:figures/full_fig_p007_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: FIG. 9: (a) The form of [PITH_FULL_IMAGE:figures/full_fig_p008_9.png] view at source ↗
Figure 11
Figure 11. Figure 11: FIG. 11: Avalanche size distributions as a function of [PITH_FULL_IMAGE:figures/full_fig_p009_11.png] view at source ↗
Figure 12
Figure 12. Figure 12: FIG. 12: (a) One-dimensional cuts of the interface at different [PITH_FULL_IMAGE:figures/full_fig_p009_12.png] view at source ↗
Figure 13
Figure 13. Figure 13: FIG. 13: Schematic diagram of the system considered: a rigid [PITH_FULL_IMAGE:figures/full_fig_p011_13.png] view at source ↗
Figure 14
Figure 14. Figure 14: FIG. 14: Schematic evolution of the spring force [PITH_FULL_IMAGE:figures/full_fig_p011_14.png] view at source ↗
Figure 15
Figure 15. Figure 15: FIG. 15: Sketch of the development of an avalanche in mean [PITH_FULL_IMAGE:figures/full_fig_p012_15.png] view at source ↗
read the original abstract

We propose a model that extends the standard depinning paradigm by incorporating an aging mechanism into the local pinning force. This favors oscillations between a stuck state of large pinning, and a slipping state of smaller pinning. We show that for mean field interactions between sites this mechanism can lead to the appearance of ``king avalanches" and global instabilities, producing a global oscillatory stick-slip stress regime. We construct the phase diagram for this mean field case and identify regions of smooth dynamics, pure stick-slip, and bistability. Crucially, when considering two-dimensional systems with short-range interactions we find that states of global stress oscillation persist, but in contrast to the mean field case, no system-size avalanches appear. Instead, we observe alternating temporal intervals of larger and lower avalanche activity that correlate with the stress oscillations.

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

3 major / 2 minor

Summary. The manuscript extends standard depinning models by adding an aging mechanism to the local pinning force that favors transitions between high-pinning stuck states and low-pinning slipping states. In the mean-field limit this produces king avalanches and a global oscillatory stick-slip regime; a phase diagram is constructed that delineates smooth, pure stick-slip, and bistable regions. In two-dimensional short-range systems the global stress oscillations survive but appear as alternating intervals of high and low avalanche activity rather than system-spanning events.

Significance. If the reported behavior proves robust, the work shows that aging can generate global instabilities and persistent stress oscillations in depinning systems, offering a possible mechanism for stick-slip dynamics in materials or seismic contexts. The explicit contrast between mean-field and two-dimensional short-range cases is a strength, as is the direct numerical demonstration that oscillations persist without requiring system-size avalanches.

major comments (3)
  1. [§2] §2 (Model): The functional form chosen for the time-dependent pinning force is introduced directly to produce stuck-slipping cycles without derivation from microscopic physics or any test of alternative aging kernels (e.g., different relaxation rates or functional shapes). Because the central claims of king avalanches and global oscillations rest on this specific choice, the absence of robustness checks makes the generality of the mechanism unclear.
  2. [§3] §3 (Mean-field phase diagram): The phase boundaries separating smooth, stick-slip, and bistable regimes are presented without quantitative error estimates, finite-size scaling, or explicit checks against alternative aging forms; this weakens the claim that the identified regions are stable features of the model.
  3. [§4] §4 (Two-dimensional results): The reported correlation between global stress oscillations and alternating intervals of high/low avalanche activity is stated without statistical measures such as correlation coefficients, error bars on activity levels, or controls for system size; these omissions make it difficult to assess how robust the persistence of oscillations is under short-range interactions.
minor comments (2)
  1. Figure captions and axis labels in the mean-field and 2D sections would benefit from explicit statements of the aging parameters used and the number of independent runs averaged.
  2. A brief comparison to existing aging or memory effects already studied in depinning literature (e.g., in earthquake or interface models) is missing from the introduction.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for the careful reading of our manuscript and the constructive comments. We appreciate the positive assessment of the potential implications for stick-slip dynamics. We address each major comment below and indicate the changes we will implement in the revised version.

read point-by-point responses

  1. Referee: [§2] §2 (Model): The functional form chosen for the time-dependent pinning force is introduced directly to produce stuck-slipping cycles without derivation from microscopic physics or any test of alternative aging kernels (e.g., different relaxation rates or functional shapes). Because the central claims of king avalanches and global oscillations rest on this specific choice, the absence of robustness checks makes the generality of the mechanism unclear.

    Authors: We agree that the specific functional form of the aging term is introduced phenomenologically rather than derived from a microscopic model. The form is chosen as a minimal way to implement a time-dependent pinning force that favors stuck-to-slipping transitions. While a full microscopic derivation lies outside the scope of this work, we have verified that the main qualitative features (oscillations and king avalanches) remain stable under moderate variations of the aging rate. In the revision we will add a paragraph in §2 explaining the motivation for the chosen kernel and include a short robustness test using an alternative exponential relaxation form, confirming persistence of the global oscillatory regime. revision: partial

  2. Referee: [§3] §3 (Mean-field phase diagram): The phase boundaries separating smooth, stick-slip, and bistable regimes are presented without quantitative error estimates, finite-size scaling, or explicit checks against alternative aging forms; this weakens the claim that the identified regions are stable features of the model.

    Authors: The phase boundaries were obtained from direct numerical integration of the mean-field equations. We acknowledge that the original presentation lacked explicit error bars and finite-size analysis. In the revised manuscript we will add error estimates obtained from ensemble averages over independent realizations and include a brief discussion of finite-size effects on the location of the boundaries. We will also add a comparison of the phase diagram for the original aging kernel versus an alternative form to demonstrate that the three regimes remain robust. revision: yes

  3. Referee: [§4] §4 (Two-dimensional results): The reported correlation between global stress oscillations and alternating intervals of high/low avalanche activity is stated without statistical measures such as correlation coefficients, error bars on activity levels, or controls for system size; these omissions make it difficult to assess how robust the persistence of oscillations is under short-range interactions.

    Authors: We agree that quantitative statistical support would strengthen the 2D results. The original figures showed the correlation visually. In the revision we will compute and report the Pearson correlation coefficient between the global stress signal and the time-dependent avalanche activity rate, together with error bars on the mean activity levels in the high- and low-activity intervals. We will also present data for several system sizes (L = 64, 128, 256) to confirm that the alternating activity pattern and the associated stress oscillations persist in the absence of system-spanning events. revision: yes

Circularity Check

0 steps flagged

No circularity; results from direct simulation of proposed model

full rationale

The paper introduces an aging mechanism into the pinning force as a modeling choice that favors stuck-slipping oscillations, then reports emergent behaviors (king avalanches, global stick-slip in mean-field; alternating avalanche activity in 2D) obtained via numerical integration of the resulting dynamics. No equation reduces any reported phenomenon to a fitted parameter or input by construction. No self-citations, uniqueness theorems, or ansatzes imported from prior work by the authors are invoked as load-bearing steps. The derivation chain is self-contained: model definition to simulation output, with the functional form serving as an explicit assumption rather than a hidden tautology.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The central claim rests on the introduction of a time-dependent aging rule for pinning forces whose precise functional form is not derived from first principles but postulated to produce the desired stuck-slipping oscillation.

axioms (1)
  • domain assumption Aging mechanism incorporated into local pinning force favors oscillations between stuck and slipping states
    This is the core modeling choice that generates the reported global instabilities.

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