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arxiv: 2601.22933 · v2 · submitted 2026-01-30 · ❄️ cond-mat.mtrl-sci · nlin.AO

Resolving Structural Avalanches in Amorphous Carbon with Arclength Continuation

Fraser Birks , Ibrahim Ghanem , Lars Pastewka , James Kermode , Maciej Buze This is my paper

Pith reviewed 2026-05-16 09:19 UTC · model grok-4.3

classification ❄️ cond-mat.mtrl-sci nlin.AO
keywords amorphous carbonshear transformationsplastic avalanchesenergy landscapenumerical continuationmachine-learned potentialstress drops
0
0 comments X

The pith

Pseudo-arclength continuation decomposes avalanches in amorphous carbon into distinct shear transformations with separated energy minima before onset.

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

The paper establishes that plastic avalanches in amorphous solids can be systematically resolved by tracing the underlying energy landscape with a continuation technique rather than standard time-stepping simulations. This approach breaks each avalanche into its component shear transformations and maps how their energies change with applied strain. A key result is that these avalanches exist as a latent chain of well-separated local minima even before the collective event begins. The same continuation framework produces an event-driven description of the dynamics, so measured quantities such as stress-drop distributions no longer depend on the chosen time increment.

Core claim

In amorphous carbon modeled by a machine-learned interatomic potential, a pseudo-arclength numerical continuation framework decomposes avalanches into constituent shear transformations and determines their strain-dependent energetics. Prior to onset, avalanches possess a latent structure consisting of well-separated local minima. The continuation method also supplies an event-driven framework for avalanche dynamics that eliminates time-step effects on statistical properties such as stress-drop distributions.

What carries the argument

Pseudo-arclength numerical continuation framework that traces continuous paths on the potential energy surface while strain is increased, locating successive minima and saddle points without relying on discrete time steps.

If this is right

  • Each avalanche decomposes into a sequence of individual shear transformations whose energies vary with strain.
  • A latent chain of distinct local minima exists prior to the collective avalanche onset.
  • Avalanche statistics such as stress-drop size distributions become independent of the simulation time step.
  • The continuation procedure supplies an event-driven alternative to conventional molecular dynamics for following plastic events.

Where Pith is reading between the lines

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

  • The same continuation approach could be applied to other amorphous materials to test whether pre-onset latent structures are a general feature of plasticity.
  • Event-driven continuation might allow direct computation of avalanche waiting times without the need to resolve fast inertial dynamics.
  • If the latent minima can be identified early, it may become possible to predict which regions will participate in the next avalanche before it triggers.

Load-bearing premise

The machine-learned interatomic potential accurately reproduces the true energy landscape of amorphous carbon and the continuation algorithm locates every relevant minimum and saddle without missing branches.

What would settle it

Running the identical strain protocol with a high-accuracy ab initio calculation on the same atomic configurations and checking whether the sequence of local minima and the resulting stress-drop statistics match those obtained with the machine-learned potential.

Figures

Figures reproduced from arXiv: 2601.22933 by Fraser Birks, Ibrahim Ghanem, James Kermode, Lars Pastewka, Maciej Buze.

Figure 1
Figure 1. Figure 1: FIG. 1. Structure and plastic events in amorphous carbon. [PITH_FULL_IMAGE:figures/full_fig_p001_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. The strain-dependent energy landscape of single [PITH_FULL_IMAGE:figures/full_fig_p002_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. The strain-dependent energy landscape of a six-bond [PITH_FULL_IMAGE:figures/full_fig_p003_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4. A comparison between AQS and continuation simu [PITH_FULL_IMAGE:figures/full_fig_p004_4.png] view at source ↗
Figure 1
Figure 1. Figure 1: FIG. 1. Dependence of the MEP on the initial path. (a,b) Initial and final [PITH_FULL_IMAGE:figures/full_fig_p008_1.png] view at source ↗
Figure 1
Figure 1. Figure 1: FIG. 1. A demonstration of the size and separability of the first 51 plastic [PITH_FULL_IMAGE:figures/full_fig_p016_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. A demonstration of the size and separability of the first 51 plastic [PITH_FULL_IMAGE:figures/full_fig_p017_2.png] view at source ↗
Figure 1
Figure 1. Figure 1: FIG. 1. Chain of events within an avalanche involving three bond transfo [PITH_FULL_IMAGE:figures/full_fig_p020_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. Chain of events within an avalanche involving six bond transform [PITH_FULL_IMAGE:figures/full_fig_p021_2.png] view at source ↗
read the original abstract

Plastic deformation in amorphous solids is carried by localized shear transformations that self-organize into avalanches. In amorphous carbon modeled with a machine-learned interatomic potential, we find that the energetics and organization of these avalanches can be resolved by systematically following the underlying energy landscape. With a pseudo-arclength numerical continuation framework, we decompose avalanches into constituent shear transformations and determine their strain-dependent energetics. Our analysis shows that, prior to onset, avalanches have a latent structure that consists of well-separated local minima. We further demonstrate that arclength continuation yields an event driven framework for following avalanche dynamics, eliminating time-step effects on statistical avalanche properties such as distributions of stress drops.

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 / 2 minor

Summary. The manuscript applies a pseudo-arclength numerical continuation framework to molecular dynamics trajectories of amorphous carbon modeled with a machine-learned interatomic potential. It claims to decompose plastic avalanches into sequences of individual shear transformations, to reveal a latent structure consisting of well-separated local minima prior to avalanche onset, and to obtain an event-driven description of avalanche dynamics that removes dependence on integration time step from statistical measures such as stress-drop distributions.

Significance. If the continuation paths are shown to be complete, the work supplies a concrete numerical route for extracting strain-dependent energetics of elementary plastic events directly from the many-body landscape. This could strengthen the link between microscopic shear transformations and macroscopic avalanche statistics in amorphous solids and offers a template that may be portable to other disordered materials once robustness is established.

major comments (2)
  1. [Methods (pseudo-arclength continuation)] Methods section describing the pseudo-arclength predictor-corrector scheme: no convergence tests or branch-switching diagnostics are reported for the 3N-dimensional configuration space. Without such checks, the central assertion that all relevant local minima are located and that the minima are “well-separated” remains vulnerable to missed secondary branches near strain values where multiple shear transformations become nearly simultaneous.
  2. [Results (latent structure of avalanches)] Results on latent avalanche structure: the claim that continuation yields a complete, time-step-independent decomposition rests on the untested assumption that the chosen tangent predictor step and corrector tolerance capture every saddle and minimum; a single omitted branch would render the reported strain-dependent energetics incomplete.
minor comments (2)
  1. [Abstract and Introduction] The abstract and introduction should explicitly name the machine-learned potential and the training database used, rather than referring only generically to “a machine-learned interatomic potential.”
  2. [Figures] Figure captions for the energy-landscape schematics should state the precise values of the continuation parameters (step size, tolerance) employed in the displayed trajectories.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their careful reading and for identifying key points where additional methodological validation would strengthen the manuscript. We address each major comment below and will revise the paper to incorporate the requested convergence tests, branch-switching diagnostics, and robustness checks.

read point-by-point responses

  1. Referee: [Methods (pseudo-arclength continuation)] Methods section describing the pseudo-arclength predictor-corrector scheme: no convergence tests or branch-switching diagnostics are reported for the 3N-dimensional configuration space. Without such checks, the central assertion that all relevant local minima are located and that the minima are “well-separated” remains vulnerable to missed secondary branches near strain values where multiple shear transformations become nearly simultaneous.

    Authors: We agree that explicit convergence tests and branch-switching diagnostics are necessary to rigorously support the completeness of the continuation paths in high-dimensional configuration space. In the revised manuscript we will add a dedicated subsection to the Methods section that reports systematic convergence with respect to arclength step size and corrector tolerance. We will also include branch-switching diagnostics confirming that no secondary branches appear in the strain intervals examined, thereby validating that all relevant local minima are captured and that the reported separation is not an artifact of the chosen numerical parameters. revision: yes

  2. Referee: [Results (latent structure of avalanches)] Results on latent avalanche structure: the claim that continuation yields a complete, time-step-independent decomposition rests on the untested assumption that the chosen tangent predictor step and corrector tolerance capture every saddle and minimum; a single omitted branch would render the reported strain-dependent energetics incomplete.

    Authors: We acknowledge that the completeness of the avalanche decomposition and the associated strain-dependent energetics must be demonstrated rather than assumed. In the revision we will augment the Results section with explicit tests showing that the identified local minima, energy barriers, and stress-drop statistics remain unchanged when the predictor step size and corrector tolerance are varied over a factor of ten. These checks will be presented both in the main text and in supplementary figures, directly addressing the concern that an omitted branch could affect the reported energetics. revision: yes

Circularity Check

0 steps flagged

No circularity: established numerical continuation applied to external energy landscape

full rationale

The paper's central claims follow from applying standard pseudo-arclength continuation to trace local minima in the configuration space of an amorphous-carbon simulation driven by a pre-trained machine-learned interatomic potential. Avalanche decomposition and the identification of latent, well-separated minima are direct numerical outputs of the predictor-corrector paths; they are not obtained by fitting any parameter to the target avalanche statistics inside the paper. No equation or result is defined in terms of itself, no fitted input is relabeled as a prediction, and no load-bearing uniqueness theorem or ansatz is imported via self-citation. The method is therefore self-contained against external benchmarks (the potential and the continuation algorithm) and receives a score of 0.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The work rests on the standard mathematical assumptions of pseudo-arclength continuation (smoothness of the energy landscape and existence of continuous solution branches) plus the domain assumption that the machine-learned potential accurately captures the relevant physics. No free parameters are introduced beyond those already present in the interatomic potential, and no new entities are postulated.

axioms (2)
  • domain assumption The potential energy surface is sufficiently smooth for pseudo-arclength continuation to trace solution branches between minima and saddles.
    Invoked when the framework is used to decompose avalanches and follow strain-dependent paths.
  • domain assumption The machine-learned interatomic potential reproduces the true energetics of shear transformations in amorphous carbon.
    Required for the latent-structure and energetics claims to hold outside the model.

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Reference graph

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