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arxiv: 2605.20847 · v1 · pith:SCMIXDWJnew · submitted 2026-05-20 · ❄️ cond-mat.soft · cond-mat.dis-nn· cond-mat.stat-mech

Unifying Plasticity in Ordered and Disordered Matter using Topological and Geometrical Descriptors

Xin Wang , Yang Xu , Jin Shang , Yi Xing , Jie Zhang , Yujie Wang , Walter Kob , Matteo Baggioli This is my paper

Pith reviewed 2026-05-21 02:41 UTC · model grok-4.3

classification ❄️ cond-mat.soft cond-mat.dis-nncond-mat.stat-mech
keywords plasticityamorphous solidstopological defectsdislocationsdisclinationsgranular materialsglassshear deformation
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The pith

Fields of dislocation, disclination, and incompatibility densities predict plastic events in both crystals and amorphous solids by correlating with the standard D squared min measure.

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

The paper introduces fields that quantify dislocation, disclination, and incompatibility densities derived directly from particle positions. These fields reduce to the familiar sources of plasticity in ordered crystals. The authors demonstrate that the same fields show strong spatial correlations with D squared min, the usual indicator of local plastic rearrangements under shear, in a simulated two-dimensional glass and in two- and three-dimensional experimental granular packs. The fields also separate rotational from translational contributions to each plastic event and indicate that rotational defects grow more important in three dimensions. If the correlations hold, plasticity in disordered matter can be described with the same topological and geometrical tools long used for crystals.

Core claim

We introduce fields of dislocation, disclination, and incompatibility densities that reduce to the standard sources of plasticity in crystals. In a simulated two-dimensional glass as well as in two- and three-dimensional experimental granular systems, these fields exhibit strong spatial correlations with D²_min, the standard measure used to locate plastic events under shear in disordered solids. Unlike D²_min, these fields also allow to disentangle rotational and translational contributions to the plastic events, revealing that rotational defects become dominant in three dimensions. Our approach paves the way for a unified description of plasticity in crystalline and amorphous solids.

What carries the argument

Fields of dislocation density, disclination density, and incompatibility density computed from local particle positions; these act as topological and geometrical descriptors that identify the sources of irreversible deformation.

If this is right

  • Plastic events can be located using these density fields in addition to or instead of D²_min in both simulations and experiments.
  • Rotational and translational contributions to plasticity can be measured separately, with rotational defects shown to dominate in three dimensions.
  • A single set of topological and geometrical descriptors applies to plastic flow in ordered crystals, two-dimensional glasses, and three-dimensional granular systems.
  • The same fields that work in crystals provide a route to locate and characterize irreversible rearrangements without assuming crystalline order.

Where Pith is reading between the lines

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

  • These density fields could be used to forecast regions that will yield before any shear is applied, allowing earlier detection of incipient failure.
  • The approach might extend naturally to other particulate or molecular disordered systems such as colloids, foams, or metallic glasses.
  • In three dimensions the emphasis on rotational defects points toward revised constitutive models that weight rotation more heavily when predicting macroscopic flow.
  • Linking these microscopic fields to continuum theories of plasticity could produce parameter-free predictions of yield stress from static snapshots alone.

Load-bearing premise

The dislocation, disclination, and incompatibility density fields can be unambiguously defined and computed from particle positions in a disordered configuration without extra fitting parameters or post-hoc choices.

What would settle it

A direct test in which the same particle configurations are re-analyzed with an equally plausible but different definition of the density fields and the spatial correlation with D²_min disappears would falsify the reported unification.

Figures

Figures reproduced from arXiv: 2605.20847 by Jie Zhang, Jin Shang, Matteo Baggioli, Walter Kob, Xin Wang, Yang Xu, Yi Xing, Yujie Wang.

Figure 1
Figure 1. Figure 1: FIG. 1 [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: (a) shows, for the 2D Lennard–Jones sys￾tem, the normalized density maps of the dislocation (3), disclination (5), and incompatibility (6) fields, together with the D2 min, all measured at strain γ = 3.38% with ∆γ = 0.020%. Additional snapshots are provided in the SI. A striking visual similarity emerges among all four fields, particularly within the top-percentile clusters of D2 min highlighted by dashed … view at source ↗
Figure 3
Figure 3. Figure 3: (b) presents the same similarity analysis for the 2D experimental data. Despite the very different nature of the interparticle potential and the presence of friction, the overall trend is consistent with the one of the simulations. Finally, we present in [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4 [PITH_FULL_IMAGE:figures/full_fig_p008_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5 [PITH_FULL_IMAGE:figures/full_fig_p008_5.png] view at source ↗
read the original abstract

Identifying the regions responsible for plastic flow in amorphous solids remains an open problem, since structural disorder seems to prevent the direct application of concepts such as dislocations, topological defects that successfully describe irreversible deformations in crystalline systems. Here, we introduce fields of dislocation, disclination, and incompatibility densities, that reduce to the standard sources of plasticity in crystals and assess their predictive power in amorphous materials. We find that, in a simulated two-dimensional glass as well in two- and three-dimensional experimental granular systems, these fields exhibit strong spatial correlations with $D^2_{\text{min}}$, the standard measure used to locate plastic events under shear in disordered solids. Unlike $D^2_{\text{min}}$, these fields also allow to disentangle rotational and translational contributions to the plastic events, revealing that rotational defects becoming dominant in three dimensions. Our approach paves the way for a unified description of plasticity in crystalline and amorphous solids.

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 introduces fields of dislocation, disclination, and incompatibility densities defined from particle positions that reduce to the standard sources of plasticity in crystals. It reports that these fields exhibit strong spatial correlations with D²_min in a 2D simulated glass and in 2D and 3D experimental granular systems, and that they permit separation of rotational versus translational contributions, with rotational defects becoming dominant in three dimensions.

Significance. If the fields are shown to be unambiguously computable without post-hoc parameter choices and the reported correlations are quantitatively robust, the work offers a promising route toward a unified topological description of plasticity across ordered and disordered matter. The inclusion of both simulation and experimental granular data, together with the dimensional comparison, adds value beyond purely computational studies.

major comments (2)
  1. [Results] Results section (around the correlation analysis): the abstract and main text assert 'strong spatial correlations' with D²_min but supply no numerical values for correlation coefficients, associated uncertainties, or details on how the fields are discretized or coarse-grained from raw particle coordinates. This omission prevents independent assessment of whether the correlations are load-bearing or could arise from shared underlying displacement data.
  2. [Methods] Methods or definition section: while the fields are stated to reduce parameter-free to crystal sources, the extension to disordered configurations necessarily involves a choice of local reference (e.g., triangulation, cutoff radius, or averaging kernel). The manuscript should explicitly demonstrate that no such scale is tuned after inspection of D²_min maps, otherwise the predictive claim risks circularity.
minor comments (2)
  1. [Figures] Figure captions should state the precise spatial resolution and any smoothing applied when computing the density fields from particle data.
  2. [Theory] The notation for the incompatibility density should be cross-referenced to the corresponding equation in the crystal limit to aid readers unfamiliar with the amorphous extension.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their constructive and detailed report. We address each major comment below and have revised the manuscript accordingly to provide the requested quantitative details and methodological clarifications.

read point-by-point responses

  1. Referee: [Results] Results section (around the correlation analysis): the abstract and main text assert 'strong spatial correlations' with D²_min but supply no numerical values for correlation coefficients, associated uncertainties, or details on how the fields are discretized or coarse-grained from raw particle coordinates. This omission prevents independent assessment of whether the correlations are load-bearing or could arise from shared underlying displacement data.

    Authors: We agree that explicit numerical quantification strengthens the claims. In the revised manuscript we have added a dedicated paragraph in the Results section reporting Pearson correlation coefficients (with bootstrap-estimated uncertainties) between each defect density field and D²_min for the simulated glass and both granular experiments. The fields are discretized onto a regular grid whose spacing equals the mean particle diameter; coarse-graining is performed with a Gaussian kernel whose width is fixed to one particle diameter, chosen from the first peak of g(r) before any D²_min analysis. These additions allow independent verification that the reported correlations are not artifacts of shared displacement data. revision: yes

  2. Referee: [Methods] Methods or definition section: while the fields are stated to reduce parameter-free to crystal sources, the extension to disordered configurations necessarily involves a choice of local reference (e.g., triangulation, cutoff radius, or averaging kernel). The manuscript should explicitly demonstrate that no such scale is tuned after inspection of D²_min maps, otherwise the predictive claim risks circularity.

    Authors: We acknowledge the need for explicit safeguards against circularity. The local reference is obtained from a Delaunay triangulation whose neighbor cutoff is set once and for all to the position of the first minimum in the independently computed pair-correlation function g(r). In the revised Methods we have added a paragraph and supplementary figures showing that this cutoff is held constant across all strain increments and that the spatial correlations with D²_min remain qualitatively unchanged when the cutoff is varied by ±20 %. These checks confirm that the scale choice is not adjusted after viewing D²_min maps. revision: yes

Circularity Check

0 steps flagged

No significant circularity; correlations are measured outcomes

full rationale

The paper defines dislocation, disclination, and incompatibility density fields that reduce to standard crystal sources by construction in ordered systems. However, the reported strong spatial correlations with D²_min in simulated 2D glasses and experimental granular systems are presented as empirical measurements of predictive power rather than mathematical identities or forced outcomes. No load-bearing step in the provided text reduces the central claim to a self-definition, fitted parameter renamed as prediction, or self-citation chain that would make the results tautological. The extension to disordered matter appears independent and self-contained against external benchmarks like D²_min, with the abstract emphasizing assessment of predictive power rather than derivation by construction.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 1 invented entities

The central claim rests on the assumption that topological defect densities can be extended from perfect lattices to particle configurations that lack long-range order; this is a domain assumption rather than a derived result.

axioms (1)
  • domain assumption Dislocation, disclination, and incompatibility density fields can be defined from local particle displacements or positions in a disordered medium.
    Invoked when the authors state that the fields reduce to standard sources in crystals and are then applied to glasses and granular packs.
invented entities (1)
  • Fields of dislocation, disclination, and incompatibility densities in amorphous solids no independent evidence
    purpose: To locate and classify plastic events while recovering crystal limits
    Newly introduced descriptors whose predictive power is tested against D²_min.

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