{"id":"9250b838-e14d-48ad-88e0-75a28292ba3f","arxiv_id":"1908.01081","paper_version":4,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":7.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":5,"one_line_summary":"During shear, the residual-stress distribution of a 2D glass acquires a system-size-dependent plateau caused by discrete stress kicks, and local yield stress changes even without local rearrangement.","lead":"Simulations of a model 2D glass show that the distribution of local distances to yielding changes under shear, developing a plateau at small distances. The work also finds that local yield stresses drift in regions that do not rearrange, a feature missing from standard coarse-grained models.","discovery_kind":"new_application","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Frozen-matrix boundary may create the plateau it attributes to mechanical-noise discreteness; no variable-R or independent-boundary test is given.","rationale":"The reader's conditional verdict is appropriate. The weakest point is the frozen-matrix boundary: the plateau and the noise cutoff are measured with the same R=5.0 protocol, and the authors' own Section V caveat concedes the plateau may appear too early because ΔσY is overestimated. This is more than a numerical nuisance: it blocks the paper's central causal attribution. The reported scaling exponents for xc and Δx_c are also not mutually consistent with a simple discreteness picture, which weakens the 'origin' claim. However, the quiescent-state validation of FM against extreme-value statistics is real evidence that FM is not universally corrupting, so the result is worth reporting conditionally. The proposed variable-R test is a clean way to decide whether the plateau is physical.","tokens_in":12771,"tokens_out":6279,"duration_ms":66395,"concrete_test":"Fix L=300 and γ=0.18, and recompute the plateau statistics (p0 as the average of P(x) for x≤10^-3, and xc as the plateau/power-law intersection) with FM regions of radius R=5.0, 7.5, 10.0, and 15.0, using the same number of independent regions for each R. If p0 or xc shifts by more than the combined bootstrap error, the plateau is controlled by the frozen boundary rather than by the bulk mechanical noise. A useful secondary check is to measure Δx_c from the same R series: if Δx_c moves with R, the FM inflation of ΔσY is the proximate cause.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The plateau claim rests on a single protocol: P(x), P(Δx), and Δx_c are all measured with the frozen-matrix (FM) setup at R=5.0. The paper itself supplies two reasons to worry. First, Section III demonstrates that R=5.0 produces an artificial second power-law regime (θ2≈1.3) from the truncation of nonaffine displacements, so the FM boundary visibly alters local relaxation. Second, Section V concedes that 'the contribution of ΔσY to Δx is somehow overestimated' and that 'the plateau thus appears sooner than in the actually sampled residual stress distributions.' If the FM boundary inflates ΔσY, it moves the measured lower cutoff Δx_c of P(Δx) to larger values; every measurement in Fig. 6 then contains the same instrumental shift, and correlating the plateau location with Δx_c is partially circular. The causal claim additionally requires an internal consistency that is not checked: if discreteness of the noise sets the plateau, the crossover should scale with the noise cutoff (xc∼Δx_c) and the plateau height with p0∼xc^θ, but the reported exponents xc∼L^-0.78 and Δx_c∼L^-1.05 disagree by a factor L^0.27, and p=0.27 with xc_exp=0.78 would imply θ≈0.35, which is not reconciled with the values of θFM used elsewhere. No R-dependence or alternative-boundary test is reported, so the plateau and its exponents remain attributable to the frozen boundary.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The manuscript uses the frozen-matrix (FM) method in a two-dimensional Lennard-Jones glass under athermal quasistatic shear to measure distributions of the local residual stress x = σY − σ0. In quenched states, P(x) shows a pseudogap form P(x) ~ x^θ with θ ≈ 0.6, consistent with extreme-value scaling of the weakest sites in unconstrained global simulations and with prior work. Under deformation, the authors report that P(x) becomes analytic at small x and develops a system-size-dependent plateau of height p0 ~ L^-p (p = 0.15 transient, p = 0.27 steady state) with a crossover xc ~ L^-0.78. They attribute this plateau to the discreteness of the mechanical noise, characterized by the lower cutoff Δxc ~ L^-1.05 of the distribution of residual-stress differences between consecutive avalanches. They also report that local yield stresses change even for regions that do not undergo plastic rearrangements, and they compare FM-derived scaling exponents with global AQS exponents, finding good agreement in the transient regime but overestimation in the steady state.","tokens_in":13081,"tokens_out":5094,"duration_ms":49792,"significance":"If the deformation-induced plateau is real, it would qualify or modify pseudogap-based scaling relations for the yielding transition, and the observation of changing local yield stress in non-yielding regions would challenge standard elastoplastic-model assumptions. The paper is commendable for cross-checking the quiescent pseudogap exponent by two independent routes (FM P(x) giving θ1 = 0.58, and global extreme-value scaling giving θ ≈ 0.61–0.65 in Fig. 2), and for using unconstrained global AQS exponents (αS, α⟨xmin⟩) as an independent falsification test of the FM-derived values. The explicit acknowledgment of FM artefacts and the discussion of conditions under which scaling relations survive (Section V) add value. However, the central plateau claim currently rests on a single protocol at R = 5.0, a region size for which the paper itself documents boundary-induced artefacts, and the reported scaling exponents are not internally consistent with the proposed noise-discreteness mechanism.","major_comments":[{"comment":"The attribution of the plateau to the discreteness of mechanical noise is internally inconsistent with the reported scaling exponents. For the form P(x) = p0 + x^θ with p0 ~ L^-p, the crossover xc where the plateau and power law balance must scale as xc ~ p0^{1/θ} ~ L^{-p/θ}. Using the steady-state values p = 0.27 and xc ~ L^-0.78 gives θ ≈ 0.35. This does not match the pseudogap exponents θFM ≈ 0.5–0.6 used in Section IV.C, nor the quiescent value θ ≈ 0.6. Furthermore, if Δxc is the microscopic discretization scale that sets the plateau, one would expect xc ~ Δxc ~ L^-1.05, not the measured xc ~ L^-0.78; the discrepancy of a factor L^0.27 is not addressed. The text's statement that the scaling of Δxc is 'reasonably close' to that of xc is not supported by the quoted exponents, and the consistency relation p = qθ should be checked explicitly or the mechanism revised.","section":"IV.B and Fig. 6"},{"comment":"The plateau is established only for R = 5.0, the same region size for which Section III documents an FM-induced second power-law regime (θ2 ≈ 1.3) caused by the truncation of nonaffine displacements at the frozen boundary. Section V concedes that the contribution of ΔσY to Δx is 'somehow overestimated' in the FM calculation and that 'the plateau thus appears sooner than in the actually sampled residual stress distributions.' Because P(x), P(Δx), and Δxc are all measured in the same FM setup, the observed correlation between the plateau entrance and Δxc (Fig. 6) is not an independent test of the causal claim. No variable-R study of the plateau or alternative boundary treatment is reported. To support the central claim of Section IV.B, the authors need to show that the plateau persists for larger R or under a different boundary condition, and that its location is not set by the FM-induced overestimate of ΔσY.","section":"III and V"},{"comment":"The paper's own global simulations provide a direct quantitative test of the plateau interpretation, and that test fails. Using αFM = d − p gives αFM = 1.85 (transient) and 1.73 (steady state), whereas the unconstrained global values are αS = 1.55 (transient) and 1.27 (steady state). The authors acknowledge this discrepancy in Section V, noting that the scaling of ⟨xmin⟩ is 'not consistent with that predicted from the plateau itself.' This admission undermines the relevance of the measured plateau for the scaling of the weakest sites, which is the quantity that the noise-discreteness mechanism is intended to explain. At minimum, the paper should reconcile the global ⟨xmin⟩ scaling with the plateau picture, or state more precisely in which observable the plateau is expected to be visible.","section":"IV.C and V"}],"minor_comments":[{"comment":"The reference for the AQS protocol is missing: 'AQS protocol []' appears without a citation. Please supply the appropriate reference or remove the empty brackets.","section":"II.B"},{"comment":"The notation is inconsistent between P(Δx), P(|Δx|), and P(σ0) in Figure 7 and the text. Since the distributions are of absolute values, please define the symbol P(|·|) once and use it uniformly.","section":"IV.B"},{"comment":"There is a typo in the text: 'reasoably close' should be 'reasonably close.'","section":"IV.B"},{"comment":"The reported exponents p = 0.15 and p = 0.27, as well as xc ~ L^-0.78 and Δxc ~ L^-1.05, are quoted without uncertainties or a description of the fitting procedure. Given that only four system sizes (L = 53, 100, 200, 300) are used, error bars or a sensitivity analysis would help assess the robustness of these values.","section":"IV.B and Fig. 6"},{"comment":"The text refers to 'Ng = 5·10^4 quenched global configurations' and 'Nℓ ≥ 2·10^5 independent local sites,' but the LaTeX macro for Nℓ appears broken in places (printed as 'N𝓁'). Please ensure the notation renders correctly.","section":"III"}],"recommendation":"major_revision","confidential_remarks":"The manuscript is honest about its limitations and the quiescent-state cross-checks are valuable. The central plateau claim, however, is not yet supported because the scaling relations among p, xc, and Δxc are internally inconsistent and because no boundary-artifact control is provided for the deformed state. The required additional analysis (larger R, or explicit reconciliation of the exponents) is within the scope of a revision, so I recommend major revision rather than rejection."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Two things to know. The paper does something genuinely new: it looks for the deformation-induced plateau in P(x) in an atomistic glass via the frozen-matrix method and finds it. Plateaus were seen in elastoplastic models, so this is a useful atomistic check. The second thing: the central causal claim—that the plateau is set by the mechanical-noise cutoff—is undercut by the authors' own numbers, and they know it. They flag the frozen-boundary artifact, the overestimated ΔσY, and the limited system sizes, but the worry goes a bit deeper. What is good: the quiescent-state analysis is careful. The pseudogap exponent is cross-checked three ways (direct FM fits, Weibull extreme-value fits, and ⟨xmin⟩~L^-α) and lands at θ≈0.6, matching literature. That is a solid calibration. The maps are informative, and the observation that σY drifts even in non-rearranging regions is genuinely new and challenges the EPM assumption ΔσY=0. The paper is also honest: Section V admits the plateau appears sooner than it should if ΔσY is overestimated. Soft spots: the plateau and its exponents rest entirely on R=5.0, one boundary protocol. The paper itself shows in Section III that R=5.0 creates an artificial second power-law regime, so the boundary is not innocent. Section V concedes the overestimate of ΔσY; this is a systematic shift that moves Δx_c and hence the purported plateau entrance. The internal consistency check fails: if discreteness sets the plateau, you'd expect x_c~Δx_c, but they report x_c~L^-0.78 and Δx_c~L^-1.05—a factor L^0.27 apart, matching the claimed p=0.27. That alone should have prompted an R-dependence or alternative-boundary test. None is reported. Net: I believe the plateau is physically real in these simulations, and the paper deserves attention from people working on elastoplastic and mean-field descriptions. But the causal interpretation—noise discreteness sets the plateau, and it changes scaling relations—is not established. The authors are closer to demonstrating it than the text admits. For peer review: yes, send it out. A serious referee will push on the exponent consistency and request R-dependence. I would cite it for the atomistic plateau and the σY-drift, not for the scaling claims.","headline":"The plateau in P(x) under shear is likely real, but this paper's own evidence does not pin its origin on noise discreteness, and the internal scaling check points the other way.","tokens_in":869,"tokens_out":1752,"would_cite":true,"duration_ms":31207,"reading_group":"maybe","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"deepseek-v4-flash","headline":"This paper argues that under athermal shear the local residual-stress distribution of an amorphous solid develops a system-size-dependent plateau at small stresses, caused by the discreteness of mechanical noise, and that local yield…","keywords":["residual stress distribution","pseudogap exponent","athermal quasistatic shear","amorphous solids","plastic flow","local yield stress","mechanical noise","avalanches"],"falsifier":"Measure $P(x)$ and the noise cutoff $\\Delta x_c(L)$ in fully unconstrained global athermal quasistatic shear simulations by tracking residual stresses in small interior subvolumes that never touch the boundary; if the plateau height $p_0$ or the cutoff exponent changes relative to the frozen-matrix values, the plateau is a boundary artefact. Alternatively, in a mesoscale model with controlled stress kicks, check whether the ratio $\\Delta x_c(L)/\\langle x_{\\min}\\rangle(L)$ grows with $L$: if it grows, the plateau dominates weak-site scaling and the $\\theta$-to-avalanche relations change; if it shrinks, the pseudogap description survives.","tokens_in":12572,"feed_emoji":"🧊","tokens_out":10327,"duration_ms":102075,"temperature":0.7,"pith_summary":"The paper asks whether the distribution of local residual stresses—the gap between a region's current stress and its yield threshold—keeps the power-law pseudogap form that theories of plastic flow assume. By deforming small circular regions of a model glass while freezing the surrounding material, the authors find the pseudogap in freshly quenched samples, with an exponent matching global yielding statistics. Once shear starts, however, the gap distribution develops a plateau at small x whose height decreases with system size, and they trace this plateau to the discreteness of the stress kicks a region receives from distant plastic events. The paper also reports that a region's local yield stress changes between events even when the region itself does not rearrange, something standard elastoplastic models leave out. A sympathetic reader would care because if the plateau is generic, finite-size scaling relations connecting the pseudogap exponent to avalanche statistics may have to be revised.","feed_headline":"Sheared glasses gain a stress-gap plateau that shrinks with size","feed_subtitle":"Atomistic simulations trace the plateau to discrete stress kicks and question scaling laws for yielding.","key_machinery":"The central tool is the frozen-matrix method: a circular region of radius roughly five particle diameters inside a two-dimensional glass is deformed under athermal quasistatic shear while a shell outside is held rigid, forcing any plastic event to occur inside the probe. Repeating this over many independent regions gives the local yield stress $\\sigma_Y$ and the residual stress $x=\\sigma_Y-\\sigma_0$. The argument is carried by the distribution $P(x)$, written as $p_0+x^\\theta$ once deformation starts, and by the companion distribution $P(\\Delta x)$ of residual-stress differences between consecutive avalanches, whose lower cutoff $\\Delta x_c$ supplies the characteristic discrete scale below which the plateau appears. Plastic events are detected with the energy-based criterion $\\kappa=(U_{\\rm aff}-U_0)/(N\\,\\delta\\gamma^2)\\ge 30$, and extreme-value statistics, through the relation $\\langle x_{\\min}\\rangle\\sim L^{-d/(1+\\theta)}$, tie local measurements to global deformation.","core_discovery":"Using the frozen-matrix method on a two-dimensional model glass under athermal quasistatic shear, the paper establishes that the distribution $P(x)$ of residual stresses $x=\\sigma_Y-\\sigma_0$ changes qualitatively once deformation starts. In the quenched state $P(x)\\sim x^{\\theta_1}$ with $\\theta_1\\approx 0.58$ in the small-$x$ region, consistent with $\\theta\\approx 0.6$ obtained from system-size scaling of the weakest site. After a few percent strain, a plateau appears at small $x$: its height scales as $p_0\\sim L^{-0.15}$ in the transient regime and $p_0\\sim L^{-0.27}$ in steady state, with the crossover to the power-law region at $x_c\\sim L^{-0.78}$. The plateau is attributed to the discreteness of the mechanical noise: the distribution of residual-stress differences between consecutive avalanches has a lower cutoff $\\Delta x_c\\sim L^{-1.05}$ that marks the entrance of the plateau. The paper also shows that the local yield stress changes on sites that do not rearrange, with $P(|\\Delta\\sigma_Y|)\\sim|\\Delta\\sigma_Y|^{-1.8}$, and argues that reliable pseudogap exponents under deformation must be extracted for $x>\\Delta x_c$.","pith_inferences":["If the plateau is set by the noise cutoff, then protocols that change the stress-kick spectrum—different interactions, spatial dimension, or an imposed external noise—should move the plateau height and crossover in a predictable way; this is testable without invoking the frozen-matrix assumption.","The measured drift of local yield stress on stable sites suggests that structural predictors of plasticity are tracking a moving target; part of the scatter in soft-spot correlations could be explained by this time-dependent threshold.","The close numerical agreement between the measured cutoff exponent ($\\approx 1.05$) and the crossover exponent ($\\approx 0.78$) is suggestive but not derived; a simulation with controlled stress kicks could determine whether the plateau entrance coincides exactly with $\\Delta x_c$ or only scales with it.","A natural extension is to measure $P(\\Delta\\sigma_Y)$ in three dimensions: if the $\\approx -1.8$ power law is universal, mesoscale descriptions should promote the local yield stress from a fixed quenched variable to an annealed, slowly fluctuating one."],"forward_implications":["In freshly quenched glasses, the frozen-matrix method recovers the pseudogap exponent $\\theta\\approx 0.6$ matching global yielding statistics, so local weak-site measurements are trustworthy at least before deformation.","Under shear, small-$x$ fits of $P(x)$ must stay above the noise cutoff $\\Delta x_c(L)$; fits that include the plateau will contaminate or bias the extracted pseudogap exponent.","If $\\Delta x_c(L)$ decays more slowly than $\\langle x_{\\min}\\rangle(L)$, the weakest-site scaling will eventually be governed by the plateau, and the standard relation between $\\theta$ and avalanche exponents $\\tau$ and $d_f$ would have to be modified.","The plateau observed in elastoplastic models is not an artefact of coarse-graining; it also appears in atomistic simulations, suggesting a common origin in discrete stress redistribution.","Local yield stress is not fixed during deformation: stable sites undergo power-law-distributed changes, so models that assume $\\Delta\\sigma_Y=0$ omit a physical source of noise."],"supporting_citations":[{"why":"Proposes the frozen-matrix idea of applying affine deformation everywhere except a small probe region; the paper's local probing protocol rests on this.","marker":"[4]"},{"why":"Shows that low local yield stresses from frozen-matrix probes coincide with the first plastic events under quasistatic shear.","marker":"[8]"},{"why":"Calibrates probe region size and correlates local yield stress maps with plastic activity, justifying the chosen probe radius.","marker":"[9]"},{"why":"Provides the energy-based criterion for detecting plastic events during athermal quasistatic shear steps.","marker":"[18]"},{"why":"Establishes extreme-value scaling and the pseudogap exponent used to validate the quiescent residual-stress distribution.","marker":"[19]"},{"why":"Gives the mean-field truncated power-law distribution of stress kicks and the size-dependent cutoff that motivates the discreteness explanation.","marker":"[22]"},{"why":"Reports the plateau form $P(x)=p_0+x^\\theta$ with size-dependent $p_0$ in mesoscale elastoplastic models, the baseline compared here.","marker":"[23]"},{"why":"Reports similar plateau and crossover scaling in another elastoplastic model, establishing the finite-size trend.","marker":"[24]"},{"why":"Shows that discrete noise steps produce deviations from scale-free behavior near an absorbing boundary, the origin invoked for the plateau.","marker":"[25]"},{"why":"Derives the scaling relations connecting the pseudogap exponent with avalanche exponents, which the plateau would modify if the noise cutoff decays slowly.","marker":"[33]"}],"fun_headline_variants":["Deformation flattens stress pseudogap into size-limited plateau","Athermal shear turns stress pseudogap into plateau, size controls","Sheared amorphous solids show size-dependent stress plateau","Pseudogap becomes plateau under athermal shear, size limits height"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The frozen matrix leaves the weakest sites statistically untouched: truncating nonaffine displacements at the frozen shell must affect only large residual stresses, not the small-x pseudogap, the deformation-induced plateau, or the drift of local yield stress.","fun_headline_variants_meta":{"raw":{"variants":["Deformation flattens stress pseudogap into size-limited plateau","Athermal shear turns stress pseudogap into plateau, size controls","Sheared amorphous solids show size-dependent stress plateau","Pseudogap becomes plateau under athermal shear, size limits height"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000459,"raw_usage":{"total_tokens":2290,"prompt_tokens":923,"completion_tokens":1367,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":539,"completion_tokens_details":{"reasoning_tokens":1295}},"tokens_in":539,"tokens_out":1367,"duration_ms":10127,"temperature":1.0,"reasoning_tokens":1295,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-14T15:24:29.220826+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Measure $P(x)$ and the noise cutoff $\\Delta x_c(L)$ in fully unconstrained global athermal quasistatic shear simulations by tracking residual stresses in small interior subvolumes that never touch the boundary; if the plateau height $p_0$ or the cutoff exponent changes relative to the frozen-matrix values, the plateau is a boundary artefact. Alternatively, in a mesoscale model with controlled stress kicks, check whether the ratio $\\Delta x_c(L)/\\langle x_{\\min}\\rangle(L)$ grows with $L$: if it grows, the plateau dominates weak-site scaling and the $\\theta$-to-avalanche relations change; if it shrinks, the pseudogap description survives.","supporting_citations":[{"cited_title":"Local elasticity map and plasticity in a model lennard-jones glass","cited_arxiv_id":null,"evidence_quote":"Proposes the frozen-matrix idea of applying affine deformation everywhere except a small probe region; the paper's local probing protocol rests on this."},{"cited_title":"11 Measuring spatial distribution of the local elastic modulus in glasses","cited_arxiv_id":null,"evidence_quote":"Shows that low local yield stresses from frozen-matrix probes coincide with the first plastic events under quasistatic shear."},{"cited_title":"Falk, Damien Vandembroucq, and Sylvain Patinet","cited_arxiv_id":null,"evidence_quote":"Calibrates probe region size and correlates local yield stress maps with plastic activity, justifying the chosen probe radius."},{"cited_title":"Lanc ¸on and L","cited_arxiv_id":null,"evidence_quote":"Provides the energy-based criterion for detecting plastic events during athermal quasistatic shear steps."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Establishes extreme-value scaling and the pseudogap exponent used to validate the quiescent residual-stress distribution."},{"cited_title":"Statistical physics of the yielding transition in amorphous solids","cited_arxiv_id":null,"evidence_quote":"Gives the mean-field truncated power-law distribution of stress kicks and the size-dependent cutoff that motivates the discreteness explanation."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Reports the plateau form $P(x)=p_0+x^\\theta$ with size-dependent $p_0$ in mesoscale elastoplastic models, the baseline compared here."},{"cited_title":"On the density of shear transforma- tions in amorphous solids","cited_arxiv_id":null,"evidence_quote":"Reports similar plateau and crossover scaling in another elastoplastic model, establishing the finite-size trend."},{"cited_title":"Mean-field description of plastic flow in amorphous solids","cited_arxiv_id":null,"evidence_quote":"Shows that discrete noise steps produce deviations from scale-free behavior near an absorbing boundary, the origin invoked for the plateau."},{"cited_title":"Ferrero, Francesco Puosi, Jean- Louis Barrat, and Kirsten Martens","cited_arxiv_id":null,"evidence_quote":"Derives the scaling relations connecting the pseudogap exponent with avalanche exponents, which the plateau would modify if the noise cutoff decays slowly."}],"review_version":1}