{"id":"36d16750-8d8b-4457-b14b-a4a3e3399726","arxiv_id":"2411.17409","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":7.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":7,"one_line_summary":"Contractile active stress in active model H drives a forward spectral cascade that turns hyperuniform phase separation into a non-hyperuniform steady state.","lead":"Direct numerical simulations of a wet active phase-separating fluid show that contractile activity, combined with fluid flow, destroys the large-scale hidden order (hyperuniformity) that normally appears during coarsening. Passive fluids and fluids with extensile activity keep the hyperuniform pattern, so the suppression is specific to the sign of the active stress.","discovery_kind":"new_application","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The reported plateau ψ(k)≈const for contractile active model H may be an artifact of the fixed-width shell average: in the 8π box the first shell (Δk=1) spans 0.25–1.25 and can mix the k→0 limit with the domain-scale peak. The paper therefore does not yet establish the asymptotic constant.","rationale":"The reader's weakest assumption was that the flat spectrum is asymptotic rather than a finite-size artifact. I agree with that direction but identify a sharper and more technical version: the shell-average estimator itself can produce an artificial plateau. Even in a larger box, a shell width of Δk=1 is not small compared with the domain-scale wavenumber, so the first shell mixes the true low-k content with the peak region. The finite-size checks in Section 3.5 compare box sizes but do not refine the spectral estimator, so they do not settle the issue. This is the single most load-bearing concern because every central claim—suppression of hyperuniformity, the H(t) transition, and the forward-cascade mechanism—is read off the same low-k spectral behavior. The flux analysis, while plausible, is an interpretation of the same affected spectra. The paper has real strengths: the distinction between contractile and extensile cases is supported by multiple diagnostics, and the larger-box runs are a genuine attempt at a finite-size check. But the plateau observation needs to be confirmed with a spectral estimator that actually resolves k much smaller than the peak wavenumber. If that test passes, the central claim stands and I would accept; as written, a conditional verdict is appropriate.","tokens_in":11092,"tokens_out":10448,"duration_ms":134438,"concrete_test":"Re-analyze the ζ=−1 steady state from the saved fields: (i) compute ψ(k) using shells of width Δk≤k0/2 down to the first resolved shell, and also plot the raw angle-resolved |φ̂(k)|² for individual modes at |k|=k0,2k0,3k0; (ii) repeat for L=8π and L=16π at matched resolution, time-averaging over at least 700 snapshots; (iii) compute the coarse-grained variance σ²(R) of φ over square sub-domains of side R. If the narrow-shell spectrum has a positive plateau for k<k*/2 and σ²(R)∼R^{-2}, the suppression is real. If it follows k^{α}, α>0, below the peak, the flat low-k signal is a shell-averaging artifact and the paper's central claim fails.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central claim depends on measuring ψ(k)=S(k)/k with S(k) defined in Eq. (13) as a shell sum over k≤|k′|<k+1. For a 2π box, k_min=1, so the 'k→0' point is actually an average over 1≤|k′|<2, which is not in the asymptotic regime. For the 8π finite-size check, k0=0.25, but if the same Δk=1 shells are used, the first shell averages over |k′|∈[0.25,1.25]. The steady-state spectral peak for contractile stress sits near the domain scale k*≈1; hence the first-shell value can be O(peak) even if the true spectrum vanishes below k*. The 2π and 8π curves in Fig. 6(f) are therefore not a controlled test of the k→0 limit. The claim 'ψ(k)→constant' needs a spectral estimator with shells narrow compared with k* and with k_min well below k*; otherwise the apparent plateau may simply be contamination of the lowest shell by the peak. This is not an internal inconsistency, but it is the weakest link in the evidence for suppression.","agreement_with_reader":"partial"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper reports direct numerical simulations of passive and active model H in two dimensions, in which a scalar order parameter is coupled to a Navier-Stokes fluid through passive or active stresses. It claims that passive model H (ζ=σ) and extensile active model H (ζ>σ) remain hyperuniform during coarsening, with spectral density ψ(k)∼k^4, whereas contractile active stress (ζ<0) arrests coarsening and drives the order-parameter spectral density to ψ(k)∼const in the steady state, i.e., a non-hyperuniform state. A scale-by-scale budget for the order-parameter spectrum is derived, and the advective transfer term is interpreted as an inverse cascade (negative flux) in the hyperuniform cases and a forward cascade (positive flux) in the contractile case. The paper also reports checks with asymmetric initial compositions and larger simulation boxes.","tokens_in":11352,"tokens_out":7160,"duration_ms":67636,"significance":"If the central claim is correct, the paper is an important counterpoint to recent results on universal hyperuniformity in dry scalar active field theories: it shows that momentum-conserving hydrodynamics combined with contractile activity can destroy the k→0 suppression of concentration fluctuations. The spectral-budget derivation is explicit and does not fit parameters to the target hyperuniformity metric, and the flux diagnostics provide a physically interpretable mechanism. The finite-size and asymmetric-quench checks are valuable. The main risk is that the conclusion is currently supported by a low-wavenumber estimator whose first shell overlaps the domain-scale peak; this must be addressed before the suppression claim is fully established.","major_comments":[{"comment":"The unit-width shell average in Eq. (13) means the lowest plotted wavenumber is not in the asymptotic regime. In the 2π box, k_min=1, so the first shell averages 1≤|k′|<2; in the 8π box, k_min=0.25, but with the same shell width the first shell averages 0.25≤|k′|<1.25. Since the steady-state spectral peak for the contractile case is near k*≈1, the apparent plateau ψ(k)≈const and the value H≈1 may be contamination from the peak rather than a true k→0 behavior. Please recompute the low-k spectral density with shells narrow compared with k* and with k_min well below k*, and show box-size convergence of the asymptotic value before claiming suppression of hyperuniformity.","section":"3.1, Eq. (13), Fig. 6(f)"},{"comment":"The hyperuniformity metric H(t)=ψ(1,t)/ψ(k_peak,t) inherits the same shell-averaging problem. A minimum H≈10^-5 and a final H≈1 are based on the first shell value ψ(1,t), which includes the peak; these quantitative statements are therefore not robust. The metric should be evaluated at a k_min far below the peak, or replaced by an extrapolated k→0 value, using narrow spectral shells.","section":"3.2, Eq. (15)"},{"comment":"The scaling exponents (α≈4 for hyperuniform cases, flux exponents ≈6 and ≈4, and growth exponents ≈1 and ≈1/3) are quoted without error bars, fit ranges, or the number of decades used, and Fig. 3(a) is a single snapshot at t=8 while Fig. 3(c) is time-averaged. Since the inverse-versus-forward cascade distinction is a central interpretive claim, please provide quantitative fit details and time-averaged spectra for both the passive and active cases.","section":"3.1 and 3.3, Figs. 1, 2, and 3"}],"minor_comments":[{"comment":"The sentence 'we compute H at each time instance and show the evolution H(t) in Fig.2(b)' should refer to Fig.2(d), since the H(t) panel is labeled (d) in the figure.","section":"3.2"},{"comment":"The first sentence of the Introduction contains the typo 'Hyperuniformy'; it should read 'Hyperuniformity'.","section":"1"},{"comment":"The phrase 'as per the law of equipartition of energy' is not justified by a constant ψ(k); a constant spectral density is not, by itself, equipartition.","section":"3.3"},{"comment":"The integral ∫₀^∞ T_adv(k)dk=0 should specify that T_adv(k) is a shell-integrated transfer rate and that the integration is over the scalar wavenumber axis, since k is used both as a vector magnitude and as a shell index.","section":"3.3, Eq. (21)"},{"comment":"There are several typographical errors that should be corrected: 'looses' in Section 3.3, 'visulization' in the Fig. 6 caption, and 'represtative' in Section 3.5.","section":"General"}],"recommendation":"major_revision","confidential_remarks":"In my view, the shell-averaging concern is the deciding issue: the paper's central claim depends on the low-k behavior, and the current estimator can mix the first shell with the domain-scale peak. The manuscript is otherwise well focused and the model is standard; I would be willing to accept after the authors supply a narrow-shell low-k analysis and statistical details for the reported exponents. There is no need to expand the paper's scope."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Colleague,\n\nThe new result here is that active model H with contractile active stress (ζ<0) loses hyperuniformity in the steady state, while passive model H and extensile active model H keep it. The paper also derives a spectral budget for the order parameter and shows that the advective flux runs forward (small k to large k) in the contractile case and inverse in the hyperuniform cases. That is a concrete, testable mechanism, and I don't think anyone has shown it for hydrodynamic scalar active field theories before.\n\nThe numerics are careful as far as they go: the spectral budget follows from the equations, the runs include asymmetric quench and larger box checks, and the flux analysis is a diagnostic rather than a fitted result. The coarsening exponents for model B (1/3) and model H (1) match known values. Good.\n\nSoft spots, in order of softness. The central claim that ψ(k) → constant as k→0 is not fully established. With a 2π box the lowest shell is k∈[1,2], which is not the asymptotic regime; the 8π box gets k_min=0.25 but uses the same unit-width shells, so the first shell still overlaps the domain-scale peak. The 2D spectra in Fig. 2(b) and 6(d) mitigate this—they show a flat, ring-free amplitude down to the accessible k, not just a shell-average artifact—but the paper can only claim a plateau over the accessible range, not the true k→0 limit. The text says 'for the limit k→0' as if that were resolved. That should be softened.\n\nAlso, the power-law exponents (α≈4, flux exponents 6 and 4) are quoted without error bars; some spectra are single-time snapshots; and no code or data are provided. These are standard referee requests, not fatal flaws.\n\nThe citation pattern is fine; the self-citations to the authors' prior work on active-scalar turbulence are relevant and not padding.\n\nBottom line: this is a real within-field result, worth refereeing seriously. I'd ask for error bars, a more careful discussion of the accessible-wavenumber limitation, and possibly narrower spectral shells in the large-box run. The mechanism is plausible and the paper should be published in some form.","headline":"Solid numerical study: contractile stress in active model H suppresses hyperuniformity with a plausible forward-flux mechanism, but the asymptotic k→0 claim is not fully established.","tokens_in":11907,"tokens_out":2739,"would_cite":true,"duration_ms":27476,"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":"Contractile activity destroys hyperuniformity in wet phase separation","keywords":["hyperuniformity","active model H","contractile active stress","phase separation","coarsening arrest","spectral energy transfer","active turbulence","hydrodynamic interactions"],"falsifier":"A direct test would be to run the contractile active model H in a box several times larger with much longer averaging, and to check whether $\\psi(k)$ develops a rising power law $\\psi(k)\\sim k^\\alpha$ with $\\alpha>0$ as $k\\to 0$ instead of remaining flat; if a positive exponent reappears, the suppression of hyperuniformity is a finite-size or finite-time artifact.","tokens_in":10856,"feed_emoji":"🌊","tokens_out":6488,"duration_ms":53998,"temperature":0.7,"pith_summary":"This paper asks whether hydrodynamic interactions preserve the universal hyperuniform patterns seen in phase-separating scalar field theories. Using direct numerical simulations of model H and active model H in two dimensions, it shows that passive hydrodynamic coupling keeps the order-parameter spectral density $\\psi(k)\\sim k^4$ at small wavenumbers, just as in Cahn-Hilliard dynamics. In the active contractile case ($\\zeta<0$), where coarsening arrests into a statistically steady state, the spectrum flattens to $\\psi(k)\\sim$ constant, meaning large-scale fluctuations are no longer suppressed and the system is non-hyperuniform. The result matters because it identifies a mechanism—advective spectral transfer driven by the active stress—that can erase a form of hidden order, with implications for how we recognize hyperuniformity in active fluids.","feed_headline":"Contractile activity destroys hyperuniformity in wet phase separation","feed_subtitle":"Contractile activity reverses the spectral cascade, flattening the order-parameter spectrum to a constant.","key_machinery":"The machinery is the shell-averaged spectral budget for the order parameter, $\\partial_t S(k,t)=I+D+T^\\phi+T^{\\rm adv}$, together with the flux $\\Pi(k)=-\\int_0^k T^{\\rm adv}(k')dk'$. The advection term $T^{\\rm adv}$ redistributes structural energy across scales without adding or removing it; its sign determines the cascade direction. In hyperuniform states the flux is negative (inverse cascade) and vanishes steeply at small $k$, leaving the $\\psi(k)\\sim k^4$ scaling untouched; in the contractile steady state the flux is positive (forward cascade) and sustains fluctuations at all scales, flattening the spectrum.","core_discovery":"The central claim is that adding hydrodynamic advection to a scalar active field theory can qualitatively change its large-scale order. In passive model H, and in active model H with extensile stress ($\\zeta>0$), the spectral density obeys $\\psi(k)\\sim k^4$ as $k\\to 0$, so the system is hyperuniform even though coarsening is much faster than in model B. With contractile stress ($\\zeta<0$), coarsening arrests into a non-equilibrium steady state and the spectrum becomes flat, $\\psi(k)\\sim$ constant, so the system is non-hyperuniform. The paper attributes this to a scale-by-scale balance: the advection term transfers structural energy from small to large wavenumbers (a forward cascade) in the contractile case, whereas it transfers energy from large to small wavenumbers (an inverse cascade) in the hyperuniform cases. The transition is robust across symmetric and asymmetric quenches and across box sizes up to $8\\pi\\times 8\\pi$.","pith_inferences":["One could test the cascade mechanism by forcing the flow externally to reverse the direction of $T^{\\rm adv}$ and checking whether hyperuniformity is recovered in the contractile regime.","This finding suggests that hyperuniformity may be a fragile property in fluids with momentum conservation, and that the hyperuniformity of a field can be tuned by controlling the sign of the active stress.","A natural extension would be to three dimensions, where the inverse-cascade phenomenology differs and the arrest may be less complete, so the suppression might be weaker.","The flat spectrum at steady state resembles equipartition of the order-parameter modes; a statistical-mechanics derivation of the flat spectrum from the balance $T^{\\rm adv}=-(I+D+T^\\phi)$ could turn the numerical observation into a solvable closure."],"forward_implications":["If the claim holds, hyperuniformity is not a universal late-time property of all phase-separating scalar fields; active hydrodynamic stress can destroy it.","The spectral flux analysis offers a diagnostic: the sign and small-$k$ scaling of $\\Pi(k)$ distinguish hyperuniform from non-hyperuniform coarsening, so one can predict the fate of a system from the advective transfer rather than waiting for long-time spectra.","Because the contractile case shows a forward cascade and anti-hyperuniform vorticity, the same mechanism may link active turbulence to a loss of order-parameter hyperuniformity in other wet active systems.","The robustness of the result to asymmetric quenches and box size suggests that the transition will be observed in experiments on contractile active emulsions or cytoskeletal networks, not only in simulations."],"supporting_citations":[{"why":"Defines active model H, the model used here, including the contractile/extensile stress tensor.","marker":"[17]"},{"why":"Showed universal hyperuniformity in dry active field theories, the baseline that wet active model H is compared against.","marker":"[4]"},{"why":"Provided the theoretical argument for $\\psi(k)\\sim k^4$ in phase-ordering systems, which this paper's flux analysis refines.","marker":"[5]"},{"why":"Established the $L(t)\\sim t^1$ hydrodynamic coarsening law in model H, used to interpret the growth regimes.","marker":"[18]"},{"why":"Earlier simulations of active-scalar fluids showing coarsening arrest and turbulence; supplies the numerical scheme and parameter choices.","marker":"[21]"},{"why":"Introduced the spectral density and hyperuniformity metric used for the order parameter, including $H(t)$ thresholds.","marker":"[11]"},{"why":"Defined the thresholds for effective and nearly hyperuniform states ($H\\leq 10^{-4}$ and $10^{-2}$).","marker":"[8]"},{"why":"Source of the shell-averaged spectrum and coarsening-length definition (Eq. 13-14) and the $L(t)\\sim t$ scaling in passive model H.","marker":"[34]"},{"why":"Provided the recent spectral-budget analysis of domain growth that the order-parameter transfer analysis extends.","marker":"[35]"}],"fun_headline_variants":["Contractile stress suppresses hyperuniformity in wet active fluids","Hydrodynamic advection flattens spectrum in active model H","Active contractility removes hyperuniform order in phase separation","Forward cascade suppresses hyperuniformity in contractile model H","Wet activity suppresses hyperuniform order via contractile stress"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The claim rests on the assumption that the flat spectra measured in finite simulation boxes, up to $8\\pi\\times 8\\pi$, and in time-averaged steady states represent what would happen in an infinite system at asymptotically small wavenumbers.","fun_headline_variants_meta":{"raw":{"variants":["Contractile stress suppresses hyperuniformity in wet active fluids","Hydrodynamic advection flattens spectrum in active model H","Active contractility removes hyperuniform order in phase separation","Forward cascade suppresses hyperuniformity in contractile model H","Wet activity suppresses hyperuniform order via contractile stress"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000314,"raw_usage":{"total_tokens":1732,"prompt_tokens":846,"completion_tokens":886,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":462,"completion_tokens_details":{"reasoning_tokens":805}},"tokens_in":462,"tokens_out":886,"duration_ms":8004,"temperature":1.0,"reasoning_tokens":805,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-12T12:08:21.113391+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"A direct test would be to run the contractile active model H in a box several times larger with much longer averaging, and to check whether $\\psi(k)$ develops a rising power law $\\psi(k)\\sim k^\\alpha$ with $\\alpha>0$ as $k\\to 0$ instead of remaining flat; if a positive exponent reappears, the suppression of hyperuniformity is a finite-size or finite-time artifact.","supporting_citations":[{"cited_title":"Active model h: scalar active matter in a momentum-conserving fluid","cited_arxiv_id":null,"evidence_quote":"Defines active model H, the model used here, including the contractile/extensile stress tensor."},{"cited_title":"Universal hyperuniformity in active field theories","cited_arxiv_id":null,"evidence_quote":"Showed universal hyperuniformity in dry active field theories, the baseline that wet active model H is compared against."},{"cited_title":"Hyperuniformity in phase ordering: the roles of activity, noise, and non-constant mobility","cited_arxiv_id":"2405.00508","evidence_quote":"Provided the theoretical argument for $\\psi(k)\\sim k^4$ in phase-ordering systems, which this paper's flux analysis refines."},{"cited_title":"Late stages of spinodal decomposition in binary mixtures","cited_arxiv_id":null,"evidence_quote":"Established the $L(t)\\sim t^1$ hydrodynamic coarsening law in model H, used to interpret the growth regimes."},{"cited_title":"Novel turbulence and coarsening arrest in active-scalar fluids","cited_arxiv_id":null,"evidence_quote":"Earlier simulations of active-scalar fluids showing coarsening arrest and turbulence; supplies the numerical scheme and parameter choices."},{"cited_title":"Nonequilibrium hyperuniform states in active turbulence","cited_arxiv_id":null,"evidence_quote":"Introduced the spectral density and hyperuniformity metric used for the order parameter, including $H(t)$ thresholds."},{"cited_title":"Random scalar fields and hyperuniformity","cited_arxiv_id":null,"evidence_quote":"Defined the thresholds for effective and nearly hyperuniform states ($H\\leq 10^{-4}$ and $10^{-2}$)."},{"cited_title":"Suppression of hyperuniformity in hydrodynamic scalar active field theories 15 Spinodal decomposition in homogeneous and isotropic turbulence","cited_arxiv_id":null,"evidence_quote":"Source of the shell-averaged spectrum and coarsening-length definition (Eq. 13-14) and the $L(t)\\sim t$ scaling in passive model H."},{"cited_title":"Spectral energy transfers in domain growth problems","cited_arxiv_id":null,"evidence_quote":"Provided the recent spectral-budget analysis of domain growth that the order-parameter transfer analysis extends."}],"review_version":1}