{"id":"0b01b8b4-e2c5-499b-9d7e-fc6b1f5ff922","arxiv_id":"2502.06312","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":6.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":7,"one_line_summary":"A continuum model of active viscoelastic fluids reproduces the two oscillatory modes previously seen only in elastic active solids.","lead":"This paper shows that two oscillatory modes of collective motion seen in active biofilms also appear in a broad class of viscoelastic fluids, not just elastic solids. The result suggests these modes are generic for active soft materials under circular confinement.","discovery_kind":"extension","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Eq. (3) omits the v·∇u advection term in the displacement dynamics; in the rotational mode this term is comparable to the retained terms, so the demonstrated modes may rest on an unvalidated linearization.","rationale":"The reader correctly identified Eq. (3) and the ad hoc confinement as weak assumptions underlying the genericity claim. My stress-test sharpens this into a concrete kinematic defect: the equation as written is not the exact material-derivative relation for a displacement field, and the omitted advection term is not negligible in the rotational mode, where u and v are both O(1) on a domain of diameter 6. This is a specific, checkable issue rather than a purely rheological plausibility concern. It does not by itself overturn the paper's conclusion, because the correct advection term might be included without destroying the modes; but it makes the current demonstration conditional on an unvalidated linearization. The reader's CONDITIONAL verdict therefore remains appropriate, with the requested numerical test as the clearest path to acceptance. I do not see evidence of inconsistency strong enough to demand rejection, and the paper does provide a physically plausible minimal model with transparent parameter definitions.","tokens_in":5429,"tokens_out":11530,"duration_ms":117742,"concrete_test":"Modify the numerical scheme to solve the full material-derivative equation D_t u = ∂t u + v·∇u = v − τd⁻¹u (using an upwind or spectral advection discretization) and rerun the νp sweeps of Fig. 2 for τd = 1 and τd → ∞. If the rotational and translational branches and the transition are essentially unchanged, the omitted advection is harmless; if the branches shift, narrow, or disappear, the current results are specific to the linearized kinematics and the genericity claim must be weakened.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central claim is that the two oscillatory modes are generic for viscoelastic fluids and solids, with elasticity only a limiting case. The mechanism for memory is carried by Eq. (3), ∂t u = v − τd⁻¹u. If u is a displacement field in the Eulerian frame, the exact kinematic relation between material displacement and velocity is D_t u = ∂t u + v·∇u = v, with the relaxation term giving D_t u = v − τd⁻¹u. The paper drops the v·∇u term, which is a small-displacement linearization. This approximation is not justified in the oscillatory rotational mode: the velocity field is azimuthal with |v| ~ O(1), the displacement u is also O(1), and with domain diameter d = 6, v·∇u is estimated as O(v0 u/d) ~ 0.1–0.3. That is of the same order as ∂t u ~ f0 v0 and as the retained relaxation term, especially near the transition region where f0 is small. Since the Hopf frequency, the τd threshold (τd ≈ 0.7), and the branch structure in Fig. 2 are all extracted from this truncated kinematic equation, the claimed genericity could be an artifact of the linearization rather than a property of viscoelastic active media. The SI provides no convergence check or comparison against the exact material-derivative form.","agreement_with_reader":"partial"},"referee_report":{"model":"deepseek-v4-flash","summary":"The manuscript studies a previously introduced continuum field theory for active media (Eqs. (1)-(3)) under circular confinement. The authors numerically solve these equations for parameters representing a viscoelastic fluid and observe two oscillatory collective modes that were reported experimentally for active elastic solids by Xu et al.: an oscillatory rotational mode and a translating mode with rotating velocity direction. By varying the displacement relaxation time tau_d, they find these modes for finite tau_d (down to tau_d approximately 0.7) as well as in the elastic limit tau_d -> infinity, and conclude that the phenomena are generic for viscoelastic active fluids and solids.","tokens_in":5749,"tokens_out":6301,"duration_ms":57472,"significance":"If the finding is robust, it meaningfully extends the scope of the experimental observations of Xu et al. from elastic solids to viscoelastic fluids, which is relevant for understanding biofilms and other biological materials. The paper provides a clear numerical demonstration for one representative parameter set (tau_d = 1) and a systematic trend in tau_d, with the qualitative distinction between the two modes well illustrated in Fig. 1. However, the claim of genericity is supported only by a limited parameter sweep, and the kinematics in Eq. (3) are linearized without explicit validation, so the current evidence is suggestive rather than conclusive.","major_comments":[{"comment":"The displacement dynamics in Eq. (3) is written as partial_t u = v - tau_d^{-1} u, which omits the advective term v dot grad u that appears in the material derivative D_t u = partial_t u + v dot grad u. In the simulated oscillatory states, the velocity and displacement fields are not infinitesimal: Fig. 1 shows |v| up to about 6 in the same scaled units, and the advective term is estimated to be of the same order as the retained terms near the transition. Since Eq. (3) is the only memory mechanism that produces the oscillations, the demonstrated modes may be an artifact of this linearization rather than a genuine property of the viscoelastic model. The Supplemental Information provides no convergence test or comparison against the full material-derivative form. I request that the authors either justify the linearization by a scale analysis for the simulated amplitudes or repeat the key simulations with the advective term included.","section":"Eq. (3) and Fig. 1"},{"comment":"The central claim of genericity for 'a broad range of viscoelastic fluids and solids' is based on a one-parameter sweep in tau_d with all other material parameters fixed (gamma_a = 1, eta = 1, mu = 1, nu_v = 1, nu_d = 10). The confinement force in SI Eq. (S1), with strength nu_conf_d0 = nu_d/2 and a linear spatial profile, is introduced ad hoc and is not tested for sensitivity. A generic statement would require at least a demonstration that the two modes persist when other parameters (e.g., gamma_a, nu_d, or the confinement strength) are varied, and that the threshold and frequencies do not depend critically on the chosen confinement profile.","section":"Fig. 2 and SI Eq. (S1)"},{"comment":"The numerical results are presented without error bars, grid-convergence tests, or validation of the pseudo-time-stepping scheme. In particular, the claimed threshold tau_d approx 0.7 and the precise frequency curves in Fig. 2 are quantitative results; the authors should report at least a grid-resolution check (e.g., 128 vs 256 grid points) and a check of the convergence of the artificial-compressibility iteration, and ideally provide the code and data for reproducibility.","section":"Supplemental Information (numerical methods)"}],"minor_comments":[{"comment":"The definition of Omega = [(grad v)^T - (grad v)] is missing the conventional factor 1/2; the dot product in the alignment term v dot [(2 + P dot P)I/3 - PP] is ambiguous and should be written with an explicit tensor contraction.","section":"Eq. (1)"},{"comment":"The curves for tau_d = 0.5 and tau_d = 0.7 are hard to distinguish in a grayscale print; consider using markers or different line styles.","section":"Fig. 2"},{"comment":"The text says the 'first two terms' on the right-hand side of Eq. (1) reflect orientational and translational diffusion, but the term -P is a decay, not a diffusion, term; rephrase for accuracy.","section":"Text following Eq. (1)"},{"comment":"The reference to the companion paper [8] is to an arXiv preprint; if published, the citation should be updated, and the relation of Eqs. (1)-(3) to that paper should be summarized more explicitly for a self-contained reading.","section":"References"}],"recommendation":"major_revision","confidential_remarks":"The paper is heavily reliant on the authors' own companion paper [8], which is not yet peer-reviewed; the editor may want to verify that the companion manuscript is in good shape. In my view, the missing advective derivative in Eq. (3) is the most serious technical concern and should be resolved before publication, as it directly affects the causality of the oscillatory mechanism."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Dear colleague,\n\nThe paper is a short numerical note showing that the two oscillatory modes Xu et al. observed in active elastic biofilms also appear in a continuum model of viscoelastic fluids with finite relaxation time. That is a genuine, if modest, extension: earlier theoretical treatments used elastic solids, and here the solid limit is shown not to be necessary. The result is probably right in broad strokes: for tau_d = 1 the authors see both modes, and the transition between them persists down to tau_d ~ 0.7, with the rotational mode disappearing below that. The observation that oscillations slow down as tau_d decreases is a nice, testable trend.\n\nThe main thing that needs attention is Eq. (3). As written, it is d_t u = v - tau_d^{-1} u, but if u is an Eulerian displacement field, the kinematic relation should involve the material derivative: D_t u = d_t u + (v·grad)u = v - tau_d^{-1} u. The authors drop the v·grad u term without comment. In the oscillatory rotational mode the velocity and displacement are both order one, and with a domain diameter of 6, the omitted term is of the same order as d_t u and the relaxation term, especially near the transition where the frequency is small. So the demonstrated modes, and the tau_d threshold in Fig. 2, could be an artifact of this linearization. I do not think the paper is fatally wrong, but the authors need to either include the advective term or give a convincing argument for why it is negligible in the relevant states.\n\nThe genericity claim also outruns the evidence. Only tau_d is varied; all other parameters are held fixed. That shows the modes are not special to the elastic limit, but it does not establish that they appear for a 'broad range' of viscoelastic fluids and solids. The confinement force is introduced ad hoc to mimic Xu et al., with a particular radial profile; that is fine for a first pass, but again it limits the generality.\n\nThe model itself is taken from the authors' own companion paper (Ref. [8], also an arXiv preprint), so the framework is not independently established here. The equations are plausible, but that puts more weight on the numeric demonstration. A more practical problem is that there is no code, no data, no error bars, and no convergence test. The SI describes the numerical scheme, but nothing that lets the reader check whether the reported amplitudes and frequencies are resolved. For a paper whose only evidence is simulation, that is a real gap, and one a referee should ask to close.\n\nOverall: the central claim is plausible and the paper is worth engaging with, but it is not, as written, a definitive demonstration of genericity. I would send it out, with instructions to address the kinematic equation, broaden or temper the genericity claim, and provide reproducibility data. These fixes are within reach for a short paper.\n\nBest,\n[Name]","headline":"Plausible numerical extension of Xu et al. modes to viscoelastic fluids, but the genericity claim is overbroad and the dropped advection term in Eq. (3) needs a defense.","tokens_in":6274,"tokens_out":3605,"would_cite":false,"duration_ms":33072,"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":"Two oscillatory modes of collective motion seen in elastic active solids also emerge in viscoelastic active fluids, making the phenomena generic to confined active biomaterials.","keywords":["active matter","viscoelastic fluids","active solids","collective motion","oscillatory modes","biofilms","continuum field theory","circular confinement"],"falsifier":"A rheological measurement of a living biofilm that shows the oscillatory rotational mode persisting while the independently measured stress-relaxation time is shorter than the model's threshold (about $\\tau_d = 0.7$ in the units of Fig. 2) would disprove the claim that this mode is generic to viscoelastic fluids.","tokens_in":5187,"feed_emoji":"🔄","tokens_out":8606,"duration_ms":68169,"temperature":0.7,"pith_summary":"The paper sets out to show that two oscillatory modes of collective motion observed in confined active biofilms—a rotation that periodically reverses direction and a uniform translation whose direction rotates—are not a special feature of elastic active solids. Working with a minimal continuum theory that couples polar order, flow, and a displacement field with a finite memory-relaxation time, the authors find both modes in viscoelastic active fluids over a broad parameter range, with elastic solids recovered only in the infinite-memory limit. The practical significance is that these phenomena should be expected in a wide class of biological fluids, soft materials, and biomaterials, and that a biofilm's solid-looking dynamics do not by themselves demonstrate solid elasticity.","feed_headline":"Viscoelastic fluids show the same oscillatory modes as solids","feed_subtitle":"A tunable memory time in a continuum model reproduces both modes, so elastic solids are just one limiting case.","key_machinery":"The load-bearing object is the displacement field $\\mathbf{u}$ with relaxation dynamics $\\partial_t \\mathbf{u} = \\mathbf{v} - \\tau_d^{-1}\\mathbf{u}$. The parameter $\\tau_d$ is the memory-relaxation time: $\\tau_d \\to \\infty$ recovers a perfectly elastic solid whose history never fades, finite $\\tau_d$ describes a viscoelastic fluid that ultimately flows, and $\\tau_d \\to 0$ is a purely viscous fluid. This single field lets one equation interpolate between solid and fluid behavior: it enters an extended Stokes equation balancing viscous stress, elastic stress from $\\mathbf{u}$, substrate friction and elastic restoring forces, and active driving. Together with a confinement force on the normal displacement at the circular boundary, this is what generates the two oscillatory modes and sets their frequency and amplitude; the paper's central move is to show that varying $\\tau_d$ at fixed activity leaves the qualitative mode structure intact well into the fluid regime.","core_discovery":"On the paper's own terms, the discovery is that the two global oscillatory modes reported for living elastic active solids are generic to active media with memory. The authors solve their coupled fields—polar order $\\mathbf{P}$ (the locally averaged migration direction), incompressible velocity $\\mathbf{v}$, and displacement $\\mathbf{u}$ (the deformation history)—under circular confinement with an elastic restoring force at the boundary, and observe the same rotation-reversing and translation-rotating modes when the displacement relaxes at a finite rate ($\\tau_d = 1$ in rescaled units), i.e., for a genuinely viscoelastic fluid. As the activity $\\nu_p$ is varied, a transition between the two modes appears for essentially all relaxation times studied, from $\\tau_d \\to \\infty$ (elastic solid) down to strongly fluid-like values; only when $\\tau_d$ drops below roughly $0.7$ does the oscillatory rotational mode disappear while the translational mode may still occur. The authors conclude that elastic behavior is only one limiting case of a broader class of oscillatory viscoelastic active matter.","pith_inferences":["The continuous interpolation between fluid and solid suggests the same framework could describe three-dimensional confinement or films with spatially varying rheology, which the paper does not test.","Replacing the single relaxation time with a full relaxation spectrum is a natural next step; the expectation would be that the modes persist as long as the slowest relaxation component is not much shorter than the oscillation period, which could be checked in rheologically characterized biofilms.","The boundary force in the model is linear and grows with distance from the center; numerically probing nonlinear or asymmetric confinement profiles could reveal how sensitively the two modes depend on the confining mechanism."],"forward_implications":["The observed oscillatory modes in bacterial biofilms do not require solid elasticity; a viscoelastic fluid description already suffices.","The activity-driven transition from rotation-reversing motion to translation-rotating motion is robust across a wide range of memory-relaxation times, so it should be a common feature of confined active materials.","As the material becomes more fluid-like (smaller $\\tau_d$), the oscillation frequency and amplitude decrease, and below a threshold ($\\tau_d \\approx 0.7$ for the parameters shown) the rotational mode disappears while the translational mode can persist.","For this class of collective phenomena, biofilms can be treated as complex viscoelastic media, and the single-relaxation-time model is a minimal description of their large-scale motion."],"supporting_citations":[{"why":"supplies the experimental observation of both oscillatory modes in a living biofilm and the elastic-solid interpretation that this work generalizes","marker":"[1]"},{"why":"provides the unified continuum field theory in Eqs. (1)-(3) on which the numerical demonstration is built","marker":"[8]"},{"why":"supports the memory-based displacement dynamics behind Eq. (3)","marker":"[12]"},{"why":"exemplifies the earlier spring-lattice active-solid models that this paper contrasts with the viscoelastic case","marker":"[6]"}],"fun_headline_variants":["Viscoelastic fluids mimic elastic solids' oscillatory modes","Generic oscillatory modes in active viscoelastic media","Elastic solids are just a limit: viscoelastic active fluids oscillate too","Circular confinement yields oscillatory modes in viscoelastic active fluids","Viscoelasticity broadens oscillatory collective motion in active matter"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The entire prediction rests on a phenomenological theory in which one relaxation time for the material's memory, together with a linear restoring force at the boundary, captures the essential physics of a real biofilm.","fun_headline_variants_meta":{"raw":{"variants":["Viscoelastic fluids mimic elastic solids' oscillatory modes","Generic oscillatory modes in active viscoelastic media","Elastic solids are just a limit: viscoelastic active fluids oscillate too","Circular confinement yields oscillatory modes in viscoelastic active fluids","Viscoelasticity broadens oscillatory collective motion in active matter"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000321,"raw_usage":{"total_tokens":1765,"prompt_tokens":863,"completion_tokens":902,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":479,"completion_tokens_details":{"reasoning_tokens":813}},"tokens_in":479,"tokens_out":902,"duration_ms":7538,"temperature":1.0,"reasoning_tokens":813,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-08T15:50:51.539558+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"A rheological measurement of a living biofilm that shows the oscillatory rotational mode persisting while the independently measured stress-relaxation time is shorter than the model's threshold (about $\\tau_d = 0.7$ in the units of Fig. 2) would disprove the claim that this mode is generic to viscoelastic fluids.","supporting_citations":[{"cited_title":"Reinken and A","cited_arxiv_id":null,"evidence_quote":"provides the unified continuum field theory in Eqs. (1)-(3) on which the numerical demonstration is built"},{"cited_title":"Oscillatory collective motion in viscoelastic and elastic active fluids and solids under circular confinement","cited_arxiv_id":"2502.06312","evidence_quote":"supports the memory-based displacement dynamics behind Eq. (3)"},{"cited_title":"Ferrante, A","cited_arxiv_id":null,"evidence_quote":"exemplifies the earlier spring-lattice active-solid models that this paper contrasts with the viscoelastic case"}],"review_version":1}