{"id":"4901563a-da4b-49be-8c80-b840769e005a","arxiv_id":"2506.16523","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":6.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":0,"one_line_summary":"Thin active nematic films with variable thickness and curvature exhibit instabilities absent in 2D models, including contractile-activity-driven nematic ordering and coupled thickness-shape deformations.","lead":"This paper derives simplified equations for thin, bendable layers of active nematics and uses them to predict new instabilities. It shows that allowing the film thickness and shape to change produces instabilities not seen in standard two-dimensional models, such as contractile activity ordering an initially isotropic cylindrical film.","discovery_kind":"new_application","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Central claim rests on Eq. (76), whose active term diverges as 1/Q^2 for P≥2 and fails to reduce to the non-deformable limit Eq. (80); if Eq. (76) is erroneous, the contractile-ordering result collapses.","rationale":"The reader identified the surface-tension assumption as the weakest assumption, but the more immediate threat to the central claim is the correctness of Eq. (76). The abstract's novel prediction that contractile activity can induce nematic order in the isotropic phase on a cylinder is a direct consequence of the active term in Eq. (76) changing sign for P≥2. That term contains a 1/Q^2 factor that makes the growth rate diverge as Q→0 for any fixed P≥2, which is unphysical: arbitrarily long axial modulations of a circumferential harmonic would grow infinitely fast. Moreover, the paper itself states that in the non-deformable limit (V=0, constant ai,ki) the growth rate is Eq. (80), but Eq. (76) does not reduce to Eq. (80) in that limit: even the P=0, Q→0 active coefficient differs (-2λm/(9μ) vs -λm/(6μ)). The flat-film result Eq. (47) at ϕ=0 gives -λm/(6μ), further suggesting a factor error. Since the derivation of Eq. (76) is not shown, the central claim is currently unsupported. The proposed concrete test—re-deriving Eq. (76) from the linearized equations and checking the two limits—would decisively settle whether the sign change is real. If the test fails, the paper's main novelty disappears, so the verdict should move to REJECT. If the authors can supply a correct derivation that removes the divergence and restores the limits, the paper could become ACCEPT or CONDITIONAL; as written, the internal inconsistency warrants rejection.","tokens_in":22685,"tokens_out":9158,"duration_ms":79851,"concrete_test":"Independently re-derive Eq. (76) from the linearized cylindrical equations (9)-(10), (55), (59)-(61). Verify two limits: (i) P=0, Q→0 should give an active coefficient equal to the flat-film value -λm/(6μ) from Eq. (47) at ϕ=0; (ii) with V=0 and constant ai,ki, it should reduce to Eq. (80). If the re-derivation removes the 1/Q^2 divergence and the P≥2 sign change, then Eq. (76) is erroneous and the contractile-ordering claim collapses.","verdict_should_be":"REJECT","load_bearing_attack":"The abstract's central claim—that in the isotropic phase both extensile and contractile activity can induce nematic order on a cylinder—rests on the dispersion relation Eq. (76). Two internal consistency checks fail. (i) In the non-deformable limit V=0, ai,ki constant, the paper states that Eq. (80) is the resulting growth rate; but Eq. (76) does not reduce to Eq. (80). For P=0, Q→0, Eq. (76) gives an active coefficient -2λm/(9μ), while Eq. (80) gives -λm/(6μ), and the flat-film result Eq. (47) at ϕ=0 also gives -λm/(6μ). (ii) For P≥2, the active term in Eq. (76) contains a factor 1/Q^2: -λm/(9Q^2 μ)(Q^2-2P^2+2)(Q^2+P^2). As Q→0, this diverges as λm P^2(2-2P^2)/(9μ Q^2) for contractile m>0, predicting an infinite growth rate at arbitrarily long axial wavelength for any non-zero activity. Such a divergence is unphysical and suggests a missing or mistyped denominator, e.g. (Q^2+P^2)^2 as in Eq. (80). Because the sign change for P≥2 that produces contractile ordering is exactly this active term, an algebraic error here would invalidate the headline claim. The derivation of Eq. (76) is not shown; only the final formula is quoted. Therefore the central result is not yet supported.","agreement_with_reader":"partial"},"referee_report":{"model":"deepseek-v4-flash","summary":"The manuscript develops asymptotic thin-film models for active nematic layers by reducing the full three-dimensional nematohydrodynamic equations in two regimes: nearly flat films with small curvature, and generally curved films with O(1) curvature. For flat films it derives effective equations for thickness, in-plane velocity, and nematic order and performs linear stability analysis of the nematic and isotropic phases. For cylindrical films it performs a similar analysis and identifies couplings between thickness, shape, and order. The paper's headline claim is that in the isotropic phase on a deformable cylinder, both extensile and contractile activity can induce nematic order, in contrast to fixed-surface active nematics.","tokens_in":22990,"tokens_out":17174,"duration_ms":185906,"significance":"The derivation from the stated 3D equations is mostly systematic, contains no fitted parameters, and the flat-film results recover known 2D active nematic limits in the appropriate reductions, which is a clear strength. The paper also produces explicit, falsifiable dispersion relations and phase diagrams. However, the central claim about contractile ordering in the isotropic cylindrical phase is not supported by the analysis as written: it rests on a quoted dispersion relation, Eq. (76), that has an unphysical long-wavelength divergence and no derivation. The value of the paper is therefore contingent on the authors being able to substantiate or correct Eq. (76).","major_comments":[{"comment":"The abstract's claim that contractile activity can induce nematic order in the isotropic phase of a cylindrical film rests on Eq. (76), but the active term in that equation is singular as Q→0 for all circumferential modes P≥2. For fixed P≥2 and contractile activity m>0, the factor (Q²−2P²+2)(Q²+P²)/Q² tends to P²(2−2P²)/Q², so the term −λm(Q²−2P²+2)(Q²+P²)/(9Q²µ) diverges to +∞. This predicts an arbitrarily large growth rate at arbitrarily long axial wavelength for any nonzero contractile activity, with no threshold; such a divergence is unphysical in a Stokes-flow thin-film model. Eq. (76) is quoted without derivation, so the divergence cannot be traced to a justified term in the asymptotic expansion. The authors must either provide the full derivation and show that the singularity is a true physical effect, or correct the formula and re-examine the contractile-ordering claim.","section":"§V.A.2, Eq. (76)"},{"comment":"Eq. (76) is also not consistent with the non-deformable limit that the paper uses as its benchmark. For P=0 and Q→0, Eq. (76) gives an active coefficient −2λm/(9µ), whereas Eq. (80) for a non-deformable cylinder and Eq. (47) for a flat layer at φ=0 both give −λm/(6µ). In addition, the Fig. 4 caption and the surrounding text attribute the contractile-ordering instability to Eq. (80), but Eq. (80) has a sign-definite active coefficient and can only be destabilized by extensile activity; the contractile result must come from Eq. (76). These internal inconsistencies indicate that either Eq. (76) is an erroneous transcription of the dispersion relation or the text describes a different calculation. As written, the central result of the paper is not supported.","section":"§V.A.2, Eqs. (76)–(80) and Fig. 4"}],"minor_comments":[{"comment":"The sentence immediately after Eq. (34) says that flows with positive divergence increase the thickness, but the right-hand side of Eq. (34) has a minus sign before h(∂1u+∂2v); positive divergence decreases the thickness. Please correct the wording.","section":"§IV, Eq. (34)"},{"comment":"The caption states that contractile systems exhibit growth of nematic order in the circumferential direction 'see Eq. (80)', but Eq. (80) is the non-deformable result that has a sign-definite active coefficient and predicts only extensile-driven growth. The citation likely should be to Eq. (76), and the sentence should be reworded after Eq. (76) is corrected.","section":"Fig. 4 caption"},{"comment":"The list of 13 unknown fields ends with 'a2,a2'; the second entry should be 'a1'.","section":"End of Sec. III"},{"comment":"The expressions for σ0_12 and σ0_22 in the SM do not match the effective stresses in Eqs. (40)-(42): the shear component should read µ(∂1v+∂2u)+mQ12 and the second normal component should read 2µ(∂1u+2∂2v)+m(Q22−Q33). Please correct these typos or check the torque-balance derivation.","section":"SM, Sec. VIII B, Eqs. (S26)-(S27)"}],"recommendation":"major_revision","confidential_remarks":"The paper fits the journal. The main concern is the unsupported cylindrical isotropic dispersion relation; the authors should be asked to rederive Eq. (76) and, if it cannot be recovered, to revise the abstract and phase diagram."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Kaveh—quick take on arXiv:2506.16523. The paper builds a systematic asymptotic theory for thin active nematic films, coupling thickness, center-surface shape, flow, and nematic order. That part is genuinely useful, and the flat-film equations reduce cleanly to known 2D results when thickness is frozen. The flat-film results also show that allowing thickness changes modifies the classical bend/splay selection, which is worth reporting.\n\nThe headline claim, though, is the cylindrical isotropic-phase result: both extensile and contractile activity can induce nematic order, in contrast to fixed surfaces. The paper attributes this to Eq. (76), the dispersion relation for the cylinder. That equation is quoted without derivation, and it doesn't survive basic consistency checks. It doesn't reduce to the non-deformable limit Eq. (80); for P=0, Q→0, it gives -2λm/9μ versus the clean -λm/6μ of the fixed-surface result. More seriously, for any P≥2 the active term scales as 1/Q^2 and diverges as Q→0, predicting infinite growth for arbitrarily long axial wavelength. That's exactly the term that flips the sign for contractile activity. Until that's re-derived, the central claim is unsupported. I'd bet on an algebraic error, not new physics.\n\nThere are smaller issues. The abstract says the flat-film analysis includes shape variations, but the stability calculation fixes the center-surface shape; only thickness is dynamic. And the torque-balance derivation in the SM has inconsistent stress coefficients (Eqs. S25–S27 don't match the main-text tensions T11, T22). That could be typos, but it doesn't help.\n\nWhat's solid: the asymptotic framework itself, the flat-film thickness coupling, and the cylindrical nematic-phase thickness instability (Eq. 71), which is separate and plausible. The paper also uses no fitted parameters, which is honest.\n\nWho's it for: people working on active shells, morphogenesis, and thin-film hydrodynamics. It deserves a serious referee, but the referee should be told to demand the derivation of Eq. (76) and a reconciliation of the limits before anything else. If the contractile-ordering result collapses, the rest is still a decent paper about thickness-coupled instabilities in active films.","headline":"A well-built asymptotic framework for active nematic films, but the cylindrical isotropic-phase claim rests on an unverified dispersion relation that fails internal consistency checks.","tokens_in":23553,"tokens_out":6394,"would_cite":false,"duration_ms":57874,"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":"Allowing a film to bend and change thickness flips the sign rule for activity-driven ordering: on a cylinder, both extensile and contractile stress can induce nematic order from an isotropic state, unlike fixed-surface active nematics.","keywords":["active nematics","thin films","asymptotic expansion","lubrication theory","linear stability","nematohydrodynamics","film thickness","curvature"],"falsifier":"A direct numerical solution of the full three-dimensional equations (1)–(3) for a contractile active nematic cylinder in the isotropic phase ($B=2/3$) at parameters where Eq. (76) predicts growth for circumferential mode $P=2$ and small axial wavenumber would settle the claim: if the order parameter $S$ does not grow and no circumferential thickness or shape bands appear, the sign-reversal result is refuted.","tokens_in":22433,"feed_emoji":"🌀","tokens_out":10776,"duration_ms":95382,"temperature":0.7,"pith_summary":"This paper derives thin-film equations for active nematic layers whose thickness and center-surface shape can change, starting from the full three-dimensional nematohydrodynamic equations with an asymptotic long-wavelength expansion. Using these equations, the authors show that deformability breaks the usual rules of two-dimensional active nematics: in a flat film the nematic phase becomes unstable in all perturbation directions for both extensile and contractile activity, and in a cylindrical film contractile activity drives a thickness instability that deforms the cylinder. The headline result is that in the isotropic phase of a cylindrical film, both extensile and contractile activity can induce nematic order, whereas active nematics on fixed surfaces only order under extensile activity. If correct, this means that thickness changes and curvature are not passive spectators but active players in morphogenetic processes such as gastrulation.","feed_headline":"Curved active films order under both extensile and contractile stress","feed_subtitle":"A thin-film theory shows deformability lets contractile stress create order, not just extensile stress.","key_machinery":"The central object is the effective film force balance obtained by integrating the three-dimensional Stokes equations across the thin dimension. In the nearly flat case this produces an in-plane tension tensor (Eqs. (40)–(42)) whose entries combine the active stress, proportional to the activity coefficient $m$, the film thickness $h$, and the in-plane nematic components $Q_{ij}$, with viscous shear terms; a thickness evolution equation $\\partial_t h = -\\nabla\\cdot(h\\mathbf{u})$ (Eq. (33)); and a torque-balance shape equation $T_{11}\\partial_1^2 H + 2T_{12}\\partial_1\\partial_2 H + T_{22}\\partial_2^2 H = 0$ (Eq. (43)). For a curved film the same expansion yields a perpendicular force balance (Eq. (59)) that ties curvature, stretch rates, thickness, and active stress together, along with compatibility relations for the surface metric. These effective equations carry the argument: every new instability follows from the sign of the activity coefficient in the resulting growth rates, and that sign changes for circumferential perturbations because of the curvature terms in the effective equations.","core_discovery":"On its own terms, the paper establishes that a deformable thin active nematic film supports a richer set of activity-driven instabilities than a fixed two-dimensional layer. In the flat-film nematic phase, the growth rates (Eqs. (44)–(45)) show contractile activity producing a uniform, direction-independent instability and extensile activity destabilizing perturbations along the order direction, so the classical bend-only-for-extensile and splay-only-for-contractile dichotomy disappears when thickness can vary. In the isotropic phase of a cylindrical film, the growth rate for the order parameter $S$ (Eq. (76)) has an activity coefficient whose sign depends on the circumferential mode number $P$: long-axis perturbations ($P=0$) grow only in extensile systems, while circumferential modes $P\\ge2$ grow in contractile systems. Because the thickness and center-surface perturbations are slaved to $\\delta S$ through Eqs. (77)–(78), any ordering instability immediately produces thickness and shape changes. The authors also show that on a non-deformable cylinder the sign of the activity coefficient never changes (Eq. (80)), isolating deformability as the cause of the reversal.","pith_inferences":["By extension, the same sign-reversal mechanism should operate on other curved films, such as spheres or tubes with varying mean curvature, because the paper's general curved-film equations (Table II) contain curvature-weighted active terms; a spherical analogue would predict contractile activity ordering the isotropic phase in high-order angular modes.","The contractile thickness instability is a concrete target for experiments with contractile actomyosin gels or microtubule-kinesin suspensions coated on cylindrical substrates: one should observe periodic axial thickenings without prior nematic order, provided surface tension is weak ($\\mathrm{Ca}\\gg1$).","If the flat-film result persists beyond linear order, the standard classification of active nematic defects by bend versus splay activity would need revision in free-standing films; the paper does not analyze defects, but its equations are set up for nonlinear simulations that could check this."],"forward_implications":["In a flat film with variable thickness, the nematic phase is unstable for perturbations in every direction under both extensile and contractile activity; contractile activity gives a leading-order growth rate independent of perturbation angle (Eq. (44)).","On a cylinder, contractile activity creates a thickness instability with growth rate $\\omega_h = m/(2\\mu)$ that deforms the cylinder even when its radius is below the orientational-instability threshold (Eq. (71)).","In the isotropic phase of a cylinder, contractile activity can produce nematic order through circumferential modes $P\\ge2$, and once order appears the film develops thickness bands and shape changes (Eqs. (76)–(78)).","The reversal is caused by deformability: for a non-deformable cylinder the activity coefficient in the isotropic growth rate keeps a single sign, recovering the extensile-only rule (Eq. (80)).","For extensile systems, the cylinder's nematic phase still shows the familiar bend instability, but only above a critical radius $R_c = (4\\mu K_Q/(-3m\\gamma))^{1/2}$; below it the ordered cylinder is stable (Eq. (70))."],"supporting_citations":[{"why":"Supplies the baseline 2D active-nematic result that bend (splay) perturbations destabilize extensile (contractile) systems, which the flat-film result contrasts with.","marker":"[35]"},{"why":"Used as the reference for normal 2D active nematics where only extensile activity grows the nematic order in the isotropic phase.","marker":"[26]"},{"why":"Together with [26], establishes the extensile-only ordering rule on fixed surfaces that the cylindrical-film result reverses.","marker":"[27]"},{"why":"Provides the fixed-cylinder active nematic instability analysis that the deformable cylindrical film builds on and extends with thickness dynamics.","marker":"[22]"},{"why":"Shows curvature dictates preferred orientation-instability directions on fixed curved geometries, the baseline for the curved-film comparison.","marker":"[17]"},{"why":"Supplies the passive thin-viscous-film equations and cylinder/sphere solutions that the active theory reduces to when activity is off.","marker":"[29]"},{"why":"Provides the asymptotic (lubrication) method used to reduce the 3D equations to the effective film dynamics.","marker":"[25]"},{"why":"Reference for the isotropic-phase instability of 2D active nematics on fixed surfaces, the contrast case for the contractile-ordering claim.","marker":"[37]"}],"fun_headline_variants":["Contractile stress creates order in thin active films","Deformable films flip active nematic instability rules","Activity drives shape and order coupling in nematic layers","Thin active films: contractile activity orders isotropic phase","Beyond 2D: thickness changes redefine active nematic instabilities"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The predictions assume surface tension is negligible (capillary number $\\mathrm{Ca}\\gg1$) so the film surfaces are stress-free, and assume the nematic tensor is uniform across the film thickness; if either assumption fails, the instabilities could be suppressed or altered.","fun_headline_variants_meta":{"raw":{"variants":["Contractile stress creates order in thin active films","Deformable films flip active nematic instability rules","Activity drives shape and order coupling in nematic layers","Thin active films: contractile activity orders isotropic phase","Beyond 2D: thickness changes redefine active nematic instabilities"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.00031,"raw_usage":{"total_tokens":1806,"prompt_tokens":1018,"completion_tokens":788,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":634,"completion_tokens_details":{"reasoning_tokens":709}},"tokens_in":634,"tokens_out":788,"duration_ms":7460,"temperature":1.0,"reasoning_tokens":709,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-15T19:26:22.401568+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"A direct numerical solution of the full three-dimensional equations (1)–(3) for a contractile active nematic cylinder in the isotropic phase ($B=2/3$) at parameters where Eq. (76) predicts growth for circumferential mode $P=2$ and small axial wavenumber would settle the claim: if the order parameter $S$ does not grow and no circumferential thickness or shape bands appear, the sign-reversal result is refuted.","supporting_citations":[{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Supplies the baseline 2D active-nematic result that bend (splay) perturbations destabilize extensile (contractile) systems, which the flat-film result contrasts with."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Used as the reference for normal 2D active nematics where only extensile activity grows the nematic order in the isotropic phase."},{"cited_title":"Godr` eche and P","cited_arxiv_id":null,"evidence_quote":"Together with [26], establishes the extensile-only ordering rule on fixed surfaces that the cylindrical-film result reverses."},{"cited_title":"Alaimo, C","cited_arxiv_id":null,"evidence_quote":"Provides the fixed-cylinder active nematic instability analysis that the deformable cylindrical film builds on and extends with thickness dynamics."},{"cited_title":"ˇSkult´ ety, D","cited_arxiv_id":null,"evidence_quote":"Shows curvature dictates preferred orientation-instability directions on fixed curved geometries, the baseline for the curved-film comparison."},{"cited_title":"Howell, European Journal of Applied Mathematics 7, 321 (1996)","cited_arxiv_id":null,"evidence_quote":"Supplies the passive thin-viscous-film equations and cylinder/sphere solutions that the active theory reduces to when activity is off."},{"cited_title":"Maroudas-Sacks, S","cited_arxiv_id":null,"evidence_quote":"Provides the asymptotic (lubrication) method used to reduce the 3D equations to the effective film dynamics."},{"cited_title":"Narayanaswamy, J","cited_arxiv_id":null,"evidence_quote":"Reference for the isotropic-phase instability of 2D active nematics on fixed surfaces, the contrast case for the contractile-ordering claim."}],"review_version":2}