{"id":"7f04c8e1-518b-4037-b0b9-36aede072c5d","arxiv_id":"2411.18185","paper_version":4,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":6.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":1,"one_line_summary":"Adding localized nonlinear losses at the open end of a modeled clarinet raises the oscillation threshold and lowers the extinction threshold, narrowing the playable blowing-pressure range.","lead":"This paper simulates a simplified clarinet model with extra turbulent losses at the open end. It finds that stronger such losses raise the minimum blowing pressure needed to start a note, while also lowering the pressure at which the note stops.","discovery_kind":"extension","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The threshold increase rests on applying the quasi-steady v|v| end-loss law to the DC operating point, not on high-amplitude acoustic calibration; if the zero-frequency slope of the end impedance is different, the 4% shift is not robust.","rationale":"I read the paper as a self-contained model study: the reflection-function derivation in Section 2.2 is algebraically consistent, the iterated-map stability framework is standard, and the monotone threshold shift is a legitimate consequence of Eq. (4) when the fixed point is nonzero. The paper does not overclaim direct experimental confirmation, and its call for future experiments is appropriate. However, the size of the claimed effect (about 4% at zeta = 0.3) is small enough that it depends entirely on the slope of the end-loss law at the DC operating point, so the least-secure step is not the map computation but the transfer of Cnl from high-amplitude calibrations to the zero-frequency/mean-flow regime. That is the same premise the reader flags, and I agree with the conditional verdict; I do not see a basis for stronger rejection because the model is internally coherent and the assumption is standard in the cited literature.","tokens_in":11762,"tokens_out":19655,"duration_ms":196095,"concrete_test":"Measure the DC pressure-flow curve of the open termination over the mean-flow range corresponding to gamma in [0.35, 0.40] at zeta = 0.3, and compare its local slope with the derivative of Eq. (4) using Cnl = 0.7. Alternatively, run the same iterated-map stability calculation with a measured frequency-dependent end impedance in place of Eq. (4); if the predicted shift at zeta = 0.3 (gamma_osc_up from 0.378 to 0.393) is not reproduced within 0.005, the quasi-steady v|v| premise is load-bearing and the central claim is conditional.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central claim of Section 5.1.2 is determined by the derivative of rhat at the fixed point x*, not by the amplitude of the oscillatory perturbation. Because x* is nonzero, rhat'(x*) depends on the slope of Eq. (4), p = rho0*Cnl*v*|v|, at the mean operating point. The value Cnl=0.7 cited for the termination was fitted from high-amplitude oscillatory measurements, and Eq. (4) is a quasi-steady turbulent-loss law; the paper provides no evidence that this law, with the same coefficient, controls the linearized impedance at the DC flow rates that set x*. If the real termination impedance is frequency dependent, hysteretic, or has a different low-Reynolds/Strouhal slope, the predicted monotone increase in gamma_osc_up could shrink, disappear, or reverse. This is not an internal inconsistency in the iterated-map derivation; it is the least-secured premise connecting the model result to a real clarinet.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper studies a Raman clarinet model with localized nonlinear losses at the open end, represented by the quasi-steady pressure-velocity relation p = rho0*Cnl*v*|v|. The authors derive a closed-form nonlinear reflection function, embed it in an iterated map, and compute the stability of the equilibrium, two-state, and long-period regimes as functions of the blowing pressure gamma, the embouchure parameter zeta, and the nonlinear loss coefficient K0. The central result is that increasing localized nonlinear losses raises the oscillation threshold (the minimal blowing pressure for onset) by a few percent while strongly lowering the extinction threshold, and the paper also characterizes bifurcation types and multistability regions as the loss coefficient varies.","tokens_in":11943,"tokens_out":11300,"duration_ms":97395,"significance":"If the central prediction is correct, the paper provides a simple qualitative account of how end losses affect clarinet playability: stronger localized losses require higher mouth pressure to start the sound and reduce the maximum sustainable pressure, narrowing the dynamic range. The derivation is transparent and the iterated-map formulation is elegant; the nonlinear reflection function interpolates continuously between the open-tube and closed-tube limits, and the threshold shift is not obtained by fitting parameters in this paper, since Cnl is taken from earlier experimental studies. The predicted monotonic rise of the oscillation threshold is a falsifiable consequence of the model and could be tested experimentally. However, the quantitative monotonicity claim rests on finite numerical scans, and the physical extrapolation of a high-amplitude fitted loss law to the low-frequency/DC operating point is not validated in the manuscript.","major_comments":[{"comment":"The predicted rise of gamma_osc_up with K0 is governed by the derivative of the nonlinear reflection function r_nl at the nonzero fixed point x* (Eqs. (7) and (11)), not by the large-amplitude behavior of Eq. (4). The coefficient Cnl = 0.7 is taken from high-amplitude oscillatory fits (Refs. 4 and 6), and the paper gives no evidence that the quasi-steady v|v| law with the same Cnl controls the linearized end impedance at the DC operating point that determines x*. If the real termination loss is frequency dependent, hysteretic, or has a different low-velocity slope, the reported 4% threshold increase could shrink, disappear, or reverse. Please either validate the low-frequency applicability of Eq. (4), show that a range of plausible low-velocity slopes preserves the monotone increase, or explicitly restrict the conclusion to the quasi-steady model.","section":"Section 2.2, Eq. (4), and Section 5.1.2, Fig. 8"},{"comment":"The claim that gamma_osc_up \"increases monotonically with K0 for all zeta in [0, 0.99]\" is a global statement drawn from a single finite grid (Delta_gamma = 1e-3, Delta_zeta = 5e-3, Delta_K0 = 5e-2) without a convergence check. Since f and its iterates have derivative discontinuities, narrow stability windows or small non-monotonic wiggles could be missed. Please provide a grid-refinement study, for example halving each step near the threshold, or give an analytic argument for monotonicity; if neither is available, soften the claim to the observed parameter range.","section":"Section 5.1.2, Fig. 8, with Table 1"},{"comment":"Fixed points are located by linear interpolation of zero-crossings on a uniform mesh whose bounds are chosen empirically (x_i in [-gamma - 0.1, gamma + 0.1]). The stability classification uses |f'(x*)| < 1, so the result is sensitive to the accuracy of x* and to the behavior of f at kinks. Please report the sensitivity of the R1/R2 boundaries to the mesh size and to the bracket choice, or use a root-finding method that handles non-smooth points.","section":"Section 3"}],"minor_comments":[{"comment":"The phrase \"in can provide\" should read \"it can provide\".","section":"Introduction, first paragraph"},{"comment":"\"Additionnally\" should be \"Additionally\".","section":"Section 5.1.1, paragraph after Fig. 6"},{"comment":"The caption does not state for which zeta the (lambda, gamma) plane is drawn, or whether it is a projection over zeta; please clarify.","section":"Figure 6 caption"},{"comment":"The notation changes from r_nl and K0 in Eq. (7) to \\hat r_nl and \\hat K0 in Eq. (11); the relation \\hat K0 = P_M K0 should be restated near Eq. (11) for readability.","section":"Eqs. (7) and (11)"},{"comment":"The phrase \"the area where R2 is unstable shrinks towards high values of zeta\" is ambiguous; if the unstable hole shrinks, state that explicitly.","section":"Section 4.2, Fig. 4"}],"recommendation":"major_revision","confidential_remarks":"The manuscript is within the journal's scope. The main scientific risk is the use of a high-amplitude fitted loss coefficient at the DC operating point that determines the oscillation threshold; I would encourage the authors to add a sensitivity analysis or a targeted low-frequency impedance measurement. Making the simulation code available would also strengthen reproducibility, since the monotonicity claim currently rests on a numerical scan."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Short version: this is a careful model paper with a new result. The authors extend the standard Raman clarinet iterated-map framework to include localized nonlinear losses at the open end, derive an explicit reflection function, and show by parametric stability analysis that increasing the nonlinear loss coefficient raises the oscillation threshold (the minimal blowing pressure to start oscillations) while lowering the extinction threshold. The threshold rise is new relative to the cited literature; the extinction effect was already known. The derivation is algebraically consistent and the stability classification follows the established iterated-map machinery. The paper is also honest: it states the quasi-static v|v| assumption and does not claim experimental validation of the threshold shift.\n\nThe soft spots are real but not fatal. First, the monotonic-increase claim across all zeta and the high-K0 behavior rest on a finite grid (Table 1) with no convergence checks, and no code or data are shipped. \"Available upon reasonable request\" is weaker than a public release. Second, as your stress-test note correctly points out, the threshold shift is controlled by the derivative of the nonlinear reflection function at the nonzero fixed-point pressure—i.e., by the slope of the v|v| law at the DC operating point. The coefficient Cnl was fitted from high-amplitude oscillatory measurements. If the real end termination has a different low-frequency or low-Reynolds impedance slope, the magnitude (or even sign) of the predicted shift could change. None of this is hidden; the paper is a model study and the undercutting implication is explicitly left as a future hypothesis. But readers should not take the 4% shift as a measured acoustic effect.\n\nBottom line: for people working on wind-instrument modeling, this is a useful and careful piece. It deserves a serious referee round. The referee should ask for the code and grid-convergence details and for a short discussion of the v|v| law's applicability at the operating point. I would cite it if I were writing in this area.","headline":"A clean model paper that shows a new, plausible effect—localized nonlinear losses raise the oscillation threshold—but the magnitude rests on an unvalidated low-frequency v|v| law; deserves serious peer review.","tokens_in":12501,"tokens_out":3663,"would_cite":true,"duration_ms":33255,"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":"Localized nonlinear losses at a clarinet's open end raise the minimal blowing pressure needed to start a tone.","keywords":["Raman clarinet model","localized nonlinear losses","oscillation threshold","extinction threshold","iterated map stability","wind instrument acoustics","nonlinear boundary condition","reflection function"],"falsifier":"Measure the onset blowing pressure of a cylindrical pipe with interchangeable open-end geometries, sharp-edged unflanged versus rounded or flanged, at fixed embouchure, using a slow linear pressure ramp and averaging over many trials to remove bifurcation delay; if the onset pressure does not rise monotonically with the inferred $C_{nl}$, or rises far more than the 4% predicted at $C_{nl}=0.7$, the central claim is refuted.","tokens_in":11523,"feed_emoji":"🎷","tokens_out":5911,"duration_ms":49897,"temperature":0.7,"pith_summary":"The paper works with a Raman clarinet, a minimal physical model in which an idealized reed is coupled to a cylindrical tube described by a reflection function, and extends it to include localized nonlinear losses at the open end. Its central result is that these losses raise the oscillation threshold: the minimal blowing pressure at which self-sustained oscillations start increases monotonically with the nonlinear-loss coefficient for all embouchures studied. The same losses also lower the extinction threshold, and do so about ten times more strongly. Because the two thresholds bound the playable pressure range, the model predicts that sharper edges at the open end make the instrument harder to start while also compressing the sound amplitude and preserving a direct onset bifurcation.","feed_headline":"Nonlinear end losses raise the clarinet's oscillation threshold","feed_subtitle":"Onset pressure climbs 4 percent at typical embouchure; the pressure at which sound stops falls 40 percent.","key_machinery":"The central object is the nonlinear reflection function $r_{nl}(\\xi)=\\lambda^2\\xi\\left(1-\\tfrac{4}{1+\\sqrt{1+\\hat{K}_0|\\xi|}}\\right)$, obtained by inverting the quasi-steady loss law and composing it with one round trip through the tube. It converts the delay-line system into the iterated map $x_{n+1}=f(x_n)$, whose fixed points locate the equilibrium and multi-state oscillation regimes. Stability of a period-$n$ regime is decided by whether the derivative of the $n$-th iterate is less than 1 in modulus, and the boundaries of these stability regions define the oscillation and extinction thresholds.","core_discovery":"For a cylindrical tube with a quasi-steady nonlinear boundary condition $p=\\rho_0 C_{nl}v|v|$ at the open end, the paper derives a passive nonlinear reflection function and folds the entire instrument into a one-dimensional iterated map $x_{n+1}=f(x_n)$. Computing fixed points and their multipliers over a fine grid of blowing pressure $\\gamma$, embouchure $\\zeta$, and dimensionless loss coefficient $\\hat{K}_0$, it finds that $\\gamma_{\\mathrm{osc}\\nearrow}$ increases monotonically with $\\hat{K}_0$ for all $\\zeta\\in[0,0.99]$. Concretely, at $\\zeta=0.3$, the threshold rises from $0.378$ at $\\hat{K}_0=0$ to $0.393$ at $\\hat{K}_0=0.325$, a 4% increase, while the extinction threshold drops by 40% for the same parameters. For $\\hat{K}_0>34$, the silent equilibrium coexists with stable oscillating regimes at high embouchure, and in the limit $\\hat{K}_0\\to\\infty$ no stable oscillation exists below $\\gamma=1$.","pith_inferences":["A time-domain simulation using a frequency-dependent radiation impedance instead of the memoryless $v|v|$ law would test whether the monotonic threshold rise survives realistic end losses.","Because the predicted onset shift is only 4%, onset experiments must control the blowing-pressure ramp rate, since bifurcation delay can mask or exaggerate the effect.","The reflection-function form could be applied to tone holes, letting makers estimate how undercutting changes local loss and hence the playable range.","The model's amplitude-compressing behavior suggests end-loss tuning as a design lever for shaping loudness response somewhat independently of pitch."],"forward_implications":["At a typical clarinet embouchure ($\\zeta=0.3$), increasing $\\hat{K}_0$ from 0 to the experimentally plausible value 0.325 raises the onset pressure by 4%, from $\\gamma_{\\mathrm{osc}\\nearrow}=0.378$ to 0.393.","The same increase cuts the extinction threshold by 40%, so the blowing-pressure range that sustains a steady tone narrows substantially.","Nonlinear losses keep the onset bifurcation direct while flattening the amplitude curve near threshold, which the paper identifies as an aid for controlling soft dynamics; linear losses, by contrast, can make the bifurcation inverse.","For $\\hat{K}_0>34$, the silent equilibrium coexists with stable oscillating regimes at high embouchure, and in the limit $\\hat{K}_0\\to\\infty$ no oscillation occurs below $\\gamma=1$.","The derived reflection function gives a simple way to include localized losses in waveguide models, which the paper suggests could inform side-hole undercutting in instrument design."],"supporting_citations":[{"why":"Supplies the iterated-map formalism, the reed nonlinear characteristic, and the stability criterion for periodic regimes that the paper uses throughout.","marker":"[13]"},{"why":"Provides the experimental fit $C_{nl}=0.7$ and the demonstration that nonlinear losses lower the extinction threshold, the baseline the paper extends to the oscillation threshold.","marker":"[6]"},{"why":"Provides the experimental comparison and the overestimation discussion that justify the maximal realistic value $\\hat{K}_0=0.325$.","marker":"[4]"},{"why":"Gives the quasi-steady turbulent-loss law at a tube exit used as the boundary condition Eq. (4).","marker":"[15]"},{"why":"Also supports the $v|v|$ quasi-steady end-loss relation used to derive the nonlinear reflection function.","marker":"[16]"},{"why":"Is the source of the bifurcation diagrams and the direct-versus-inverse threshold distinction that the paper reproduces and extends to nonlinear losses.","marker":"[12]"}],"fun_headline_variants":["Nonlinear losses push clarinet onset pressure up 4%","Clarinet's oscillation threshold rises with nonlinear losses","End losses raise clarinet's starting pressure, cut stop pressure","Nonlinear end losses shift clarinet thresholds: onset up, stop down","4% higher onset, 40% lower stop: nonlinear clarinet losses"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The predicted rise of the oscillation threshold rests on modelling the open-end losses as a memoryless, quasi-steady relation $p=\\rho_0 C_{nl} v|v|$ with a single constant $C_{nl}$; if the real losses are frequency dependent, hysteretic, or of another form, the monotonic increase may not survive.","fun_headline_variants_meta":{"raw":{"variants":["Nonlinear losses push clarinet onset pressure up 4%","Clarinet's oscillation threshold rises with nonlinear losses","End losses raise clarinet's starting pressure, cut stop pressure","Nonlinear end losses shift clarinet thresholds: onset up, stop down","4% higher onset, 40% lower stop: nonlinear clarinet losses"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000659,"raw_usage":{"total_tokens":2979,"prompt_tokens":874,"completion_tokens":2105,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":490,"completion_tokens_details":{"reasoning_tokens":2026}},"tokens_in":490,"tokens_out":2105,"duration_ms":11607,"temperature":1.0,"reasoning_tokens":2026,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-12T11:26:28.179286+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Measure the onset blowing pressure of a cylindrical pipe with interchangeable open-end geometries, sharp-edged unflanged versus rounded or flanged, at fixed embouchure, using a slow linear pressure ramp and averaging over many trials to remove bifurcation delay; if the onset pressure does not rise monotonically with the inferred $C_{nl}$, or rises far more than the 4% predicted at $C_{nl}=0.7$, the central claim is refuted.","supporting_citations":[{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Supplies the iterated-map formalism, the reed nonlinear characteristic, and the stability criterion for periodic regimes that the paper uses throughout."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Provides the experimental fit $C_{nl}=0.7$ and the demonstration that nonlinear losses lower the extinction threshold, the baseline the paper extends to the oscillation threshold."},{"cited_title":"and Frappé, C.The Journal of the Acoustical Society of America122(2), 1173–1179 August (2007)","cited_arxiv_id":null,"evidence_quote":"Provides the experimental comparison and the overestimation discussion that justify the maximal realistic value $\\hat{K}_0=0.325$."},{"cited_title":"and Van Wijngaarden, L.Journal of Fluid Mechanics99(2), 293–319 (1980)","cited_arxiv_id":null,"evidence_quote":"Gives the quasi-steady turbulent-loss law at a tube exit used as the boundary condition Eq. (4)."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Also supports the $v|v|$ quasi-steady end-loss relation used to derive the nonlinear reflection function."},{"cited_title":"and Kergomard, J.Acta Acustica united with Acustica101(2), 279–291 (2015)","cited_arxiv_id":null,"evidence_quote":"Is the source of the bifurcation diagrams and the direct-versus-inverse threshold distinction that the paper reproduces and extends to nonlinear losses."}],"review_version":1}