{"id":"173ba9fb-d86f-4b84-83b6-a6fb92a170ab","arxiv_id":"2608.06675","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":6.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":1,"one_line_summary":"For oblique disc impacts, tangential and kinetic restitution coefficients are non-unique functions of impact angle, friction, and initial angular velocity, even when normal restitution is well defined.","lead":"Simulations of a disc bouncing off a plate show that the tangential and kinetic restitution coefficients depend strongly on impact angle, friction, and initial spin, so the same numerical value can describe very different collisions. This matters because many event-driven simulations of granular materials use a single fixed restitution coefficient as a material property.","discovery_kind":"extension","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The central claim rests on an unvalidated DEM contact law; until the θ/ω-dependent eT/ekin patterns are reproduced with a standard contact model or experiments, the non-uniqueness conclusion may be an artifact of the simulation.","rationale":"I read the paper as a controlled DEM study whose main point is definitional and practical: within a frictional, dissipative disc–plate collision, eT and ekin are many-to-one functions of (θ, μ, ωin), so a fixed value does not identify a material. For the argument to hold as a statement about real systems, the contact model must capture the relevant physics; the authors explicitly limit it to rigid bodies with overlap stand-in and no internal degrees of freedom. This is exactly the reader's weakest assumption, and I agree it is load-bearing. However, the concern does not invalidate the paper's internal logic: non-uniqueness is demonstrated within the stated model, and the qualitative conclusion is consistent with existing analytical relations such as Eq. 2. The missing experimental validation and missing reproducibility items (parameter table, error bars, data/code, empty citations) strengthen the conditionality but do not force rejection. Secondary issues—such as the Conclusions referring to 'spherical particles' when the simulations are two-dimensional discs—should be corrected but do not break the central argument. Therefore the reader's CONDITIONAL verdict stands unchanged.","tokens_in":6163,"tokens_out":6675,"duration_ms":65475,"concrete_test":"Re-run the full θ–μ–ω sweep with a standard, separately validated Hertz–Mindlin contact model (Hertzian normal stiffness with viscoelastic damping, tangential stiffness with Coulomb sliding) under the same impact velocities, μ/γ ranges, and geometry. If eT(θ) and ekin(θ) still show non-monotonic angle dependence, rolling-regime micro-slip oscillations, and ω-induced divergence (eT ≫ 1 or ≪ 0), the non-uniqueness claim is robust; if the patterns change qualitatively, they are properties of the overlap-area force law rather than of restitution coefficients. A secondary check would compare the same observables to the experimental oblique-impact data cited in [18].","verdict_should_be":"UNCHANGED","load_bearing_attack":"The load-bearing premise is that the overlap-proportional contact force with Coulomb friction is a faithful proxy for real disc impacts. This is not a peripheral assumption: the Conclusions generalize from the simulation to 'material parameters' and say eT and ekin are 'ill-suited as control parameters for numerical simulations.' The Simulation section itself states 'the particle and the plate are rigid, no internal degrees of freedom or plastic deformation are being considered.' If real discs dissipate or redistribute energy through internal vibration, plastic yield, or roughness in ways this model forbids, the specific signature of non-uniqueness reported here—micro-slip oscillations in the rolling regime, collapse of all μ-curves onto pure rolling/sliding bounds, and the extreme eT range −4.17 to 5.37 under initial spin—could be an artifact of the contact law rather than a generic property of restitution coefficients. The absence of a parameter table, error bars, and release of data/code, plus no comparison with experimental oblique-impact measurements, leaves no way to distinguish physical behavior from numerical or algorithmic behavior. The paper even contains unresolved empty citations ('well known []', 'companion paper []'), compounding the validation gap.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"This Letter reports two-dimensional DEM simulations of a disc impacting a horizontal plate, with systematic variation of impact angle θ, friction coefficient μ, normal damping γ, and initial angular velocity ω. The paper defines normal, tangential, and kinematic restitution coefficients and shows that eT and ekin vary non-monotonically with θ, converge onto rolling/sliding bounds at large θ, exhibit micro-slip oscillations in the rolling regime, and are substantially altered by initial spin. The authors conclude that eT and ekin are not unique material parameters but highly situational quantities, and that prescribing single values of eT or ekin in event-driven simulations is problematic.","tokens_in":6414,"tokens_out":4574,"duration_ms":45138,"significance":"If the conclusions hold, the paper addresses a genuine gap in the granular-impact literature: most work focuses on the normal restitution coefficient, while tangential and kinematic coefficients are routinely used in event-driven simulations and kinetic theories despite being poorly characterized. The reported bounds by pure rolling and pure sliding, the θ-dependent minima, and the sensitivity to initial angular velocity are practically relevant observations that go beyond typical textbook treatments. The paper is, however, purely computational and currently lacks the parameter reporting, validation, and reproducibility details needed to establish that these patterns are generic properties of dissipative frictional collisions rather than artifacts of one contact model. With those additions the work could be a useful contribution, but in its present form the significance is conditional.","major_comments":[{"comment":"The Simulation section does not report the numerical parameters needed to reproduce or judge the simulations: Young's modulus, normal damping γ values, disc radius and mass, time step, polygon discretization, and plate properties are all absent, and Fig. 2 refers to 'different γ' without giving any values. Without a parameter table and convergence checks, the quantitative curves and the central non-uniqueness claim cannot be verified, and the reader cannot distinguish physical behavior from numerical artifacts. Please provide a full parameter table, together with at least one time-step and mesh-refinement convergence test.","section":"Simulation section"},{"comment":"The claim that eT oscillates around a pure-rolling value by roughly 2% due to 'micro-slip events' is a key qualitative finding, but it is supported only by a visual reading of Fig. 2. There is no quantitative definition of oscillation amplitude, no statement of θ resolution, no error bars, and no test showing that the oscillations persist under refinement of the contact algorithm or time step. Since the non-uniqueness argument relies on these oscillations being physical, a quantitative and reproducible characterization is required.","section":"Results, rolling-regime oscillations"},{"comment":"The generalization from this specific contact model to real materials is too strong. The Simulation section explicitly states that 'no internal degrees of freedom (e.g. vibration) are allowed' and 'no internal degrees of freedom or plastic deformation are being considered.' If real discs dissipate or redistribute energy through internal vibration, plastic yield, or surface roughness, the reported collapse to rolling/sliding bounds and the extreme eT range (−4.17 to 5.37) under initial spin may be artifacts of the overlap-proportional rigid-body contact law. The Conclusions should either restrict the claim to this model class or add a test showing that a contact model including internal degrees of freedom or a validated elastoplastic contact law reproduces the same functional patterns.","section":"Simulation section and Conclusions"},{"comment":"The Conclusions state that 'the normal coefficient of restitution is essentially unique for each material,' but this is not supported by the paper's own results: Fig. 2a and the accompanying text report that eN decreases for steeper impact angles and shifts with γ. If 'essentially unique' is intended to mean only independence of μ, the term needs to be defined precisely; otherwise the contrast with eT and ekin is ambiguous and the uniqueness claim for eN is not quantitatively established.","section":"Conclusions and Fig. 2a"}],"minor_comments":[{"comment":"Several citations are incomplete: the Introduction has 'well known []', the Simulation section has 'companion paper []', and the Implication section has 'impact kinematics []'. These empty references must be filled before submission.","section":"Introduction, Simulation, Implications"},{"comment":"The Conclusions refer to 'spherical particles', but the simulations are of two-dimensional discs; please correct the terminology.","section":"Conclusions"},{"comment":"The sign convention in Eq. (1) is unclear: the text says the sign is negative for eN and positive for eT, but the relation Δν = ±e·Δν′ is not accompanied by explicit definitions of Δν and Δν′ in terms of pre- and post-collision normal and tangential velocity components. Define all symbols in one place.","section":"Equation (1)"},{"comment":"The caption says 'The dotted lines represent μ = [0, 1] and different γ', which is not a complete description. Please specify line styles, parameter values, and whether the curves are raw data or averaged results.","section":"Fig. 2 caption"},{"comment":"The sentence 'Gravity is disabled during the simulation...' appears twice in consecutive paragraphs; please remove the duplicate.","section":"Simulation section"}],"recommendation":"major_revision","confidential_remarks":"The manuscript reads like a compressed version of a larger study, and the empty references and duplicated sentence suggest it was submitted before final polishing. The central question is worthy, but as a Letter it asks the reader to trust a simulation apparatus that is only described by reference to prior work. Adding a supplementary material with the parameter table, data, and validation results, and softening the conclusions to the model class actually simulated, would make the case much stronger. The current version is not ready for publication in its present form."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Krengel's letter has a real finding, but it is more situational than the title and conclusions suggest. The 2D DEM sweep shows that eT and ekin depend strongly on impact angle, friction, and initial angular velocity, with micro-slip oscillations in the rolling regime and eT ranging from -4.17 to 5.37 under initial spin. That goes well beyond the sliding-regime formula in Eq. 2, and the collapse of all mu-curves onto pure rolling/sliding bounds is a clean, testable statement. The coefficients are measured outputs of forward simulations, not fitted inputs, so there is no circularity in the main claim.\n\nCredit where due: the paper identifies a genuine gap in how restitution coefficients are treated in event-driven simulations and rockfall models, and the initial-spin effect on eT, including eT>1 and eT<0, is not in the cited literature. The qualitative patterns are likely reproducible within this model.\n\nSoft spots are real though. The load-bearing premise is that overlap-proportional contact with Coulomb friction is a faithful proxy for a real disc impact. The paper itself says no internal degrees of freedom or plastic deformation are considered. That makes 'highly situational material parameters' a claim about this contact model, not necessarily about materials. The extreme eT values may be artifacts of the contact law. There are also no error bars or repeat statistics, no table of Young's modulus, gamma values, disc mass or radius, and no code or data release. Two citations are empty ('well known []', 'companion paper []'). The conclusion calls the particles 'spherical' when the model is 2D discs—a wording problem that also signals the generalization to spheres is unearned.\n\nNone of this kills the central point. Within the model, fixed eT/ekin inputs are ill-defined. A serious referee should see it, but the paper needs the parameter table, reproducibility material, and a toned-down abstract and conclusion before it is publishable. I would cite the micro-slip oscillation behavior once the numerics are checked.","headline":"Useful DEM evidence that eT/ekin are situational rather than material constants, but the unvalidated contact model and missing reproducibility details make the sweeping conclusions premature.","tokens_in":6924,"tokens_out":2394,"would_cite":true,"duration_ms":23381,"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":"For frictional disc impacts, the tangential and kinematic restitution coefficients are situational parameters, not material constants.","keywords":["oblique impact","restitution coefficient","discrete element simulation","granular matter","tangential restitution","microslip","initial angular velocity","non-uniqueness"],"falsifier":"Take one disc material with a fixed, independently measured normal restitution $e_N$, and sweep the impact angle $\\theta$ from near-grazing to near-normal while measuring $e_T$ and $e_\\mathrm{kin}$ for controlled values of friction and initial spin. If for that material each value of $e_T$ or $e_\\mathrm{kin}$ corresponds to exactly one $(\\theta,\\mu,\\omega_\\mathrm{in})$ configuration, the non-uniqueness claim is falsified; if identical values recur across widely different configurations, it is confirmed.","tokens_in":5962,"feed_emoji":"🥏","tokens_out":7833,"duration_ms":69164,"temperature":0.7,"pith_summary":"The paper claims that the tangential and kinematic coefficients of restitution, $e_T$ and $e_\\mathrm{kin}$, of a disc impacting a flat plate are not fixed material properties. Using two-dimensional discrete-element simulations, it shows that the same numerical value of $e_T$ or $e_\\mathrm{kin}$ arises from many different combinations of impact angle, friction coefficient, normal dissipation, and initial angular velocity. The normal coefficient $e_N$, in contrast, remains essentially unique for a given material within this model. The author concludes that $e_T$ and $e_\\mathrm{kin}$ are highly situational parameters and are ill-suited as control parameters for simulations of granular matter, because a measured value does not identify the collision it came from.","feed_headline":"Disc impacts show tangential restitution is no material constant","feed_subtitle":"The same coefficient can describe many different collisions, so event-driven simulations should not treat it as a material constant.","key_machinery":"The argument is carried by a two-dimensional discrete-element collision model in which a disc strikes a horizontal plate: contact forces are proportional to the area of the overlap polygon, friction is Coulomb with coefficient $\\mu$, the normal direction dissipates energy through a factor $\\gamma$, and the bodies are rigid with no internal degrees of freedom such as vibration and no plastic deformation. This controlled setup lets the paper isolate how the three restitution coefficients depend on $\\theta$, $\\mu$, $\\gamma$, and initial angular velocity $\\omega_\\mathrm{in}$. The second piece of machinery is the pre-rolling relation $e_T = 1-\\mu(1+e_N)\\cot(90^\\circ-\\theta)$, which the paper shows is valid only until the contact enters the rolling regime.","core_discovery":"On its own terms, the paper's central discovery is that for oblique disc impacts, $e_T$ and $e_\\mathrm{kin}$ are non-monotonic and non-unique functions of the impact angle $\\theta$ and the friction coefficient $\\mu$, bounded by the ideal cases of pure sliding ($\\mu\\to 0$) and pure rolling ($\\mu\\to\\infty$). $e_T$ follows the literature relation $e_T = 1 - \\mu(1+e_N)\\cot(90^\\circ-\\theta)$ only until a critical angle $\\theta_c$; beyond it, $e_T$ oscillates around a rolling value due to micro-slip events. $e_\\mathrm{kin}$ dips to a $\\mu$-dependent minimum and then rises to a $\\gamma$-dependent plateau. Adding an initial angular velocity $\\omega_\\mathrm{in}$ moves the onset of rolling and, for steep impacts, pushes $e_T$ far outside the range $[0,1]$, from about $-4.17$ to $5.37$ in the simulations. From this the paper concludes that neither $e_T$ nor $e_\\mathrm{kin}$ can serve as a unique material parameter for numerical simulations of oblique frictional impacts.","pith_inferences":["If the non-uniqueness carries over to three-dimensional and non-spherical particles, as the author anticipates, then orientation adds yet another state variable, making restitution-coefficient descriptions even less tractable.","A direct test would be to repeat the same parameter sweep with contact laws that include internal vibration or plastic deformation; if the curves collapse or become unique, the non-uniqueness is a property of the contact law rather than of granular collisions generally.","The result suggests that scatter in published tangential-restitution measurements across laboratories may reflect undocumented differences in impact conditions rather than material variability."],"forward_implications":["A fixed tangential or kinematic restitution coefficient cannot be transported from one measurement to another simulation as if it were a material constant.","Event-driven and kinetic-theory calculations that use single restitution coefficients will misrepresent oblique frictional impacts, especially when rotation is present before contact.","Reports of tangential restitution should specify impact angle, friction properties, and initial angular velocity, otherwise the number is ambiguous.","The simple pre-rolling formula for the tangential coefficient fails once rolling begins, so attempts to derive a tangential from a normal restitution coefficient alone are not viable for steep impacts."],"supporting_citations":[{"why":"Supplies the pre-rolling formula that the paper tests and then shows fails once rolling begins.","marker":"[17]"},{"why":"Provides the discrete-element simulation algorithm used for all reported restitution coefficients.","marker":"[15]"},{"why":"Defines the impact setup and parameter choices for the planar disc collisions.","marker":"[16]"},{"why":"Gives the contact-mechanics basis for micro-slip at the rolling-sliding transition that drives e_T oscillations.","marker":"[19]"},{"why":"Earlier tangential restitution model for dashpot contacts that motivates the definition of e_T the paper re-examines.","marker":"[2]"},{"why":"Experimental rebound measurements used to support the energy transfer from tangential motion into rotation.","marker":"[18]"}],"fun_headline_variants":["Tangential restitution: situational, not a constant","Oblique disc impacts: restitution lacks uniqueness","Disc impact restitution: non-unique, angle-dependent","Restitution coefficients mislead in oblique disc collisions","Why tangential restitution isn't a material property"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The conclusion rests on whether the simulation's contact law represents real disc collisions: the model forbids internal vibration and plastic deformation, so if real discs lose energy through those channels, the particular pattern of non-uniqueness seen here could be an artifact of the contact law.","fun_headline_variants_meta":{"raw":{"variants":["Tangential restitution: situational, not a constant","Oblique disc impacts: restitution lacks uniqueness","Disc impact restitution: non-unique, angle-dependent","Restitution coefficients mislead in oblique disc collisions","Why tangential restitution isn't a material property"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000201,"raw_usage":{"total_tokens":1393,"prompt_tokens":973,"completion_tokens":420,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":589,"completion_tokens_details":{"reasoning_tokens":349}},"tokens_in":589,"tokens_out":420,"duration_ms":4591,"temperature":1.0,"reasoning_tokens":349,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-10T22:41:38.337364+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Take one disc material with a fixed, independently measured normal restitution $e_N$, and sweep the impact angle $\\theta$ from near-grazing to near-normal while measuring $e_T$ and $e_\\mathrm{kin}$ for controlled values of friction and initial spin. If for that material each value of $e_T$ or $e_\\mathrm{kin}$ corresponds to exactly one $(\\theta,\\mu,\\omega_\\mathrm{in})$ configuration, the non-uniqueness claim is falsified; if identical values recur across widely different configurations, it is confirmed.","supporting_citations":[{"cited_title":"Sondergaard, K","cited_arxiv_id":null,"evidence_quote":"Supplies the pre-rolling formula that the paper tests and then shows fails once rolling begins."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Provides the discrete-element simulation algorithm used for all reported restitution coefficients."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Gives the contact-mechanics basis for micro-slip at the rolling-sliding transition that drives e_T oscillations."},{"cited_title":"Becker, T","cited_arxiv_id":null,"evidence_quote":"Earlier tangential restitution model for dashpot contacts that motivates the definition of e_T the paper re-examines."},{"cited_title":"Gorham and A","cited_arxiv_id":null,"evidence_quote":"Experimental rebound measurements used to support the energy transfer from tangential motion into rotation."}],"review_version":1}