{"id":"a31794a0-f30c-482d-b429-f0f7a772ae4c","arxiv_id":"2606.00560","paper_version":1,"verdict":"UNVERDICTED","confidence":"LOW","novelty_score":5.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":2,"one_line_summary":"Numerical trajectory simulations and Fokker-Planck solutions show cusp-like steady-state velocity distributions and Deff ~ r^{-2} diffusion for large resetting rates independent of drag form, with mean first-passage time minimized by an optimal resetting rate only in shear-thickening media.","lead":"The paper numerically examines inertial run-and-tumble particles with velocity resetting to zero in one-dimensional non-Newtonian media. A smart generalist might read it to see how resetting rates affect diffusion and search times in complex fluids used in biology or materials processing.","discovery_kind":"new_application","skeptic_critique":{"model":"grok-4.3","headline":"Numerical reliability of MFPT(r) curves is the load-bearing step for the media-type distinction","rationale":"The reader's weakest_assumption already isolates the numerical accuracy of the MFPT computation as the critical unverified step; the present analysis confirms that this is precisely where the central qualitative claim (media-dependent existence of optimal resetting) is least anchored, while the Ps(v) and Deff results have an internal consistency check.","tokens_in":1939,"tokens_out":317,"duration_ms":13577,"concrete_test":"Recompute MFPT versus r for both media using (i) 10× more trajectories and (ii) a velocity grid twice as fine in the numerical solver; verify whether the location and depth of the minimum in shear-thickening and its absence in shear-thinning remain within statistical error bars.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The headline distinction (optimal r exists in shear-thickening but not shear-thinning) rests on numerical evaluation of mean first-passage times. The paper reports trajectory-based Ps(v) agreeing with numerical FP solution, but does not state the method, grid resolution, or sampling used for MFPT; any velocity discretization, absorbing-boundary implementation, or finite-sample bias that differs between the two g(v) forms could create or erase the reported minimum. Because the independence claims for Ps(v) and Deff ~ r^{-2} are supported by explicit cross-checks while the MFPT claim is not, the media-type contrast is the least secure element.","agreement_with_reader":"agree"},"referee_report":{"model":"grok-4.3","summary":"The paper examines an athermal inertial run-and-tumble particle in one dimension subject to velocity resetting at rate r while moving in a non-Newtonian medium with nonlinear drag g(v). The run-and-tumble motion is driven by symmetric dichotomous noise of strength Σ and flip rate λ. The authors solve the Fokker-Planck equation numerically and sample trajectories to obtain the steady-state velocity distribution Ps(v), which develops a cusp at v=0 for large r; they further report that the long-time motion is diffusive with effective diffusivity Deff scaling as r^{-2}, both features independent of the specific g(v), λ, and Σ. In contrast, the mean first-passage time to a target velocity vt depends qualitatively on the medium: an optimal resetting rate exists for shear-thickening g(v) but not for shear-thinning g(v).","tokens_in":2093,"tokens_out":589,"duration_ms":14918,"significance":"If the reported distinction in mean first-passage time is numerically robust, the results demonstrate that the rheological character of the drag can qualitatively change the resetting-rate optimization for first-passage processes in active particles. The explicit cross-check between trajectory sampling and numerical Fokker-Planck integration for Ps(v) and the Deff scaling provides a concrete strength for those claims.","major_comments":[{"comment":"The headline claim that an optimal resetting rate exists only in shear-thickening media rests on the numerical evaluation of MFPT(r). No details are supplied on the discretization scheme, grid resolution, absorbing-boundary implementation, number of trajectories, or convergence tests used for the MFPT computation (in contrast to the explicit trajectory-vs-FP comparison stated for Ps(v)). This omission directly affects the reliability of the media-type distinction.","section":"Section on mean first-passage time (likely §4)"},{"comment":"The statement that Ps(v) and Deff ~ r^{-2} hold 'irrespective of the specific form of g(v)' is supported by the reported numerical agreement, but the MFPT results are presented only for two representative g(v) forms without a systematic scan over additional functional forms or parameter values to confirm the qualitative contrast persists.","section":"Abstract and MFPT discussion"}],"minor_comments":[{"comment":"The abstract states that results hold 'irrespective of ... the values of λ and Σ' yet the figures appear to use fixed λ and Σ; a brief statement clarifying the range explored would improve clarity.","section":"Abstract"},{"comment":"Error bars or convergence diagnostics are not mentioned for the trajectory-sampled Ps(v) or Deff even though the abstract highlights agreement with the numerical FP solution.","section":"Numerical methods and results sections"}],"recommendation":"major_revision","confidential_remarks":null},"author_rebuttal":{"model":"grok-4.3","summary":"We thank the referee for the detailed review and constructive feedback on our manuscript. The comments highlight important aspects of the numerical methodology and the scope of the MFPT analysis that require clarification. We address each major comment point by point below and will revise the manuscript accordingly to improve transparency and robustness.","responses":[{"response":"We agree that the manuscript lacks sufficient detail on the MFPT numerics, which is a valid concern for assessing the reliability of the shear-thickening versus shear-thinning distinction. In the revised version, we will add a dedicated subsection describing the numerical procedure: the finite-difference discretization of the time-dependent Fokker-Planck equation, the spatial grid resolution and domain size, the implementation of absorbing boundary conditions at the target velocity vt (including how probability flux is removed), the number of independent trajectory realizations used for cross-validation, and the convergence tests with respect to grid size and time step. These additions will directly address the reliability issue without altering the reported qualitative results.","revision_made":"yes","referee_comment":"[Section on mean first-passage time (likely §4)] The headline claim that an optimal resetting rate exists only in shear-thickening media rests on the numerical evaluation of MFPT(r). No details are supplied on the discretization scheme, grid resolution, absorbing-boundary implementation, number of trajectories, or convergence tests used for the MFPT computation (in contrast to the explicit trajectory-vs-FP comparison stated for Ps(v)). This omission directly affects the reliability of the media-type distinction."},{"response":"The two representative forms were chosen because they exemplify the distinct rheological classes (shear-thickening with g(v) increasing faster than linear, shear-thinning with g(v) increasing slower than linear), and the MFPT behavior traces to the sign of the second derivative of g(v) near the origin. While this provides a clear illustration, we acknowledge that a broader exploration would strengthen the claim. In the revision we will therefore include MFPT(r) curves for two additional g(v) forms (a different power-law exponent in each class and a saturating nonlinear drag) over a range of Σ and λ values, confirming that the existence of an optimal resetting rate remains confined to the shear-thickening class.","revision_made":"yes","referee_comment":"[Abstract and MFPT discussion] The statement that Ps(v) and Deff ~ r^{-2} hold 'irrespective of the specific form of g(v)' is supported by the reported numerical agreement, but the MFPT results are presented only for two representative g(v) forms without a systematic scan over additional functional forms or parameter values to confirm the qualitative contrast persists."}],"tokens_in":1587,"tokens_out":567,"duration_ms":19401,"standing_objections":[]},"desk_editor":{"model":"grok-4.3","letter":"The main things to know are that the steady-state velocity distribution develops a cusp at zero and the long-time diffusion coefficient scales as r^{-2} for large resetting rate, both independent of the nonlinear drag form g(v). The authors also report that mean first-passage time to a target velocity shows a minimum at some optimal r only in shear-thickening media, not in shear-thinning ones.\n\nThey do a solid job cross-checking direct particle trajectories against numerical solution of the Fokker-Planck equation for Ps(v), which supports the cusp and the scaling claims holding across different g(v), lambda, and Sigma. That independence is the cleanest new element and comes from independent numerical routes rather than fitting.\n\nThe softer part is the first-passage time results that drive the media-type contrast. The abstract gives no information on the discretization, boundary handling, or sampling used for the MFPT, and the stress-test note correctly flags that any difference in numerical treatment between the two g(v) forms could affect whether a minimum appears. Without those checks the distinction is less secure than the distribution and diffusion parts.\n\nThis is a focused numerical study for people working on inertial active particles or transport in non-Newtonian fluids. A reader already thinking about run-and-tumble models with resetting would find the scaling results useful and might want to reproduce the MFPT curves themselves. It is worth sending for peer review so the numerical details on the passage times can be examined.","headline":"The cusp and Deff ~ r^{-2} scaling look robust across drag laws from the trajectory-FP cross-checks, but the shear-thickening vs thinning distinction in optimal resetting rate rests on thinner numerical support for the MFPT curves.","tokens_in":2611,"tokens_out":388,"would_cite":false,"duration_ms":13877,"reading_group":"maybe","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"grok-4.3","headline":"Velocity resetting at high rates produces a cusp singularity at zero velocity and makes long-time motion diffusive with diffusivity falling as r to the minus two, independent of the drag law, while the mean time to a target velocity has an","keywords":["run-and-tumble particles","velocity resetting","non-Newtonian media","first-passage time","effective diffusion","velocity distribution","shear-thickening","shear-thinning"],"falsifier":"A simulation or experiment in which the effective diffusion coefficient fails to scale as r to the minus two for large r, or in which an optimal resetting rate appears in shear-thinning media, would falsify the reported results.","tokens_in":2833,"feed_emoji":"📉","tokens_out":571,"duration_ms":12711,"temperature":0.7,"pith_summary":"The paper studies an inertial run-and-tumble particle whose velocity is reset to zero at constant rate r while it experiences nonlinear drag from a non-Newtonian medium. The steady velocity distribution is obtained from direct trajectories and from numerical solution of the Fokker-Planck equation; both methods agree. For large r the distribution develops a cusp at v equals zero and the particle diffuses at long times with an effective diffusivity that decays as r to the minus two, and these features hold for any drag function and any tumbling parameters. The mean first-passage time to a chosen target velocity, however, depends on the rheological character of the medium: an optimal resetting rate exists only when the medium is shear-thickening.","feed_headline":"Resetting rate controls cusp and r^{-2} diffusion in non-Newtonian run-and-tumble motion","feed_subtitle":"Mean time to target velocity shows a minimum at intermediate r only in shear-thickening media.","key_machinery":"Steady-state velocity distribution Ps(v) obtained from particle trajectories and numerical Fokker-Planck solution, together with mean first-passage time statistics under symmetric dichotomous noise and nonlinear drag g(v).","core_discovery":"In the presence of velocity resetting at rate r the steady-state velocity distribution Ps(v) of the particle exhibits a cusp-like singularity at v=0 for large r, leading to diffusive behavior at long times with Deff decaying as r^{-2}, independent of the drag function g(v). The mean first-passage time to a target velocity vt depends on the medium type: an optimal r minimizes it in shear-thickening media but not in shear-thinning ones.","pith_inferences":[],"forward_implications":[],"fun_headline_variants":["Resetting induces cusp at v=0 and r^{-2} diffusion in non-Newtonian media","Velocity distribution develops cusp singularity for large resetting rates","Long-time diffusion coefficient decays as r^{-2} independent of g(v)","Optimal r minimizes first-passage time only in shear-thickening media","No optimal resetting rate for first-passage time in shear-thinning media"],"cache_read_input_tokens":2112,"weakest_assumption_plain":"The numerical solution of the Fokker-Planck equation and the trajectory sampling both faithfully represent the underlying stochastic process without extra approximations that would erase the difference in optimal resetting behavior between the two media types.","fun_headline_variants_meta":{"raw":{"variants":["Resetting induces cusp at v=0 and r^{-2} diffusion in non-Newtonian media","Velocity distribution develops cusp singularity for large resetting rates","Long-time diffusion coefficient decays as r^{-2} independent of g(v)","Optimal r minimizes first-passage time only in shear-thickening media","No optimal resetting rate for first-passage time in shear-thinning media"]},"model":"grok-4.3","cost_usd":0.008765,"raw_usage":{"total_tokens":4007,"prompt_tokens":787,"num_sources_used":0,"completion_tokens":93,"cost_in_usd_ticks":87649500,"prompt_tokens_details":{"text_tokens":787,"audio_tokens":0,"image_tokens":0,"cached_tokens":256},"completion_tokens_details":{"audio_tokens":0,"reasoning_tokens":3127,"accepted_prediction_tokens":0,"rejected_prediction_tokens":0}},"tokens_in":787,"tokens_out":93,"duration_ms":19936,"temperature":1.0,"reasoning_tokens":3127,"cache_read_input_tokens":256,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-06-28T18:26:57.445780+00:00","model_set":{"reader":"grok-4.3"},"falsifier":"A simulation or experiment in which the effective diffusion coefficient fails to scale as r to the minus two for large r, or in which an optimal resetting rate appears in shear-thinning media, would falsify the reported results.","supporting_citations":[],"review_version":1}