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REVIEW 3 major objections 4 minor 61 references

Reciprocal swimming in granular media: the role of jamming and swimmer inertia

T0 review · 3 major / 4 minor · reviewed 2026-08-04 · deepseek-v4-flash

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Pith's one-line read A reciprocal, time-symmetric scallop-like swimmer can still move through granular media: slow flaps push forward through jamming, while fast flaps reverse direction through inertia.

desk verdict Solid DEM study with two real propulsion mechanisms, but the headline linear law leans on an untested force threshold and fitted exponents; worth a serious referee, not yet a quantitative law. read the letter →

arxiv 2510.22081 v2 pith:WLXX6AKU submitted 2025-10-24 cond-mat.soft physics.flu-dyn

Amir Nazemi , Hongyi Xiao This is my paper · ORCID
classification cond-mat.softphysics.flu-dyn
keywords reciprocalswimminggranularmediajammingscalloptheoremdiscreteelementmethodforcechainsswimmerinertialocomotion
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

This paper uses particle simulations to show that a scallop-like swimmer performing reciprocal (time-reversible) wing flaps can propel itself through dry granular media by two distinct mechanisms. In the slow quasi-static regime, the medium jams more strongly at the end of the closing stroke than at the end of the opening stroke, so the number of strong particle contacts in the fully closed state exceeds that in the fully open state; this excess contact count is linearly proportional to the net forward distance per cycle. In the fast dynamic regime, the swimmer's inertia matters: after each stroke it coasts, and because the closed-wing configuration offers less resistance, the backward coast lasts longer, producing net backward motion. The paper combines both contributions into a single relation, Δy/L = αΔN_c − β(T_c/T)^n, with fitted constants, and shows frictional and frictionless data collapse onto it. A sympathetic reader cares because it identifies measurable order parameters that link microscopic jamming and inertial coasting to macroscale swimming direction and speed.

What carries the argument

The central object is the strong-contact count N_c, defined as the number of inter-particle contacts whose force magnitude exceeds a threshold F_c = 1.0 mN (chosen as the top 0.1% of the force distribution in the base case); the order parameter ΔN_c is its difference between the fully closed and fully open states. It captures the jammed stagnant zones that form around the wings and resist translation. The second object is the coasting time T_c = m_s/(P_s L T), a characteristic time for the swimmer to come to rest under medium resistance; the ratio T_c/T measures how much inertia matters within one flapping period. Together these two quantities appear additively in Eq. 8, separating the jammi

What would settle it

Rerun the quasi-static parameter sweep with F_c set to, say, the top 0.01%, top 1%, or a fixed multiple of the mean contact force, and check whether Δy/L versus ΔN_c remains on the same straight line; alternatively, in an experiment with a photoelastic granular medium, count force chains above a threshold and compare the predicted displacement per cycle against the measured one.

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Extended reading notes

Core claim

In the quasi-static regime, the cycle-averaged normalized net displacement per cycle, Δy/L, is proportional to ΔN_c = N_c(θ_c) − N_c(θ_o), the difference in the number of contacts carrying forces above a fixed threshold between the fully closed and fully open wing states; the slope is α = 8.63×10^-6 across varied gap widths, a one-wing swimmer, an inert mid-body, and frictional versus frictionless media, with every nonzero case favoring the opening stroke. This linear relation is the paper's quantitative demonstration that jamming-induced hysteresis breaks the symmetry between the two reciprocal strokes and generates forward locomotion. In the dynamic regime, where the flapping period approa

Load-bearing premise

The linear jamming law rests on the hand-chosen force threshold F_c = 1.0 mN used to define a 'strong contact'; if the linearity or the fitted slope α changes when that threshold is moved, the paper's quantitative jamming claim loses its support.

Editorial extensions

If this is right

  • In the quasi-static regime, net displacement per cycle can be predicted from a single force-network statistic, ΔN_c, without tracking full particle trajectories.
  • Because the jamming term is linear and additive, geometry changes that raise ΔN_c, such as adding an inert mid-body, proportionately increase forward locomotion.
  • Friction is necessary for the jamming mechanism: with frictionless particles, ΔN_c is essentially zero and forward locomotion disappears.
  • In the dynamic regime, increasing swimmer mass or shortening flapping period shifts locomotion from forward to backward, with a power-law dependence on T_c/T.
  • The two mechanisms are separable: measured displacement minus αΔN_c collapses onto a single master curve in both frictional and frictionless media.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • A natural extension the paper leaves implicit: ΔN_c could be measured in physical experiments using photoelastic or X-ray imaging of force chains, turning the linear law into a testable design rule for real granular robots rather than a simulation-only result.
  • The threshold dependence of ΔN_c is untested; an obvious follow-up is to check whether the linear law and slope α survive when F_c is varied over an order of magnitude or redefined per case as a different percentile of the force distribution.
  • The additive form of Eq. 8 suggests a control knob: for a given swimmer mass, one could choose a flapping frequency at which the jamming and inertial contributions cancel, producing a near-zero net displacement.
  • Because the inertial mechanism operates even in frictionless media, it may generalize to any dense suspension in which the swimmer's density differs from the medium, bridging the granular results and inertial swimming in ordinary viscous fluids.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

3 major / 4 minor

Summary. The paper uses DEM simulations of a scallop-like reciprocal swimmer in a granular medium to identify two propulsion mechanisms. In the quasi-static regime, the authors quantify jamming-induced symmetry breaking via ΔN_c, the difference in the number of strong contacts (|F| > F_c) between fully closed and fully open wing states, and report a linear relation Δy/L = α ΔN_c with α = 8.63×10^-6 across varied gap widths, mid-body geometry, and friction. In a dynamic regime characterized by a coasting time T_c, they report that net displacement follows Δy/L = α ΔN_c − β(T_c/T)^n with fitted β = 0.24 and n = 0.44, collapsing frictional and frictionless data onto a master curve. The paper validates the base case against prior experiments and includes controls (frictionless medium, one-wing, mid-body).

Significance. If the reported quantitative relations are robust, the paper makes a valuable contribution: it connects mesoscopic force-chain asymmetry (a jamming signature) to net locomotion in a reciprocal granular swimmer, and it demonstrates a distinct inertial propulsion mechanism with a compact order parameter. The simulations are well controlled, with explicit tests of friction, geometry, and inertia, and the qualitative claims are supported by multiple independent observables (coordination number, force chains, swimmer kinematics). The authors are honest that β and n are fitted, and they caution against extrapolating Eq. (8). The main risk is that the central quantitative law depends on a hand-chosen strong-force threshold F_c that is not tested for sensitivity.

major comments (3)
  1. [Sec. III B, Eq. (6), Fig. 4(b)] The central linear relation Δy/L = αΔN_c is defined using a threshold F_c = 1.0 mN chosen as the top 0.1% of the base-case contact force distribution. This threshold is fixed across all cases, but DEM contact forces scale with Young's modulus, overlap, and packing. The paper does not test how α or the linearity changes when F_c is varied, nor whether a rescaled threshold is needed in the dynamic regime or for different E. If the linear law is an artifact of this particular threshold, the quantitative support for the jamming mechanism fails. Please add a sensitivity analysis varying F_c over at least a decade (including values tied to the force distribution of each case) and show that the linear relation and the inferred α are stable. Report the uncertainty in α from the fit.
  2. [Sec. III C, Eq. (8), Fig. 6(b)] The master curve Eq. (8) is built by subtracting αΔN_c from the dynamic data. This assumes that jamming and inertial contributions add linearly, which is an ad hoc superposition rather than a derived relation. Moreover, β and n are fitted with no uncertainty, and the collapse in Fig. 6(b) is shown only for the training data. To make the inertial scaling convincing, provide uncertainties for β and n, state whether the same power law is obtained if the jamming subtraction uses a different α or threshold, and ideally perform an out-of-sample check (e.g., a configuration not included in the fit).
  3. [Sec. III C, Fig. 5(c), Fig. 6(a)] The transition from quasi-static to dynamic regime is claimed to occur at T_c/T ≈ 4×10^-3, but the criterion for this crossover is not defined quantitatively. The text describes a plateau and a transition by inspection. If the crossover location is to be used as a physical prediction, please specify an objective criterion (e.g., where the inertial term exceeds the jamming term or where retardation time becomes a fixed fraction of T).
minor comments (4)
  1. [Fig. 5(c)] The axis label for the vertical axis appears garbled as '( - )' in the provided text; please fix the math rendering. Also clarify whether the plotted quantity is (|Δy_R^c| − |Δy_R^o|)/L.
  2. [Sec. III C, Eq. (7)] The hydrostatic-like pressure P_s = ρ φ_0 g Z_0 is introduced after its first use in Eq. (7). Define P_s explicitly before or immediately with Eq. (7) so the reader can verify the dimensional analysis.
  3. [Fig. 4(b)] Please clarify in the caption or text whether the frictionless point (green triangle) is included in the linear fit for α. If it is included, report its leverage; if excluded, state so. Also add error bars for Δy/L in Fig. 4(b) and Fig. 6, not just in Fig. 4(a).
  4. [Sec. III B, Fig. 3] The threshold used to select mobile particles and strong forces is described as 'consistent' across cases. Please state the exact threshold values (force and velocity) in the caption or text.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the order parameters are measured independently of the displacement they are correlated with.

full rationale

The paper's central quantitative claims are empirical correlations between separately measured observables, not derivations that reduce to their own inputs. The quasi-static order parameter ΔN_c is defined in Eq. (6) as the difference between the number of strong contacts at the closed and open states, with the force threshold F_c fixed at the top 0.1% of the base-case contact-force distribution. This quantity is measured from contact-force statistics, independent of the swimmer displacement Δy/L. The linear relation Δy/L = αΔN_c in Fig. 4b is a fitted empirical collapse across varied gap widths, mid-body geometry, and friction; α is a fitted slope, not an input. Similarly, the dynamic regime uses a coasting time T_c defined in Eq. (7) from swimmer mass, period, and hydrostatic pressure, again independent of the measured displacement. Equation (8) is explicitly an empirical master-curve fit with β and n labeled as fitted parameters. No equation is self-referential, and no fitted parameter is renamed as a prediction. The only self-citation, [22], provides independent experimental kinematics and CT data used for validation; it is not the load-bearing justification for the jamming or inertia correlations. The force-threshold choice is arbitrary and its sensitivity is not tested, but that is a robustness/correctness concern, not circularity, because the threshold is not chosen to reproduce Δy and the paper holds it fixed across all cases. The inertial term is also compared against an existing theoretical prediction [40], which is external support. Overall, the derivation chain is self-contained: simulations produce kinematics and contact forces, and the paper fits correlations between them without building the measured outputs into the definitions of the control parameters.

Assumptions & free parameters 4 free parameters · 5 assumptions · 0 invented entities

The central quantitative claims rest on a small number of fitted parameters (α, β, n, threshold F_c) and on modeling assumptions (single translational DOF, reduced modulus, linear additivity of the two mechanisms, area-proportional drag during coasting). No invented physical entities are introduced.

free parameters (4)
  • F_c (strong-force threshold) = 1.0 mN (top 0.1% of base-case contact forces)
    Defines ΔN_c; chosen from the base case's force distribution, not from theory. The linear relation and slope α may depend on this threshold; robustness not tested.
  • α (linear coefficient) = 8.63×10^-6
    Fitted slope of Δy/L vs ΔN_c in Fig. 4b; no uncertainty or out-of-sample validation.
  • β (inertial amplitude) = 0.24
    Fitted prefactor in Eq. 8 for the inertial contribution.
  • n (inertial exponent) = 0.44
    Fitted power-law exponent in Eq. 8; no theoretical derivation given.
assumptions (5)
  • domain assumption DEM contact model (Hertz normal, viscous dissipation, Coulomb friction) captures the essential jamming physics of dry granular media.
    Used throughout; standard in granular DEM but the reduced Young's modulus (1 MPa) and linear/viscous dissipation are approximations (Sec. II).
  • ad hoc to paper The characteristic coasting time T_c = m_s/(P_s L T) with P_s = ρφ_0 g Z_0 is the correct order-one time scale for the swimmer to stop under medium resistance.
    Eq. (7); a dimensional-analysis estimate whose prefactor is arbitrary (absorbed into β). Used to define the inertial order parameter.
  • ad hoc to paper Jamming and inertial contributions to net displacement add linearly (Eq. 8).
    The master-curve collapse assumes the two mechanisms are independent and additive; not derived, and cross-effects (inertia modifying jamming) are not examined.
  • domain assumption The medium resistance during coasting is proportional to the swimmer's exposed area 2L^2 sin(θ).
    Used in Sec. III C to explain why coasting after closing (smaller θ) is longer; not directly measured.
  • domain assumption The swimmer's translational dynamics are restricted to the y direction (single DOF).
    Section II; the simulation disables x and z translation and rotation, which could affect real free swimmers.

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Pith. "Pith review of Reciprocal swimming in granular media: the role of jamming and swimmer inertia." pith.science (2026). https://pith.science/paper/WLXX6AKU

@misc{pith2026251022081,
  author       = {Pith},
  title        = {Pith review of: Reciprocal swimming in granular media: the role of jamming and swimmer inertia},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/WLXX6AKU}},
  note         = {Machine review of arXiv:2510.22081}
}
read the original abstract

We use particle simulations to reveal two distinct propulsion mechanisms for a scallop-like swimmer to propel itself in granular media by reciprocally flapping its wings. Based on the discrete element method, we examine the structure, kinematics, and contact forces of particles near the swimmer to quantify how jamming manifests as stagnant zones near the swimmer in a frictional granular medium, which are less intense during the opening stroke than the closing. This broken symmetry is quantified by the difference in the number of strong particle contact forces formed during opening and closing, which shows a linear relation with the swimmer's net displacement across various swimmer and medium configurations, all favoring the opening stroke. We identify a secondary propulsion mechanism in a dynamic regime with significant swimmer inertia, as the flapping period approaches the coasting time for a moving swimmer to come to rest under the medium resistance. In this case, the swimmer's net displacement is correlated to the ratio between these two time scales, and the swimming direction favors the closing stroke due to the smaller medium resistance as the swimmer coasts with closed wings.

Figures

Figures reproduced from arXiv: 2510.22081 by the authors.

Figure 1
Figure 1. FIG. 1. Schematics of the simulation setup and particle contact models. (a) 3D view of the setup. (b) Top-down view of the [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. FIG. 2. Swimmer and particle kinematics from the experiment [22] and from DEM simulations, see configurations in Table [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
Figure 3
Figure 3. FIG. 3. Force transmission and structural analyses for the base simulation case. (a) Particle velocity and inter-particle contact [PITH_FULL_IMAGE:figures/full_fig_p005_3.png] view at source ↗
Figures from the paper (3 more)
Figure 4
Figure 4. Figure 4: FIG. 4. The influence of jamming on net locomotion. (a) Cycle-averaged swimmer net displacement ∆ [PITH_FULL_IMAGE:figures/full_fig_p006_4.png]
Figure 5
Figure 5. Figure 5: FIG. 5. Locomotion in the dynamic regime. (a) The normalized swimmer displacement ∆ [PITH_FULL_IMAGE:figures/full_fig_p007_5.png]
Figure 6
Figure 6. Figure 6: FIG. 6. Quantified relations between swimmer locomotion and inertial coasting. (a) Normalized swimmer displacement vs the [PITH_FULL_IMAGE:figures/full_fig_p008_6.png]

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Pith tools

Reviewed August 4, 2026 · model on record in the stance chip above.