Pith. sign in

REVIEW 4 major objections 6 minor 42 references

Chondrule dust rim growth: Influence of restructuring using molecular dynamics simulations

T0 review · 4 major / 6 minor · reviewed 2026-08-10 · deepseek-v4-flash

Pith's one-line read Collisions above roughly 10 cm/s compact or destroy chondrule dust rims, so the rims only grow where disk turbulence is weak.

desk verdict A solid, incremental MD study of rim restructuring with a useful collision library and Monte Carlo growth model, but the headline 10 cm/s threshold is not actually supported by the paper's own energy data and needs fixing before publication. read the letter →

arxiv 2501.04625 v1 pith:CM4IVS2N submitted 2025-01-08 astro-ph.EP cond-mat.softphysics.space-ph

classification astro-ph.EPcond-mat.softphysics.space-ph PACS 79.20.Ap96.25.Pq95.30.Wi96.50.Dj
keywords chondrulesfine-grainedrimshit-and-stickcollisionsgranularmechanicsmoleculardynamicsrimcompactiondiskturbulenceMonteCarlosimulation
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 asks what happens to the dusty rims that grow around chondrules when incoming dust hits hard enough to restructure rather than stick. Using molecular-dynamics simulations of roughly 6000 collisions between ice grains and porous dust piles, it finds the hit-and-stick regime has a threshold near 10 cm/s: below about $10^{-12}$ J of collision energy a rim barely changes, between $10^{-12}$ and $10^{-10}$ J it compacts, and above $10^{-8}$ J it is disrupted. Because collision energy is set by relative velocities that disk turbulence drives, the paper then predicts, through machine-learned collision outcomes fed into a Monte Carlo growth model, that rims grow steadily only in weak turbulence with $\alpha \leq 10^{-5}$, are eroded for $\alpha$ from $10^{-3}$ to $10^{-4}$, and cannot accumulate in stronger turbulence. If correct, the presence and structure of fine-grained chondrule rims become a readable record of how strongly the local disk gas was stirring when the rims formed.

What carries the argument

The machinery is a granular contact model tracked by molecular dynamics: grains in a collision feel elastic repulsion, velocity-dependent dissipation, a constant adhesive pull-off force, and rolling and torsional friction, with the simulation run until the impact energy is dissipated. The collision library built from these runs records the number of monomers displaced or lost from the rim, the distance from the impact point reached by restructuring, and the resulting change in rim height and porosity. Those data train a random-forest classifier and regressor that predict whether rim mass increases or decreases for a given collision, and the predictor is embedded in a Monte Carlo model that draws incoming dust particles according to the collision rate and relative velocity set by the turbulence parameter $\alpha$.

What would settle it

Laboratory collisions between pre-formed dust rims and individual grains or aggregates, spanning impact speeds from 0.1 to 100 cm/s and measuring rim thickness and porosity before and after each hit, would directly test the 10 cm/s boundary; if silicate rims compact or erode at energies that do not track the ice-based thresholds scaled by 3.8, the derived turbulence limits need revision.

Watch

Extended reading notes

Core claim

The central claim is that chondrule rim growth is governed by kinetic-energy thresholds rather than by sticking probability alone. For collisions with kinetic energy below $10^{-12}$ J, corresponding to relative speeds of about 0.13 to 27 m/s for the modeled particles, the rim is essentially undisturbed. From about $10^{-12}$ J up to $10^{-10}$ J, impacts compact the rim, decreasing both its thickness and porosity; above $10^{-8}$ J, impacts disrupt the rim and expel monomers. Connected to disk turbulence through a turbulent-velocity scaling, these outcomes translate into sustained rim growth for $\alpha \leq 10^{-5}$, erosion for $\alpha = 10^{-3}$ to $10^{-4}$, and no net rim accumulation for $\alpha \geq 10^{-2}$. The paper notes that silicate dust binds about 3.8 times more weakly than the water ice used in the simulations, so the kinetic-energy thresholds are expected to scale by the same factor when transferred to silicates.

Load-bearing premise

All quantitative thresholds are computed for water-ice grains and then carried over to the silicate dust of real chondrule rims by assuming the two materials differ only by a factor of 3.8 in binding energy; if that material scaling is wrong, the 10 cm/s threshold and the turbulence boundaries shift.

Editorial extensions

If this is right

  • Rims grow steadily only in quiet disk regions, so a chondrule with a fine-grained rim is evidence that its rim-forming environment had $\alpha \leq 10^{-5}$.
  • Rims grown in more turbulent regions will be thinner and denser, because impacts between $10^{-12}$ and $10^{-10}$ J compact the rim instead of adding porosity.
  • At intermediate turbulence ($\alpha = 10^{-3}$ to $10^{-4}$) rim mass fluctuates around a small nonzero value, giving repeatedly eroded and re-formed rims over time.
  • Above $10^{-8}$ J, collisions can eject most of the rim, so the same turbulence that drives dust accretion onto a chondrule can also strip the rim once the relative velocities are high enough.

Reading between the lines

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

  • The authors do not pursue it, but the compaction and erosion thresholds give a way to invert observed fine-grained rim porosity and thickness in meteorites into a local nebular turbulence level.
  • The 3.8 ice-to-silicate scaling is a linear extrapolation; a testable extension would rerun the collision library with silicate surface energies to see whether the thresholds move by more than that factor when dissipation also changes.
  • Because the dust grains modeled have radii of 0.5 to 10 microns, the 10 cm/s threshold is tied to that grain-size range; submicron or millimeter dust would likely shift the hit-and-stick boundary.
  • The prediction that rims cannot form when $\alpha \geq 10^{-2}$ suggests a plausible sorting mechanism in the solar nebula: rimmed and unrimmed chondrules found together in one meteorite could have formed in regions with different turbulence before being mixed.
Share X Bluesky LinkedIn Reddit HN

Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

4 major / 6 minor

Summary. This paper uses LIGGGHTS granular-mechanics simulations of water-ice dust collisions onto a patch representing a chondrule rim. From about 6,000 simulated collisions it characterizes how many monomers are displaced or lost and how rim thickness and porosity change as a function of collision kinetic energy. It then trains a random forest model on these outcomes and feeds it into a Monte Carlo simulation of rim growth under different turbulence levels, concluding that rims grow for α ≤ 1e-5, are eroded at intermediate α, and cannot form at high α. The paper also claims a hit-and-stick threshold of approximately 10 cm/s.

Significance. If the energy-resolved collision outcomes and the turbulence thresholds are correct, the paper would provide a concrete bridge between granular-mechanics collision simulations and observationally relevant chondrule rim growth. The construction of a large collision library, the explicit treatment of restructuring versus fragmentation, and the machine-learning/Monte Carlo pipeline are valuable and, in principle, reusable. The energy thresholds (1e-12, 1e-10, and 1e-8 J) are plausible and are grounded in the simulated outcomes. However, the headline velocity threshold and the material scaling to silicates are not established by the data as presented, so the current version overstates its central claim.

major comments (4)
  1. [Abstract; Section V] The paper's headline claim is inconsistent with its own energy analysis. The abstract states 'We establish a threshold of approximately 10 cm/s for the hit-and-stick collision regime,' but Section V defines the onset of restructuring as KE = 1e-12 J and translates this to relative velocities of 0.13 to 27 m/s for the particles in the library; 10 cm/s = 0.1 m/s lies below that stated range. Using the quoted ice density ρ = 1 g/cm3, a 10 μm radius monomer has KE = 2.1e-14 J at 10 cm/s, two orders of magnitude below 1e-12 J, so most simulated projectiles would be in the 'very little restructuring' regime at 10 cm/s. The 10 cm/s threshold is thus not a property of the simulated data; it is at best a threshold for the most massive aggregates. The threshold should be presented in kinetic energy, or as a size-dependent velocity, and the 'approximately 10 cm/s' statement should be either derived from an explicit velocity-binned analysis or removed.
  2. [Section II.C; Section V] The quantitative results are computed for water ice and then applied to chondrule silicates via the final-paragraph statement that the binding energy of ice is 3.8 times that of silicate and 'the threshold kinetic energies may be expected to increase by a similar factor.' This linear scaling is not derived from the simulations or from a model of contact mechanics; the thresholds depend on the adhesive force, rolling friction, and dissipation in a way that need not be linear in a single binding-energy ratio. Because the abstract's velocity threshold and the Monte Carlo conclusions are meant to apply to chondrule rims, the paper should either justify the 3.8 factor explicitly, provide at least bounding silicate simulations, or clearly label the silicate thresholds as conjectures rather than results.
  3. [Section IV] The Monte Carlo growth curves in Figs. 13 and 14 are the basis for the conclusion that rim growth is sustained only for α ≤ 1e-5, but the reliability of the machine-learning model for this application is not fully demonstrated. The random forest is trained and evaluated on an 80/20 split of the same collision library, which tests interpolation within that library but not extrapolation to the collision conditions actually sampled by Eq. (8); no out-of-sample or stratified validation (e.g., by particle size or velocity bin) is reported for the classifier, and the growth curves are shown without error bars or sensitivity to the model's MAE/RMSE. Please add a validation scheme that mimics the Monte Carlo sampling distribution, propagate the prediction uncertainty into Fig. 13, or explicitly state that the α thresholds are indicative.
  4. [Section II.C] The numerical values of the two tuned model parameters, the dissipation constant A and the tangential damping coefficient ηtang, are not reported. A is said to be fitted to the experimentally measured coefficient of restitution of ice grains and ηtang is said to depend on the time step, but neither the fitted value nor the time step is given. These parameters directly affect the energy thresholds in Section III, so reporting them is necessary for reproducibility and for assessing how robust the 1e-12, 1e-10, and 1e-8 J boundaries are to the fitting choices.
minor comments (6)
  1. [Section III, near Fig. 9] The sentence 'This is indeed true, with the average size of the lost monomers with the trend becoming more slightly more pronounced for collision energies KE > 1e-10 J, as shown in Fig. 9' is ungrammatical and unclear; please rewrite it.
  2. [Section IV] There is a typo in 'the rim undergoes periodic distruction'; it should read 'destruction'.
  3. [Fig. 13] Panel (b) appears to be missing axis labels; if the abscissa is the number of collisions, please label it and add units, and likewise indicate the ordinate.
  4. [Section II.B] The displacement criterion is defined as a change in position relative to the chondrule core by more than 1%, but the simulated system is a flat patch on the chondrule surface; please define the reference coordinate for the core more precisely in this geometry.
  5. [References] Reference [34] lists 'Y. Marrochhi' and 'G. Librourel'; these names appear to be misspelled and should be checked against the published article.
  6. [General] The paper does not include a data availability statement; making the collision library and the machine-learning/Monte Carlo scripts available would strengthen reproducibility and allow the community to test the extrapolation concerns raised above.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the collision thresholds are emergent simulation outputs anchored to an independent restitution measurement, and the ML surrogate is used transparently.

full rationale

The paper's derivation chain is self-contained and does not reduce to its inputs by construction. The collision library is generated by a granular-mechanics code (LIGGGHTS) with material parameters for water ice, and the single fitted dissipation constant A is calibrated to an experimentally measured coefficient of restitution of ice grains; it is not fitted to the rim-growth threshold being claimed. The KE thresholds (10^-12 J, 10^-10 J, 10^-8 J) are presented as empirical binned outcomes of roughly 6000 simulated collisions, not as imposed inputs. The random-forest model is explicitly described as trained on the collision data (80% train/20% test) and used as a surrogate in the Monte Carlo growth simulation; this is a transparent interpolation of the simulated collision physics rather than a circular prediction, though it means the growth conclusions inherit the simulation model's assumptions and are not independently externally validated. Self-citations ([7], [8], [33]) appear for methodology, prior dust-pile settings, and the authors' earlier extensions, but they are not load-bearing justifications of the new threshold. A non-circular consistency concern exists: the abstract's 'approximately 10 cm/s' is hard to reconcile with the Conclusions' statement that KE = 10^-12 J corresponds to relative velocities of 0.13-27 m/s for the particles used; for typical monomer sizes in the library, 10 cm/s lies below that energy threshold. That is a translation/consistency issue, not a circular reduction.

Assumptions & free parameters 2 free parameters · 4 assumptions · 0 invented entities

The quantitative claims rest on the granular-mechanics model of Ringl and Urbassek (Ref. 18), one fitted dissipation constant, a water-ice material model, a cylindrical patch approximation, and a random forest surrogate. No new physical entities are introduced. The 10 cm/s threshold is presented as an outcome, but it is not directly tied to a velocity-resolved measurement in the paper.

free parameters (2)
  • Dissipation constant A = not stated numerically
    Fitted to the experimentally measured coefficient of restitution of ice grains (Section II.C); enters the viscoelastic normal force in Eq. (1) and affects energy dissipation in all collisions.
  • Tangential damping coefficient eta_tang = 0.1 m/dt
    Chosen by test simulation to stabilize grain contacts (Section II.A); affects sliding friction through Eq. (6) and therefore restructuring and loss outcomes.
assumptions (4)
  • ad hoc to paper Water ice is a valid surrogate for chondrule silicate dust, with thresholds scaled by a 3.8 binding-energy factor.
    Section II.C sets all material parameters to water ice; Section V extrapolates to silicates using only a linear binding-energy scaling without silicate simulations.
  • domain assumption A cylindrical patch of rim with 50 micron radial extent represents the full isotropically accreting chondrule surface.
    Section II.B restricts the simulation to a patch and uses a drag force for particles leaving the patch, which limits the observed restructuring range to pile dimensions.
  • domain assumption Constant normal adhesion equal to the DMT pull-off force adequately describes grain contacts.
    Section II.A, Eq. (2) and surrounding text simplify DMT/JKR adhesion to a constant pull-off force, valid only for small, high-rigidity grains.
  • domain assumption The random forest model trained on an 80/20 split of the collision library generalizes to collision histories encountered in the Monte Carlo growth simulation.
    Section IV reports test-set MAE and RMSE but no out-of-distribution validation or uncertainty propagation for the growth curves.

how reviews work

0 comments
Cite this review

Pith. "Pith review of Chondrule dust rim growth: Influence of restructuring using molecular dynamics simulations." pith.science (2026). https://pith.science/paper/CM4IVS2N

@misc{pith2026250104625,
  author       = {Pith},
  title        = {Pith review of: Chondrule dust rim growth: Influence of restructuring using molecular dynamics simulations},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/CM4IVS2N}},
  note         = {Machine review of arXiv:2501.04625}
}
abstract

We investigate the influence of disruptive collisions on chondrule rim growth, emphasizing the role of kinetic energy in determining the outcomes of these interactions. We establish a threshold of approximately 10 cm/s for the "hit-and-stick" collision regime, beyond which significant changes occur in the structure of rimmed chondrules. Our findings highlight that at low collision energies (KE $< 10^{-12}$ J), minimal structural alteration takes place, while higher energies (KE up to $10^{-10}$ J) lead to compaction of the rim, reducing both its thickness and porosity. Collisions with energies exceeding $10^{-8}$ J result in the complete disruption of the rim, with particles being expelled from it. These results are correlated with the turbulence levels within the disk, as kinetic energy scales with the relative velocities of colliding particles. Leveraging machine learning models trained on our collision data, we predict changes in rim characteristics and employ these predictions in a Monte Carlo simulation to explore rim growth dynamics. Our simulations reveal that rim development is sustained in low-turbulence environments ($\alpha \leq 10^{-5}$), while intermediate turbulence levels ($\alpha$ = $10^{-3}$ to $10^{-4}$) lead to erosion, preventing further rim accumulation in high-turbulence contexts.

Figures

Figures reproduced from arXiv: 2501.04625 by the authors.

Figure 1
Figure 1. We characterize the collision outcomes as either caus￾ing restructuring or fragmentation. In the case of re￾structuring, individual monomers within the pile roll or slide on the surface of other monomers until they reach a new stable configuration as the energy is dissipated. We are interested in both the total number of monomers that are displaced as well as the range of restructuring, defined as the maximum distan… view at source ↗
Figure 1
Figure 1. FIG. 1: Snapshots of a sample collision with views from the si [PITH_FULL_IMAGE:figures/full_fig_p004_1.png] view at source ↗
Figure 2
Figure 2. FIG. 2: Final result of the collision shown in Fig. 1. (a) Show [PITH_FULL_IMAGE:figures/full_fig_p005_2.png] view at source ↗
Figures from the paper (7 more)
Figure 3
Figure 3. Figure 3: FIG. 3: The ratio of monomers that are displaced within or [PITH_FULL_IMAGE:figures/full_fig_p005_3.png]
Figure 7
Figure 7. Figure 7: FIG. 7: Physical characteristics of the rims pre- and post [PITH_FULL_IMAGE:figures/full_fig_p006_7.png]
Figure 5
Figure 5. Figure 5: FIG. 5: a) Comparison of restructuring caused by collisions [PITH_FULL_IMAGE:figures/full_fig_p006_5.png]
Figure 8
Figure 8. Figure 8: FIG. 8: Change in the physical characteristics of a chondrul [PITH_FULL_IMAGE:figures/full_fig_p006_8.png]
Figure 10
Figure 10. Figure 10: FIG. 10: Percent change in the thickness of the rim as a func [PITH_FULL_IMAGE:figures/full_fig_p007_10.png]
Figure 12
Figure 12. Figure 12: FIG. 12: Average change in (a) rim thickness and (b) rim [PITH_FULL_IMAGE:figures/full_fig_p008_12.png]
Figure 14
Figure 14. Figure 14: FIG. 14: Average rate of growth of the chondrule rim mass. [PITH_FULL_IMAGE:figures/full_fig_p009_14.png]

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

42 extracted references · 42 canonical work pages

  1. [1]

    Blum, Research in Astron

    J. Blum, Research in Astron. Astrophys. 10, 1199 (2010)

  2. [2]

    Reipurth, D

    B. Reipurth, D. Jewitt, and K. Keil, Protostars and plan- ets V (University of Arizona Press, 2007)

  3. [3]

    B. C. Johnson, D. A. Minton, H. J. Melosh, and M. T. Zuber, Nature 517, 339 (2015), ISSN 1476-4687

  4. [4]

    Hasegawa, S

    Y. Hasegawa, S. Wakita, Y. Matsumoto, and S. Oshino, The Astrophysical Journal 816, 8 (2015)

  5. [5]

    Wakita, Y

    S. Wakita, Y. Matsumoto, S. Oshino, and Y. Hasegawa, The Astrophysical Journal 834, 125 (2017)

  6. [6]

    C. W. Ormel, J. N. Cuzzi, and A. G. G. M. Tielens, The Astrophysical Journal 679, 1588 (2008)

  7. [7]

    Xiang, A

    C. Xiang, A. Carballido, R. Hanna, L. Matthews, and T. Hyde, Icarus 321, 99 (2019), ISSN 0019-1035

  8. [8]

    Xiang, A

    C. Xiang, A. Carballido, L. S. Matthews, and T. W. Hyde, The Astrophysical Journal 950, 11 (2023)

Show all 42 references
  1. [9]

    examined the chemical composition and microstruc- ture of matrix material and chondrule rims in the chon- drite ALHA77307, finding results that support the nebu- lar dust accretion model. Hanna and Ketcham [10] used X-ray tomography on the Murchison meteorite to study the morph...

  2. [10]

    R. D. Hanna and R. A. Ketcham, Earth and Planetary Science Letters 481, 201 (2018), ISSN 0012-821X

  3. [11]

    P. A. Bland, L. E. Howard, D. J. Prior, J. Wheeler, R. M. Hough, and K. A. Dyl, Nature Geoscience 4, 244 (2011), ISSN 1752-0908

  4. [12]

    A. J. Brearley, Geochimica et Cosmochimica Acta 57, 1521 (1993), ISSN 0016-7037

  5. [13]

    Gunkelmann, A

    N. Gunkelmann, A. Kataoka, C. P. Dullemond, and H. M. Urbassek, A&A 599, L4 (2017)

  6. [14]

    Most modeling studies on chondrule rim growth and dust coagulation assume that collisions occur in the hit-and-stick regime [6, 10]

    using granular mechanics simulation showed that 2 the bouncing velocity increases with greater filling fac- tors and thicker dust rims. Most modeling studies on chondrule rim growth and dust coagulation assume that collisions occur in the hit-and-stick regime [6, 10]. The assum...

  7. [15]

    Beitz, C

    E. Beitz, C. G¨ uttler, A. Nakamura, A. Tsuchiyama, and J. Blum, Icarus 225, 558 (2013), ISSN 0019-1035

  8. [16]

    Weidling, C

    R. Weidling, C. G ˜A¼ttler, J. Blum, and F. Brauer, As- tron. J. 696, 2036 (2009)

  9. [17]

    Umst¨ atter, N

    P. Umst¨ atter, N. Gunkelmann, C. P. Dullemond, and H. M. Urbassek, Monthly Notices of the Royal Astro- nomical Society 483, 4938 (2018), ISSN 0035-8711

  10. [18]

    displaced

    in the open source LIGGGHTS code [19]. LIGGGHTS is an extension of the popular molecular dynamics code LAMMPS [20] for the simulation of gran- ular media. The acronym means ‘LAMMPS Improved for General Granular and Granular Heat Transfer Sim- ulations’. LIGGGHTS provides high ...

  11. [19]

    Michoulier, J.-F

    S. Michoulier, J.-F. Gonzalez, and D. J. Price, Com- paction during fragmentation and bouncing produces real- istic dust grain porosities in protoplanetary discs (2024), 2406.15622

  12. [20]

    R. J. Geretshauser, F. Meru, R. Speith, and W. Kley, Astron. & Astrophys. 531, A166 (2011)

  13. [21]

    Ringl and H

    C. Ringl and H. M. Urbassek, Computer Physics Com- 11 munications 183, 986 (2012)

  14. [22]

    Kloss, C

    C. Kloss, C. Goniva, A. Hager, S. Amberger, and S. Pirker, Prog. Comput. Fluid Dy. 12, 140 (2012)

  15. [23]

    LAMMPS, http://lammps.sandia.gov/ (2008)

  16. [24]

    Ringl, E

    C. Ringl, E. M. Bringa, D. S. Bertoldi, and H. M. Ur- bassek, Astrophysical Journal 752, 151 (2012)

  17. [25]

    Ringl, E

    C. Ringl, E. M. Bringa, and H. M. Urbassek, Phys. Rev. E 86, 061313 (2012)

  18. [26]

    P¨ oschel and T

    T. P¨ oschel and T. Schwager, Computational granular dy- namics: models and algorithms (Springer, 2005)

  19. [27]

    N. V. Brilliantov, F. Spahn, J.-M. Hertzsch, and T. P¨ oschel, Phys. Rev. E 53, 5382 (1996)

  20. [28]

    B. V. Derjaguin, V. M. Muller, and Y. P. Toporov, Jour- nal of Colloid and Interface Science 53, 314 (1975)

  21. [29]

    Maugis, Contact, adhesion and rupture of elastic solids (Springer, Berlin, 2000)

    D. Maugis, Contact, adhesion and rupture of elastic solids (Springer, Berlin, 2000)

  22. [30]

    Blum, Advances in Physics 55, 881 (2006)

    J. Blum, Advances in Physics 55, 881 (2006)

  23. [31]

    K. L. Johnson, K. Kendall, and A. D. Roberts, Proceed- ings of the Royal Society of London. A. mathematical and physical sciences 324, 301 (1971)

  24. [32]

    K. L. Johnson, Contact mechanics (Cambridge Univer- sity Press, Cambridge, 1985)

  25. [33]

    Burnham and A

    N. Burnham and A. A. Kulik, in Handbook of Mi- cro/Nano Tribology, edited by B. Bhushan (CRC Press, Boca Raton, 1999), chap. 5, p. 247, 2nd ed

  26. [34]

    Dominik and A

    C. Dominik and A. G. G. M. Tielens, Astrophys. J. 480, 647 (1997)

  27. [35]

    P. K. Haff and B. T. Werner, Powder Technology 48, 239 (1986)

  28. [36]

    Xiang, A

    C. Xiang, A. Carballido, L. S. Matthews, and T. W. Hyde, Icarus 354, 114053 (2021)

  29. [37]

    Marrochhi, M

    Y. Marrochhi, M. Chaussidon, L. Piani, and G. Li- brourel, Science Advances 2, e1601001 (2016)

  30. [38]

    A. H. F. Guimaraes, N. Albers, F. Spahn, M. Seiss, E. Vieira-Neto, and N. V. Brilliantov, Icarus 220, 660 (2012)

  31. [39]

    J. S. Mathis, W. Rumpl, and K. H. Nordsieck, The As- trophysical Journal 217, 425 (1977)

  32. [40]

    C. W. Ormel, M. Spaans, and A. G. G. M. Tielens, As- tronomy & Astrophysics 461, 215 (2007)

  33. [41]

    J. N. Cuzzi, A. R. Dobrovolskis, and J. M. Champney, Icarus 106, 102 (1993), ISSN 0019-1035

  34. [42]

    J. N. Cuzzi, Icarus 168, 484 (2004), ISSN 0019-1035

Pith tools

Reviewed August 10, 2026 · model on record in the stance chip above.