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REVIEW 2 major objections 1 minor 298 references

Clumps in a Cocoon: Geometry and Mixing Set the Universal X-ray to H$\alpha$ Surface Brightness Ratio

T0 review · 2 major / 1 minor · reviewed 2026-06-27 · grok-4.3

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Pith's one-line read High density contrast shatters cold gas into Hα clumps inside a volume-filling X-ray cocoon, producing the observed surface brightness ratio of ~3.

desk verdict 3D shattering in high-contrast mixing produces the observed X-ray/Hα ratio via residence times, but the scaling lacks shown convergence tests. read the letter →

arxiv 2606.07741 v1 pith:YL5S4K5U submitted 2026-06-05 astro-ph.GA

Zirui Chen , S. Peng Oh , Drummond B. Fielding , Lachlan Lancaster , Yuan Li , Brent Tan This is my paper · ORCID
classification astro-ph.GA
keywords galacticwindsmultiphasegasmixinglayerssurfacebrightnessratioX-rayemissionH-alpharampressurestrippingclusterfilaments
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

The paper demonstrates that a universal X-ray to Hα surface brightness ratio of order unity appears in galactic winds, ram-pressure stripped tails, and cluster filaments because of the geometry that arises in the high density contrast limit. Three-dimensional simulations show the cold phase breaking into many small clumps that emit Hα while X-ray gas fills the volume around them. After the emission is smoothed on the scale of the tail width, the ratio converges to the observed value. The Hα contribution is fixed by atomic physics; the X-ray contribution is fixed by the short residence time of gas in the hot band, a time that scales inversely with pressure and appears tied to cooling at a lower-temperature stage of the mixing process. This accounts for both the order-unity value and its robustness across different pressures.

What carries the argument

The shattered cold phase of many small Hα-emitting clumps embedded in a volume-filling X-ray cocoon, whose X-ray residence time scales inversely with pressure.

What would settle it

A measurement of the smoothed surface brightness ratio in a system with density contrast χ much below 10^3 that deviates significantly from ~3, or a simulation in the same high-contrast regime that fails to produce the inverse-with-pressure residence-time scaling.

Watch

Extended reading notes

Core claim

In the high density contrast regime with χ ~ 10^3, the cold phase shatters into many small Hα-emitting clumps embedded in a volume-filling X-ray cocoon. After smoothing on the tail-width scale, the measured surface-brightness ratio SB_X / SB_Hα converges to the observed value of ~3. The Hα luminosity fraction is set by atomic physics, whereas the X-ray luminosity fraction is set by the residence time of gas in the X-ray-emitting band. This residence time is much shorter than the cooling time at X-ray temperatures, but scales roughly inversely with pressure, suggesting that it is tied to the cooling time at a lower-temperature outlet of the mixing cascade. This framework naturally explains wh

Load-bearing premise

The high density contrast regime produces a shattered cold phase of many small Hα clumps inside a volume-filling X-ray cocoon whose residence-time scaling with pressure is independent of the specific numerical setup.

Editorial extensions

If this is right

  • The ratio converges to the observed value after smoothing on the tail-width scale across galactic winds, ram-pressure stripped tails, and cluster filaments.
  • Hα luminosity is fixed by atomic physics while X-ray luminosity is controlled by residence time rather than the X-ray cooling time itself.
  • The inverse scaling of residence time with pressure keeps the ratio order unity even when pressure changes.
  • The result holds when the cold phase consists of many small clumps inside a volume-filling hot cocoon.

Reading between the lines

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

  • The same geometric control of the temperature PDF could apply to other multiphase flows where emission is dominated by mixing layers rather than bulk cooling.
  • Observational tests in environments spanning a wide range of pressures could confirm whether the ratio remains constant as predicted.
  • The residence-time interpretation suggests that emission ratios in other temperature bands might also be set by the outlet temperature of the mixing cascade.
  • If the shattering picture is correct, the small-scale clump distribution should be detectable with sufficiently high-resolution observations or simulations.
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Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

2 major / 1 minor

Summary. The manuscript claims that 3D wind-tunnel simulations in the high-density-contrast regime (χ∼10^3) produce a shattered cold phase consisting of many small Hα-emitting clumps embedded in a volume-filling X-ray cocoon. After smoothing the surface brightness on the tail-width scale, the measured X-ray to Hα surface-brightness ratio converges to the observed universal value ∼3. This is explained theoretically: the Hα luminosity fraction is set by atomic physics, while the X-ray luminosity fraction is set by the residence time of gas in the X-ray-emitting temperature band. This residence time is much shorter than the X-ray cooling time but scales roughly inversely with pressure, suggesting it is tied to the cooling time at a lower-temperature outlet of the mixing cascade. The framework accounts for the order-unity ratio being robust to changes in gas pressure.

Significance. If the central result holds, the work provides a geometric explanation for the observed universal X-ray/Hα surface-brightness ratio in galactic winds, ram-pressure-stripped tails, and cluster filaments, emphasizing the role of 3D shattering and mixing-layer geometry over plane-parallel models. The connection to prior work on temperature PDFs (Chen & Oh 2026) and the residence-time interpretation tied to the mixing cascade represent a potentially important conceptual advance. The simulations' ability to recover an order-unity ratio without free parameters is a strength if convergence can be demonstrated.

major comments (2)
  1. [Simulation results paragraph] Simulation results paragraph (abstract and main text description of wind-tunnel runs): the claim that the surface-brightness ratio converges to the observed value after smoothing on the tail-width scale is presented without quantitative error bars, resolution study, or convergence tests with respect to grid resolution, artificial viscosity, or sub-grid mixing parameters. This is load-bearing for the assertion that the residence-time scaling with pressure is independent of the specific numerical setup in the χ∼10^3 shattered-clump regime.
  2. [Theoretical interpretation paragraph] Theoretical interpretation paragraph: the residence time is stated to scale 'roughly inversely with pressure' and to 'suggest' a link to the cooling time at a lower-temperature outlet of the mixing cascade, but no explicit derivation of the scaling, quantitative comparison to the cooling function, or analytic relation is provided. This is central to the claim that the ratio is order unity and robust to pressure variations.
minor comments (1)
  1. [Abstract] The abstract references 'Chen & Oh 2026' without a corresponding entry in the bibliography; the full citation should be added for completeness.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their constructive report and for recognizing the potential significance of the geometric explanation for the universal surface-brightness ratio. We address each major comment below. Where the comments identify areas needing additional quantitative support, we will revise the manuscript accordingly.

read point-by-point responses

  1. Referee: Simulation results paragraph (abstract and main text description of wind-tunnel runs): the claim that the surface-brightness ratio converges to the observed value after smoothing on the tail-width scale is presented without quantitative error bars, resolution study, or convergence tests with respect to grid resolution, artificial viscosity, or sub-grid mixing parameters. This is load-bearing for the assertion that the residence-time scaling with pressure is independent of the specific numerical setup in the χ∼10^3 shattered-clump regime.

    Authors: We agree that the current presentation would benefit from explicit quantitative support. In the revised manuscript we will add error bars derived from multiple snapshots and independent runs, together with a dedicated resolution study (including variations in grid resolution and artificial viscosity) demonstrating that the measured SB_X/SB_Hα ratio and its pressure scaling remain stable in the χ∼10^3 regime once the tail-width smoothing scale is reached. These additions will be placed in the main text or a new appendix. revision: yes

  2. Referee: Theoretical interpretation paragraph: the residence time is stated to scale 'roughly inversely with pressure' and to 'suggest' a link to the cooling time at a lower-temperature outlet of the mixing cascade, but no explicit derivation of the scaling, quantitative comparison to the cooling function, or analytic relation is provided. This is central to the claim that the ratio is order unity and robust to pressure variations.

    Authors: The referee is correct that the scaling is currently presented on the basis of the simulation measurements without a full analytic derivation. We will revise the theoretical section to include an explicit derivation showing how the residence time in the X-ray band scales as τ_res ∝ P^{-1} when tied to the cooling time at the lower-temperature outlet of the mixing cascade, together with a direct quantitative comparison to the cooling function Λ(T) at the relevant temperatures. This will make the connection to the order-unity ratio and its robustness to pressure fully analytic. revision: yes

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity; derivation relies on new simulations and atomic physics

full rationale

The paper's central result is obtained from new 3D wind-tunnel simulations in the χ~10^3 regime, where the measured SB_X/SB_Hα ratio after tail-width smoothing converges to the observed ~3 value. The theoretical split attributes Hα luminosity to atomic physics and X-ray luminosity to a residence-time scaling (~1/P) extracted from those simulations, with the link to lower-temperature cooling time presented as a suggestion rather than a closed derivation. The citation to Chen & Oh 2026 is used only for motivation on geometry controlling the temperature PDF and is not required to establish the SB ratio or its pressure robustness; no equation reduces by construction to a fitted input, self-definition, or prior self-citation chain. The work is therefore self-contained against the external observational benchmark.

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

Review performed on abstract only; no explicit free parameters, invented entities, or additional axioms are stated beyond the domain assumption of the high-contrast shattering regime.

assumptions (2)
  • domain assumption High density contrast χ~10^3 produces shattering of cold phase into small clumps with volume-filling X-ray cocoon
    Invoked to justify the simulation setup and the resulting surface-brightness ratio.
  • domain assumption X-ray luminosity fraction is controlled by residence time in the X-ray band rather than cooling time at X-ray temperatures
    Central to the theoretical account of why the ratio is order unity and pressure-independent.

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Cite this review

Pith. "Pith review of Clumps in a Cocoon: Geometry and Mixing Set the Universal X-ray to H$\alpha$ Surface Brightness Ratio." pith.science (2026). https://pith.science/paper/YL5S4K5U

@misc{pith2026260607741,
  author       = {Pith},
  title        = {Pith review of: Clumps in a Cocoon: Geometry and Mixing Set the Universal X-ray to H$\alpha$ Surface Brightness Ratio},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/YL5S4K5U}},
  note         = {Machine review of arXiv:2606.07741}
}
abstract

Recent observations reveal a universal X-ray to H$\alpha$ surface-brightness ratio, ${\rm SB}_{\rm X}/{\rm SB}_{\rm H\alpha}\sim 3$, in galactic winds, ram-pressure stripped tails, and cluster filaments. This is surprising because H$\alpha$ traces cold ($\sim 10^4$ K) gas while X-rays trace much hotter ($\sim 10^{6}$--$10^{7}$ K) gas. Plane-parallel mixing-layer models do not recover this ratio, and can be off by orders of magnitude. Motivated by recent work showing that geometry controls the temperature PDF of multiphase gas (Chen & Oh 2026), we run 3D wind-tunnel simulations in the high density contrast ($\chi\sim 10^3$) regime. In this limit, the cold phase shatters into many small H$\alpha$-emitting clumps, while X-ray-emitting gas forms a volume-filling cocoon around them. After smoothing on the tail-width scale, the measured surface-brightness ratio converges to the observed value, which can be understood theoretically. The H$\alpha$ luminosity fraction is set by atomic physics, whereas the X-ray luminosity fraction is set by the residence time of gas in the X-ray-emitting band. This residence time is much shorter than the cooling time at X-ray temperatures, but scales roughly inversely with pressure, suggesting that it is tied to the cooling time at a lower-temperature outlet of the mixing cascade. This framework naturally explains why the observed ratio is order unity, and robust to changes in gas pressure.

Figures

Figures reproduced from arXiv: 2606.07741 by the authors.

Figure 1
Figure 1. H𝛼 (top) and X-ray (bottom) surface brightness maps for a zoomed￾in section of the cloud tail in our wind tunnel simulation. The H𝛼 emitting gas consists of numerous small clumps, while the X-ray emitting gas is volume-filling and forms an elongated, cocoon-like structure that envelopes the H𝛼 emitting clumps. We refer to this morphology as "clumps in a cocoon" throughout this letter. We choose a simulation snapshot… view at source ↗
Figure 3
Figure 3. Mass-weighted PDFs of the residence time 𝑡𝑋 in the X-ray￾emitting temperature band, defined as 106 K < 𝑇 < 8 × 106 K and con￾taining ≃ 90% of the total X-ray emission. The distribution is measured using an Eulerian passive scalar that is incremented by Δ𝑡 every timestep while gas remains in the X-ray band and reset to zero otherwise. Black shows the fiducial run with 𝑃/𝑘𝐵 = 3 × 104 K cm−3 , which is appropriate for … view at source ↗

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Works this paper leans on

298 extracted references · 247 canonical work pages

  1. [1]

    D., Lancaster, L., & Diesing, R

    doi:10.3847/1538-4357/ade711 , eid =. arXiv , author =:2505.08907 , journal =

    work page doi:10.3847/1538-4357/ade711

  2. [2]

    K., & Gronke, M

    , keywords =. doi:10.1093/mnras/stad3125 , eprint =

    work page doi:10.1093/mnras/stad3125

  3. [3]

    2023, MNRAS, 526, 4245, doi: 10.1093/mnras/stad3011

    , keywords =. doi:10.1093/mnras/stad3011 , eprint =

    work page doi:10.1093/mnras/stad3011

  4. [4]

    doi:10.1093/mnras/stad1716 , eprint =

    , keywords =. doi:10.1093/mnras/stad1716 , eprint =

    work page doi:10.1093/mnras/stad1716

  5. [5]

    Transport, collective motion, and Brownian motion

    Mori, Hazime , date-added =. Transport, Collective Motion, and Brownian Motion , volume =. 1965 , bdsk-url-1 =. doi:10.1143/PTP.33.423 , journal =

    work page doi:10.1143/ptp.33.423 1965

  6. [6]

    and Gariepy, Ronald F

    Evans, Lawrence C. and Gariepy, Ronald F. , date-added =. Measure Theory and Fine Properties of Functions , year =

  7. [7]

    2025, arXiv e-prints, arXiv:2509.03802, doi: 10.48550/arXiv.2509.03802

    doi:10.48550/arXiv.2509.03802 , eid =. arXiv , author =:2509.03802 , journal =

    work page doi:10.48550/arxiv.2509.03802

  8. [8]

    First passage and first hitting times of L

    Palyulin, Vladimir V and Blackburn, George and Lomholt, Michael A and Watkins, Nicholas W and Metzler, Ralf and Klages, Rainer and Chechkin, Aleksei V , date-added =. First passage and first hitting times of L. New Journal of Physics , number =

Show all 298 references
  1. [9]

    Molecular hydrodynamics , year =

    Boon, Jean Pierre and Yip, Sidney , date-added =. Molecular hydrodynamics , year =

  2. [10]

    2025 , bdsk-url-1 =

    Hybrid Simulations of Supersonic Shear Flows: I) Particle Acceleration , url =. 2025 , bdsk-url-1 =. arXiv , author =:2511.10739 , primaryclass =

    2025

  3. [11]

    Approximation by exponential sums revisited , volume =

    Beylkin, Gregory and Monz. Approximation by exponential sums revisited , volume =. Applied and Computational Harmonic Analysis , number =

  4. [12]

    Fast Evaluation of the Caputo Fractional Derivative and its Applications to Fractional Diffusion Equations , volume =

    Jiang, Shidong and Zhang, Jiwei and Zhang, Qian and Zhang, Zhimin , date-added =. Fast Evaluation of the Caputo Fractional Derivative and its Applications to Fractional Diffusion Equations , volume =. 2017 , bdsk-url-1 =. doi:10.4208/cicp.OA-2016-0136 , journal =

    2017 doi

  5. [13]

    Discretized fractional calculus , volume =

    Lubich, Ch , date-added =. Discretized fractional calculus , volume =. SIAM Journal on Mathematical Analysis , number =

  6. [14]

    arXiv , author =:2502.01726 , journal =

    doi:10.3847/1538-4357/adbca7 , eid =. arXiv , author =:2502.01726 , journal =

    doi

  7. [15]

    arXiv , author =:2205.01986 , journal =

    doi:10.1103/PhysRevE.107.065206 , eid =. arXiv , author =:2205.01986 , journal =

    doi

  8. [16]

    arXiv , author =:2409.16053 , journal =

    doi:10.48550/arXiv.2409.16053 , eid =. arXiv , author =:2409.16053 , journal =

    doi

  9. [17]

    doi:10.1038/s41550-022-01868-9 , eprint =

    Nature Astronomy , keywords =. doi:10.1038/s41550-022-01868-9 , eprint =

    doi

  10. [18]

    doi:10.1038/s41550-019-0724-0 , eprint =

    Nature Astronomy , keywords =. doi:10.1038/s41550-019-0724-0 , eprint =

    doi

  11. [19]

    arXiv , author =:2509.07104 , journal =

    doi:10.48550/arXiv.2509.07104 , eid =. arXiv , author =:2509.07104 , journal =

    doi arXiv

  12. [20]

    doi:10.1093/mnras/stz2760 , eprint =

    , keywords =. doi:10.1093/mnras/stz2760 , eprint =

    doi

  13. [21]

    doi:10.1086/502676 , journal =

    doi

  14. [22]

    doi:10.1086/344687 , journal =

    doi

  15. [23]

    arXiv , author =:2510.02443 , journal =

    doi:10.48550/arXiv.2510.02443 , eid =. arXiv , author =:2510.02443 , journal =

    doi arXiv

  16. [24]

    arXiv , author =:2503.02329 , journal =

    doi:10.3847/1538-4357/ade0bc , eid =. arXiv , author =:2503.02329 , journal =

    doi

  17. [25]

    arXiv , author =:2504.15345 , journal =

    doi:10.48550/arXiv.2504.15345 , eid =. arXiv , author =:2504.15345 , journal =

    doi arXiv

  18. [26]

    arXiv , author =:2507.00136 , journal =

    doi:10.48550/arXiv.2507.00136 , eid =. arXiv , author =:2507.00136 , journal =

    doi

  19. [27]

    doi:10.1093/mnras/staf1474 , eprint =

    , keywords =. doi:10.1093/mnras/staf1474 , eprint =

    doi

  20. [28]

    arXiv , author =:2505.18155 , journal =

    doi:10.48550/arXiv.2505.18155 , eid =. arXiv , author =:2505.18155 , journal =

    doi

  21. [29]

    arXiv , author =:2509.15320 , journal =

    doi:10.48550/arXiv.2509.15320 , eid =. arXiv , author =:2509.15320 , journal =

    doi

  22. [30]

    Solution to the Cosmic Ray Anisotropy Problem , url =

    Mertsch, Philipp and Funk, Stefan , date-added =. Solution to the Cosmic Ray Anisotropy Problem , url =. Physical Review Letters , month = jan, number =. 2015 , bdsk-url-1 =. doi:10.1103/physrevlett.114.021101 , issn =

    2015 doi

  23. [32]

    doi:10.1093/mnras/stac3207 , eprint =

    , keywords =. doi:10.1093/mnras/stac3207 , eprint =

    doi

  24. [33]

    arXiv , author =:2411.16415 , journal =

    doi:10.3847/1538-4357/ad96af , eid =. arXiv , author =:2411.16415 , journal =

    doi

  25. [34]

    arXiv , author =:2107.07569 , journal =

    doi:10.1051/0004-6361/202140665 , eid =. arXiv , author =:2107.07569 , journal =

    doi

  26. [35]

    Quirk , date-added =

    James J. Quirk , date-added =. An alternative to unstructured grids for computing gas dynamic flows around arbitrarily complex two-dimensional bodies , url =. Computers & Fluids , number =. 1994 , bdsk-url-1 =. doi:https://doi.org/10.1016/0045-7930(94)90031-0 , issn =

    1994 doi

  27. [36]

    arXiv , author =:2203.06479 , journal =

    doi:10.3389/fphy.2022.858841 , eid =. arXiv , author =:2203.06479 , journal =

    2022 doi

  28. [37]

    arXiv , author =:2507.19044 , journal =

    doi:10.48550/arXiv.2507.19044 , eid =. arXiv , author =:2507.19044 , journal =

    doi

  29. [38]

    doi:10.1093/mnras/stac2909 , eprint =

    , keywords =. doi:10.1093/mnras/stac2909 , eprint =

    doi

  30. [39]

    Reichherzer, Patrick and Bott, Archie F. A. and Ewart, Robert J. and Gregori, Gianluca and Kempski, Philipp and Kunz, Matthew W. and Schekochihin, Alexander A. , date-added =. Efficient micromirror confinement of sub-teraelectronvolt cosmic rays in galaxy clusters , volume =. ...

    2025 doi

  31. [40]

    , date-added =

    Doob, Joseph L. , date-added =. Stochastic Processes , year =

  32. [41]

    arXiv , author =:2507.10651 , journal =

    doi:10.48550/arXiv.2507.10651 , eid =. arXiv , author =:2507.10651 , journal =

    doi

  33. [42]

    arXiv , author =:2506.10277 , journal =

    doi:10.48550/arXiv.2506.10277 , eid =. arXiv , author =:2506.10277 , journal =

    doi

  34. [43]

    arXiv , author =:2104.03089 , journal =

    doi:10.1051/0004-6361/202140611 , eid =. arXiv , author =:2104.03089 , journal =

    doi

  35. [44]

    arXiv , author =:1610.05332 , journal =

    doi:10.3847/0004-637X/833/1/5 , eid =. arXiv , author =:1610.05332 , journal =

    doi arXiv

  36. [45]

    arXiv , author =:1504.04418 , journal =

    doi:10.1088/0004-637X/806/1/81 , eid =. arXiv , author =:1504.04418 , journal =

    doi arXiv

  37. [46]

    doi:10.1007/978-3-319-10416-4 , editor =

    Solar Prominences , date-added =. doi:10.1007/978-3-319-10416-4 , editor =

    doi

  38. [47]

    arXiv , author =:2002.12539 , journal =

    doi:10.3847/2041-8213/ab7824 , eid =. arXiv , author =:2002.12539 , journal =

    doi

  39. [48]

    doi:10.1086/503668 , eprint =

    , keywords =. doi:10.1086/503668 , eprint =

    doi

  40. [49]

    arXiv , author =:2412.03649 , journal =

    doi:10.48550/arXiv.2412.03649 , eid =. arXiv , author =:2412.03649 , journal =

    doi

  41. [50]

    arXiv , author =:2502.17549 , journal =

    doi:10.48550/arXiv.2502.17549 , eid =. arXiv , author =:2502.17549 , journal =

    doi

  42. [51]

    doi:10.1093/mnras/stae2771 , eprint =

    , keywords =. doi:10.1093/mnras/stae2771 , eprint =

    doi

  43. [52]

    arXiv , author =:2306.03141 , journal =

    doi:10.1007/s00159-023-00149-2 , eid =. arXiv , author =:2306.03141 , journal =

    doi

  44. [53]

    arXiv , author =:0801.1450 , journal =

    doi:10.1103/PhysRevD.77.123003 , eid =. arXiv , author =:0801.1450 , journal =

    doi arXiv

  45. [54]

    doi:10.1126/science.aan4880 , eprint =

    Science , keywords =. doi:10.1126/science.aan4880 , eprint =

    doi

  46. [55]

    arXiv , author =:1702.08436 , journal =

    doi:10.1103/PhysRevD.96.103013 , eid =. arXiv , author =:1702.08436 , journal =

    doi arXiv

  47. [56]

    doi:10.1051/0004-6361/202449334 , eid =

    , keywords =. doi:10.1051/0004-6361/202449334 , eid =

    doi

  48. [57]

    doi:10.1088/0004-637X/693/2/L118 , journal =

    doi

  49. [58]

    doi:10.1086/525523 , journal =

    doi

  50. [59]

    arXiv , author =:2101.01438 , journal =

    doi:10.1103/PhysRevD.103.063035 , eid =. arXiv , author =:2101.01438 , journal =

    doi

  51. [60]

    arXiv , author =:2501.18696 , journal =

    doi:10.48550/arXiv.2501.18696 , eid =. arXiv , author =:2501.18696 , journal =

    doi

  52. [61]

    doi:10.1093/mnrasl/slae074 , eprint =

    , keywords =. doi:10.1093/mnrasl/slae074 , eprint =

    doi

  53. [62]

    doi:10.1086/151503 , journal =

    doi

  54. [63]

    doi:10.1086/499219 , eprint =

    , keywords =. doi:10.1086/499219 , eprint =

    doi

  55. [64]

    Barthelemy, Pierre and Bertolotti, Jacopo and Wiersma, Diederik S , date-added =. A L. Nature , number =

  56. [65]

    doi:10.1088/0004-637X/778/1/35 , eid =

    , keywords =. doi:10.1088/0004-637X/778/1/35 , eid =

    doi

  57. [66]

    arXiv , author =:1709.08269 , journal =

    doi:10.3847/1538-4357/aa8ee8 , eid =. arXiv , author =:1709.08269 , journal =

    doi arXiv

  58. [67]

    arXiv , author =:1901.03439 , journal =

    doi:10.3847/2041-8213/ab8122 , eid =. arXiv , author =:1901.03439 , journal =

    doi

  59. [68]

    arXiv , author =:1609.04851 , journal =

    doi:10.1103/PhysRevLett.118.055103 , eid =. arXiv , author =:1609.04851 , journal =

    doi arXiv

  60. [69]

    arXiv , author =:1809.01168 , journal =

    doi:10.1103/PhysRevLett.121.255101 , eid =. arXiv , author =:1809.01168 , journal =

    doi arXiv

  61. [70]

    Vinogradov , date-added =

    Dmitry V. Vinogradov , date-added =. Cumulant approach of arbitrary truncated Levy flight , url =. Physica A: Statistical Mechanics and its Applications , keywords =. 2010 , bdsk-url-1 =. doi:https://doi.org/10.1016/j.physa.2010.09.014 , issn =

    2010 doi

  62. [71]

    arXiv , author =:2203.07265 , journal =

    doi:10.1051/0004-6361/202243546 , eid =. arXiv , author =:2203.07265 , journal =

    doi

  63. [72]

    arXiv , author =:1404.5306 , journal =

    doi:10.1088/2041-8205/788/1/L13 , eid =. arXiv , author =:1404.5306 , journal =

    doi arXiv

  64. [73]

    doi:10.1093/mnras/stad671 , eprint =

    , keywords =. doi:10.1093/mnras/stad671 , eprint =

    doi

  65. [74]

    arXiv , author =:2104.13093 , journal =

    doi:10.1007/s42452-021-04891-z , eid =. arXiv , author =:2104.13093 , journal =

    doi

  66. [75]

    de Burgh-Day, C. O. and Leeuwenburg, T. , date-added =. Machine learning for numerical weather and climate modelling: a review , url =. 2023 , bdsk-url-1 =. doi:10.5194/gmd-16-6433-2023 , journal =

    2023 doi

  67. [76]

    arXiv , author =:2107.10858 , journal =

    doi:10.3847/1538-4357/ac49e1 , eid =. arXiv , author =:2107.10858 , journal =

    doi

  68. [77]

    Arkenstone ‚

    Smith, Matthew C and Fielding, Drummond B and Bryan, Greg L and Kim, Chang-Goo and Ostriker, Eve C and Somerville, Rachel S and Stern, Jonathan and Su, Kung-Yi and Weinberger, Rainer and Hu, Chia-Yu and Forbes, John C and Hernquist, Lars and Burkhart, Blakesley and Li, Yuan , ...

    2023 doi

  69. [78]

    arXiv , author =:1112.0656 , journal =

    doi:10.1088/0004-637X/745/2/152 , eid =. arXiv , author =:1112.0656 , journal =

    doi arXiv

  70. [79]

    Scalar turbulence , volume =

    Shraiman, Boris I and Siggia, Eric D , date-added =. Scalar turbulence , volume =. Nature , number =

  71. [80]

    arXiv , author =:2211.06434 , journal =

    doi:10.3847/2041-8213/accf1f , eid =. arXiv , author =:2211.06434 , journal =

    doi

  72. [81]

    doi:10.1146/annurev-astro-120419-014455 , eprint =

    , keywords =. doi:10.1146/annurev-astro-120419-014455 , eprint =

    doi

  73. [82]

    arXiv , author =:2301.10717 , journal =

    doi:10.3847/1538-4357/acdc27 , eid =. arXiv , author =:2301.10717 , journal =

    doi

  74. [83]

    Zaburdaev, Vasily and Denisov, Sergey and Klafter, Joseph , date-added =. L. Reviews of Modern Physics , number =

  75. [84]

    Comment on ``Stochastic process with ultraslow convergence to a Gaussian: the truncated L

    Shlesinger, Michael F , date-added =. Comment on ``Stochastic process with ultraslow convergence to a Gaussian: the truncated L. Physical Review Letters , number =

  76. [85]

    Analytic approach to the problem of convergence of truncated L

    Koponen, Ismo , date-added =. Analytic approach to the problem of convergence of truncated L. Physical Review E , number =

  77. [86]

    Discriminating between anomalous diffusion and transient behavior in microheterogeneous environments , volume =

    Berezhkovskii, Alexander M and Dagdug, Leonardo and Bezrukov, Sergey M , date-added =. Discriminating between anomalous diffusion and transient behavior in microheterogeneous environments , volume =. Biophysical journal , number =

  78. [87]

    A biological interpretation of transient anomalous subdiffusion

    Saxton, Michael J , date-added =. A biological interpretation of transient anomalous subdiffusion. I. Qualitative model , volume =. Biophysical journal , number =

  79. [88]

    Univariate geometric stable laws , volume =

    Kozubowski, Tomasz J and Rachev, Svetlozar T , date-added =. Univariate geometric stable laws , volume =. Journal of Computational Analysis and Applications , pages =

  80. [89]

    Monte Carlo simulation of uncoupled continuous-time random walks yielding a stochastic solution of the space-time fractional diffusion equation , volume =

    Fulger, Daniel and Scalas, Enrico and Germano, Guido , date-added =. Monte Carlo simulation of uncoupled continuous-time random walks yielding a stochastic solution of the space-time fractional diffusion equation , volume =. Physical Review E---Statistical, Nonlinear, and Soft...

  81. [90]

    doi:10.1007/978-3-662-59623-4_1 , journal =

    doi

  82. [91]

    Matrix approach to discrete fractional calculus II: partial fractional differential equations , volume =

    Podlubny, Igor and Chechkin, Aleksei and Skovranek, Tomas and Chen, YangQuan and Jara, Blas M Vinagre , date-added =. Matrix approach to discrete fractional calculus II: partial fractional differential equations , volume =. Journal of Computational Physics , number =

  83. [92]

    What is the fractional Laplacian? A comparative review with new results , volume =

    Lischke, Anna and Pang, Guofei and Gulian, Mamikon and Song, Fangying and Glusa, Christian and Zheng, Xiaoning and Mao, Zhiping and Cai, Wei and Meerschaert, Mark M and Ainsworth, Mark and others , date-added =. What is the fractional Laplacian? A comparative review with new r...

  84. [93]

    Numerical methods for fractional diffusion , volume =

    Bonito, Andrea and Borthagaray, Juan Pablo and Nochetto, Ricardo H and Ot. Numerical methods for fractional diffusion , volume =. Computing and Visualization in Science , number =

  85. [94]

    Random walks on lattices

    Montroll, Elliott W and Weiss, George H , date-added =. Random walks on lattices. II , volume =. Journal of Mathematical Physics , number =

  86. [95]

    Stochastic pathway to anomalous diffusion , volume =

    Klafter, Joseph and Blumen, Alexander and Shlesinger, Michael F , date-added =. Stochastic pathway to anomalous diffusion , volume =. Physical Review A , number =

  87. [96]

    Fractional transport in strongly turbulent plasmas , volume =

    Isliker, Heinz and Vlahos, Loukas and Constantinescu, Dana , date-added =. Fractional transport in strongly turbulent plasmas , volume =. Physical Review Letters , number =

  88. [97]

    Stable distributions , year =

    Borak, Szymon and H. Stable distributions , year =

  89. [98]

    The dynamical foundation of fractal stream chemistry: The origin of extremely long retention times , volume =

    Scher, Harvey and Margolin, Gennady and Metzler, Ralf and Klafter, Joseph and Berkowitz, Brian , date-added =. The dynamical foundation of fractal stream chemistry: The origin of extremely long retention times , volume =. Geophysical Research Letters , number =

  90. [99]

    Anomalous diffusion in living yeast cells , volume =

    Toli. Anomalous diffusion in living yeast cells , volume =. Physical review letters , number =

  91. [100]

    Dispersive (non-Gaussian) transient transport in disordered solids , volume =

    Pfister, Gerhard and Scher, Harvey , date-added =. Dispersive (non-Gaussian) transient transport in disordered solids , volume =. Advances in Physics , number =

  92. [101]

    Random walk to a nonergodic equilibrium concept , volume =

    Bel, Golan and Barkai, Eli , date-added =. Random walk to a nonergodic equilibrium concept , volume =. Physical Review E---Statistical, Nonlinear, and Soft Matter Physics , number =

  93. [102]

    Anomalous transport , year =

    Klages, Rainer and Radons, G. Anomalous transport , year =

  94. [103]

    arXiv , author =:2406.03542 , journal =

    doi:10.48550/arXiv.2406.03542 , eid =. arXiv , author =:2406.03542 , journal =

    doi

  95. [104]

    arXiv , author =:2106.08362 , journal =

    doi:10.3847/1538-4357/ac2de9 , eid =. arXiv , author =:2106.08362 , journal =

    doi

  96. [105]

    doi:10.1086/428919 , eprint =

    , keywords =. doi:10.1086/428919 , eprint =

    doi

  97. [106]

    doi:10.1086/345827 , eprint =

    , keywords =. doi:10.1086/345827 , eprint =

    doi

  98. [107]

    Atmospheric diffusion shown on a distance-neighbour graph , volume =

    Richardson, Lewis Fry , date-added =. Atmospheric diffusion shown on a distance-neighbour graph , volume =. Proceedings of the Royal Society of London. Series A, Containing Papers of a Mathematical and Physical Character , number =

  99. [108]

    doi:10.1086/308492 , journal =

    doi

  100. [109]

    arXiv , author =:1307.1346 , journal =

    doi:10.1088/0004-637X/779/2/140 , eid =. arXiv , author =:1307.1346 , journal =

    doi arXiv

  101. [110]

    arXiv , author =:1103.1882 , journal =

    doi:10.1088/0004-637X/743/1/51 , eid =. arXiv , author =:1103.1882 , journal =

    doi arXiv

  102. [111]

    doi:10.1086/307233 , eprint =

    , keywords =. doi:10.1086/307233 , eprint =

    doi

  103. [112]

    Anomalous diffusion in disordered media: Statistical mechanisms, models and physical applications , url =

    Jean-Philippe Bouchaud and Antoine Georges , date-added =. Anomalous diffusion in disordered media: Statistical mechanisms, models and physical applications , url =. Physics Reports , number =. 1990 , bdsk-url-1 =. doi:https://doi.org/10.1016/0370-1573(90)90099-N , issn =

    1990 doi

  104. [113]

    Dubkov, Alexander A and Spagnolo, Bernardo and Uchaikin, Vladimir V , date-added =. L. International Journal of Bifurcation and Chaos , number =

  105. [114]

    The random walk's guide to anomalous diffusion: a fractional dynamics approach , volume =

    Metzler, Ralf and Klafter, Joseph , date-added =. The random walk's guide to anomalous diffusion: a fractional dynamics approach , volume =. Physics reports , number =

  106. [115]

    An introduction to fractional diffusion , year =

    Henry, Bruce I and Langlands, Trevor AM and Straka, Peter , booktitle =. An introduction to fractional diffusion , year =

  107. [116]

    Reynolds, Andy M and Rhodes, Christopher J , date-added =. The L. Ecology , number =

  108. [117]

    doi:10.1093/mnras/stae276 , eprint =

    , keywords =. doi:10.1093/mnras/stae276 , eprint =

    doi

  109. [118]

    doi:10.1093/mnras/stad2609 , eprint =

    , keywords =. doi:10.1093/mnras/stad2609 , eprint =

    doi

  110. [119]

    arXiv , author =:2304.03023 , journal =

    doi:10.1017/S0022377823000946 , eid =. arXiv , author =:2304.03023 , journal =

    doi

  111. [120]

    doi:10.1038/s41550-020-1094-3 , eprint =

    Nature Astronomy , keywords =. doi:10.1038/s41550-020-1094-3 , eprint =

    doi

  112. [121]

    doi:10.1023/A:1026150809598 , journal =

    doi

  113. [122]

    doi:10.1088/0004-637X/721/1/74 , journal =

    doi

  114. [123]

    arXiv , author =:1504.08129 , journal =

    doi:10.1088/0004-637X/807/2/158 , eid =. arXiv , author =:1504.08129 , journal =

    doi arXiv

  115. [124]

    arXiv , author =:1312.3792 , journal =

    doi:10.1051/0004-6361/201322572 , eid =. arXiv , author =:1312.3792 , journal =

    doi arXiv

  116. [125]

    doi:10.1038/24798 , journal =

    doi

  117. [127]

    arXiv , author =:2003.10947 , journal =

    doi:10.1051/0004-6361/202037616 , eid =. arXiv , author =:2003.10947 , journal =

    2003 doi

  118. [128]

    arXiv , author =:1706.01804 , journal =

    doi:10.1051/0004-6361/201730660 , eid =. arXiv , author =:1706.01804 , journal =

    doi arXiv

  119. [129]

    Fang and C

    X. Fang and C. Xia and R. Keppens , date-added =. MULTIDIMENSIONAL MODELING OF CORONAL RAIN DYNAMICS , url =. 2013 , bdsk-url-1 =. doi:10.1088/2041-8205/771/2/L29 , journal =

    2013 doi

  120. [130]

    doi:10.1023/A:1012722021820 , journal =

    doi

  121. [131]

    doi:10.3389/fspas.2022.820116 , eid =

    Frontiers in Astronomy and Space Sciences , month = mar, pages =. doi:10.3389/fspas.2022.820116 , eid =

    2022 doi

  122. [132]

    doi:10.1088/1361-6587/ab5406 , eid =

    Plasma Physics and Controlled Fusion , keywords =. doi:10.1088/1361-6587/ab5406 , eid =

    doi

  123. [133]

    doi:10.1093/mnras/staa3131 , eprint =

    , keywords =. doi:10.1093/mnras/staa3131 , eprint =

    doi

  124. [134]

    arXiv , author =:1001.0551 , journal =

    doi:10.1051/0004-6361/201014010 , eid =. arXiv , author =:1001.0551 , journal =

    doi arXiv

  125. [135]

    arXiv , author =:1807.02968 , journal =

    doi:10.1016/j.cpc.2019.106942 , eid =. arXiv , author =:1807.02968 , journal =

    2019 doi

  126. [136]

    doi:10.1086/171262 , journal =

    doi

  127. [137]

    doi:10.1016/S0920-5632(99)00518-6 , journal =

    doi

  128. [138]

    doi:10.1063/1.1324345 , editor =

    Acceleration and Transport of Energetic Particles Observed in the Heliosphere , date-added =. doi:10.1063/1.1324345 , editor =

    doi

  129. [139]

    Meerschaert and Charles Tadjeran , date-added =

    Mark M. Meerschaert and Charles Tadjeran , date-added =. Finite difference approximations for fractional advection--dispersion flow equations , url =. Journal of Computational and Applied Mathematics , keywords =. 2004 , bdsk-url-1 =. doi:https://doi.org/10.1016/j.cam.2004.01....

    2004 doi

  130. [140]

    arXiv , author =:2209.12902 , journal =

    doi:10.3847/1538-4357/acbef9 , eid =. arXiv , author =:2209.12902 , journal =

    doi

  131. [141]

    arXiv , author =:2209.00019 , journal =

    doi:10.3847/1538-4357/acb3b1 , eid =. arXiv , author =:2209.00019 , journal =

    doi

  132. [142]

    doi:10.1038/s41467-020-16660-4 , eid =

    Nature Communications , month = jun, pages =. doi:10.1038/s41467-020-16660-4 , eid =

    doi

  133. [143]

    arXiv , author =:1710.02106 , journal =

    doi:10.3847/2041-8213/aa9a33 , eid =. arXiv , author =:1710.02106 , journal =

    doi arXiv

  134. [144]

    doi:10.1093/mnras/stac3214 , eprint =

    , keywords =. doi:10.1093/mnras/stac3214 , eprint =

    doi

  135. [145]

    arXiv , author =:2203.10880 , journal =

    doi:10.1051/0004-6361/202243574 , eid =. arXiv , author =:2203.10880 , journal =

    doi

  136. [146]

    arXiv , author =:1909.09052 , journal =

    doi:10.1088/1475-7516/2019/11/048 , eid =. arXiv , author =:1909.09052 , journal =

    2019 doi

  137. [147]

    doi:10.1016/j.ppnp.2017.01.004 , eprint =

    Progress in Particle and Nuclear Physics , keywords =. doi:10.1016/j.ppnp.2017.01.004 , eprint =

    2017 doi

  138. [148]

    arXiv , author =:1111.2536 , journal =

    doi:10.1103/PhysRevLett.109.071101 , eid =. arXiv , author =:1111.2536 , journal =

    doi arXiv

  139. [149]

    doi:10.1016/j.cpc.2011.01.017 , eprint =

    Computer Physics Communications , keywords =. doi:10.1016/j.cpc.2011.01.017 , eprint =

    2011 doi

  140. [150]

    arXiv , author =:2201.01316 , journal =

    doi:10.3847/1538-4357/ac5595 , eid =. arXiv , author =:2201.01316 , journal =

    doi

  141. [151]

    arXiv , author =:1203.0570 , journal =

    doi:10.1103/PhysRevLett.108.211102 , eid =. arXiv , author =:1203.0570 , journal =

    doi arXiv

  142. [152]

    arXiv , author =:1903.11584 , journal =

    doi:10.1142/S0218271819300222 , eid =. arXiv , author =:1903.11584 , journal =

    1903 doi

  143. [153]

    doi:10.1111/j.1745-3933.2005.00057.x , eprint =

    , keywords =. doi:10.1111/j.1745-3933.2005.00057.x , eprint =

    2005 doi

  144. [154]

    doi:10.1086/508706 , eprint =

    , keywords =. doi:10.1086/508706 , eprint =

    doi

  145. [155]

    arXiv , author =:2003.08390 , journal =

    doi:10.3847/2041-8213/ab8d2c , eid =. arXiv , author =:2003.08390 , journal =

    doi

  146. [156]

    arXiv , author =:2108.05355 , journal =

    doi:10.3847/1538-4357/ac2f41 , eid =. arXiv , author =:2108.05355 , journal =

    doi

  147. [157]

    doi:10.1038/s41550-021-01516-8 , eprint =

    Nature Astronomy , keywords =. doi:10.1038/s41550-021-01516-8 , eprint =

    doi

  148. [158]

    arXiv , author =:1710.10703 , journal =

    doi:10.3847/1538-4357/aaf6eb , eid =. arXiv , author =:1710.10703 , journal =

    doi arXiv

  149. [159]

    arXiv , author =:2311.04275 , journal =

    doi:10.48550/arXiv.2311.04275 , eid =. arXiv , author =:2311.04275 , journal =

    doi

  150. [160]

    arXiv , author =:1807.09279 , journal =

    doi:10.3847/1538-4357/aad55c , eid =. arXiv , author =:1807.09279 , journal =

    doi arXiv

  151. [161]

    doi:10.1093/mnras/staa302 , eprint =

    , keywords =. doi:10.1093/mnras/staa302 , eprint =

    doi

  152. [162]

    doi:10.1111/j.1365-2966.2008.12922.x , eprint =

    , keywords =. doi:10.1111/j.1365-2966.2008.12922.x , eprint =

    2008 doi

  153. [163]

    doi:10.48550/arXiv.1302.4485 , eprint =

    , keywords =. doi:10.48550/arXiv.1302.4485 , eprint =

    doi arXiv

  154. [164]

    arXiv , author =:2402.03419 , journal =

    doi:10.48550/arXiv.2402.03419 , eid =. arXiv , author =:2402.03419 , journal =

    doi

  155. [165]

    arXiv , author =:2311.05691 , journal =

    doi:10.48550/arXiv.2311.05691 , eid =. arXiv , author =:2311.05691 , journal =

    doi

  156. [166]

    doi:10.1146/annurev-astro-041923-043618 , eprint =

    , keywords =. doi:10.1146/annurev-astro-041923-043618 , eprint =

    doi

  157. [167]

    arXiv , author =:2309.05699 , journal =

    doi:10.3847/2041-8213/acf85b , eid =. arXiv , author =:2309.05699 , journal =

    doi

  158. [168]

    Theoretical analysis and simulations of the generalized Lotka-Volterra model , volume =

    Malcai, Ofer and Biham, Ofer and Richmond, Peter and Solomon, Sorin , date-added =. Theoretical analysis and simulations of the generalized Lotka-Volterra model , volume =. Physical Review E , number =

  159. [169]

    Power-law distributions and L

    Malcai, Ofer and Biham, Ofer and Solomon, Sorin , date-added =. Power-law distributions and L. Physical Review E , number =

  160. [170]

    and Moin, Parviz , date-added =

    Chan, Wai Hong Ronald and Johnson, Perry L. and Moin, Parviz , date-added =. The turbulent bubble break-up cascade. Part 1. Theoretical developments , volume =. 2021 , bdsk-url-1 =. doi:10.1017/jfm.2020.1083 , journal =

    2021 doi

  161. [171]

    Dodd and Perry L

    Wai Hong Ronald Chan and Michael S. Dodd and Perry L. Johnson and Parviz Moin , date-added =. Identifying and tracking bubbles and drops in simulations: A toolbox for obtaining sizes, lineages, and breakup and coalescence statistics , url =. Journal of Computational Physics , ...

    2021 doi

  162. [172]

    Scaling behaviour in the dynamics of an economic index , volume =

    Mantegna, Rosario N and Stanley, H Eugene , date-added =. Scaling behaviour in the dynamics of an economic index , volume =. Nature , number =

  163. [173]

    Stochastic process with ultraslow convergence to a Gaussian: the truncated L

    Mantegna, Rosario N and Stanley, H Eugene , date-added =. Stochastic process with ultraslow convergence to a Gaussian: the truncated L. Physical Review Letters , number =

  164. [174]

    doi:10.1016/j.physrep.2010.12.004 , journal =

    2010 doi

  165. [175]

    American Astronomical Society Meeting Abstracts , date-added =

  166. [176]

    doi:10.1093/mnras/stad1874 , eprint =

    , keywords =. doi:10.1093/mnras/stad1874 , eprint =

    doi

  167. [177]

    doi:10.1146/annurev-astro-052920-125203 , eprint =

    , keywords =. doi:10.1146/annurev-astro-052920-125203 , eprint =

    doi

  168. [178]

    arXiv , author =:2301.04156 , journal =

    doi:10.3847/1538-4357/aceef9 , eid =. arXiv , author =:2301.04156 , journal =

    doi

  169. [179]

    arXiv , author =:2208.02261 , journal =

    doi:10.3847/1538-4357/aca021 , eid =. arXiv , author =:2208.02261 , journal =

    doi

  170. [180]

    doi:10.1093/mnras/stad2720 , eprint =

    , keywords =. doi:10.1093/mnras/stad2720 , eprint =

    doi

  171. [181]

    doi:10.1038/nature21677 , eprint =

    , keywords =. doi:10.1038/nature21677 , eprint =

    doi

  172. [182]

    doi:10.1093/mnras/stz1481 , eprint =

    , keywords =. doi:10.1093/mnras/stz1481 , eprint =

    doi

  173. [183]

    doi:10.1088/0004-637X/715/2/1575 , eprint =

    , keywords =. doi:10.1088/0004-637X/715/2/1575 , eprint =

    doi

  174. [184]

    doi:10.1093/mnras/sty2021 , eprint =

    , keywords =. doi:10.1093/mnras/sty2021 , eprint =

    doi

  175. [185]

    arXiv , author =:1609.02561 , journal =

    doi:10.3847/1538-4357/833/1/46 , eid =. arXiv , author =:1609.02561 , journal =

    doi arXiv

  176. [186]

    On the particle size spectrum of a condensing vapor , volume =

    Friedlander, SK , date-added =. On the particle size spectrum of a condensing vapor , volume =. The Physics of Fluids , number =

  177. [187]

    Similarity considerations for the particle-size spectrum of a coagulating, sedimenting aerosol , volume =

    Friedlander, SK , date-added =. Similarity considerations for the particle-size spectrum of a coagulating, sedimenting aerosol , volume =. Journal of Atmospheric Sciences , number =

  178. [188]

    Quasi-stationary approximations for the size distribution of aerosols , volume =

    Jeffrey, DJ , date-added =. Quasi-stationary approximations for the size distribution of aerosols , volume =. Journal of the Atmospheric Sciences , number =

  179. [189]

    Self-similar particle-size distributions during coagulation: theory and experimental verification , volume =

    Hunt, James R , date-added =. Self-similar particle-size distributions during coagulation: theory and experimental verification , volume =. Journal of Fluid Mechanics , pages =

  180. [190]

    Zeitschrift fur Physik , month = jan, pages =

  181. [191]

    arXiv , author =:1009.3011 , journal =

    doi:10.1051/0004-6361/201015228 , eid =. arXiv , author =:1009.3011 , journal =

    doi arXiv

  182. [192]

    doi:10.1006/icar.1996.0170 , journal =

    1996 doi

  183. [193]

    Williams and G.W

    D.R. Williams and G.W. Wetherill , date-added =. Size Distribution of Collisionally Evolved Asteroidal Populations: Analytical Solution for Self-Similar Collision Cascades , url =. Icarus , number =. 1994 , bdsk-url-1 =. doi:https://doi.org/10.1006/icar.1994.1010 , issn =

    1994 doi

  184. [194]

    The Connection between Bubble Size Spectra and Energy Dissipation Rates in the Upper Ocean , url =

    Chris Garrett and Ming Li and David Farmer , date-added =. The Connection between Bubble Size Spectra and Energy Dissipation Rates in the Upper Ocean , url =. 2000 , bdsk-url-1 =. doi:https://doi.org/10.1175/1520-0485(2000)030<2163:TCBBSS>2.0.CO;2 , journal =

    2000 doi

  185. [195]

    arXiv , author =:1902.00798 , journal =

    doi:10.3389/fspas.2019.00005 , eid =. arXiv , author =:1902.00798 , journal =

    2019 doi

  186. [196]

    arXiv , author =:1112.4841 , journal =

    doi:10.1088/0004-637X/747/2/86 , eid =. arXiv , author =:1112.4841 , journal =

    doi arXiv

  187. [197]

    arXiv , author =:1309.7139 , journal =

    doi:10.1088/0004-637X/784/2/115 , eid =. arXiv , author =:1309.7139 , journal =

    doi arXiv

  188. [198]

    doi:10.1086/309318 , eprint =

    , keywords =. doi:10.1086/309318 , eprint =

    doi

  189. [199]

    doi:10.1086/174188 , journal =

    doi

  190. [200]

    doi:10.1086/145707 , journal =

    doi

  191. [201]

    arXiv , author =:1306.5194 , journal =

    doi:10.1088/2041-8205/775/1/L32 , eid =. arXiv , author =:1306.5194 , journal =

    doi arXiv

  192. [202]

    arXiv , author =:1803.05446 , journal =

    doi:10.3847/1538-4357/aac884 , eid =. arXiv , author =:1803.05446 , journal =

    doi arXiv

  193. [203]

    doi:10.1093/mnras/stw2499 , eprint =

    , keywords =. doi:10.1093/mnras/stw2499 , eprint =

    doi

  194. [204]

    doi:10.1093/mnras/staa812 , eprint =

    , keywords =. doi:10.1093/mnras/staa812 , eprint =

    doi

  195. [205]

    arXiv , author =:2211.01395 , journal =

    doi:10.3847/1538-4357/acc73f , eid =. arXiv , author =:2211.01395 , journal =

    doi

  196. [206]

    arXiv , author =:1011.3514 , journal =

    doi:10.1088/0067-0049/192/1/9 , eid =. arXiv , author =:1011.3514 , journal =

    doi arXiv

  197. [207]

    doi:10.1093/mnras/stac2528 , eprint =

    , keywords =. doi:10.1093/mnras/stac2528 , eprint =

    doi

  198. [208]

    doi:10.1086/367828 , eprint =

    , keywords =. doi:10.1086/367828 , eprint =

    doi

  199. [209]

    doi:10.1093/mnras/staa550 , eprint =

    , keywords =. doi:10.1093/mnras/staa550 , eprint =

    doi

  200. [210]

    doi:10.1093/mnras/stac3426 , eprint =

    , keywords =. doi:10.1093/mnras/stac3426 , eprint =

    doi

  201. [211]

    arXiv , author =:1507.00882 , journal =

    doi:10.1088/0004-637X/807/2/142 , eid =. arXiv , author =:1507.00882 , journal =

    doi arXiv

  202. [212]

    doi:10.1093/mnras/stab1607 , eprint =

    , keywords =. doi:10.1093/mnras/stab1607 , eprint =

    doi

  203. [213]

    arXiv , author =:1905.06341 , journal =

    doi:10.3847/1538-4357/ab21be , eid =. arXiv , author =:1905.06341 , journal =

    1905 doi

  204. [214]

    arXiv , author =:1906.10693 , journal =

    doi:10.3847/2041-8213/ab30cb , eid =. arXiv , author =:1906.10693 , journal =

    doi

  205. [215]

    doi:10.1051/0004-6361:20042080 , eprint =

    , keywords =. doi:10.1051/0004-6361:20042080 , eprint =

    doi

  206. [216]

    High-fidelity simulation of atomization in a gas turbine injector high shear nozzle , year =

    Kim, D and Ham, F and Bose, S and Le, H and Herrmann, M and Li, X and Soteriou, MC and Kim, W , booktitle =. High-fidelity simulation of atomization in a gas turbine injector high shear nozzle , year =

  207. [217]

    Computational study of atomization and fuel drop size distributions in high-speed primary breakup , volume =

    Bravo, Luis and Kim, D and Ham, F and Su, S , date-added =. Computational study of atomization and fuel drop size distributions in high-speed primary breakup , volume =. Atomization and Sprays , number =

  208. [218]

    Simulation of liquid fuel atomization by a complex high-shear swirling injector , volume =

    Ham, Frank and Kim, Dokyun and Bose, Sanjeeb and Le, Hung and Herrmann, Marcus , booktitle =. Simulation of liquid fuel atomization by a complex high-shear swirling injector , volume =

  209. [219]

    doi:10.1086/161433 , journal =

    doi

  210. [220]

    doi:10.1093/mnras/stad236 , eprint =

    , keywords =. doi:10.1093/mnras/stad236 , eprint =

    doi

  211. [221]

    arXiv , author =:2305.14424 , journal =

    doi:10.48550/arXiv.2305.14424 , eid =. arXiv , author =:2305.14424 , journal =

    doi

  212. [222]

    doi:10.1093/mnras/sts704 , eprint =

    , keywords =. doi:10.1093/mnras/sts704 , eprint =

    doi

  213. [223]

    Fundamentals of the hydrodynamic mechanism of splitting in dispersion processes , volume =

    Hinze, Julius O , date-added =. Fundamentals of the hydrodynamic mechanism of splitting in dispersion processes , volume =. AIChE journal , number =

  214. [224]

    On the breakage of drops in a turbulent flow , volume =

    Kolmogorov, Andrey , booktitle =. On the breakage of drops in a turbulent flow , volume =

  215. [225]

    Air entrainment and surface fluctuations in a turbulent ship hull boundary layer , volume =

    Masnadi, Naeem and Erinin, Martin A and Washuta, Nathan and Nasiri, Farshad and Balaras, Elias and Duncan, James H , date-added =. Air entrainment and surface fluctuations in a turbulent ship hull boundary layer , volume =. Journal of Ship Research , number =

  216. [226]

    and Moin, Parviz and Urzay, Javier , date-added =

    Chan, Wai Hong Ronald and Johnson, Perry L. and Moin, Parviz and Urzay, Javier , date-added =. The turbulent bubble break-up cascade. Part 2. Numerical simulations of breaking waves , volume =. 2021 , bdsk-url-1 =. doi:10.1017/jfm.2020.1084 , journal =

    2021 doi

  217. [227]

    doi:10.1046/j.1365-8711.2001.04270.x , eprint =

    , keywords =. doi:10.1046/j.1365-8711.2001.04270.x , eprint =

    2001 doi

  218. [228]

    arXiv , author =:2005.06651 , journal =

    doi:10.3847/1538-4365/ab929b , eid =. arXiv , author =:2005.06651 , journal =

    2005 doi

  219. [229]

    doi:10.1093/mnras/sty920 , eprint =

    , keywords =. doi:10.1093/mnras/sty920 , eprint =

    doi

  220. [230]

    doi:10.1093/mnras/stac3708 , eprint =

    , keywords =. doi:10.1093/mnras/stac3708 , eprint =

    doi

  221. [231]

    doi:10.1038/s42254-019-0127-2 , eprint =

    Nature Reviews Physics , keywords =. doi:10.1038/s42254-019-0127-2 , eprint =

    doi

  222. [232]

    doi:10.1093/mnras/stz1773 , eprint =

    , keywords =. doi:10.1093/mnras/stz1773 , eprint =

    doi

  223. [233]

    doi:10.1093/mnras/stac319 , eprint =

    , keywords =. doi:10.1093/mnras/stac319 , eprint =

    doi

  224. [234]

    arXiv , author =:1612.03935 , journal =

    doi:10.3847/1538-4357/aa7e2d , eid =. arXiv , author =:1612.03935 , journal =

    doi arXiv

  225. [235]

    doi:10.1086/428723 , eprint =

    , keywords =. doi:10.1086/428723 , eprint =

    doi

  226. [236]

    doi:10.1093/mnras/stac1610 , eprint =

    , keywords =. doi:10.1093/mnras/stac1610 , eprint =

    doi

  227. [237]

    doi:10.1093/mnras/stab3351 , eprint =

    , keywords =. doi:10.1093/mnras/stab3351 , eprint =

    doi

  228. [238]

    Soviet Astronomy Letters , month = mar, pages =

  229. [239]

    arXiv , author =:2210.09532 , journal =

  230. [240]

    arXiv , author =:2205.01732 , journal =

  231. [241]

    doi:10.1093/mnrasl/slab100 , eprint =

    , keywords =. doi:10.1093/mnrasl/slab100 , eprint =

    doi

  232. [242]

    arXiv , author =:1901.10481 , journal =

    doi:10.3847/1538-4357/ab4bca , eid =. arXiv , author =:1901.10481 , journal =

    1901 doi

  233. [243]

    doi:10.1093/mnras/stw2267 , eprint =

    , keywords =. doi:10.1093/mnras/stw2267 , eprint =

    doi

  234. [244]

    arXiv , author =:2107.03395 , journal =

    doi:10.3847/1538-4357/ac2d29 , eid =. arXiv , author =:2107.03395 , journal =

    doi

  235. [245]

    arXiv , author =:1903.00004 , journal =

    doi:10.3847/1538-4357/ab4255 , eid =. arXiv , author =:1903.00004 , journal =

    1903 doi

  236. [246]

    doi:10.1086/587486 , eprint =

    , keywords =. doi:10.1086/587486 , eprint =

    doi

  237. [247]

    doi:10.1093/mnras/staa3544 , eprint =

    , keywords =. doi:10.1093/mnras/staa3544 , eprint =

    doi

  238. [248]

    arXiv , author =:2204.05316 , journal =

  239. [249]

    doi:10.1086/523664 , eprint =

    , keywords =. doi:10.1086/523664 , eprint =

    doi

  240. [250]

    doi:10.1093/mnras/stw409 , eprint =

    , keywords =. doi:10.1093/mnras/stw409 , eprint =

    doi

  241. [251]

    doi:10.1093/mnrasl/slw091 , eprint =

    , keywords =. doi:10.1093/mnrasl/slw091 , eprint =

    doi

  242. [252]

    arXiv , author =:2202.05283 , journal =

  243. [253]

    doi:10.1093/mnras/stab3462 , eprint =

    , keywords =. doi:10.1093/mnras/stab3462 , eprint =

    doi

  244. [254]

    arXiv , author =:2108.09356 , journal =

    doi:10.3847/1538-4357/ac1db2 , eid =. arXiv , author =:2108.09356 , journal =

    doi

  245. [255]

    arXiv , author =:2207.13838 , journal =

  246. [256]

    arXiv , author =:1610.06565 , journal =

    doi:10.3847/1538-4357/835/1/72 , eid =. arXiv , author =:1610.06565 , journal =

    doi arXiv

  247. [257]

    doi:10.1086/164857 , journal =

    doi

  248. [258]

    Pathways to Discovery in Astronomy and Astrophysics for the 2020s , url =

    National Academies of Sciences, Engineering, and Medicine , date-added =. Pathways to Discovery in Astronomy and Astrophysics for the 2020s , url =. doi:10.17226/26141 , isbn =

    doi

  249. [259]

    doi:10.1038/s41550-020-01234-7 , eprint =

    Nature Astronomy , keywords =. doi:10.1038/s41550-020-01234-7 , eprint =

    doi

  250. [260]

    and Torchinsky, Jason L

    Huang, Tianhong and Stechmann, Samuel N. and Torchinsky, Jason L. , date-added =. Framework for idealized climate simulations with spatiotemporal stochastic clouds and planetary-scale circulations , url =. Phys. Rev. Fluids , month =. 2022 , bdsk-url-1 =. doi:10.1103/PhysRevFl...

    2022 doi

  251. [261]

    arXiv , author =:1903.02595 , journal =

    1903 arXiv

  252. [262]

    doi:10.1093/mnras/stab1884 , eprint =

    , keywords =. doi:10.1093/mnras/stab1884 , eprint =

    doi

  253. [263]

    doi:10.1093/mnras/sty2948 , eprint =

    , keywords =. doi:10.1093/mnras/sty2948 , eprint =

    doi

  254. [264]

    doi:10.1093/mnras/sty1285 , eprint =

    , keywords =. doi:10.1093/mnras/sty1285 , eprint =

    doi

  255. [265]

    doi:10.1093/mnras/stx3014 , eprint =

    , keywords =. doi:10.1093/mnras/stx3014 , eprint =

    doi

  256. [266]

    doi:10.1111/j.1365-2966.2011.19524.x , eprint =

    , keywords =. doi:10.1111/j.1365-2966.2011.19524.x , eprint =

    2011 doi

  257. [267]

    doi:10.1093/mnras/stv786 , eprint =

    , keywords =. doi:10.1093/mnras/stv786 , eprint =

    doi

  258. [268]

    doi:10.1038/nature07648 , eprint =

    , keywords =. doi:10.1038/nature07648 , eprint =

    doi

  259. [269]

    doi:10.1088/0004-637X/703/1/785 , eprint =

    , keywords =. doi:10.1088/0004-637X/703/1/785 , eprint =

    doi

  260. [270]

    doi:10.1093/mnras/staa2421 , eprint =

    , keywords =. doi:10.1093/mnras/staa2421 , eprint =

    doi

  261. [271]

    doi:10.1093/mnras/stac2390 , eprint =

    , keywords =. doi:10.1093/mnras/stac2390 , eprint =

    doi

  262. [272]

    doi:10.1093/mnras/stz2347 , eprint =

    , keywords =. doi:10.1093/mnras/stz2347 , eprint =

    doi

  263. [273]

    The Physics of the Interstellar Medium and Intergalactic Medium , date-added =

  264. [274]

    doi:10.1126/science.aay0073 , eprint =

    Science , keywords =. doi:10.1126/science.aay0073 , eprint =

    doi

  265. [275]

    arXiv , author =:1912.08491 , journal =

    doi:10.3847/2041-8213/ab7237 , eid =. arXiv , author =:1912.08491 , journal =

    doi

  266. [276]

    arXiv , author =:1011.0037 , journal =

    doi:10.1088/0004-637X/729/2/106 , eid =. arXiv , author =:1011.0037 , journal =

    doi arXiv

  267. [277]

    doi:10.1088/0004-637X/717/1/1 , eprint =

    , keywords =. doi:10.1088/0004-637X/717/1/1 , eprint =

    doi

  268. [278]

    arXiv , author =:1308.3244 , journal =

    doi:10.1088/0004-637X/784/1/38 , eid =. arXiv , author =:1308.3244 , journal =

    doi arXiv

  269. [279]

    arXiv , author =:2205.08174 , journal =

  270. [280]

    arXiv , author =:1608.04227 , journal =

    doi:10.1051/0004-6361/201629526 , eid =. arXiv , author =:1608.04227 , journal =

    doi arXiv

  271. [281]

    doi:10.1093/mnras/stac1123 , eprint =

    , keywords =. doi:10.1093/mnras/stac1123 , eprint =

    doi

  272. [282]

    doi:10.1093/mnras/stab179 , eprint =

    , keywords =. doi:10.1093/mnras/stab179 , eprint =

    doi

  273. [283]

    doi:10.1086/322408 , journal =

    doi

  274. [284]

    arXiv , author =:1902.10219 , journal =

    doi:10.3847/1538-4357/ab1648 , eid =. arXiv , author =:1902.10219 , journal =

    1902 doi arXiv

  275. [285]

    arXiv , author =:1811.01951 , journal =

    doi:10.3847/1538-4357/ab328a , eid =. arXiv , author =:1811.01951 , journal =

    doi

  276. [286]

    arXiv , author =:2112.14782 , journal =

    doi:10.3847/1538-4357/ac56e1 , eid =. arXiv , author =:2112.14782 , journal =

    doi

  277. [287]

    doi:10.1093/mnras/staa1849 , eprint =

    , keywords =. doi:10.1093/mnras/staa1849 , eprint =

    doi

  278. [288]

    doi:10.1093/mnras/stab1264 , eprint =

    , keywords =. doi:10.1093/mnras/stab1264 , eprint =

    doi

  279. [289]

    doi:10.1093/mnras/stab3274 , eprint =

    , keywords =. doi:10.1093/mnras/stab3274 , eprint =

    doi

  280. [290]

    doi:10.1093/mnras/stab3273 , eprint =

    , keywords =. doi:10.1093/mnras/stab3273 , eprint =

    doi

  281. [291]

    arXiv , author =:2106.14889 , journal =

    doi:10.3847/1538-4357/ac7ebd , eid =. arXiv , author =:2106.14889 , journal =

    doi

  282. [292]

    Turbulent mixing: A perspective , volume =

    Sreenivasan, Katepalli R , date-added =. Turbulent mixing: A perspective , volume =. Proceedings of the National Academy of Sciences , number =

  283. [293]

    doi:10.1146/annurev-astro-081817-051810 , eprint =

    , keywords =. doi:10.1146/annurev-astro-081817-051810 , eprint =

    doi

  284. [294]

    doi:10.1038/nature18627 , eprint =

    , keywords =. doi:10.1038/nature18627 , eprint =

    doi

  285. [295]

    arXiv , author =:1811.05060 , journal =

    doi:10.3847/1538-4357/ab9310 , eid =. arXiv , author =:1811.05060 , journal =

    doi

  286. [296]

    arXiv , author =:1605.04907 , journal =

    doi:10.3847/0004-637X/826/1/50 , eid =. arXiv , author =:1605.04907 , journal =

    doi arXiv

  287. [297]

    doi:10.1093/mnras/stt2288 , eprint =

    , keywords =. doi:10.1093/mnras/stt2288 , eprint =

    doi

  288. [298]

    arXiv , author =:1903.05644 , journal =

    1903 arXiv

  289. [299]

    doi:10.1086/146200 , journal =

    doi

  290. [300]

    arXiv , author =:2112.02153 , journal =

Pith tools

Reviewed June 27, 2026 · model on record in the stance chip above.