Pith. sign in

REVIEW 3 major objections 6 minor 1 cited by

Anisotropic anomalous diffusion in microgravity dusty plasma. Part One: Nonextensive Statistical Analysis

T0 review · 3 major / 6 minor · reviewed 2026-08-12 · deepseek-v4-flash

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗ Review JSON

Pith's one-line read Dust in an ISS plasma diffuses superdiffusively along the electric field and crosses into Lévy transport at higher pressure.

desk verdict Unique PK-4 analysis and a useful drift-correction method, but the Lévy crossover claim rests on Eq. 8 outside its own domain, so the abstract overstates the MSD evidence. read the letter →

arxiv 2411.15705 v3 pith:BPA5WRZL submitted 2024-11-24 physics.plasm-ph

Bradley R. Andrew , Luca Guazzotto , Lorin Matthews , Hyde Truell , E. G. Kostadinova This is my paper · ORCID
classification physics.plasm-ph PACS 52.27.Lw52.25.Fi05.40.Fb
keywords dustyplasmaanomalousdiffusionTsallisnonextensivestatisticsq-GaussiandistributionLévyprocessmicrogravityPK-4meansquareddisplacement
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 analyzes video tracking of individual dust particles from the Plasmakristall-4 (PK-4) experiment on the International Space Station to establish that dust diffusion in a microgravity dusty plasma is anisotropic and anomalous. Using mean squared displacement (MSD) curves and histograms of particle displacements and velocities, the authors find that particle motion parallel to the applied electric field is superdiffusive, and at higher neutral-gas pressure it crosses over to Lévy-type diffusion with occasional large jumps. Motion across the field is also anomalous, but the histograms are best described by a Bi-q-Gaussian, meaning two coexisting populations: one near-classical and one superdiffusive. The paper further claims that increasing pressure pushes the dust toward thermal equilibrium, while increasing discharge current drives it away. These results matter because they tie macroscopic transport regimes to the ion-wakefield anisotropy produced by the polarity-switched field and demonstrate that Tsallis nonextensive statistics can classify diffusion regimes from a single experiment.

What carries the argument

The machinery is Tsallis nonextensive statistics applied to the nonlinear Fokker-Planck equation. The paper uses the q-Gaussian solution of the porous-medium-type equation (Eq. 5) to fit displacement and velocity histograms, with the fitted nonextensive exponent $q_p$ (positions) and $q_v$ (velocities) quantifying how far the distributions are from Gaussian. The second moment of that q-Gaussian solution gives the scaling $\mathrm{MSD} \propto \tau^{2/(3-q)}$ (Eq. 8), which yields the classification $q > 5/3$, equivalently $\alpha > 3/2$, for a Lévy process. For the perpendicular direction, the key object is the Bi-q-Gaussian, a sum of two q-Gaussians that captures the coexistence of a bulk population and a fat-tailed halo.

What would settle it

A direct test would be to re-fit the axial MSD curves for the 70 Pa cases with a truncated Lévy-stable model and compare the inferred stability index with the criterion $q > 5/3$; if the Lévy index disagrees with the q-Gaussian classification, or if the MSD exponent no longer follows $\alpha = 2/(3-q)$, the crossover claim loses its support.

Watch

Extended reading notes

Core claim

The central claim is that the direction of transport in PK-4 dusty plasma determines the diffusion regime, with the mechanism being the anisotropic ion wakefield around each dust grain. In the axial direction, parallel to the electric field, MSD exponents satisfy $\alpha_\parallel > 1$ for all nine pressure-current cases and exceed the Lévy threshold $\alpha = 3/2$ in several cases, especially at 70 Pa, so the paper concludes that parallel transport is superdiffusive with a crossover to Lévy processes at higher pressure. In the perpendicular direction the MSD is smaller, shows brief subdiffusive trapping at short time delays, and the displacement and velocity histograms are best fitted by the sum of two q-Gaussians, a roughly Gaussian sub-population and a fat-tailed halo, which the paper interprets as two distinct thermodynamic populations, one classically diffusing and one superdiffusive but not Lévy. The paper also claims that the nonextensive parameter $q_{v\parallel}$ stays close to 1 even while parallel diffusion is large, indicating strong energy exchange and near-equilibrium, whereas $q_{v\perp}$ lies further from 1, signaling departure from equilibrium, and that pressure and current act as opposing controls on the equilibrium state.

Load-bearing premise

The Lévy classification from MSD uses the scaling $\alpha = 2/(3-q)$ obtained from the second moment of the q-Gaussian solution, but that second moment diverges for $q \geq 5/3$, so the relation is applied in the very regime where its derivation is no longer valid.

Editorial extensions

If this is right

  • If the classification is right, parallel dust transport is superdiffusive in every pressure-current case examined, and crosses into Lévy-type jumping at the highest pressure (70 Pa).
  • Cross-field transport remains anomalous but non-Lévy: a near-classical bulk population and a superdiffusive halo population coexist, which explains the Bi-q-Gaussian histograms.
  • Pressure and current are opposing equilibrium controls: raising pressure cools and thermalizes the dust, while raising current increases the wakefield-driven nonequilibrium.
  • Sub-domain analysis implies that single q-Gaussian fits can describe local regions even when global cross-field histograms require two populations, so global averages can obscure locally distinct thermodynamic states.
  • The same Tsallis framework can classify diffusion regimes in other strongly coupled systems from a single experimental run, since the q exponents and MSD exponent are extracted from the same tracks.

Reading between the lines

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

  • A direct extension would be to vary the polarity-switching frequency (500 Hz here) and test whether $\alpha_\parallel$ shifts, because the wakefield asymmetry that drives superdiffusion is created by the switching itself.
  • Mapping the q-Gaussian to kappa distributions via $\kappa = 1/(q-1)$ suggests the cross-field Bi-q-Gaussian is the dusty-plasma analog of the solar-wind core-plus-halo structure, so the same data could be re-fitted with kappa distributions.
  • The claim that electrostatic-fluctuation energy explains high dust temperatures predicts that floating-potential fluctuations of order $10^{-5}$ V should be measurable; simulations of the local wakefield potential could test this quantitatively.
  • Because the global Bi-q-Gaussian may be an averaging artifact of pooling domains with different $q_v$, one test is to construct global histograms only from domains whose local $q_v$ values agree and check whether a single q-Gaussian suffices.
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

3 major / 6 minor

Summary. The paper analyzes nine pressure-current datasets from the PK-4 microgravity dusty plasma experiment, using particle tracking data to compute mean squared displacements (MSDs) and displacement/velocity histograms. The authors fit the histograms to Tsallis q-Gaussian and bi-q-Gaussian distributions to extract nonextensive exponents qp and qv, and fit MSD curves to obtain anomalous diffusion exponents α. They report anisotropic anomalous diffusion: motion parallel to the electric field is superdiffusive and, for some high-pressure cases, crosses over to Lévy behavior, while cross-field motion is described by a superposition of two populations. They also use qv values and velocity histograms to infer nonequilibrium tendencies, temperature gradients, and a possible link between temperature gradients and the nonextensive parameter through Eq. (16).

Significance. If the central claim were fully supported, the paper would provide a valuable characterization of direction-dependent anomalous diffusion in a microgravity complex plasma, with the nonextensive framework connecting PDF shape to transport exponents. The paper's strengths include a carefully described data pipeline (particle tracking, nonhomogeneous drift subtraction with velocity-autocorrelation validation, and histogram fitting with goodness-of-fit metrics), open-source code availability, and the use of ISS experimental data. However, the central claim is currently weakened by an internal inconsistency in the MSD-based Lévy criterion, the lack of uncertainties on the key fitted parameters, and the small number of PDF cases that directly support the crossover. These issues are load-bearing for the abstract's statement that both MSDs and PDFs indicate a crossover.

major comments (3)
  1. [§3.2, §5.1, Eq. (8)] The MSD-based Lévy criterion α>3/2 is not a valid consequence of the Tsallis scaling relation. The paper states in §3.2 that the second moment of the q-Gaussian diverges for 5/3≤q<3, so Eq. (8) is undefined in exactly the Lévy regime that the criterion is used to identify. For q<5/3, the exponent 2/(3−q) from Eq. (8) is bounded above by 3/2, so the inequality α>3/2 cannot be produced by a finite-variance q-Gaussian. Consequently, the dashed α=3/2 line in Fig. 7 is not an independent confirmation of the qp>5/3 histogram classification, and the abstract's claim that 'Both MSDs and PDFs indicate a crossover' is not supported by the present analysis. This point should be addressed by either deriving a valid MSD-based Lévy criterion or explicitly presenting the qp fits as the only Lévy indicator.
  2. [§5.2, Table 2] No uncertainties are reported for any of the fitted parameters α, qp, or qv in Table 2, and the crossover to Lévy behavior rests on only two values of qp∥ (1.81 for 70 Pa/1 mA and 1.70 for 70 Pa/0.7 mA). With roughly 20k data points per case, bootstrap or fit-covariance uncertainties should be straightforward to provide; without them, the reader cannot judge whether qp∥=1.70 is statistically distinguishable from 5/3, which is load-bearing for the claimed crossover. The absence of error bars also makes it difficult to assess the trends in Figs. 7 and 9.
  3. [§6.1] The discussion acknowledges that only the 70 Pa/1 mA case has qp∥>5/3, while the MSD exponents α∥>3/2 for nearly all parallel cases. For cases such as 46 Pa/1 mA (qp∥=1.44, α∥=2.40), the relation α=2/(3−q) from Eq. (8) fails badly, indicating that the MSD fit is not described by the same q-Gaussian as the displacement histogram. This internal inconsistency means the statement in the conclusions that 'for several pressure-current cases, superdiffusion crosses over to a Lévy process' is not supported by the data; at most the PDF fits indicate a crossover for two high-pressure cases. The manuscript should either soften the claim or provide a mechanism that reconciles the MSD and PDF exponents.
minor comments (6)
  1. [§1] Typographical errors include 'microgravty' and 'non-Mazwellian'; these should be 'microgravity' and 'non-Maxwellian'.
  2. [§4.1] The text mentions 'MHDS' plots; this appears to be a typo for 'MSD'.
  3. [Fig. 5] The y-axis label 'mean squared displacement (µm/s)' has incorrect units; MSD should be in µm².
  4. [Eq. (11)] The limiting expression for the q-Gaussian as q→1 appears to have a misplaced factor of m in the denominator; please verify the formula.
  5. [Table 3] The three sub-tables for 30 Pa, 46 Pa, and 70 Pa appear to have identical entries in the first and third rows, which is likely a copy-paste error; the 46 Pa table should be checked.
  6. [§5.2] The notation for the scaling relation α=2/(3−q) is used inconsistently; standardizing the symbols for the MSD exponent would improve readability.

Circularity Check

1 steps flagged · score 5.0 of 10

The MSD-based Lévy criterion in §5.1 is derived from the same q-Gaussian second moment used to define qp>5/3, so the claimed MSD/PDF agreement is not an independent confirmation; Eq. 8 is also invalid in the regime it is used to certify.

  1. self definitional [Section 3.2 (Eqs. 8-9) and Section 5.1; abstract]
    "Anomalous diffusion is described by taking the second moment of Eq. 5, which yields ... ⟨(x − x0)2⟩ = Bq(Dτ)^{2/(3−q)} ... Recall that Tsallis’ theory claims that the diffusion is a Lévy process when q >5/3. Using the scaling relation MSD = ⟨r2⟩ ∝ τ^{2/(3−qp)} [61] yields the criterion α >3/2 for a Lévy process."

    The α>3/2 criterion is obtained by setting qp=5/3 in Eq. 8, which is exactly the q-Gaussian second moment whose divergence defines the Lévy condition ('The variances of these distributions are finite for q <5/3 but diverge for 5/3≤q<3'). Thus the MSD 'indicator' is not an independent observable; it is the qp>5/3 criterion restated through the model's own scaling. Moreover, Eq. 8 is derived as that second moment, so it has no validity for qp≥5/3; using it to certify α>3/2 is an extrapolation into the divergent regime. Hence the abstract's 'Both MSDs and PDFs indicate a crossover' is not two independent lines of evidence: the MSD line inherits the q-Gaussian model's definition and cannot independently confirm the histogram classification.

full rationale

The paper's central classification has one genuine self-consistency problem. In §5.1 the Lévy threshold for the MSD exponent (α>3/2) is not an independent diagnostic: it is obtained from Eq. 8, the q-Gaussian second-moment scaling, by the same condition (q=5/3) that defines the PDF Lévy crossover. Equation 8 is the second moment that the paper itself states diverges for 5/3≤q<3, so applying it to certify α>3/2 uses the model in a regime where the derived formula has no validity. The abstract's 'Both MSDs and PDFs indicate a crossover' therefore overstates the evidence; the MSD indicator is model-internal and not an independent confirmation. That said, the qp and qv histogram fits are direct measurements of the data, Table 2 reports the fitted values, and the paper openly records disagreements between α∥ and qp∥ (e.g., α∥>3/2 for nearly all parallel cases while only two high-pressure cases have qp∥>5/3). The central crossover claim therefore retains independent empirical content from the PDF analysis, and the self-citations to companion structure papers ([59], [83]) are not load-bearing for the Lévy conclusion. On balance, the circularity is partial: the MSD-based evidence reduces to the q-Gaussian model by construction, but the PDF evidence does not.

Assumptions & free parameters 6 free parameters · 7 assumptions · 0 invented entities

The central classification rests on fitted q and α values without uncertainty estimates, and on a scaling relation that is not valid in the Lévy regime it is used to define. No new physical entities are postulated.

free parameters (6)
  • qp (nonextensive position exponent), parallel and perpendicular = qp||: 1.25 to 1.81; qp⊥1: 0.94 to 1.40; qp⊥2: 1.10 to 1.60 (Table 2)
    Fitted to displacement histograms at time delay 5 s; values above 5/3 are used to identify Lévy processes.
  • qv (nonextensive velocity exponent), parallel and perpendicular = qv||: 1.13 to 1.41; qv⊥1: 1.11 to 1.30; qv⊥2: 1.38 to 2.31 (Table 2)
    Fitted to velocity histograms; used to assess equilibrium and suprathermal tails.
  • MSD exponents α|| and α⊥ = α||: 1.50 to 2.40; α⊥: 0.88 to 1.45 (Table 2)
    Fitted to MSD curves at time delay 4 to 5 s; values above 3/2 are used to label Lévy processes.
  • Diffusion coefficients D and thermal velocities v_th = Ranges shown in Figures 10, 14, 15
    Extracted from q-Gaussian fit variances; used for temperature and diffusion trend claims.
  • Time delay τ = 5 s for displacement histograms = 5 s
    Histograms built at this delay; α extracted at 4 to 5 s. Choice affects all derived qp and the comparison to α.
  • Number of NHDS subdomains = 12
    Chosen to balance drift-subtraction accuracy and computation time; affects residual trajectories and MSD magnitudes.
assumptions (7)
  • standard math The q-Gaussian form (Eqs. 5, 10) solves the nonlinear Fokker-Planck equation and normalizes via Eq. 7.
    Taken from Frank and Tsallis; underpins all histogram fits.
  • ad hoc to paper The scaling MSD = Bq(Dτ)^(2/(3-q)) (Eq. 8) is valid for the fitted q values, including q ≥ 5/3.
    The paper's own text states variances diverge for 5/3 ≤ q < 3, so the second-moment scaling is not defined there; it is nevertheless used to derive the α > 3/2 Lévy criterion and to compare α with qp.
  • domain assumption After nonhomogeneous drift subtraction, residual dust motion is purely diffusive.
    Validated through velocity autocorrelation for one case, but assumed for all others.
  • domain assumption The dust is unresponsive to the 500 Hz polarity-switched field and experiences only anisotropic ion-wake interactions.
    Standard PK-4 assumption; underlies attribution of anisotropy to wakefields.
  • domain assumption Cross-field histograms are superpositions of two q-Gaussians (Eq. 14), not a single q-Gaussian or another family.
    Justified by R2 and NRMSE, but no model-selection criterion or parameter uncertainties are given.
  • domain assumption Temperature conversion Tq(5q-3)/2 = TM (Eq. 12) applies to these dust distributions.
    Taken from [54]; no validation for the dust component.
  • ad hoc to paper Eq. 16 relating qv to thermophoretic and electric forces is qualitatively applicable to PK-4.
    Authors state it has not been verified experimentally; used for qualitative support only.

how reviews work

0 comments
Cite this review

Pith. "Pith review of Anisotropic anomalous diffusion in microgravity dusty plasma. Part One: Nonextensive Statistical Analysis." pith.science (2026). https://pith.science/paper/BPA5WRZL

@misc{pith2026241115705,
  author       = {Pith},
  title        = {Pith review of: Anisotropic anomalous diffusion in microgravity dusty plasma. Part One: Nonextensive Statistical Analysis},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/BPA5WRZL}},
  note         = {Machine review of arXiv:2411.15705}
}
read the original abstract

Anisotropic anomalous dust diffusion in microgravity dusty plasma is investigated using experimental data from the Plasmakristall-4 (PK-4) facility on board the International Space Station. The PK-4 experiment uses video cameras to track individual dust particles, which allows the collection of large amounts of statistical information on the dust particle positions and velocities. These statistics are used to quantify anomalous dust diffusion caused by anisotropies in the plasma-mediated dust-dust interactions in PK-4. Anisotropies are caused by an externally applied polarity-switched electric field, which modifies the ion wakefields surrounding the dust grains. Video data for nine sets of pressure-current conditions are used to recover Mean Squared Displacement (MSD) plots after subtracting particle drift. Position and velocity histograms are fitted to Tsallis nonextensive probability distribution functions (PDFs). Both MSDs and PDFs indicate a crossover from suprathermal to L\'evy diffusion in the axial direction at higher pressure conditions. In addition, increasing the pressure enhances dust thermal equilibrium, while increasing the current drives the system away from equilibrium.

Figures

Figures reproduced from arXiv: 2411.15705 by the authors.

Figure 1
Figure 1. PK-4 Experimental Setup. Dust moves into camera FoV. [PITH_FULL_IMAGE:figures/full_fig_p004_1.png] view at source ↗
Figure 2
Figure 2. Analytical plot of the q-Gaussian distribution for three cases. [PITH_FULL_IMAGE:figures/full_fig_p007_2.png] view at source ↗
Figure 3
Figure 3. a) Dust particle tracks (µm) found using @msdanalyzer broken into 12 domains. b) Dust tracks (µm) after normal drift subtraction. c) Dust tracks (µm) after nonhomogeneous drift subtraction (NHDS). d) Average drift trajectories found in each domain in A). Experimental conditions were 70 Pa 0.35 mA [PITH_FULL_IMAGE:figures/full_fig_p009_3.png] view at source ↗
Figures from the paper (17 more)
Figure 4
Figure 4. Figure 4: Velocity Autocorrelation of the 70 Pa 0.35 mA case before (red) and after NHDS (blue). [PITH_FULL_IMAGE:figures/full_fig_p009_4.png]
Figure 5
Figure 5. Figure 5: MSD plots for all cases after drift subtraction zoomed in to help distinguish different curves. [PITH_FULL_IMAGE:figures/full_fig_p012_5.png]
Figure 6
Figure 6. Figure 6: Fits to mean square displacement for different time delays for the 70Pa, 1mA case. a) MSD [PITH_FULL_IMAGE:figures/full_fig_p012_6.png]
Figure 7
Figure 7. Figure 7: a) α∥ and b) α⊥ for all pressure-current cases. The exponent α extracted from MSD∥ and MSD⊥ at time delay between 4 s and 5 s is plotted for all cases in [PITH_FULL_IMAGE:figures/full_fig_p013_7.png]
Figure 8
Figure 8. Figure 8: Position distribution fit example from case 70 Pa 0.7 mA for displacements in a) parallel [PITH_FULL_IMAGE:figures/full_fig_p013_8.png]
Figure 9
Figure 9. Figure 9: Coefficients extracted from nonextensive [PITH_FULL_IMAGE:figures/full_fig_p014_9.png]
Figure 10
Figure 10. Figure 10: Diffusion coefficients (/mum/s) obtained from fits to the displacement histogram using q-Gaussian and Bi-q-Gaussian. a) parallel, b) perpendicular, c) perpendicular from Gaussian-like sub￾population, and d) perpendicular from ‘tail-halo’ population. Next, we examined …
Figure 11
Figure 11. Figure 11: Percent difference between α found from MSD curves and α found from qp using Eq. 8. a) parallel component, b) perpendicular component from a single q-Gaussian, c) Gaussian-like ‘sub￾population’, and d) ‘tail-halo’. A dashed line at 20% is used to help compare the figu…
Figure 12
Figure 12. Figure 12: Velocity component histograms and distribution fits for the 30 Pa, 0.7mA case. a) Velocity [PITH_FULL_IMAGE:figures/full_fig_p016_12.png]
Figure 13
Figure 13. Figure 13: Nonequilibrium coefficients extracted from fits to velocity histograms for all pressure-current [PITH_FULL_IMAGE:figures/full_fig_p017_13.png]
Figure 14
Figure 14. Figure 14: Temperatures for all pressure-current cases found using a Maxwellian fit to the a) parallel [PITH_FULL_IMAGE:figures/full_fig_p017_14.png]
Figure 15
Figure 15. Figure 15: Temperatures TM q for all pressure-current cases found using non-Maxwellian fits to the parallel and perpendicular components of the velocity histograms. Temperature in the parallel direction a) was obtained using a single q-Gaussian fit. Temperatures in the perpendic…
Figure 16
Figure 16. Figure 16: Velocity distributions for a) ∥ and b) ⊥ directions obtained from histogram fits of domain 11 for the case 30 Pa 0.7 mA. Notice that the q-Gaussian (magenta) curve provides a much closer fit than the one shown in [PITH_FULL_IMAGE:figures/full_fig_p019_16.png]
Figure 17
Figure 17. Figure 17: a) T∥ and b) T⊥ show temperatures in units of Kelvin for 20 domains calculated for the 30 Pa 0.7 mA case. Each domain contained about 500 dust tracks, a minimum of 10 time frames per trajectory, which yields statistically significant amount of data for the velocity fi…
Figure 18
Figure 18. Figure 18: Electric potential in the vicinity of dust particles calculated by the DRIAD simulation. The [PITH_FULL_IMAGE:figures/full_fig_p020_18.png]
Figure 19
Figure 19. Figure 19: Components of the Bi-q-Gaussian illustrating two distinct populations: a) red [PITH_FULL_IMAGE:figures/full_fig_p022_19.png]
Figure 20
Figure 20. Figure 20: Analytical plot of the "knee and ankle" distribution a) with normal axis,b) a log scale, and [PITH_FULL_IMAGE:figures/full_fig_p023_20.png]

Discussion (0). Continue with ORCID to comment.

Forward citations

Cited by 1 Pith paper

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Structural States of Filamentary Microgravity Dusty Plasma

    physics.plasm-ph 2025-05 conditional novelty 5.0 of 10

    Dust filaments in microgravity dusty plasma show pressure-dependent ordering patterns analogous to nematic and smectic liquid crystal phases.

Reference graph

Works this paper leans on

86 extracted references · 75 canonical work pages · cited by 1 Pith paper

  1. [1]

    P. K. Shukla. A survey of dusty plasma physics.Physics of Plasmas, 2001

    2001

  2. [2]

    R. L. Merlino, J. R. Heinrich, S.-H. Hyun, and J. K. Meyer. Nonlinear dust acoustic waves and shocks. Physics of Plasmas, 19(5), March 2012

    2012

  3. [3]

    S. A. Khrapak, B. A. Klumov, P. Huber, V. I. Molotkov, A. M. Lipaev, V. N. Naumkin, A. V. Ivlev, H. M. Thomas, M. Schwabe, G. E. Morfill, Yu. Malentschenko, S. Volkov, et al. Fluid-solid phase transitions in three-dimensional complex plasmas under microgravity conditions.Physical Review E, 2012

    2012

  4. [4]

    Made to order: Researchers discover a new form of crystalline matter

    American Physical Society. Made to order: Researchers discover a new form of crystalline matter. https://phys.org/news/2015-11-crystalline.html, 2015. Accessed: 2024-08-14

    2015

  5. [5]

    Kostadinova, Emerson Gehr, Bradley Andrew, Lorin S

    Evdokiya G. Kostadinova, Emerson Gehr, Bradley Andrew, Lorin S. Matthews, Truell W. Hyde, and Abbie Terrell. Liquid plasma crystals on the ISS. InAIAA SCITECH 2023 Forum. American Institute of Aeronautics and Astronautics, January 2023

    2023

  6. [6]

    M. G. Hariprasad, P. Bandyopadhyay, V. S. Nikolaev, D. A. Kolotinskii, S. Arumugam, G. Arora, S. Singh, A. Sen, and A. V. Timofeev. Self-sustained non-equilibrium co-existence of fluid and solid states in a strongly coupled complex plasma system.Scientific Reports, 12(1), August 2022

    2022

  7. [7]

    Ivlev, Philip C

    Alexei V. Ivlev, Philip C. Brandt, Gregor E. Morfill, Christoph Rath, Hubertus M. Thomas, Glenn Joyce, Vladimir E. Fortov, Andrey M. Lipaev, Vladimir I. Molotkov, and Oleg F. Petrov. Elec- trorheological complex plasmas.IEEE Transactions on Plasma Science, 38(4):733–740, April 2010. Conference Name: IEEE Transactions on Plasma Science

    work page 2010

  8. [8]

    V. N. Tsytovich, U. De Angelis, R. Bingham, and D. Resendes. Long-range correlations in dusty plasmas. Physics of Plasmas, 1997

    1997

Show all 86 references
  1. [9]

    Smith, J

    B. Smith, J. Vasut, T. Hyde, L. Matthews, J. Reay, M. Cook, and J. Schmoke. Dusty plasma correlation function experiment.Advances in Space Research, 34(11):2379–2383, 2004

    2004

  2. [10]

    Correia, Emerson J

    Matheus V. Correia, Emerson J. Freitas, Leonardo R. E. Cabral, and Clécio C. de Souza Silva. Structural phases of classical 2d clusters with competing two-body and three-body interactions. Journal of Physics: Condensed Matter, 35(41):415404, July 2023. 27

    2023

  3. [11]

    Lazar, Shahzad Mahmood, Aman-ur-Rehman, and S

    Kashif Arshad, M. Lazar, Shahzad Mahmood, Aman-ur-Rehman, and S. Poedts. Kinetic study of electrostatic twisted waves instability in nonthermal dusty plasmas. Physics of Plasmas, 24(2):023701, 2017

    2017

  4. [12]

    O. F. Petrov, V. E. Fortov, O. S. Vaulina, A. V. Chernyshev, S. N. Antipov, A. V. Gavrikov, and I. A. Shakhova. Experimental study of dusty plasma kinetics.Physica Scripta, 72(2):205–207, 2005

    2005

  5. [13]

    Goree, M

    Bin Liu, J. Goree, M. Y. Pustylnik, H. M. Thomas, V. E. Fortov, A. M. Lipaev, A. D. Usachev, V. I. Molotkov, O. F. Petrov, and M. H. Thoma. Particle velocity distribution in a three-dimensional dusty plasma under microgravity conditions.AIP Conference Proceedings, 1925(1):020003, 2018

    1925

  6. [14]

    PhD thesis, The University of Iowa, 2010

    Yan Feng.Microscopic dynamics in two-dimensional strongly-coupled dusty plasmas. PhD thesis, The University of Iowa, 2010

    2010

  7. [15]

    Joshi, M

    E. Joshi, M. Y. Pustylnik, M. H. Thoma, H. M. Thomas, and M. Schwabe. Recrystallization in string-fluid complex plasmas.Physical Review Research, 5(1):013086, March 2023

    2023

  8. [16]

    E. G. Kostadinova, R. Banka, J. L. Padgett, C. D. Liaw, L. S. Matthews, and T. W. Hyde. Fractional Laplacian spectral approach to turbulence in a dusty plasma monolayer.Physics of Plasmas, 28(12):123703, 2021

    2021

  9. [17]

    Observation of kolmogorov turbulence due to multiscale vortices in dusty plasma experiments.Physics of Plasmas, 31(1):013701, 2024

    Sachin Sharma, Rauoof Wani, Prabhakar Srivastav, Meenakshee Sharma, Sayak Bose, Yogesh Saxena, and Sanat Tiwari. Observation of kolmogorov turbulence due to multiscale vortices in dusty plasma experiments.Physics of Plasmas, 31(1):013701, 2024

    2024

  10. [18]

    A review on the vortex and coherent structures in dusty plasma medium

    Mangilal Choudhary. A review on the vortex and coherent structures in dusty plasma medium. Physics of Plasmas, 31(1):013702, 2024

    2024

  11. [19]

    Stronglycoupledplasmaphysicsandhighenergy-densitymatter

    M.S.Murillo. Stronglycoupledplasmaphysicsandhighenergy-densitymatter. Physics of Plasmas, 11(5):2964–2971, 2004

    2004

  12. [20]

    A. V. Ivlev, G. E. Morfill, H. M. Thomas, C. Räth, G. Joyce, P. Huber, R. Kompaneets, V. E. Fortov, A. M. Lipaev, V. I. Molotkov, T. Reiter, M. Turin, and P. Vinogradov. First observation of electrorheological plasmas.Physical Review Letters, 100(9):095003, March 2008

    2008

  13. [21]

    Phasetransitioninelectrorheologicalplasmas

    ChristopherDietz, JohannesBudak, TobiasKamprich, MichaelKretschmer, andMarkusH.Thoma. Phasetransitioninelectrorheologicalplasmas. Contributions to Plasma Physics, 61(10):e202100079, 2021

    2021

  14. [22]

    Beckers, J

    J. Beckers, J. Berndt, D. Block, M. Bonitz, P. J. Bruggeman, L. Couëdel, G. L. Delzanno, Y. Feng, R. Gopalakrishnan, F. Greiner et al. Physics and applications of dusty plasmas: The perspectives

  15. [23]

    Perspective: Dusty plasma experiments—a learning tool for physics graduate students

    Mangilal Choudhary. Perspective: Dusty plasma experiments—a learning tool for physics graduate students. European Journal of Physics, 42(6):065203, 2021

    2021

  16. [24]

    Robert L. Merlino. Dusty plasmas: from Saturn’s rings to semiconductor processing devices. Advances in Physics: X, 6(1):1873859, 2021

    2021

  17. [25]

    E. G. Kostadinova, K. Busse, N. Ellis, J. Padgett, C. D. Liaw, L. S. Matthews, and T. W. Hyde. Delocalization in infinite disordered two-dimensional lattices of different geometry.Physical Review B, 96(23):235408, 2017

    2017

  18. [26]

    E. G. Kostadinova, C. D. Liaw, L. S. Matthews, and T. W. Hyde. Physical interpretation of the spectral approach to delocalization in infinite disordered systems. Materials Research Express, 3(12):125904, 2016

    2016

  19. [27]

    E. G. Kostadinova, F. Guyton, A. Cameron, K. Busse, C. D. Liaw, L. S. Matthews, and T. W. Hyde. Transport properties of disordered two-dimensional complex plasma crystal.Contributions to Plasma Physics, 58(2-3):209–216, 2018. 28

    2018

  20. [28]

    Goree, and Yan Feng

    Bin Liu, J. Goree, and Yan Feng. Non-Gaussian statistics and superdiffusion in a driven-dissipative dusty plasma. Physical Review E, 78(2):026405, 2008

    2008

  21. [29]

    M. Y. Pustylnik, M. A. Fink, V. Nosenko, T. Antonova, T. Hagl, H. M. Thomas, A. V. Zob- nin, A. M. Lipaev, A. D. Usachev, V. I. Molotkov et al. Plasmakristall-4: New complex (dusty) plasma laboratory on board the International Space Station. Review of Scientific Instruments, 8...

    2016

  22. [30]

    V. N. Naumkin, D. I. Zhukhovitskii, A. M. Lipaev, A. V. Zobnin, A. D. Usachev, O. F. Petrov, H. M. Thomas, M. H. Thoma, O. I. Skripochka, and A. A. Ivanishin. Excitation of progressing dust ionization waves on pk-4 facility.Physics of Plasmas, 28(10):103701, 2021

    2021

  23. [31]

    Mendoza, D

    A. Mendoza, D. Jiménez Martí, L. S. Matthews, B. Rodríguez Saenz, P. Hartmann, E. Kostadinova, M. Rosenberg, and T. W. Hyde. Ion density waves driving the formation of filamentary dust structures. Physics of Plasmas, 31(1):013701, 2024

    2024

  24. [32]

    Goree, Bin Liu, M

    J. Goree, Bin Liu, M. Y. Pustylnik, H. M. Thomas, V. E. Fortov, A. M. Lipaev, V. I. Molotkov, A. D. Usachev, O. F. Petrov, M. H. Thoma, E. Thomas, U. Konopka, and S. Prokopiev. Correlation and spectrum of dust acoustic waves in a radio-frequency plasma using pk-4 on the intern...

    2020

  25. [33]

    Bin Liu, John Goree, M. Y. Pustylnik, H. M. Thomas, V. E. Fortov, A. M. Lipaev, A. D. Usachev, O. F. Petrov, A. V. Zobnin, and M. H. Thoma. Time-dependent shear motion in a strongly coupled dustyplasmainpk-4ontheinternationalspacestation(iss). IEEE Transactions on Plasma Scien...

    2021

  26. [34]

    Lunarexosphere: Dust-in-plasma? dustyplasma? Journal of Space Operations and Communicator, 20(4), 2024

    RonaldH.Freeman. Lunarexosphere: Dust-in-plasma? dustyplasma? Journal of Space Operations and Communicator, 20(4), 2024

    2024

  27. [35]

    PeterHartmann, MarleneRosenberg, ZoltanJuhasz, LorinS.Matthews, DustinL.Sanford, Katrina Vermillion, Jorge Carmona-Reyes, and Truell W. Hyde. Ionization waves in the pk-4 direct current neon discharge. Plasma Sources Science and Technology, 29(11):115014, November 2020

    2020

  28. [36]

    Matthews, Peter Hartmann, Marlene Rosenberg, Evdokiya Kostadinova, Jorge Carmona-Reyes, Truell W

    Katrina Vermillion, Dustin Sanford, Lorin S. Matthews, Peter Hartmann, Marlene Rosenberg, Evdokiya Kostadinova, Jorge Carmona-Reyes, Truell W. Hyde, Andrey M. Lipaev, Alexandr D. Usachev et al. Influence of temporal variations in plasma conditions on the electric potential nea...

    2022

  29. [37]

    Kostadinova, Peter Hartmann, Lorin S

    Katrina Vermillion, Abbie Terrell, Emerson Gehr, Evdokiya G. Kostadinova, Peter Hartmann, Lorin S. Matthews, and Truell W. Hyde. Numerical modeling of the plasmakristall-4 experiment on the iss. InAIAA SCITECH 2023 Forum. American Institute of Aeronautics and Astronautics, Jan...

    2023

  30. [38]

    TNF and IL-1 exhibit distinct ubiquitin requirements for inducing NEMO–IKK supramolecular structures.Jour- nal of Cell Biology, 204(2):231–245, January 2014

    Nadine Tarantino, Jean-Yves Tinevez, Elizabeth Faris Crowell, Bertrand Boisson, Ricardo Hen- riques, Musa Mhlanga, Fabrice Agou, Alain Israël, and Emmanuel Laplantine. TNF and IL-1 exhibit distinct ubiquitin requirements for inducing NEMO–IKK supramolecular structures.Jour- na...

    2014

  31. [39]

    Liberating Lévy walk research from the shackles of optimal foraging.Physics of Life Reviews, 14:59–83, September 2015

    Andy Reynolds. Liberating Lévy walk research from the shackles of optimal foraging.Physics of Life Reviews, 14:59–83, September 2015

    2015

  32. [40]

    Benhamou

    M. Benhamou. Lecture on the anomalous diffusion in Condensed Matter Physics.Materials and Devices, 3(1):1–12, 2018

    2018

  33. [41]

    Goree, and Bin Liu

    Yan Feng, J. Goree, and Bin Liu. Identifying anomalous diffusion and melting in dusty plasmas. Physical Review E, 81(3):036403, March 2010

    2010

  34. [42]

    Anoma- lous Diffusion: A Basic Mechanism for the Evolution of Inhomogeneous Systems

    FernandoA.Oliveira, RogelmaM.S.Ferreira, LucianoC.Lapas, andMendeliH.Vainstein. Anoma- lous Diffusion: A Basic Mechanism for the Evolution of Inhomogeneous Systems. Frontiers in Physics, 7:18, February 2019. 29

    2019

  35. [43]

    Daniels, Christian Beck, and Eberhard Bodenschatz

    Karen E. Daniels, Christian Beck, and Eberhard Bodenschatz. Defect turbulence and generalized statistical mechanics. Physica D: Nonlinear Phenomena, 193(1-4):208–217, June 2004

    2004

  36. [44]

    A. M. Reynolds and M. Veneziani. Rotational dynamics of turbulence and Tsallis statistics.Physics Letters A, 327(1):9–15, June 2004

    2004

  37. [45]

    AGING IN EARTHQUAKE MODELS Complexity, Metastability and Nonexten- sivity

    Urgur Tirnakli. AGING IN EARTHQUAKE MODELS Complexity, Metastability and Nonexten- sivity. World Scientific, 2005

    2005

  38. [46]

    A. Y. Abul-Magd. Nonextensive random matrix theory approach to mixed regular-chaotic dynam- ics. Physical Review E, 71(6):066207, June 2005

    2005

  39. [47]

    Ivanova, H

    K. Ivanova, H. N. Shirer, T. P. Ackerman, and E. E. Clothiaux. Dynamical model and nonextensive statistical mechanics of liquid water path fluctuations in stratus clouds.Journal of Geophysical Research: Atmospheres, 112(D15):D15207, August 2007

    2007

  40. [48]

    Douglas, S

    P. Douglas, S. Bergamini, and F. Renzoni. Tunable Tsallis Distributions in Dissipative Optical Lattices. Physical Review Letters, 96(11):110601, March 2006

    2006

  41. [49]

    Bediaga, E

    I. Bediaga, E. M. F. Curado, and J. M. de Miranda. A nonextensive thermodynamical equilibrium approach in hadrons. Physica A: Statistical Mechanics and its Applications, 286(1-2):156–163, October 2000

    2000

  42. [50]

    L. P. Karakatsanis, G. P. Pavlos, and M. N. Xenakis. Tsallis non-extensive statistics, intermittent turbulence, SOC and chaos in the solar plasma. part two: Solar flares dynamics. Physica A: Statistical Mechanics and its Applications, 392(18):3920–3944, September 2013

    2013

  43. [51]

    G. P. Pavlos, L. P. Karakatsanis, and M. N. Xenakis. Tsallis non-extensive statistics, intermittent turbulence, SOC and chaos in the solar plasma, part one: Sunspot dynamics.Physica A: Statistical Mechanics and its Applications, 391(24):6287–6319, 2012

    2012

  44. [52]

    Danny Summers and Richard M. Thorne. The modified plasma dispersion function.Physics of Fluids B: Plasma Physics, 3(8):1835–1847, August 1991

    1991

  45. [53]

    A nonextensive approach for the instability of current-driven ion-acoustic waves in space plasmas.Physics of Plasmas, 16(7):072903, July 2009

    Zhipeng Liu, Liyan Liu, and Jiulin Du. A nonextensive approach for the instability of current-driven ion-acoustic waves in space plasmas.Physics of Plasmas, 16(7):072903, July 2009

    2009

  46. [54]

    Linear analysis of whistler mode instability in anisotropic q- nonextensive distributed plasmas: a numerical approach

    Muhammad Bilal, Aman ur Rehman, Mushtaq Ahmad, Muhammad Ahsan Shahzad, Muhammad Sarfraz, and Shahzad Mahmood. Linear analysis of whistler mode instability in anisotropic q- nonextensive distributed plasmas: a numerical approach. Physica Scripta, 98(9):095607, August 2023

    2023

  47. [55]

    Thecollisionfrequenciesintheplasmaswiththepower-lawq-distributions in nonextensive statistics.Physica A: Statistical Mechanics and its Applications, 566:125623, 2021

    YueWangandJiulinDu. Thecollisionfrequenciesintheplasmaswiththepower-lawq-distributions in nonextensive statistics.Physica A: Statistical Mechanics and its Applications, 566:125623, 2021

    2021

  48. [56]

    Dust charging processes in the nonequilibrium dusty plasma with nonextensive power-law distribution.Physics of Plasmas, 19(2):023702, February 2012

    Jingyu Gong and Jiulin Du. Dust charging processes in the nonequilibrium dusty plasma with nonextensive power-law distribution.Physics of Plasmas, 19(2):023702, February 2012

    2012

  49. [57]

    Dust acoustic instability driven by drifting ions and electrons in the dust plasma with lorentzian kappa distribution.Physics of Plasmas, 16(12):123707, December 2009

    Zhipeng Liu and Jiulin Du. Dust acoustic instability driven by drifting ions and electrons in the dust plasma with lorentzian kappa distribution.Physics of Plasmas, 16(12):123707, December 2009

    2009

  50. [58]

    Fiji: An Open-Source Platform for Biological-Image Analysis.Nature Methods, 9(7):676–682, July 2012

    Johannes Schindelin, Ignacio Arganda-Carreras, Erwin Frise, Verena Kaynig, Mark Longair, Tobias Pietzsch, Stephan Preibisch, Curtis Rueden, Stephan Saalfeld, Benjamin Schmid et al. Fiji: An Open-Source Platform for Biological-Image Analysis.Nature Methods, 9(7):676–682, July 2012

    2012

  51. [59]

    Structural states of filamentary microgravity dusty plasma

    Emerson Gehr, Abbie Terrell, Katrina Vermillion, and Alexandria Mendoza. Structural states of filamentary microgravity dusty plasma. In review forPhysics of Plasmas, 2025

    2025

  52. [60]

    Springer Series in Synergetics

    Till Daniel Frank.Nonlinear Fokker-Planck Equations: Fundamentals and Applications. Springer Series in Synergetics. Springer, 2005. 30

    2005

  53. [61]

    Introduction to Nonextensive Statistical Mechanics: Approaching a Complex World

    Constantino Tsallis. Introduction to Nonextensive Statistical Mechanics: Approaching a Complex World. Springer, New York, 2009

    2009

  54. [62]

    J. L. Padgett, E. G. Kostadinova, C. D. Liaw, K. Busse, L. S. Matthews, and T. W. Hyde. Anoma- lous diffusion in one-dimensional disordered systems: A discrete fractional Laplacian method.Jour- nal of Physics A: Mathematical and Theoretical, 53(18):185701, April 2020

    2020

  55. [63]

    Some properties of q-Gaussian distributions.arXiv preprint arXiv:2101.00516, 2021

    Nahla Ben Salah. Some properties of q-Gaussian distributions.arXiv preprint arXiv:2101.00516, 2021

    2021 arXiv

  56. [64]

    Identification of time scales of the violation of the Stokes–Einstein relation in Yukawa liquids.Physics of Plasmas, 28(4):043703, April 2021

    Zahra Ghannad. Identification of time scales of the violation of the Stokes–Einstein relation in Yukawa liquids.Physics of Plasmas, 28(4):043703, April 2021

    2021

  57. [65]

    Possible generalization of Boltzmann-Gibbs statistics.Journal of Statistical Physics, 52(1-2):479–487, July 1988

    Constantino Tsallis. Possible generalization of Boltzmann-Gibbs statistics.Journal of Statistical Physics, 52(1-2):479–487, July 1988

    1988

  58. [66]

    Shivanandan, A

    A. Shivanandan, A. Radenovic, and I. F. Sbalzarini. MosaicIA: An ImageJ/Fiji plugin for spatial pattern and interaction analysis.BMC Bioinformatics, 14:349, December 2013

    2013

  59. [67]

    Avinash, R

    K. Avinash, R. L. Merlino, and P. K. Shukla. Anomalous dust temperature in dusty plasma experiments. Physics Letters A, 375(30-31):2854–2857, July 2011

    2011

  60. [68]

    Nonextensivity in nonequilibrium plasma systems with Coulombian long-range interac- tions

    Jiulin Du. Nonextensivity in nonequilibrium plasma systems with Coulombian long-range interac- tions. Physics Letters A, 329(3):262–273, November 2004

    2004

  61. [69]

    The nonextensive parameter for nonequilibrium plasmas in magnetic field

    Yu Haining and Du Jiulin. The nonextensive parameter for nonequilibrium plasmas in magnetic field. Physica A: Statistical Mechanics and its Applications, 410:302–309, August 2014

    2014

  62. [70]

    R. A. Treumann, C. H. Jaroschek, and M. Scholer. Stationary plasma states far from equilibrium. Physics of Plasmas, 11(4):1317–1325, April 2004

    2004

  63. [71]

    Livadiotis, M

    G. Livadiotis, M. I. Desai, and L. B. Wilson. Generation of Kappa distributions in solar wind at 1 au. The Astrophysical Journal, 853(2):142, February 2018

    2018

  64. [72]

    M. P. Leubner and Z. Vörös. A nonextensive entropy approach to solar wind intermittency.The Astrophysical Journal, 618(1):547–555, January 2005

    2005

  65. [73]

    Anjos, and Ernesto P

    Constantino Tsallis, Joao C. Anjos, and Ernesto P. Borges. Fluxes of cosmic rays: A delicately balanced stationary state.Physics Letters A, 310(5-6):372–376, December 2003

    2003

  66. [74]

    L. F. Burlaga and A. F. Viñas. Tsallis distributions of the large-scale magnetic field strength fluctuations in the solar wind from 7 to 87 au.Journal of Geophysical Research: Space Physics, 110(A7):A07106, July 2005

    2005

  67. [75]

    A. V. Ivlev, G. E. Morfill, U. Konopka, and M. Kretschmer. Electrorheology of complex plasmas. Physical Review Letters, 106(15):155001, 2011. DOI: 10.1103/PhysRevLett.106.155001

    2011 doi

  68. [76]

    M. Y. Pustylnik, S. A. Khrapak, A. G. Khrapak, M. H. Thoma, H. M. Thomas, G. E. Morfill, A. M. Lipaev, A. D. Usachev, V. I. Molotkov, O. F. Petrov, A. V. Zobnin, and V. E. Fortov. Electrorheological phenomena in dusty plasma.Physical Review Research, 2(3):033314, 2020. DOI: 10...

    2020 doi

  69. [77]

    D. I. Zhukhovitskii. On the controversy of dust ionization waves.Physics of Plasmas, 29(7):073701,

  70. [78]

    M. Y. Pustylnik. Dust ionization wave analysis and response to critiques. Physics of Plasmas, 29(11):114701, 2022. DOI: 10.1063/5.0116237

    2022 doi

  71. [79]

    L. S. McCabe, J. Williams, S. C. Thakur, U. Konopka, E. G. Kostadinova, M. Y. Pustylnik, H. M. Thomas, M. H. Thoma, and E. Thomas. Experiments and modeling of dust particle heating resulting from changes in polarity switching in the PK-4 microgravity laboratory.arXiv preprint,

  72. [80]

    Hartmann, M

    P. Hartmann, M. Rosenberg, Z. Juhasz, L. S. Matthews, D. L. Sanford, K. Vermillion, J. Carmona- Reyes and T. W. Hyde Ionization waves in the PK-4 direct current neon discharge.Plasma Sources Science and Technology, 2020. https://iopscience.iop.org/article/10.1088/1361-6595/ abb955

    2020 doi

  73. [81]

    L. S. Matthews, T. W. Hyde, K. Vermillion, D. Sanford, P. Hartmann, M. Rosen- berg, E. G. Kostadinova, and J. Carmona-Reyes. Effect of ionization waves on dust chain formation in a DC discharge. Journal of Plasma Physics , 2020. https://www.cambridge.org/core/journals/journal-...

    2020

  74. [82]

    Vermillion, D

    K. Vermillion, D. Sanford, L. S. Matthews, P. Hartmann, M. Rosenberg, E. G. Kostadinova, J. Carmona-Reyes, T. W. Hyde, A. M. Lipaev, A. D. Usachev et al. Influence of temporal variations in plasma on dust-dust interactions. Physics of Plasmas, 2022. https://pubs.aip.org/aip/po...

    2022

  75. [83]

    Liquid Plasma Crystals on the ISS,

    E. G. Kostadinova, E. Gehr, B. Andrew, L. S. Matthews, T. W. Hyde, and A. Terrell, “Liquid Plasma Crystals on the ISS,” inAIAA SCITECH 2023 Forum, p. 2615, 2023. 32

    2023

  76. [2022]

    DOI: 10.1063/5.0098892

    doi

  77. [2023]

    Physics of Plasmas, 30(12):120601, December 2023

    2023

  78. [2025]

    https://arxiv.org/abs/2501.12248. 31

    arXiv

Pith tools

Reviewed August 12, 2026 · model on record in the stance chip above.