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arxiv: 2604.15084 · v1 · submitted 2026-04-16 · ❄️ cond-mat.other

Static heterogeneity generates apparent universality in first-passage bursty dynamics

Morten M{\o}ller , Philipp Rahe , Sadegh Ghaderzadeh , Elena Besley , Philip Moriarty This is my paper

Pith reviewed 2026-05-10 08:42 UTC · model grok-4.3

classification ❄️ cond-mat.other
keywords first-passage dynamicsbursty processespower-law distributionsspatial heterogeneityscanning tunneling microscopykinetic Monte Carlomolecular diffusioninter-event times
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0 comments X

The pith

STM tip-induced spatial heterogeneity produces an apparent α∼1 power law in molecular first-passage times.

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

The paper tests whether the widely reported α∼1 scaling in bursty inter-event times reflects intrinsic scale-free dynamics or instead emerges from underlying rate heterogeneity. In a controlled physical system of 2D molecular diffusion observed by scanning tunneling microscopy, the measured inter-pulse distributions take the same truncated power-law form seen in human activities such as email and web browsing. Maximum-likelihood fits favor a Kohlrausch-Williams-Watts tempered power law, and kinetic Monte Carlo simulations reproduce the data when static spatial heterogeneity from the STM tip is included. The simulations show that the α∼1 regime is limited to a finite time window and disappears once the heterogeneity is removed, indicating that the scaling is an emergent effect rather than evidence of universality. A sympathetic reader would care because the same heterogeneity mechanism could explain many reported power laws across social and biological systems without requiring scale invariance.

Core claim

In two-dimensional molecular diffusion detected by the tip of a scanning tunnelling microscope, the inter-pulse time distribution exhibits an apparent α∼1 scaling that is reproduced by kinetic Monte Carlo simulations solely through tip-induced spatial heterogeneity; the scaling is confined to a finite time window and is better described by a Kohlrausch-Williams-Watts tempered power law than by a pure power law, demonstrating that the behavior arises from position-dependent rates rather than from scale-free dynamics.

What carries the argument

Tip-induced static spatial heterogeneity, which imposes a fixed distribution of local first-passage times whose superposition generates the observed tempered power-law inter-pulse statistics.

If this is right

  • Many reported α∼1 distributions in human dynamics may reflect heterogeneous rates rather than intrinsic universality.
  • Pure power laws are disfavored; tempered forms provide a better description once heterogeneity is accounted for.
  • The apparent universality classes α=1 and α=3/2 can be distinguished by whether spatial or rate heterogeneity is present.
  • Kinetic Monte Carlo models that include position-dependent rates can be used to test for true scale invariance in other bursty systems.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The same heterogeneity mechanism may operate in other physical systems with spatial rate variations, such as diffusion in porous media or on heterogeneous surfaces.
  • Mapping local rates directly in an experiment could allow recovery of the underlying exponential waiting-time distribution once heterogeneity is corrected for.
  • Similar re-analysis of social datasets could test whether removing estimated rate heterogeneity eliminates the reported power-law tails.

Load-bearing premise

The STM tip creates a dominant and fixed spatial heterogeneity in molecular detection rates that is accurately captured by the kinetic Monte Carlo model and fully accounts for the measured inter-pulse statistics.

What would settle it

Perform the same molecular diffusion experiment with a detection method that imposes no spatial bias, such as a uniform optical probe or a non-local measurement, and test whether the α∼1 scaling in inter-pulse times disappears.

read the original abstract

Processes involving bursts of activity separated by quiescent periods occur across diverse systems and scales. In human dynamics, these phenomena have been described by power-law inter-event time distributions, $P(t)\sim t^{-\alpha}$, with putative universality classes $\alpha=1$ and $\alpha=\frac{3}{2}$ having been proposed. Whether the observed $\alpha = 1$ scaling reflects intrinsic scale-free dynamics or instead emerges from heterogeneous underlying rates has been debated at length. We address this question in a canonical physical system for first-passage dynamics: two-dimensional molecular diffusion detected by the tip of a scanning tunnelling microscope. The resulting inter-pulse time distributions exhibit the same apparent truncated power-law form reported for human activities such as email communication, web browsing, and library loans. Maximum-likelihood estimation and model comparison decisively favor a Kohlrausch-Williams-Watts--tempered power law, $P(t)\propto t^{-\alpha}\exp\left(-(t/t_c)^\beta\right)$, with $\alpha \sim 1$. Kinetic Monte Carlo simulations reproduce this behavior, showing that the apparent $\alpha \sim 1$ scaling is confined to a finite time window and arises from tip-induced spatial heterogeneity, not scale invariance.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 2 minor

Summary. The manuscript examines inter-pulse time distributions in a physical system of two-dimensional molecular diffusion detected by scanning tunneling microscopy (STM). It claims that the observed truncated power-law form with apparent exponent α ∼ 1 arises from static spatial heterogeneity induced by the STM tip, rather than intrinsic scale-free dynamics. This is supported by maximum-likelihood estimation and model comparison favoring a Kohlrausch-Williams-Watts tempered power law, together with kinetic Monte Carlo (KMC) simulations that reproduce the behavior when tip-induced heterogeneity is incorporated.

Significance. If the central claim holds, the work supplies a concrete, experimentally accessible physical example in which heterogeneity alone generates the apparent α ∼ 1 scaling and its finite-time truncation, directly addressing long-standing debates about universality classes in bursty first-passage processes. The combination of real STM data, statistical model selection, and forward KMC simulations that recover the experimental phenomenology is a clear strength, offering a mechanistic route to interpret similar distributions reported in human dynamics and other complex systems.

major comments (2)
  1. [KMC simulations] KMC simulations section: the model does not incorporate STM-specific detection thresholds, amplitude cutoffs, or tip-convolution effects that are common in experimental current traces. Without an explicit control simulation using uniform rates plus realistic noise and detection criteria, it remains unclear whether heterogeneity is both necessary and sufficient to produce the observed truncated power-law, or whether measurement selection effects could independently generate the same phenomenology.
  2. [Statistical analysis] Statistical analysis and model comparison: the claim that MLE and model comparison 'decisively favor' the tempered power-law lacks reported quantitative diagnostics (likelihood ratios, AIC/BIC differences, or bootstrap error estimates on α and β). This makes it difficult to assess the robustness of the preference for α ∼ 1 over pure power-law or other alternatives.
minor comments (2)
  1. [Abstract] The abstract states that KMC 'reproduces this behavior' but does not specify which quantitative metrics (e.g., fitted α, tc, or Kolmogorov-Smirnov distance) were matched between simulation and experiment.
  2. [Methods] Notation for the tempered power-law form P(t) ∝ t^{-α} exp[−(t/tc)^β] should be consistently defined with explicit parameter ranges and units in the main text.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive and positive assessment of our manuscript. We address each major comment point by point below and have revised the manuscript accordingly where the concerns are valid.

read point-by-point responses

  1. Referee: [KMC simulations] KMC simulations section: the model does not incorporate STM-specific detection thresholds, amplitude cutoffs, or tip-convolution effects that are common in experimental current traces. Without an explicit control simulation using uniform rates plus realistic noise and detection criteria, it remains unclear whether heterogeneity is both necessary and sufficient to produce the observed truncated power-law, or whether measurement selection effects could independently generate the same phenomenology.

    Authors: We agree that an explicit control is needed to isolate the role of heterogeneity. Our current KMC implementation already encodes tip-induced spatial variation in local hopping rates (derived from the experimental tip geometry and bias), with detection occurring when a diffusing molecule enters the effective tunneling volume. However, to demonstrate necessity, we will add a new control simulation using spatially uniform rates, realistic additive noise matching the experimental current traces, and the same amplitude threshold and convolution kernel. This will be presented in a revised Figure and accompanying text to show that uniform rates plus detection effects alone do not recover the truncated power-law with α ≈ 1. revision: yes

  2. Referee: [Statistical analysis] Statistical analysis and model comparison: the claim that MLE and model comparison 'decisively favor' the tempered power-law lacks reported quantitative diagnostics (likelihood ratios, AIC/BIC differences, or bootstrap error estimates on α and β). This makes it difficult to assess the robustness of the preference for α ∼ 1 over pure power-law or other alternatives.

    Authors: We accept this criticism. The original manuscript relied on qualitative statements of model preference. In the revision we will add a dedicated subsection reporting (i) log-likelihood ratios between the tempered power-law and pure power-law (and exponential) models, (ii) AIC and BIC differences with explicit values, and (iii) bootstrap-derived 95% confidence intervals on α and β obtained from 1000 resamples of the experimental inter-event times. These diagnostics will be tabulated and referenced in the main text. revision: yes

Circularity Check

0 steps flagged

No significant circularity; derivation relies on independent KMC forward simulation of heterogeneity

full rationale

The paper's central claim—that apparent α∼1 scaling emerges from tip-induced spatial heterogeneity—is supported by direct comparison of experimental inter-pulse distributions to KMC simulations that implement heterogeneous rates as an input mechanism. No step reduces a claimed prediction to a fitted parameter by construction, nor does any load-bearing premise collapse to a self-citation or self-defined ansatz. The simulations are forward models whose outputs are compared to data rather than tuned to reproduce the scaling tautologically. The derivation chain therefore remains self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Based solely on the abstract, no explicit free parameters, axioms, or invented entities are detailed beyond the empirical fitting of the tempered power-law form; the heterogeneity is physically motivated rather than postulated ad hoc.

pith-pipeline@v0.9.0 · 5527 in / 1241 out tokens · 30488 ms · 2026-05-10T08:42:30.784440+00:00 · methodology

discussion (0)

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Reference graph

Works this paper leans on

99 extracted references · 99 canonical work pages

  1. [1]

    Schweitzer, Sociophysics.Physics Today71(2), 40–46 (2018)

    F. Schweitzer, Sociophysics.Physics Today71(2), 40–46 (2018)

    work page 2018

  2. [2]

    Bouchaud, From statistical physics to social sciences: the pitfalls of multi-disciplinarity

    J.-P. Bouchaud, From statistical physics to social sciences: the pitfalls of multi-disciplinarity. Journal of Physics: Complexity4(4), 041001 (2023)

    work page 2023

  3. [3]

    M. W. Macy, B. K. Szymanski, J. A. Ho lyst, The Ising model celebrates a century of interdis- ciplinary contributions.npj Complex1(1) (2024)

    work page 2024

  4. [4]

    P. W. Anderson, More Is Different.Science177(4047), 393–396 (1972)

    work page 1972

  5. [5]

    J. L. Silverberg, M. Bierbaum, J. P. Sethna, I. Cohen, Collective Motion of Humans in Mosh and Circle Pits at Heavy Metal Concerts.Phys. Rev. Lett.110, 228701 (2013)

    work page 2013

  6. [6]

    J. J. Buend ´ıa, H. Lopez, G. Sanchis, L. C. Pardo, Modelling human behaviour in a bumper car ride using molecular dynamics tools: a student project.European Journal of Physics38(3), 035802 (2017)

    work page 2017

  7. [7]

    Patriarca, E

    M. Patriarca, E. Heinsalu, D. S ´anchez, The physics of languages.Physics World36(8), 25 (2023)

    work page 2023

  8. [8]

    S. A. Levin, H. V. Milner, C. Perrings, The dynamics of political polarization.Proceedings of the National Academy of Sciences118(50), e2116950118 (2021)

    work page 2021

  9. [9]

    Barreira da Silva Rocha, Evolutionary dynamics of nationalism and migration.Physica A: Statistical Mechanics and its Applications392(15), 3183–3197 (2013)

    A. Barreira da Silva Rocha, Evolutionary dynamics of nationalism and migration.Physica A: Statistical Mechanics and its Applications392(15), 3183–3197 (2013)

    work page 2013

  10. [10]

    Barab ´asi, The origin of bursts and heavy tails in human dynamics.Nature435(7039), 207–211 (2005)

    A.-L. Barab ´asi, The origin of bursts and heavy tails in human dynamics.Nature435(7039), 207–211 (2005)

    work page 2005

  11. [11]

    Karsai, H.-H

    M. Karsai, H.-H. Jo, K. Kaski,Bursty Human Dynamics(Springer International Publishing) (2018)

    work page 2018

  12. [12]

    V ´azquez, Exact Results for the Barab ´asi Model of Human Dynamics.Phys

    A. V ´azquez, Exact Results for the Barab ´asi Model of Human Dynamics.Phys. Rev. Lett.95, 248701 (2005). 24

    work page 2005

  13. [13]

    V ´azquez,et al., Modeling bursts and heavy tails in human dynamics.Phys

    A. V ´azquez,et al., Modeling bursts and heavy tails in human dynamics.Phys. Rev. E73, 036127 (2006)

    work page 2006

  14. [14]

    Johansen, Comment on A.-L

    A. Johansen, Comment on A.-L. Barab ´asi, Nature 435 207-211 (2005) (2006)

    work page 2005

  15. [15]

    D. B. Stouffer, R. D. Malmgren, L. A. N. Amaral, Comment on Barab ´asi, Nature 435, 207 (2005) (2005)

    work page 2005

  16. [16]

    A. L. Barabasi, K. I. Goh, A. Vazquez, Reply to Comment on ”The origin of bursts and heavy tails in human dynamics” (2005)

    work page 2005

  17. [17]

    Jacomy, Epistemic clashes in network science: Mapping the tensions between idiographic and nomothetic subcultures.Big Data & Society7(2), 2053951720949577 (2020)

    M. Jacomy, Epistemic clashes in network science: Mapping the tensions between idiographic and nomothetic subcultures.Big Data & Society7(2), 2053951720949577 (2020)

    work page 2020

  18. [18]

    A. D. Broido, A. Clauset, Scale-free networks are rare.Nat. Commun.10(1), 1017 (2019)

    work page 2019

  19. [19]

    scale-free

    E. F. Keller, Revisiting “scale-free” networks.Bioessays27(10), 1060–1068 (2005)

    work page 2005

  20. [20]

    Corral, Long-Term Clustering, Scaling, and Universality in the Temporal Occurrence of Earthquakes.Phys

    A. Corral, Long-Term Clustering, Scaling, and Universality in the Temporal Occurrence of Earthquakes.Phys. Rev. Lett.92, 108501 (2004)

    work page 2004

  21. [21]

    J. M. Beggs, N. Timme, Being critical of criticality in the brain.Front. Physiol.3, 163 (2012)

    work page 2012

  22. [22]

    Karsai,et al., Small but slow world: How network topology and burstiness slow down spreading.Phys

    M. Karsai,et al., Small but slow world: How network topology and burstiness slow down spreading.Phys. Rev. E83, 025102 (2011)

    work page 2011

  23. [23]

    T. Gernat,et al., Automated monitoring of behavior reveals bursty interaction patterns and rapid spreading dynamics in honeybee social networks.Proceedings of the National Academy of Sciences115(7), 1433–1438 (2018)

    work page 2018

  24. [24]

    Sorribes, B

    A. Sorribes, B. G. Armendariz, D. Lopez-Pigozzi, C. Murga, G. G. de Polavieja, The origin of behavioral bursts in decision-making circuitry.PLoS Comput. Biol.7(6), e1002075 (2011)

    work page 2011

  25. [25]

    Ghosh, Non-equilibrium dynamics of stochastic gene regulation.J

    A. Ghosh, Non-equilibrium dynamics of stochastic gene regulation.J. Biol. Phys.41(1), 49–58 (2015). 25

    work page 2015

  26. [26]

    A. G. Hawkes, A. Jalali, D. Colquhoun, The distributions of the apparent open times and shut times in a single channel record when brief events cannot be detected.Philosophical Transactions of the Royal Society of London, Series A: Physical and Engineering Sciences 332(1627), 511–538 (1990)

    work page 1990

  27. [27]

    Takeuchi, Y

    M. Takeuchi, Y. Sano, Burstiness of human physical activities and their characterisation.J. Comput. Soc. Sci.7(1), 625–641 (2024)

    work page 2024

  28. [28]

    Jiang,et al., Calling patterns in human communication dynamics.Proceedings of the National Academy of Sciences110(5), 1600–1605 (2013)

    Z.-Q. Jiang,et al., Calling patterns in human communication dynamics.Proceedings of the National Academy of Sciences110(5), 1600–1605 (2013)

    work page 2013

  29. [29]

    Dalton, I

    E. Dalton, I. Clancy, D. Corcoran, A. Arshak, G. Gooberman, On-Off Intermittency and Criticality in Early Stage Electromigration.Phys. Rev. Lett.104, 214101 (2010)

    work page 2010

  30. [30]

    Mathiesen, L

    J. Mathiesen, L. Angheluta, P. T. H. Ahlgren, M. H. Jensen, Excitable human dynamics driven by extrinsic events in massive communities.Proceedings of the National Academy of Sciences 110(43), 17259–17262 (2013)

    work page 2013

  31. [31]

    J. Choi, T. Hiraoka, H.-H. Jo, Individual-driven versus interaction-driven burstiness in human dynamics: The case of Wikipedia edit history.Phys. Rev. E104, 014312 (2021)

    work page 2021

  32. [32]

    C. W. Lynn, L. Papadopoulos, D. D. Lee, D. S. Bassett, Surges of Collective Human Activity Emerge from Simple Pairwise Correlations.Phys. Rev. X9, 011022 (2019)

    work page 2019

  33. [33]

    Oliveira, A

    J. Oliveira, A. Vazquez, Impact of interactions on human dynamics.Physica A: Statistical Mechanics and its Applications388(2), 187–192 (2009)

    work page 2009

  34. [34]

    R. D. Malmgren, D. B. Stouffer, A. E. Motter, L. A. N. Amaral, A Poissonian explanation for heavy tails in e-mail communication.Proceedings of the National Academy of Sciences 105(47), 18153–18158 (2008)

    work page 2008

  35. [35]

    R. D. Malmgren, D. B. Stouffer, A. S. L. O. Campanharo, L. A. N. Amaral, On Universality in Human Correspondence Activity.Science325(5948), 1696–1700 (2009)

    work page 2009

  36. [36]

    G. J. Ross, T. Jones, Understanding the heavy-tailed dynamics in human behavior.Phys. Rev. E91, 062809 (2015). 26

    work page 2015

  37. [37]

    Redner,A guide to first-passage processes(Cambridge University Press, Cambridge, Eng- land) (2012)

    S. Redner,A guide to first-passage processes(Cambridge University Press, Cambridge, Eng- land) (2012)

    work page 2012

  38. [38]

    Binnig, H

    G. Binnig, H. Fuchs, E. Stoll, Surface diffusion of oxygen atoms individually observed by STM.Surface Science169(2), L295–L300 (1986)

    work page 1986

  39. [39]

    M. L. Lozano, M. C. Tringides, Surface Diffusion Measurements from STM Tunneling Current Fluctuations.Europhysics Letters30(9), 537 (1995)

    work page 1995

  40. [40]

    X. Wang, Q. Li, M. C. Tringides, Effect of an STM tip on the surface-diffusion measurement: A Monte Carlo study.Phys. Rev. B57, 7275–7280 (1998)

    work page 1998

  41. [41]

    Wander, J

    A. Wander, J. Harrison, D. King, Extracting adsorbate diffusion dynamics from an STM experiment: a Monte Carlo study of flicker noise.Surface Science397(1), 406–420 (1998)

    work page 1998

  42. [42]

    Barth, Transport of adsorbates at metal surfaces: from thermal migration to hot precursors

    J. Barth, Transport of adsorbates at metal surfaces: from thermal migration to hot precursors. Surface Science Reports40(3), 75–149 (2000)

    work page 2000

  43. [43]

    S. Baud, X. Bouju, C. Ramseyer, H. Tang, Atomic diffusion inside an STM junction: simulations by kinetic Monte Carlo coupled to tunneling current calculations.Surface Science523(3), 267– 278 (2003)

    work page 2003

  44. [44]

    Hahne, J

    S. Hahne, J. Ikonomov, M. Sokolowski, P. Maass, Determining molecule diffusion coefficients on surfaces from a locally fixed probe: Analysis of signal fluctuations.Phys. Rev. B87, 085409 (2013)

    work page 2013

  45. [45]

    Hahne, P

    S. Hahne, P. Maass, Diffusion Coefficients from Signal Fluctuations: Influence of Molecular Shape and Rotational Diffusion.The Journal of Physical Chemistry A118(12), 2237–2243 (2014)

    work page 2014

  46. [46]

    Hahne, Determination of single molecule diffusion from signal fluctuations, PhD thesis, Universit¨at Osnabr¨ uck (2014), accessed: 2026-04-02

    S. Hahne, Determination of single molecule diffusion from signal fluctuations, PhD thesis, Universit¨at Osnabr¨ uck (2014), accessed: 2026-04-02

    work page 2014

  47. [47]

    Schiel, P

    C. Schiel, P. Rahe, P. Maass, On the Possibility of Exploring Tip-Molecule Interactions with STM Experiments.Journal of The Electrochemical Society169(9), 096515 (2022). 27

    work page 2022

  48. [48]

    Tracking

    D. W. Pohl, R. M ¨oller, “Tracking”’ tunneling microscopy.Review of Scientific Instruments 59(6), 840–842 (1988)

    work page 1988

  49. [49]

    B. S. Swartzentruber, Direct Measurement of Surface Diffusion Using Atom-Tracking Scanning Tunneling Microscopy.Phys. Rev. Lett.76, 459–462 (1996)

    work page 1996

  50. [50]

    Rahe,et al., Flexible drift-compensation system for precise 3D force mapping in severe drift environments.Review of Scientific Instruments82(6), 063704 (2011)

    P. Rahe,et al., Flexible drift-compensation system for precise 3D force mapping in severe drift environments.Review of Scientific Instruments82(6), 063704 (2011)

    work page 2011

  51. [51]

    Materials and methods are available as supplementary material

    work page

  52. [52]

    Tautz, Structure and bonding of large aromatic molecules on noble metal surfaces: The example of PTCDA.Progress in Surface Science82(9), 479–520 (2007)

    F. Tautz, Structure and bonding of large aromatic molecules on noble metal surfaces: The example of PTCDA.Progress in Surface Science82(9), 479–520 (2007)

    work page 2007

  53. [53]

    Mercurio,et al., Adsorption height determination of nonequivalent C and O species of PTCDA on Ag(110) using x-ray standing waves.Phys

    G. Mercurio,et al., Adsorption height determination of nonequivalent C and O species of PTCDA on Ag(110) using x-ray standing waves.Phys. Rev. B87, 045421 (2013)

    work page 2013

  54. [54]

    Ikonomov, O

    J. Ikonomov, O. Bauer, M. Sokolowski, Highly ordered thin films of perylene-3,4,9,10- tetracarboxylic acid dianhydride (PTCDA) on Ag(100).Surface Science602(12), 2061–2068 (2008)

    work page 2061

  55. [55]

    Ikonomov, C

    J. Ikonomov, C. H. Schmitz, M. Sokolowski, Diffusion-limited island decay of PTCDA on Ag(100): Determination of the intermolecular interaction.Phys. Rev. B81, 195428 (2010)

    work page 2010

  56. [56]

    Ikonomov, P

    J. Ikonomov, P. Bach, R. Merkel, M. Sokolowski, Surface diffusion constants of large organic molecules determined from their residence times under a scanning tunneling microscope tip. Phys. Rev. B81, 161412 (2010)

    work page 2010

  57. [57]

    B ¨ohringer,et al., Corrugation reversal in scanning tunneling microscope images of organic molecules.Phys

    M. B ¨ohringer,et al., Corrugation reversal in scanning tunneling microscope images of organic molecules.Phys. Rev. B57, 4081–4087 (1998)

    work page 1998

  58. [58]

    P. L. L ´evesque,et al., Correlation Between Substrate Morphology and the Initial Stages of Epitaxial Organic Growth: PTCDA/Ag(111).The Journal of Physical Chemistry C120(34), 19271–19279 (2016)

    work page 2016

  59. [59]

    Seidel, C

    C. Seidel, C. Awater, X. Liu, R. Ellerbrake, H. Fuchs, A combined STM, LEED and molecular modelling study of PTCDA grown on Ag(110).Surface Science371(1), 123–130 (1997). 28

    work page 1997

  60. [60]

    Blenn, P

    N. Blenn, P. V. Mieghem, Are human interactivity times lognormal?CoRRabs/1607.02952 (2016)

    work page arXiv 2016

  61. [61]

    Clauset, C

    A. Clauset, C. R. Shalizi, M. E. J. Newman, Power-Law Distributions in Empirical Data.SIAM Review51(4), 661–703 (2009)

    work page 2009

  62. [62]

    C. R. Shalizi, So You Think You Have a Power Law – Well Isn’t That Special?; http://bactra.org/weblog/491.html (2007), accessed: 03-02-2026

    work page 2007

  63. [63]

    Akaike, A new look at the statistical model identification.IEEE Transactions on Automatic Control19(6), 716–723 (1974)

    H. Akaike, A new look at the statistical model identification.IEEE Transactions on Automatic Control19(6), 716–723 (1974)

    work page 1974

  64. [64]

    Kohlrausch, Theorie des elektrischen R¨ uckstandes in der Leidener Flasche.Annalen der Physik167(2), 179–214 (1854)

    R. Kohlrausch, Theorie des elektrischen R¨ uckstandes in der Leidener Flasche.Annalen der Physik167(2), 179–214 (1854)

    work page

  65. [65]

    Williams, D

    G. Williams, D. C. Watts, Non-symmetrical dielectric relaxation behaviour arising from a simple empirical decay function.Trans. Faraday Soc.66, 80–85 (1970)

    work page 1970

  66. [66]

    J. H. Wu, Q. Jia, The heterogeneous energy landscape expression of KWW relaxation.Sci. Rep.6(1), 20506 (2016)

    work page 2016

  67. [67]

    J. C. Phillips, Stretched exponential relaxation in molecular and electronic glasses.Reports on Progress in Physics59(9), 1133 (1996)

    work page 1996

  68. [68]

    fat tails

    J. Laherr `ere, D. Sornette, Stretched exponential distributions in nature and economy: “fat tails” with characteristic scales.Eur. Phys. J. B2(4), 525–539 (1998)

    work page 1998

  69. [69]

    R. Chen, Apparent stretched-exponential luminescence decay in crystalline solids.Journal of Luminescence102-103, 510–518 (2003), proceedings of the 2002 International Conference on Luminescence and Optical Spectroscopy of Condensed Matter

    work page 2003

  70. [70]

    Cipelletti, S

    L. Cipelletti, S. Manley, R. C. Ball, D. A. Weitz, Universal Aging Features in the Restructuring of Fractal Colloidal Gels.Phys. Rev. Lett.84, 2275–2278 (2000)

    work page 2000

  71. [71]

    Cipelletti, L

    L. Cipelletti, L. Ramos, Slow dynamics in glassy soft matter.Journal of Physics: Condensed Matter17(6), R253 (2005). 29

    work page 2005

  72. [72]

    Wagner,et al., Quantitative imaging of electric surface potentials with single-atom sensi- tivity.Nat

    C. Wagner,et al., Quantitative imaging of electric surface potentials with single-atom sensi- tivity.Nat. Mater.18(8), 853–859 (2019)

    work page 2019

  73. [73]

    J. A. Stroscio, D. M. Eigler, Atomic and Molecular Manipulation with the Scanning Tunneling Microscope.Science254(5036), 1319–1326 (1991)

    work page 1991

  74. [74]

    T. T. Tsong, G. Kellogg, Direct observation of the directional walk of single adatoms and the adatom polarizability.Phys. Rev. B12, 1343–1353 (1975)

    work page 1975

  75. [75]

    G. J. Simpson, V. Garc´ıa-L´opez, A. D. Boese, J. M. Tour, L. Grill, Directing and understanding the translation of a single molecule dipole.J. Phys. Chem. Lett.14(10), 2487–2492 (2023)

    work page 2023

  76. [76]

    Matvija,et al., Electric-field-controlled phase transition in a 2D molecular layer.Sci

    P. Matvija,et al., Electric-field-controlled phase transition in a 2D molecular layer.Sci. Rep. 7(1), 7357 (2017)

    work page 2017

  77. [77]

    Rozbo ˘ril, I

    F. Rozbo ˘ril, I. O ˘st´adal, P. Sobot´ık, P. Koc´an, Self-assembly of a two-dimensional molecular layer in a nonhomogeneous electric field: Kinetic Monte Carlo simulations.Phys. Rev. E99, 032110 (2019)

    work page 2019

  78. [78]

    Bauer,et al., Role of functional groups in surface bonding of planar𝜋-conjugated molecules

    O. Bauer,et al., Role of functional groups in surface bonding of planar𝜋-conjugated molecules. Phys. Rev. B86, 235431 (2012)

    work page 2012

  79. [79]

    Alkauskas, A

    A. Alkauskas, A. Baratoff, C. Bruder, Site-selective adsorption of naphthalene-tetracarboxylic- dianhydride on Ag(110): First-principles calculations.Phys. Rev. B73, 165408 (2006)

    work page 2006

  80. [80]

    E. V. Tsiper, Z. G. Soos, Charge redistribution and polarization energy of organic molecular crystals.Phys. Rev. B64, 195124 (2001)

    work page 2001

Showing first 80 references.