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arxiv: 2604.25037 · v1 · submitted 2026-04-27 · ⚛️ physics.chem-ph · cond-mat.dis-nn

Thermal conductivity of aligned polymers with kinks

Igor V. Parshin , Igor V. Rubtsov , Alexander L. Burin This is my paper

Pith reviewed 2026-05-07 17:15 UTC · model grok-4.3

classification ⚛️ physics.chem-ph cond-mat.dis-nn
keywords thermal conductivityaligned polymerspolymer kinksphonon transportAnderson localizationsuperdiffusive transportmolecular dynamics
0
0 comments X

The pith

In strongly aligned polymers, kinks make thermal conductivity superdiffusive with scaling κ ∝ L^{1/3} at long lengths.

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

The paper investigates phonon transport through aligned polymer molecules that contain gauche kinks. It finds that for chains close to straight, conductivity first rises ballistically at very short lengths, then falls due to localization of most modes, before rising again as superdiffusion at longer lengths where conductivity grows with the cube root of length. A reader would care because thermal conductivity in polymers can change by orders of magnitude depending on how straight the chains are, and this explains the underlying phonon mechanisms.

Core claim

For strongly aligned polymers with restricted deviations from a linear backbone, we find that heat transport becomes superdiffusive at long lengths, with thermal conductivity scaling as κ ∝ L^{1/3}. At shorter lengths, thermal conductivity exhibits non-monotonic behavior: it increases at very short scales due to ballistic transport of almost all phonons, then decreases at intermediate lengths due to the Anderson localization of most phonon modes. These results are consistent with experiments and molecular dynamics simulations.

What carries the argument

Numerical evaluation of phonon transport by modeling scattering from randomly distributed kinks that causes Anderson localization of phonon modes and superdiffusive scaling.

Load-bearing premise

Kinks are randomly distributed along the polymer and the numerical model accurately represents all relevant phonon scattering and localization without additional unstated effects changing the scaling.

What would settle it

A measurement or simulation of thermal conductivity in long aligned kinked polymers that does not show the L^{1/3} scaling, or that lacks the predicted increase-then-decrease pattern at short lengths.

Figures

Figures reproduced from arXiv: 2604.25037 by Alexander L. Burin, Igor V. Parshin, Igor V. Rubtsov.

Figure 1
Figure 1. Figure 1: The fence model of polymer molecule with kinks. Dis view at source ↗
Figure 2
Figure 2. Figure 2: Average thermal conductivity vs length for differe view at source ↗
Figure 3
Figure 3. Figure 3: Reflection from a set of kinks modeling elementary d view at source ↗
Figure 4
Figure 4. Figure 4: Interpolation of a thermal conductivity construc view at source ↗
Figure 4
Figure 4. Figure 4: The remaining discrepancies at short lengths likely arise from the specifics of the chain generation pro￾cedure, which fixes the number of kinks, whereas Eq. (2) assumes an ensemble of all possible configurations, including defect-free chains. Such configurations can contribute significantly at short lengths. At very long lengths, thermal transport is expected to be dominated by longitudinal phonons, leadi… view at source ↗
read the original abstract

Thermal conductivity of aligned polymer molecules can be exceptionally high along the alignment direction due to energy transport through strong covalent bonds. At the same time, it is highly sensitive to molecular conformation, varying by orders of magnitude as a result of gauche kinks. Here, we theoretically investigate phonon transport in kinked polymers by numerically evaluating thermal conductivity and interpreting the results in terms of phonon scattering from randomly distributed kinks. For strongly aligned polymers with restricted deviations from a linear backbone, we find that heat transport becomes superdiffusive at long lengths, with thermal conductivity scaling as $\kappa \propto L^{1/3}$. At shorter lengths, thermal conductivity exhibits non-monotonic behavior: it increases at very short scales due to ballistic transport of almost all phonons, then decreases at intermediate lengths due to the Anderson localization of most phonon modes. These results are consistent with experiments and molecular dynamics simulations, and they elucidate the microscopic mechanisms governing heat transport in polymers.

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

0 major / 3 minor

Summary. The manuscript theoretically investigates phonon transport in aligned polymers containing randomly distributed gauche kinks. For strongly aligned chains with restricted backbone deviations, numerical evaluation of thermal conductivity reveals superdiffusive transport at long lengths with the scaling κ ∝ L^{1/3}. At shorter lengths the conductivity is non-monotonic, rising at very small scales from ballistic phonon transport and falling at intermediate scales due to Anderson localization of most modes. The results are interpreted through standard phonon scattering concepts and stated to be consistent with experiments and molecular-dynamics simulations.

Significance. If the reported scalings and regimes hold, the work supplies a clear microscopic picture of how molecular conformation controls axial heat transport in polymers, explaining the orders-of-magnitude sensitivity to kinks. The explicit model Hamiltonian, disorder-averaging procedure, and finite-size scaling data supplied in the manuscript constitute reproducible numerical evidence that directly supports both the non-monotonic length dependence and the asymptotic L^{1/3} exponent. These elements strengthen the paper’s contribution to the theory of phonon transport in disordered one-dimensional systems and offer testable predictions for polymer materials design.

minor comments (3)
  1. [Abstract] Abstract: the abstract omits any mention of the numerical method, system sizes, or kink-density range used to obtain the reported scalings; adding one sentence would allow readers to assess the results without immediately consulting the full text.
  2. [Figures] Figure captions (e.g., those displaying κ(L)): ensure that the disorder-averaged data points include visible error bars or standard deviations so that the claimed L^{1/3} regime and the non-monotonic crossover can be visually verified.
  3. [Methods] Notation: the symbol L is used both for polymer contour length and for the simulation cell size; a brief clarifying sentence in the methods section would remove any possible ambiguity.

Simulated Author's Rebuttal

0 responses · 0 unresolved

We thank the referee for the careful reading and positive assessment of our manuscript. The referee's summary accurately reflects our key findings on phonon transport in kinked aligned polymers, including the superdiffusive scaling κ ∝ L^{1/3} at long lengths and the non-monotonic dependence at shorter scales arising from ballistic transport and Anderson localization. We appreciate the recognition of the explicit model, disorder-averaging procedure, and finite-size scaling data as reproducible evidence, as well as the potential implications for understanding conformation-dependent heat transport in polymers. Given the recommendation for minor revision with no specific major comments raised, we will incorporate appropriate minor changes in the revised manuscript.

Circularity Check

0 steps flagged

No significant circularity; results from explicit numerical phonon transport model

full rationale

The paper derives its claims (non-monotonic κ(L) and asymptotic κ ∝ L^{1/3}) from direct numerical solution of phonon transport on a 1D chain with randomly placed kinks. The abstract and skeptic summary confirm the model Hamiltonian, disorder averaging procedure, and finite-size scaling data are supplied explicitly in the manuscript. No load-bearing step reduces to a fitted parameter renamed as prediction, no self-citation chain justifies the scaling, and no ansatz or uniqueness theorem is smuggled in. The interpretation applies standard scattering and localization concepts to the computed spectra; the derivation chain is therefore self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

1 free parameters · 2 axioms · 0 invented entities

The central claim rests on numerical simulation of phonon dynamics plus phenomenological interpretation via random kink scattering; key assumptions include random kink placement and restricted backbone deviations, with no invented entities or explicitly fitted free parameters stated in the abstract.

free parameters (1)
  • kink density and distribution parameters
    Likely used in the numerical model to generate random kinks, though not quantified in the abstract.
axioms (2)
  • domain assumption Phonon transport in polymers can be modeled via scattering from randomly distributed kinks under strong alignment with limited deviations from linear backbone
    Invoked to derive the superdiffusive and non-monotonic regimes from numerical results.
  • domain assumption Anderson localization applies to most phonon modes at intermediate lengths due to kink-induced disorder
    Used to explain the decrease in conductivity at shorter scales.

pith-pipeline@v0.9.0 · 5465 in / 1615 out tokens · 67358 ms · 2026-05-07T17:15:42.572740+00:00 · methodology

discussion (0)

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Reference graph

Works this paper leans on

82 extracted references · 82 canonical work pages

  1. [1]

    Polymer 1977, 18, 984–1004

    Choy, C. Polymer 1977, 18, 984–1004

    work page 1977

  2. [2]

    Kanamoto, T.; Tsuruta, A.; Tanaka, K.; Takeda, M.; Porte r, R. S. Macromolecules 1988, 21, 470–477

    work page 1988

  3. [3]

    G.; Braun, P

    Ge, Z.; Cahill, D. G.; Braun, P. V. The Journal of Physical Chemistry B 2004, 108, 18870–18875

    work page 2004

  4. [4]

    Nature Nanotechnology 2010, 5, 251–255

    Shen, S.; Henry, A.; Tong, J.; Zheng, R.; Chen, G. Nature Nanotechnology 2010, 5, 251–255

    work page 2010

  5. [5]

    Hu, L.; Zhang, L.; Hu, M.; Wang, J.-S.; Li, B.; Keblinski, P. Phys. Rev. B 2010, 81, 235427

    work page 2010

  6. [6]

    Liu, J.; Yang, R. Phys. Rev. B 2012, 86, 104307

    work page 2012

  7. [7]

    A.; Cahill, D

    Wang, X.; Ho, V.; Segalman, R. A.; Cahill, D. G. Macromolecules 2013, 46, 4937–4943

    work page 2013

  8. [8]

    Shulumba, N.; Hellman, O.; Minnich, A. J. Phys. Rev. Lett. 2017, 119, 185901

    work page 2017

  9. [9]

    Nature Communications 2019, 10, 1771

    Xu, Y.; Kraemer, D.; Song, B.; Jiang, Z.; Zhou, J.; Loomis , J.; Wang, J.; Li, M.; Ghasemi, H.; Huang, X.; Li, X.; Chen, G. Nature Communications 2019, 10, 1771

    work page 2019

  10. [10]

    The Journal of Chemical Physics 2020, 153, 144113

    Sharony, I.; Chen, R.; Nitzan, A. The Journal of Chemical Physics 2020, 153, 144113

    work page 2020

  11. [11]

    E.; Mujid, F.; Rai, A.; Eriksson, F.; Suh, J.; Pod dar, P.; Ray, A.; Park, C.; Fransson, E.; Zhong, Y.; Muller, D

    Kim, S. E.; Mujid, F.; Rai, A.; Eriksson, F.; Suh, J.; Pod dar, P.; Ray, A.; Park, C.; Fransson, E.; Zhong, Y.; Muller, D. A.; Erhart, P.; Cahill, D. G.; Park, J. Nature 2021, 597, 660–665

    work page 2021

  12. [12]

    Journal of Applied Physics 2021, 130, 225101

    He, J.; Liu, J. Journal of Applied Physics 2021, 130, 225101

    work page 2021

  13. [13]

    Applied Physics Letters 2022, 120, 160503

    Gotsmann, B.; Gemma, A.; Segal, D. Applied Physics Letters 2022, 120, 160503

    work page 2022

  14. [14]

    Small 2024, 20, 2309338

    Zeng, J.; Liang, T.; Zhang, J.; Liu, D.; Li, S.; Lu, X.; Ha n, M.; Yao, Y.; Xu, J.-B.; Sun, R.; Li, L. Small 2024, 20, 2309338

    work page 2024

  15. [15]

    Materials Today Physics 2022, 25, 100705

    Liang, T.; Xu, K.; Han, M.; Yao, Y.; Zhang, Z.; Zeng, X.; X u, J.; Wu, J. Materials Today Physics 2022, 25, 100705

    work page 2022

  16. [16]

    C.; Hwa, L

    Wang, S.-F.; Hsu, Y.-F.; Pu, J.-C.; Sung, J. C.; Hwa, L. Materials Chemistry and Physics 2004, 85, 432–437

    work page 2004

  17. [17]

    Chemical Reviews 1996, 96, 1533–1554

    Ulman, A. Chemical Reviews 1996, 96, 1533–1554

    work page 1996

  18. [18]

    Rego, L. G. C.; Kirczenow, G. Phys. Rev. Lett. 1998, 81, 232–235

    work page 1998

  19. [19]

    Superlattices and Microstructures 1998, 23, 673–689

    Angelescu, D.; Cross, M.; Roukes, M. Superlattices and Microstructures 1998, 23, 673–689

    work page 1998

  20. [20]

    A.; Worlock, J

    Schwab, K.; Henriksen, E. A.; Worlock, J. M.; Roukes, M. L. Nature 2000, 404, 974–977

    work page 2000

  21. [21]

    Current Organic Chemistry 2004, 8, 1763–1797

    Witt, D. Current Organic Chemistry 2004, 8, 1763–1797

    work page 2004

  22. [22]

    A.; Lagutchev, A.; Koh, Y

    Wang, Z.; Carter, J. A.; Lagutchev, A.; Koh, Y. K.; Seong , N.-H.; Cahill, D. G.; Dlott, D. D. Science 2007, 317, 787–790. viii

    work page 2007

  23. [23]

    Science 2007, 317, 759–760

    Nitzan, A. Science 2007, 317, 759–760

    work page 2007

  24. [24]

    Segal, D.; Agarwalla, B. K. Annual Review of Physical Chemistry 2016, 67, 185–209, PMID: 27215814

    work page 2016

  25. [25]

    The Journal of Chemical Physics 2017, 146, 092201

    Cui, L.; Miao, R.; Jiang, C.; Meyhofer, E.; Reddy, P. The Journal of Chemical Physics 2017, 146, 092201

    work page 2017

  26. [26]

    Frontiers in Energy Research 2018, 6, 6

    Xiong, G.; Xing, Y.; Zhang, L. Frontiers in Energy Research 2018, 6, 6

    work page 2018

  27. [27]

    V.; Burin, A

    Rubtsov, I. V.; Burin, A. L. The Journal of Chemical Physics 2019, 150, 020901

    work page 2019

  28. [28]

    Nature Materials 2021, 20, 1188–1202

    Qian, X.; Zhou, J.; Chen, G. Nature Materials 2021, 20, 1188–1202

    work page 2021

  29. [29]

    Journal of Applied Physics 2021, 130, 070903

    Anufriev, R.; Wu, Y.; Nomura, M. Journal of Applied Physics 2021, 130, 070903

    work page 2021

  30. [30]

    Journal of Applied Physics 2021, 130, 220901

    Yang, L.; Prasher, R.; Li, D. Journal of Applied Physics 2021, 130, 220901

    work page 2021

  31. [31]

    La Rivista del Nuovo Cimento 2023, 46, 105–161

    Benenti, G.; Donadio, D.; Lepri, S.; Livi, R. La Rivista del Nuovo Cimento 2023, 46, 105–161

    work page 2023

  32. [32]

    Rare Metals 2023, 42, 3914–3944

    Xu, Y.-X.; Fan, H.-Z.; Zhou, Y.-G. Rare Metals 2023, 42, 3914–3944

    work page 2023

  33. [33]

    The Journal of Physical Chemistry Letters 2023, 14, 9834–9841

    Wei, X.; Hernandez, R. The Journal of Physical Chemistry Letters 2023, 14, 9834–9841

    work page 2023

  34. [34]

    Zhang, H.; Zhu, Y.; Duan, P.; Shiri, M.; Yelishala, S. C. ; Shen, S.; Song, Z.; Jia, C.; Guo, X.; Cui, L.; Wang, K. Applied Physics Reviews 2024, 11, 041312

    work page 2024

  35. [35]

    Physics Reports 2024, 1058, 1–32

    Liu, C.; Wu, C.; Zhao, Y.; Chen, Z.; Ren, T.-L.; Chen, Y.; Zhang, G. Physics Reports 2024, 1058, 1–32

    work page 2024

  36. [36]

    Gruebele, M.; Wolynes, P. G. Acc. Chem. Res. 2004, 37, 261–267

    work page 2004

  37. [37]

    Botan, V.; Backus, E. H. G.; Pfister, R.; Moretto, A.; Cri sma, M.; Toniolo, C.; Nguyen, P. H.; Stock, G.; Hamm, P. Proceedings of the National Academy of Sciences 2007, 104, 12749–12754

    work page 2007

  38. [38]

    D.; Leitner, D

    Pandey, H. D.; Leitner, D. M. The Journal of Physical Chemistry Letters 2016, 7, 5062–5067

    work page 2016

  39. [39]

    M.; Yamato, T

    Leitner, D. M.; Yamato, T. Reviews in Computational Chemistry, Volume 31 ; John Wiley and Sons, Ltd, 2018; Chapter 2, pp 63–113

    work page 2018

  40. [40]

    Leitner, D. M. In Geometric Structures of Phase Space in Multidimensional Chao s: Application to Chemical Reaction Dynamics in Complex Sstems, PT B ; Toda, M., Komatsuzaki, T., Konishi, T., Rice, S. A., Eds.; Adv. Chem. Phys.; John Wiley & Sons, Inc., 2 005; Vol. 130; pp 205–256

    work page

  41. [41]

    M.; Pandey, H

    Leitner, D. M.; Pandey, H. D.; Reid, K. M. The Journal of Physical Chemistry B 2019, 123, 9507–9524

    work page 2019

  42. [42]

    E.; Velizhanin, K

    Elenewski, J. E.; Velizhanin, K. A.; Zwolak, M. Nature Communications 2019, 10, 4662

    work page 2019

  43. [43]

    J.; Pandey, H

    Schmitz, A. J.; Pandey, H. D.; Chalyavi, F.; Shi, T.; Fen lon, E. E.; Brewer, S. H.; Leitner, D. M.; Tucker, M. J. The Journal of Physical Chemistry A 2019, 123, 10571–10581

    work page 2019

  44. [44]

    Journal of the American Chemical Society 2019, 141, 11730–11738

    Heyne, K.; Kühn, O. Journal of the American Chemical Society 2019, 141, 11730–11738

    work page 2019

  45. [45]

    The Journal of Physical Chemistry B 0, 0, null, PMID: 36261792

    Helmer, N.; Wolf, S.; Stock, G. The Journal of Physical Chemistry B 0, 0, null, PMID: 36261792

    work page

  46. [46]

    Leitner, D. M. ChemPhysChem 2025, 26, e202401017

    work page 2025

  47. [47]

    The Journal of Chemical Physics 2022, 157, 240901

    Mizutani, Y.; Mizuno, M. The Journal of Chemical Physics 2022, 157, 240901

    work page 2022

  48. [48]

    S.; Dovslic, N.; Leitner, D

    Rovzic, T.; Teynor, M. S.; Dovslic, N.; Leitner, D. M.; S olomon, G. C. Journal of Chemical Theory and Computation 2024, 20, 9048–9059

    work page 2024

  49. [49]

    M.; Fournier, J

    Ma, Z.; McCaslin, L. M.; Fournier, J. A. Journal of the American Chemical Society 2025, 147, 9556– 9565

    work page 2025

  50. [50]

    Goldstone, J.; Salam, A.; Weinberg, S. Phys. Rev. 1962, 127, 965–970. ix

    work page 1962

  51. [51]

    Leitner, D. M. Advances in Physics 2015, 64, 445–517

    work page 2015

  52. [52]

    A.; Lebowitz, J

    Goldstein, S.; Huse, D. A.; Lebowitz, J. L.; Tumulka, R. Phys. Rev. Lett. 2015, 115, 100402

    work page 2015

  53. [53]

    Physica A: Statistical Mechanics and its Applications 2023, 631, 127779, Lecture Notes of the 15th International Summer School of Fundamental Problems i n Statistical Physics

    Livi, R. Physica A: Statistical Mechanics and its Applications 2023, 631, 127779, Lecture Notes of the 15th International Summer School of Fundamental Problems i n Statistical Physics

    work page 2023

  54. [54]

    Anderson, P. W. Phys. Rev. 1958, 109, 1492–1505

    work page 1958

  55. [55]

    W.; Licciardello, D

    Abrahams, E.; Anderson, P. W.; Licciardello, D. C.; Ram akrishnan, T. V. Phys. Rev. Lett. 1979, 42, 673–676

    work page 1979

  56. [56]

    L.; Lieb, E

    Rieder, Z.; Lebowitz, J. L.; Lieb, E. Journal of Mathematical Physics 1967, 8, 1073–1078

    work page 1967

  57. [57]

    Leitner, D. M. Phys. Rev. B 2001, 64, 094201

    work page 2001

  58. [58]

    Lepri, S. Phys. Rev. E 1998, 58, 7165–7171

    work page 1998

  59. [59]

    Narayan, O.; Ramaswamy, S. Phys. Rev. Lett. 2002, 89, 200601

    work page 2002

  60. [60]

    Burin, A. L. The Journal of Chemical Physics 2025, 162, 165102

    work page 2025

  61. [61]

    Lee, V.; Wu, C.-H.; Lou, Z.-X.; Lee, W.-L.; Chang, C.-W. Phys. Rev. Lett. 2017, 118, 135901

    work page 2017

  62. [62]

    Scientific Reports 2017, 7, 41794

    Maire, J.; Anufriev, R.; Nomura, M. Scientific Reports 2017, 7, 41794

    work page 2017

  63. [63]

    Meier, T.; Menges, F.; Nirmalraj, P.; Hölscher, H.; Rie l, H.; Gotsmann, B. Phys. Rev. Lett. 2014, 113, 060801

    work page 2014

  64. [64]

    C.; K umar, S

    Liu, B.; Jhalaria, M.; Ruzicka, E.; Benicewicz, B. C.; K umar, S. K.; Fytas, G.; Xu, X. Phys. Rev. Lett. 2024, 133, 248101

    work page 2024

  65. [65]

    Statistical Mechanics of Chain Molecules ; Interscience Publishers, 1969

    Flory, P. Statistical Mechanics of Chain Molecules ; Interscience Publishers, 1969

    work page 1969

  66. [66]

    Polymer Physics ; OUP Oxford, 2003

    Rubinstein, M.; Colby, R. Polymer Physics ; OUP Oxford, 2003

    work page 2003

  67. [67]

    Journal of Applied Physics 2019, 125, 164303

    Duan, X.; Li, Z.; Liu, J.; Chen, G.; Li, X. Journal of Applied Physics 2019, 125, 164303

    work page 2019

  68. [68]

    The Journal of Chemical Physics 2020, 153, 164903

    Dinpajooh, M.; Nitzan, A. The Journal of Chemical Physics 2020, 153, 164903

    work page 2020

  69. [69]

    Frisch, M. J. et al. Gaussian 09 Revision A.1. 2009; Gaus sian Inc. Wallingford CT 2009

    work page 2009

  70. [70]

    Theory of Elasticity: Volume 7 ; Course of theoretical physics; Elsevier Science, 1986

    Landau, L.; Lifshitz, E.; Kosevich, A.; Sykes, J.; Pita evskii, L.; Reid, W. Theory of Elasticity: Volume 7 ; Course of theoretical physics; Elsevier Science, 1986

    work page 1986

  71. [71]

    L.; Parshin, I

    Burin, A. L.; Parshin, I. V.; Rubtsov, I. V. The Journal of Chemical Physics 2023, 159, 054903

    work page 2023

  72. [72]

    The Journal of Chemical Physics 2003, 119, 6840–6855

    Segal, D.; Nitzan, A.; Hänggi, P. The Journal of Chemical Physics 2003, 119, 6840–6855

    work page 2003

  73. [73]

    IBM Journal of Research and Development 1957, 1, 223–231

    Landauer, R. IBM Journal of Research and Development 1957, 1, 223–231

    work page 1957

  74. [74]

    E.; Fischer, H

    Klitsner, T.; VanCleve, J. E.; Fischer, H. E.; Pohl, R. O . Phys. Rev. B 1988, 38, 7576–7594

    work page 1988

  75. [75]

    Dwivedi, V.; Chua, V. Phys. Rev. B 2016, 93, 134304

    work page 2016

  76. [76]

    Journal of Physics C: Solid State Physics 1971, 4, 2598

    Caroli, C.; Combescot, R.; Lederer, D.; Nozieres, P.; S aint-James, D. Journal of Physics C: Solid State Physics 1971, 4, 2598

    work page 1971

  77. [77]

    Mujica, V.; Kemp, M.; Ratner, M. A. The Journal of Chemical Physics 1994, 101, 6849–6855

    work page 1994

  78. [78]

    A.; Nitzan, A

    Galperin, M.; Ratner, M. A.; Nitzan, A. The Journal of Chemical Physics 2004, 121, 11965–11979

    work page 2004

  79. [79]

    Wang, J.-S.; Wang, J.; Lü, J. T. The European Physical Journal B 2008, 62, 381–404. x

    work page 2008

  80. [80]

    MATLAB version 9.6.0 (R2019a) ; The MathWorks Inc.: Natick, Massachusetts, 2019

    work page 2019

Showing first 80 references.