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Energy diffusion of simple networks under the spatiotemporal thermostats

  • Regular Article - Statistical and Nonlinear Physics
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Abstract

We investigate the energy transport in simple networks consisting of one-dimensional nonlinear chain with self-coupled loop. The impacts of the loop length and coupling strength on the heat flux and spatiotemporal correlation functions of energy–momentum fluctuations are discussed via Langevin thermostats generated by spatiotemporal noise. For thermostats at different temperatures, the spatiotemporal ones can weaken the total heat flux of the system in comparison with the normal Langevin ones. The total heat flux will increase when the dispersal kernel or the loop length or the coupling strength increases, while the heat flux in the loop does not change as the dispersal kernel or the loop length increases, and decrease as the coupling strength increases. Then the underlying mechanism of heat flux can be well explained by the phonon spectra and Fourier’s law. For the thermostats at the same temperatures, it is shown that the peak of the propagating front for the trunk (PT) and the peak of the propagating front from the coupling position to the outer trunk (PC) do not change almost for the normal Langevin and spatiotemporal thermostats. The PT decreases and PC increases when the loop length or coupling strength increases. Our results may contribute to further understanding of thermal information appearing in coupled nanotubes, polymer chains and biological networks.

Graphical abstract

Heat flux J vs the coupling strength k. The red circle, blue triangle and green five-pointed star refer to the total heat flux, heat flux in the self-coupled loop and shortcut, respectively. The length of the FPU-\(\beta \) lattice \(N = 500,\) coupling at \(i = 151, j =350\).

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This manuscript has no associated data or the data will not be deposited. [Authors comment: The paper contents are purely theoretical, and did not need any data.]

References

  1. R. Livi, S. Lepri, Nature 421(6921), 327 (2003)

    Article  ADS  Google Scholar 

  2. S. Lepri, R. Livi, A. Politi, Phys. Rep. 377(1), 1–80 (2003)

    Article  ADS  MathSciNet  Google Scholar 

  3. A. Dhar, Adv. Phys. 57(5), 457–537 (2008)

    Article  ADS  Google Scholar 

  4. C.W. Chang, D. Okawa, A. Majumdar, A. Zettl, Science 314, 1121 (2006)

    Article  ADS  Google Scholar 

  5. S. Lepri, Lect. Notes Phys. 921, 1 (2016)

    Article  MathSciNet  Google Scholar 

  6. S. de Groot, P. Mazur, Non-equilibrium Thermodynamics (Dover, New York, 1984)

    MATH  Google Scholar 

  7. E. Fermi, J. Pasta, S. Ulam, Studies of nonlinear problems, in Collected Papers of E. Fermi, vol. 2 (University of Chicago Press, Chicago, 1965), pp. 978–988

  8. H. Kaburaki, M. Machida, Phys. Lett. A 181, 85 (1993)

    Article  ADS  Google Scholar 

  9. A. Fillipov, B. Hu, B. Li, A. Zeltser, J. Phys. A 31(38), 7719–7728 (1998)

    Article  ADS  Google Scholar 

  10. K. Aoki, D. Kusnezov, Phys. Rev. Lett. 86(18), 4029–4032 (2001)

    Article  ADS  Google Scholar 

  11. N. Li, J. Ren, L. Wang, G. Zhang, P. Hänggi, B. Li, Rev. Mod. Phys. 84(3), 1045 (2012)

    Article  ADS  Google Scholar 

  12. X. Gu, Y. Wei, X. Yin, B. Li, R. Yang, Rev. Mod. Phys. 90(4), 041002 (2018)

    Article  ADS  Google Scholar 

  13. J. Wattis, J. Phys. A 26, 1193 (1993)

    Article  ADS  MathSciNet  Google Scholar 

  14. G. Friesecke, J. Wattis, Commun. Math. Phys. 161, 391 (1994)

    Article  ADS  Google Scholar 

  15. F. Zhang, D. Isbister, D. Evans, Phys. Rev. E 61, 3541 (2000)

    Article  ADS  Google Scholar 

  16. F. Zhang, D. Isbister, D. Evans, Phys. Rev. E 64, 021102 (2001)

    Article  ADS  Google Scholar 

  17. N. Li, P. Tong, B. Li, Europhys. Lett. 75, 49 (2006)

    Article  ADS  Google Scholar 

  18. N. Li, B. Li, Europhys. Lett. 78, 34001 (2007)

    Article  ADS  Google Scholar 

  19. N. Li, B. Li, AIP Adv. 2, 041408 (2012)

    Article  ADS  Google Scholar 

  20. N. Li, B. Li, Phys. Rev. E 87, 042125 (2013)

    Article  ADS  Google Scholar 

  21. S. Liu, J. Liu, P. Hänggi, C. Wu, B. Li, Phys. Rev. B 90, 174304 (2014)

    Article  ADS  Google Scholar 

  22. J. Liu, S. Liu, N. Li, B. Li, C. Wu, Phys. Rev. E 91, 042910 (2015)

    Article  ADS  MathSciNet  Google Scholar 

  23. H. Zhao, Phys. Rev. Lett. 96, 140602 (2006)

    Article  ADS  Google Scholar 

  24. N. Li, B. Li, S. Flach, Phys. Rev. Lett. 105, 054102 (2010)

    Article  ADS  Google Scholar 

  25. Y. Ming, L. Ye, H. Chen, S. Mao, H. Li, Z. Ding, Phys. Rev. E 97, 012221 (2018)

    Article  ADS  MathSciNet  Google Scholar 

  26. F. Bonetto, J. Lebowitz, L. Rey-Bellet, Mathematical Physics (Imperial College Press, London, 2000)

    Google Scholar 

  27. S. Nose, J. Chem. Phys. 81(1), 511–519 (1984)

    Article  ADS  Google Scholar 

  28. W. Hoover, Phys. Rev. A 31(3), 1695–1697 (1985)

    Article  ADS  Google Scholar 

  29. W. Zhong, Y. Shao, L. Li, F. Wang, Z. He, Europhys. Lett. 82(2), 20003 (2008)

    Article  ADS  Google Scholar 

  30. M. Scheffer, J. Bascompte, W. Brock, V. Brovkin, S. Carpenter, V. Dakos, H. Held, E. van Nes, M. Rietkerk, G. Sugihara, Nature 461(7260), 53–9 (2009)

    Article  ADS  Google Scholar 

  31. T. Singh, S. Banerjee, Int. J. Biomath. 13(4), 2050044 (2020)

    Article  MathSciNet  Google Scholar 

  32. A. Alés, J. López, J. Stat. Mech. 2020(3), 033210 (2020)

    Article  Google Scholar 

  33. J. Piccinini, I. Perez Ipiña, H. Laufs, M.L. Kringelbach, G. Deco, Y. Sanz Perl, E. Tagliazucchi, Chaos 31, 023128 (2021)

    Article  ADS  Google Scholar 

  34. G. Denaro, D. Valenti, A. La Cognata, B. Spagnolo, A. Bonanno, G. Basilone, S. Mazzola, S.W. Zgozi, S. Aronica, C. Brunet, Ecol. Complex. 13(1), 21–34 (2013)

    Article  Google Scholar 

  35. V. Guttal, C. Jayaprakash, Theor. Ecol. 2(1), 3–12 (2009)

    Article  Google Scholar 

  36. F. Sagués, J.M. Sancho, J. Garca-Ojalvo, Rev. Mod. Phys. 79(3), 829 (2007)

    Article  ADS  Google Scholar 

  37. J. Ma, P. Yuan, J. Wang, Y. Wang, G. Xie, H. Zhu, L. Qian, Nat. Commun. 6(1), 1–8 (2015)

    ADS  Google Scholar 

  38. R. Pastor-Satorras, A. Vázquez, A. Vespignani, Phys. Rev. Lett. 87, 258701 (2001)

    Article  ADS  Google Scholar 

  39. T. Zhou, G. Yan, B. Wang, Phys. Rev. E 71, 046141 (2005)

  40. K. Xiong, C. Zeng, Z. Liu, B. Li, Phys. Rev. E 98(2), 022115 (2018)

    Article  ADS  Google Scholar 

  41. K. Xiong, J. Zhou, M. Tang, C. Zeng, Z. Liu, Phys. Rev. E 98(6), 062144 (2018)

    Article  ADS  Google Scholar 

  42. K. Xiong, Z. Liu, C. Zeng, B. Li, Natl. Sci. Rev. 7, 270–277 (2020)

    Article  Google Scholar 

  43. C.F. Moukarzel, M. Argollo de Menezes, Phys. Rev. E 65, 056709 (2002)

    Article  ADS  Google Scholar 

  44. I. Sendiña-Nadal, S. Alonso, V. Pérez-Muñuzuri, M. Gómez-Gesteira, V. Pérez-Villar, L. Ramíez-Piscina, J. Casademunt, J.M. Sancho, F. Sagués, Phys. Rev. Lett. 84, 2734 (2000)

    Article  ADS  Google Scholar 

  45. S. Alonso, F. Sagués, J.M. Sancho, Phys. Rev. E 65, 066107 (2002)

    Article  ADS  Google Scholar 

  46. S. de Franciscis, A. d’Onofrio, Phys. Rev. E 86, 021118 (2012)

    Article  ADS  Google Scholar 

  47. G. Denaro, D. Valenti, B. Spagnolo, G. Basilone, S. Mazzola, S.W. Zgozi, S. Aronica, A. Bonanno, PLoS One 8(6), e66785 (2013)

    Article  ADS  Google Scholar 

  48. V. Pérez-Muñuzuri, F. Sagués, J.M. Sancho, Phys. Rev. E 62, 94–99 (2000)

    Article  ADS  Google Scholar 

  49. M.A. Santos, J.M. Sancho, Phys. Rev. E 64, 016129 (2001)

    Article  ADS  Google Scholar 

  50. H. Wang, Q. Ouyang, Phys. Rev. E 65, 046206 (2002)

    Article  ADS  Google Scholar 

  51. C. Gardiner, Handbook of Stochastic Methods for Physics, Chemistry and the Natural Sciences, 3rd edn. (Springer, Heidelberg, 2003)

    Google Scholar 

  52. M. Kot, M. Lewis, P. Driessche, Ecology 77, 2027–2042 (1996)

    Article  Google Scholar 

  53. Z. Liu, B. Li, Phys. Rev. E 76, 051118 (2007)

    Article  ADS  Google Scholar 

  54. E. Swartz, R. Pohl, Rev. Mod. Phys. 61, 605 (1989)

    Article  ADS  Google Scholar 

  55. R. Klages, G. Radons, I. Sokolov, Anomalous Transport: Foundations and Applications (Wiley-VCH, Weinheim, 2008)

    Book  Google Scholar 

  56. S. Dorogovtsev, J. Mendes, Adv. Phys. 51, 1079 (2002)

    Article  ADS  Google Scholar 

  57. S. Ciuchi, F. de Pasquale, B. Spagnolo, Phys. Rev. E 54, 706–716 (1996)

    Article  ADS  Google Scholar 

  58. N. Pizzolato, A. Fiasconaro, D.P. Adorno, B. Spagnolo, Phys. Biol. 7(3), 034001 (2010)

    Article  ADS  Google Scholar 

  59. C. Guarcello, D. Valenti, A. Carollo, B. Spagnolo, J. Stat. Mech. Theory E 2016, 054012 (2016)

    Article  Google Scholar 

  60. A. Carollo, B. Spagnolo, D. Valenti, Sci. Rep. 8, 9852 (2018)

    Article  ADS  Google Scholar 

  61. A. Mikhaylov, A. Pimashkin, Y. Pigareva, S. Gerasimova, E. Gryaznov, S. Shchanikov, A. Zuev, M. Talanov, I. Lavrov, V. Demin, V. Erokhin, S. Lobov, I. Mukhina, V. Kazantsev, H. Wu, B. Spagnolo, Front. Neurosci. 14, 358 (2020)

    Article  Google Scholar 

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Acknowledgements

We thank Prof. Z. Liu, Dr. Y. Luo and T. Huang for valuable discussions. This work was supported by the National Natural Science Foundation of China under Grant no. 12005166, the Yunnan Fundamental Research Projects (Grant no. 2019FI002 and 202101AS070018), Yunnan Province Ten Thousand Talents Plan Young and Elite Talents Project, and Yunnan Province Computational Physics and Applied Science and Technology Innovation Team, and the Natural Science Foundation of Shaanxi Provincial Department of Education under Grant no. 20JK0764.

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Authors and Affiliations

  1. Faculty of Science, Kunming University of Science and Technology, Kunming, 650500, People’s Republic of China

    Shuan Wang, Chunhua Zeng & Fengzao Yang

  2. College of Science, Xi’an University of Science and Technology, Xi’an, 710054, People’s Republic of China

    Kezhao Xiong

  3. Paul M. Rady Department of Mechanical Engineering and Department of Physics, University of Colorado, Boulder, CO, 80309-0427, USA

    Baowen Li

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  1. Shuan Wang
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Contributions

SW: writing—original draft preparation; CZ: original idea, funding acquisition; FY, KX and BL: reviewing and editing. All authors contributed to the preparation of the manuscript.

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Correspondence to Chunhua Zeng.

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Wang, S., Zeng, C., Yang, F. et al. Energy diffusion of simple networks under the spatiotemporal thermostats. Eur. Phys. J. B 94, 236 (2021). https://doi.org/10.1140/epjb/s10051-021-00247-z

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