Skip to main content
SpringerLink
Log in

Controlling the diffusion of bistable active clusters in one-dimensional channels

  • Regular Article - Statistical and Nonlinear Physics
  • Published:
The European Physical Journal B Aims and scope Submit manuscript

Abstract

A two-cluster system with a bistable potential is constructed in one-dimensional channels. Using molecular dynamics and Monte Carlo methods, we study the collective diffusion properties of the bistable cluster system. It is shown that the internal structure of the bistable cluster can greatly influence the diffusion behavior, which is different from simple particle systems. The collective diffusion coefficients of two states can differ by two orders of magnitude. An explanation is found from the distance distribution between two clusters. This study provides theoretical guidance for understanding the particularity of complex active structures in diffusion behavior. If the results are extended to active matter, it can be understood that the active matter can regulate the diffusion ability by changing its own morphology or stability.

Graphical abstract

In this manuscript, we have investigated the effects of complex structures on collective diffusion behavior in one dimensional channels as the followings: (1) The collective diffusion coefficient of bistable cluster depends strongly on the internal structure of the cluster. If this is true, it means that the previous simplification of a multi-particle system should be readdressed to new discussions. (2) The influence of cluster bistability on the collective diffusion coefficient varies by two orders of magnitude, just like a switch “on and off”. Assuming that the cluster is an active matter that can adjust its form, then controlling the transport of active matter will be possible.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5

Similar content being viewed by others

Data Availability Statement

This manuscript has no associated data, or the data will not be deposited. [Authors comment: Our results are calculated by our own program and are easily repeatable. Therefore, it is not necessary to store all the original data.]

References

  1. L. Gammaitoni, P. Hänggi, P. Jung, F. Marchesoni, Stochastic resonance. Rev. Mod. Phys. 70, 223 (1998)

    Article  ADS  Google Scholar 

  2. A.A. Zharov, I.V. Shadrivov, Y.S. Kivshar, Nonlinear properties of Left-Handed metamaterials. Phys. Rev. Lett. 91, 037401 (2003)

    Article  ADS  Google Scholar 

  3. W.-J. Zhu, T.-C. Li, W.-R. Zhong, B.-Q. Ai, Rectification and separation of mixtures of active and passive particles driven by temperature difference. J. Chem. Phys. 152, 184903 (2020)

    Article  ADS  Google Scholar 

  4. X. Fang, K. Kruse, L. Ting, J. Wang, Nonequilibrium physics in biology. Rev. Mod. Phys. 91, 045004 (2019)

    Article  ADS  MathSciNet  Google Scholar 

  5. Z. Dong, H.-J. Kim, H. Cui, C. Li, C.-W. Qiu, J.S. Ho, Wireless magnetic actuation with a Bistable parity-time-symmetric circuit. Phys. Rev. Appl. 15, 024023 (2021)

    Article  ADS  Google Scholar 

  6. M. Liu, Y. Sun, D.A. Powell, I.V. Shadrivov, M. Lapine, R.C. McPhedran, Y.S. Kivshar, Nonlinear response via intrinsic rotation in metamaterials. Phys. Rev. B 87, 235126 (2013)

    Article  ADS  Google Scholar 

  7. A. Zaikin, J. García-Ojalvo, R. Báscones, E. Ullner, J. Kurths, Doubly stochastic coherence via noise-induced symmetry in Bistable neural models. Phys. Rev. Lett. 90, 030601 (2003)

    Article  ADS  Google Scholar 

  8. H. Ge, H. Qian, Thermodynamic limit of a nonequilibrium steady state: Maxwell-type construction for a Bistable biochemical system. Phys. Rev. Lett. 103, 148103 (2009)

    Article  ADS  Google Scholar 

  9. W.R. Zhong, Y.Z. Shao, Z.H. He, Pure multiplicative stochastic resonance of a theoretical anti-tumor model with seasonal modulability. Phys. Rev. E 73, 060902 (2006)

    Article  ADS  Google Scholar 

  10. I. Berenstein, C. Beta, Flow-induced transitions in Bistable systems. Phys. Rev. E 86, 056205 (2012)

    Article  ADS  Google Scholar 

  11. D. Powell, I. Shadrivov, Y. Kivshar, Multistability in nonlinear left-handed transmission lines. Appl. Phys. Lett. 92, 264104 (2008)

    Article  ADS  Google Scholar 

  12. K. Zhang, J. Wang, Landscape and flux theory of non-equilibrium open economy. Phys. A 482, 189 (2017)

    Article  MathSciNet  Google Scholar 

  13. Z.-C. Xu, Z. Dong-qin, A. Bao-quan, B. Hu, Z. Wei-rong, Transport diffusion in one dimensional molecular systems: power law and validity of Ficks law. AIP Adv. 5, 107145 (2015)

    Article  ADS  Google Scholar 

  14. A. Fick, Ueber diffusion. Ann. der Phys. 170, 59 (1855)

    Article  ADS  Google Scholar 

  15. E.L. Cussler, Diffusion: mass transfer in fluid systems, 3rd edn. (Cambridge University Press, New York, 2007)

    Google Scholar 

  16. J. Wang, G. Casati, G. Benenti, Inverse currents in Hamiltonian coupled transport. Phys. Rev. Lett. 124, 110607 (2020)

    Article  ADS  MathSciNet  Google Scholar 

  17. F. Salles, H. Jobic, T. Devic, P.L. Llewellyn, C. Serre, G. Férey, G. Maurin, Self and transport diffusivity of CO2 in the metal organic framework MIL-47(V) explored by quasi-elastic neutron scattering experiments and molecular dynamics simulations. ACS Nano 4, 143 (2010)

    Article  Google Scholar 

  18. C. Zaum, K. Morgenstern, Understanding the enhancement of surface diffusivity by dimerization. Phys. Rev. Lett. 121, 185901 (2018)

    Article  ADS  Google Scholar 

  19. A.M. Kusova, A.E. Sitnitsky, D.A. Faizullin, Y.F. Zuev, Protein translational diffusion and intermolecular interactions of globular and intrinsically unstructured proteins. J. Phys. Chem. A 123(46), 10190 (2019)

    Article  Google Scholar 

  20. W. Jost, Diffusion in solids, liquids, gases (Academic Press Inc., New York, 1952)

    Google Scholar 

  21. L. Badowski, M.A. Załuska-Kotur, Z.W. Gortel, Collective diffusion in an interacting one-dimensional lattice gas: arbitrary interactions, activation energy, and nonequilibrium diffusion. Phys. Rev. B 72, 24 (2005)

    Article  Google Scholar 

  22. N. Gnan, E. Zaccarelli, The microscopic role of deformation in the dynamics of soft colloids. Nat. Phys. 15, 683 (2019)

    Article  Google Scholar 

  23. C. Bechinger, R.D. Leonardo, H. Löwen et al., Active particles in complex and crowded environments. Rev. Mod. Phys. 88, 045006 (2016)

    Article  ADS  MathSciNet  Google Scholar 

  24. B.-Q. Ai, Z.-G. Shao, W.-R. Zhong, Mixing and demixing of binary mixtures of polar chiral active particles. Soft Matter 14, 4388 (2018)

    Article  ADS  Google Scholar 

  25. B.-Q. Ai, W.-J. Zhu, Y.-F. He, W.-R. Zhong, Giant negative mobility of inertial particles caused by the periodic potential in steady laminar flows. J. Chem. Phys. 149, 164903 (2018)

  26. J. Philibert, One and a half century of diffusion: fick. Einstein, before and beyond. Diffus Fundam 4, 1 (2006)

    Google Scholar 

  27. A. Dom’ınguez, Signature of time-dependent hydrodynamic interactions on collective diffusion in colloidal monolayers. Phys. Rev. E 90, 062314 (2014)

    Article  ADS  Google Scholar 

  28. N. Guisoni, K.I. Mazzitello, L. Diambra, Alternating regimes of motion in a model with cell-cell interactions. Phys. Rev. E 101, 062408 (2020)

    Article  ADS  Google Scholar 

  29. B. Lin, B. Cui, X. Xinliang, R. Zangi, H. Diamant, S.A. Rice, Divergence of the long-wavelength collective diffusion coefficient, in quasi-one- and quasi-two-dimensional colloidal suspensions. Phys. Rev. E 89, 022303 (2014)

    Article  ADS  Google Scholar 

  30. M. Tokuyama, T. Furubayashi, J. Kawamura, Statistical-mechanical theory of self-diffusion in dilute suspensions of macroions. Phys. A 486, 681 (2017)

    Article  MathSciNet  Google Scholar 

  31. G. Balázsi, A. van Oudenaarden, J.J. Collins, Cellular decision-making, biological noise, from microbes to mammals. Cell 144, 910 (2011)

    Article  Google Scholar 

  32. Y. Tsori, Bistable colloidal orientation in polar liquid near a charged wall. J. Coll. Inter. Sci. 559, 45 (2020)

    Article  ADS  Google Scholar 

  33. L. Girifalco, M. Hodak, R. Lee, Carbon nanotubes, Buckyballs, ropes, and a universal graphitic potential. Phys. Rev. B 62, 13104 (2000)

    Article  ADS  Google Scholar 

  34. M.P. Allen, D.J. Tildesley, Computer simulation of liquids (Oxford University Press, New York, 1987)

    MATH  Google Scholar 

  35. A.P. Thompson, D.M. Ford, G.S. Heffelfinger, Direct molecular simulation of gradient-driven diffusion. J. Chem. Phys. 109, 6406 (1998)

    Article  ADS  Google Scholar 

  36. D.P. Landau, K. Binder, A guide to Monte Carlo simulation in statistical physics (Cambrige University Press, Cambridge, 2004)

    MATH  Google Scholar 

  37. D.J. Adams, Grand canonical ensemble monte Carlo for a Lennerd-Jones fluid. Mol. Phys. 29, 307 (1975)

    Article  ADS  Google Scholar 

  38. S. Boinepalli, P. Attard, Grand canonical molecular dynamics. J. Chem. Phys. 119, 12769 (2003)

    Article  ADS  Google Scholar 

  39. F. Roger, C. David Nicholson, N. Quirke, Direct molecular dynamics simulation of flow down a chemical potential gradient in a slit-shaped micropore. Phys. Rev. Lett. 74, 2463 (1995)

    Article  ADS  Google Scholar 

  40. P.-R. Chen, Xu. Zhi-Cheng, Gu. Yu, W.-R. Zhong, Collective diffusion in carbon nanotubes: crossover between one-dimension and three-dimension. Chin. Phys. B 25, 086601 (2016)

    Article  ADS  Google Scholar 

  41. S. Lepri, R. Livi, A. Politi, Thermal conduction in classical low-dimensional lattices. Phys. Rep. 377, 1 (2003)

    Article  ADS  MathSciNet  Google Scholar 

Download references

Acknowledgements

We would like to thank the high-performance computing platform at Jinan University and Siyuan clusters in the Department of Physics. ZWR sincerely thanks Prof. Bambi Hu for his encouragement on this topic a few years ago, which prompted this author to not give up even in the most difficult times. We hereby express our deep gratitude to him.

Author information

Authors and Affiliations

  1. Siyuan Laboratory, Department of Physics, Jinan University, Guangzhou, 510632, China

    Wei-rong Zhong

  2. Guangdong Provincial Key Laboratory of Quantum Engineering and Quantum Materials, School of Physics and Telecommunication Engineering, South China Normal University, Guangzhou, 510006, China

    Bao-quan Ai

Authors
  1. Wei-rong Zhong
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Bao-quan Ai
    View author publications

    You can also search for this author in PubMed Google Scholar

Contributions

ZWR and ABQ designed the research, performed the research, and wrote the manuscript.

Corresponding author

Correspondence to Wei-rong Zhong.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Zhong, Wr., Ai, Bq. Controlling the diffusion of bistable active clusters in one-dimensional channels. Eur. Phys. J. B 95, 43 (2022). https://doi.org/10.1140/epjb/s10051-021-00248-y

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1140/epjb/s10051-021-00248-y

Search

Navigation