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Diffusion on hierarchical systems of weakly-coupled networks

Author

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  • Siudem, Grzegorz
  • Hołyst, Janusz A.

Abstract

We analyzed diffusion dynamics on weakly-coupled networks (interconnected networks) by means of separation of time scales. Using an adiabatic approximation we reduced the system dynamics to a Markov chain with aggregated variables and derived a transport equation that is analogous to Fick’s First Law and includes a driving force. Entropy production is a sum of microscopic entropy transport, which results from the particle’s migration between networks of different topologies and macroscopic entropy production of the Markov chain. Equilibrium particles partition between different sub-networks depends only on internal sub-network parameters. By changing structure of networks one can not only modify diffusion constants but can also induce or reverse the direction of the particles’ flow between different networks. Our framework, confirmed by numerical simulations, is also useful for considering diffusion in nested systems corresponding to hierarchical networks with several different time scales thus it can serve to uncover hidden hierarchy levels from observations of diffusion processes.

Suggested Citation

  • Siudem, Grzegorz & Hołyst, Janusz A., 2019. "Diffusion on hierarchical systems of weakly-coupled networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 513(C), pages 675-686.
    • Handle: RePEc:eee:phsmap:v:513:y:2019:i:c:p:675-686
    DOI: 10.1016/j.physa.2018.08.078
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    Cited by:

    1. Buda, Andrzej & Kwapień, Jarosław, 2022. "Agent-based modelling of the global phonographic market," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 598(C).
    2. Deng, Yang & Jia, Zhen & Deng, Guangming & Zhang, Qiongfen, 2020. "Eigenvalue spectrum and synchronizability of multiplex chain networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 537(C).
    3. Agnieszka Geras & Grzegorz Siudem & Marek Gagolewski, 2022. "Time to vote: Temporal clustering of user activity on Stack Overflow," Journal of the Association for Information Science & Technology, Association for Information Science & Technology, vol. 73(12), pages 1681-1691, December.

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