Diffusion on hierarchical systems of weakly-coupled networks

Grzegorz Siudem , Janusz Hołyst


We analyzed diffusion dynamics on weakly-coupled networks (interconnected networks)by means of separation of time scales. Using an adiabatic approximation we reduced thesystem dynamics to a Markov chain with aggregated variables and derived a transportequation that is analogous to Fick’s First Law and includes a driving force. Entropy produc-tion is a sum of microscopic entropy transport, which results from the particle’s migrationbetween networks of different topologies and macroscopic entropy production of theMarkov chain. Equilibrium particles partition between different sub-networks dependsonly on internal sub-network parameters. By changing structure of networks one can notonly 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 hierarchicalnetworks with several different time scales thus it can serve to uncover hidden hierarchylevels from observations of diffusion processes.
Publication typeOriginal work published as abstract
Author Grzegorz Siudem (FP / PCSD)
Grzegorz Siudem,,
- Physics of Complex Systems Divison
, Janusz Hołyst (FP / LPESS)
Janusz Hołyst,,
- Center of Physics in Economics and Social Sciences
Corporate authorWydział Fizyki Politechniki Warszawskiej (Wydz.Fizyki PW)
Journal seriesPhysica A-Statistical Mechanics and Its Applications, ISSN 0378-4371, (A 30 pkt)
Issue year2019
Publication size in sheets0.55
Keywords in EnglishComplex networks, Hierarchical systems, Diffusion dynamic
ASJC Classification3104 Condensed Matter Physics; 2613 Statistics and Probability
URL https://doi.org/10.1016/j.physa.2018.08.078
projectComputing Real-World Phenomena with Dynamically Changing Complex Networks . Project leader: Hołyst Janusz, , Phone: 22 234 7133, start date 01-06-2009, end date 30-11-2012, FP7-ICT-2009-5, Completed
WF 7 Framework Programme (7 FP) [7 Program Ramowy (7 PR)]
Self-Organised information PrOcessing, CriticaLity and Emergence in multilevel Systems . Project leader: Hołyst Janusz, , Phone: 22 234 7133, start date 01-12-2012, end date 30-11-2015, 317534, Completed
WF 7 Framework Programme (7 FP) [7 Program Ramowy (7 PR)]
Reverse EngiNeering of sOcial Information pRocessing. Project leader: Hołyst Janusz, , Phone: 22 234 7133, application date 28-04-2015, start date 01-01-2016, end date 31-12-2019, 691152, Implemented
WF Horizon 2020 [Horyzont 2020]
Languageen angielski
1-s2.0-S0378437118310203-main.pdf 600.21 KB
Score (nominal)0
ScoreMinisterial score = 30.0, 19-11-2018, ArticleFromJournal
Ministerial score (2013-2016) = 30.0, 19-11-2018, ArticleFromJournal
Publication indicators Scopus Citations = 0; Scopus SNIP (Source Normalised Impact per Paper): 2016 = 1.324; WoS Impact Factor: 2017 = 2.132 (2) - 2017=2.076 (5)
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