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Diffusion–Advection Equations on a Comb: Resetting and Random Search

Author

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  • Trifce Sandev

    (Research Center for Computer Science and Information Technologies, Macedonian Academy of Sciences and Arts, Bul. Krste Misirkov 2, 1000 Skopje, Macedonia
    Institute of Physics & Astronomy, University of Potsdam, D-14776 Potsdam-Golm, Germany
    Institute of Physics, Faculty of Natural Sciences and Mathematics, Ss. Cyril and Methodius University, Arhimedova 3, 1000 Skopje, Macedonia)

  • Viktor Domazetoski

    (Research Center for Computer Science and Information Technologies, Macedonian Academy of Sciences and Arts, Bul. Krste Misirkov 2, 1000 Skopje, Macedonia)

  • Alexander Iomin

    (Department of Physics, Technion, Haifa 32000, Israel)

  • Ljupco Kocarev

    (Research Center for Computer Science and Information Technologies, Macedonian Academy of Sciences and Arts, Bul. Krste Misirkov 2, 1000 Skopje, Macedonia
    Faculty of Computer Science and Engineering, Ss. Cyril and Methodius University, P.O. Box 393, 1000 Skopje, Macedonia)

Abstract

This review addresses issues of various drift–diffusion and inhomogeneous advection problems with and without resetting on comblike structures. Both a Brownian diffusion search with drift and an inhomogeneous advection search on the comb structures are analyzed. The analytical results are verified by numerical simulations in terms of coupled Langevin equations for the comb structure. The subordination approach is one of the main technical methods used here, and we demonstrated how it can be effective in the study of various random search problems with and without resetting.

Suggested Citation

  • Trifce Sandev & Viktor Domazetoski & Alexander Iomin & Ljupco Kocarev, 2021. "Diffusion–Advection Equations on a Comb: Resetting and Random Search," Mathematics, MDPI, vol. 9(3), pages 1-24, January.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:3:p:221-:d:485338
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    References listed on IDEAS

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    5. Viktor Stojkoski & Trifce Sandev & Lasko Basnarkov & Ljupco Kocarev & Ralf Metzler, 2020. "Generalised geometric Brownian motion: Theory and applications to option pricing," Papers 2011.00312, arXiv.org.
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    Cited by:

    1. Lenzi, M.K. & Lenzi, E.K. & Guilherme, L.M.S. & Evangelista, L.R. & Ribeiro, H.V., 2022. "Transient anomalous diffusion in heterogeneous media with stochastic resetting," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 588(C).
    2. Pece Trajanovski & Petar Jolakoski & Ljupco Kocarev & Trifce Sandev, 2023. "Ornstein–Uhlenbeck Process on Three-Dimensional Comb under Stochastic Resetting," Mathematics, MDPI, vol. 11(16), pages 1-28, August.

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