IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v9y2021i3p221-d485338.html
   My bibliography  Save this article

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

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/9/3/221/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/9/3/221/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Arkhincheev, V.E, 2000. "Anomalous diffusion and charge relaxation on comb model: exact solutions," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 280(3), pages 304-314.
    2. 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.
    3. Méndez, Vicenç & Iomin, Alexander, 2013. "Comb-like models for transport along spiny dendrites," Chaos, Solitons & Fractals, Elsevier, vol. 53(C), pages 46-51.
    4. Emilia Bazhlekova & Ivan Bazhlekov, 2019. "Subordination Approach to Space-Time Fractional Diffusion," Mathematics, MDPI, vol. 7(5), pages 1-12, May.
    5. Iomin, A. & Méndez, V., 2016. "Does ultra-slow diffusion survive in a three dimensional cylindrical comb?," Chaos, Solitons & Fractals, Elsevier, vol. 82(C), pages 142-147.
    6. Vladimir V. Palyulin & Vladimir N. Mantsevich & Rainer Klages & Ralf Metzler & Aleksei V. Chechkin, 2017. "Comparison of pure and combined search strategies for single and multiple targets," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 90(9), pages 1-16, September.
    7. Dzhanoev, A.R. & Sokolov, I.M., 2018. "The effect of the junction model on the anomalous diffusion in the 3D comb structure," Chaos, Solitons & Fractals, Elsevier, vol. 106(C), pages 330-336.
    8. Iomin, A., 2021. "Anomalous diffusion in umbrella comb," Chaos, Solitons & Fractals, Elsevier, vol. 142(C).
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    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.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Liu, Lin & Chen, Siyu & Bao, Chunxu & Feng, Libo & Zheng, Liancun & Zhu, Jing & Zhang, Jiangshan, 2023. "Analysis of the absorbing boundary conditions for anomalous diffusion in comb model with Cattaneo model in an unbounded region," Chaos, Solitons & Fractals, Elsevier, vol. 174(C).
    2. Dzhanoev, A.R. & Sokolov, I.M., 2018. "The effect of the junction model on the anomalous diffusion in the 3D comb structure," Chaos, Solitons & Fractals, Elsevier, vol. 106(C), pages 330-336.
    3. Feng, Zongbao & Wu, Xianguo & Chen, Hongyu & Qin, Yawei & Zhang, Limao & Skibniewski, Miroslaw J., 2022. "An energy performance contracting parameter optimization method based on the response surface method: A case study of a metro in China," Energy, Elsevier, vol. 248(C).
    4. Gwang Goo Lee & Sung-Won Ham, 2023. "Prediction of Carbon Price in EU-ETS Using a Geometric Brownian Motion Model and Its Application to Analyze the Economic Competitiveness of Carbon Capture and Storage," Energies, MDPI, vol. 16(17), pages 1-13, August.
    5. Jolakoski, Petar & Pal, Arnab & Sandev, Trifce & Kocarev, Ljupco & Metzler, Ralf & Stojkoski, Viktor, 2023. "A first passage under resetting approach to income dynamics," Chaos, Solitons & Fractals, Elsevier, vol. 175(P1).
    6. Curto, José Dias & Serrasqueiro, Pedro, 2022. "Averaging financial ratios," Finance Research Letters, Elsevier, vol. 48(C).
    7. Stojkoski, Viktor, 2024. "Measures of physical mixing evaluate the economic mobility of the typical individual," Chaos, Solitons & Fractals, Elsevier, vol. 180(C).
    8. Suleiman, Kheder & Song, Qixuan & Zhang, Xuelan & Liu, Shengna & Zheng, Liancun, 2022. "Anomalous diffusion in a circular comb with external velocity field," Chaos, Solitons & Fractals, Elsevier, vol. 155(C).
    9. dos Santos, Maike A.F., 2019. "Analytic approaches of the anomalous diffusion: A review," Chaos, Solitons & Fractals, Elsevier, vol. 124(C), pages 86-96.
    10. Wang, Feifei & Chen, Diyi & Xu, Beibei & Zhang, Hao, 2016. "Nonlinear dynamics of a novel fractional-order Francis hydro-turbine governing system with time delay," Chaos, Solitons & Fractals, Elsevier, vol. 91(C), pages 329-338.
    11. Yeşiltaş, Özlem, 2023. "The Black–Scholes equation in finance: Quantum mechanical approaches," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 623(C).
    12. Johannes Hendrik Venter & Pieter Juriaan De Jongh, 2022. "Trading Binary Options Using Expected Profit and Loss Metrics," Risks, MDPI, vol. 10(11), pages 1-21, November.
    13. Csáki, Endre & Csörgo, Miklós & Földes, Antónia & Révész, Pál, 2011. "On the local time of random walk on the 2-dimensional comb," Stochastic Processes and their Applications, Elsevier, vol. 121(6), pages 1290-1314, June.
    14. Viktor Stojkoski & Petar Jolakoski & Arnab Pal & Trifce Sandev & Ljupco Kocarev & Ralf Metzler, 2021. "Income inequality and mobility in geometric Brownian motion with stochastic resetting: theoretical results and empirical evidence of non-ergodicity," Papers 2109.01822, arXiv.org.
    15. Wang, Zhaoyang & Lin, Ping & Wang, Erhui, 2021. "Modeling multiple anomalous diffusion behaviors on comb-like structures," Chaos, Solitons & Fractals, Elsevier, vol. 148(C).
    16. Endre Csáki & Antónia Földes, 2020. "Random Walks on Comb-Type Subsets of $$\mathbb {Z}^2$$ Z 2," Journal of Theoretical Probability, Springer, vol. 33(4), pages 2233-2257, December.
    17. Jin Hong Kuan, 2022. "Liquidity Provision Payoff on Automated Market Makers," Papers 2209.01653, arXiv.org.
    18. Ma, Pengcheng & Najafi, Alireza & Gomez-Aguilar, J.F., 2024. "Sub mixed fractional Brownian motion and its application to finance," Chaos, Solitons & Fractals, Elsevier, vol. 184(C).
    19. Kemp, Jordan T. & Bettencourt, Luís M.A., 2022. "Statistical dynamics of wealth inequality in stochastic models of growth," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 607(C).
    20. Petar Jolakoski & Arnab Pal & Trifce Sandev & Ljupco Kocarev & Ralf Metzler & Viktor Stojkoski, 2022. "The fate of the American dream: A first passage under resetting approach to income dynamics," Papers 2212.13176, arXiv.org.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:gam:jmathe:v:9:y:2021:i:3:p:221-:d:485338. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.