IDEAS home Printed from https://ideas.repec.org/a/eee/chsofr/v143y2021ics0960077920309632.html
   My bibliography  Save this article

Fractional calculus approach for the phase dynamics of Josephson junction

Author

Listed:
  • Ali, Imtiaz
  • Rasheed, Amer
  • Anwar, Muhammad Shoaib
  • Irfan, Muhammad
  • Hussain, Zakir

Abstract

This article presents the phase dynamics of an inline long Josephson junction in voltage state under the influence of constant external magnetic field. Fractional calculus approach is used to model the evolution of the phase difference between the macroscopic wave functions of the two superconductors across the junction. The governing non-linear partial differential equation is then solved using finite difference-finite element schemes. Other quantities of interest like Josephson current density and voltage across the junction are also computed. The effects of various parameters in the model on phase difference,Josephson current density and voltage are analyzed graphically with the help of numerical simulations.

Suggested Citation

  • Ali, Imtiaz & Rasheed, Amer & Anwar, Muhammad Shoaib & Irfan, Muhammad & Hussain, Zakir, 2021. "Fractional calculus approach for the phase dynamics of Josephson junction," Chaos, Solitons & Fractals, Elsevier, vol. 143(C).
    • Handle: RePEc:eee:chsofr:v:143:y:2021:i:c:s0960077920309632
    DOI: 10.1016/j.chaos.2020.110572
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0960077920309632
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.chaos.2020.110572?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Chen, Ting & Wang, Derong, 2020. "Combined application of blockchain technology in fractional calculus model of supply chain financial system," Chaos, Solitons & Fractals, Elsevier, vol. 131(C).
    2. Jean-Guy Caputo & Nikos Flytzanis & Emmanuel Vavalis, 1995. "A Semi-Linear Elliptic Pde Model For The Static Solution Of Josephson Junctions," International Journal of Modern Physics C (IJMPC), World Scientific Publishing Co. Pte. Ltd., vol. 6(02), pages 241-262.
    Full references (including those not matched with items on IDEAS)

    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. Dutta, Pankaj & Choi, Tsan-Ming & Somani, Surabhi & Butala, Richa, 2020. "Blockchain technology in supply chain operations: Applications, challenges and research opportunities," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 142(C).
    2. Chien-Hua Tsai, 2023. "Supply chain financing scheme based on blockchain technology from a business application perspective," Annals of Operations Research, Springer, vol. 320(1), pages 441-472, January.
    3. Meiyan Li & Yingjun Fu, 2022. "Prediction of Supply Chain Financial Credit Risk Based on PCA-GA-SVM Model," Sustainability, MDPI, vol. 14(24), pages 1-21, December.
    4. Ratri Parida & Manoj Kumar Dash & Anil Kumar & Edmundas Kazimieras Zavadskas & Sunil Luthra & Eyob Mulat‐weldemeskel, 2022. "Evolution of supply chain finance: A comprehensive review and proposed research directions with network clustering analysis," Sustainable Development, John Wiley & Sons, Ltd., vol. 30(5), pages 1343-1369, October.
    5. Chao, Xiangrui & Ran, Qin & Chen, Jia & Li, Tie & Qian, Qian & Ergu, Daji, 2022. "Regulatory technology (Reg-Tech) in financial stability supervision: Taxonomy, key methods, applications and future directions," International Review of Financial Analysis, Elsevier, vol. 80(C).
    6. Rico-Peña, Juan Jesús & Arguedas-Sanz, Raquel & López-Martin, Carmen, 2023. "Models used to characterise blockchain features. A systematic literature review and bibliometric analysis," Technovation, Elsevier, vol. 123(C).
    7. Wei, Leilei & Wang, Huanhuan, 2023. "Local discontinuous Galerkin method for multi-term variable-order time fractional diffusion equation," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 203(C), pages 685-698.
    8. Yu Gong & Yun Zhang & Mohammed Alharithi, 2022. "Supply Chain Finance and Blockchain in Operations Management: A Literature Review," Sustainability, MDPI, vol. 14(20), pages 1-21, October.
    9. Muhamad Deni Johansyah & Asep Kuswandi Supriatna & Endang Rusyaman & Jumadil Saputra, 2022. "The Existence and Uniqueness of Riccati Fractional Differential Equation Solution and Its Approximation Applied to an Economic Growth Model," Mathematics, MDPI, vol. 10(17), pages 1-21, August.
    10. Lei Xie & Hongshuai Han, 2020. "Capacity Sharing and Capacity Investment of Environment-Friendly Manufacturing: Strategy Selection and Performance Analysis," IJERPH, MDPI, vol. 17(16), pages 1-20, August.
    11. Haoyang Tan & Qiang Zhang, 2021. "Application of Blockchain Hierarchical Model in the Realm of Rural Green Credit Investigation," Sustainability, MDPI, vol. 13(3), pages 1-9, January.
    12. Ávalos-Ruíz, L.F. & Zúñiga-Aguilar, C.J. & Gómez-Aguilar, J.F. & Cortes-Campos, H.M. & Lavín-Delgado, J.E., 2023. "A RGB image encryption technique using chaotic maps of fractional variable-order based on DNA encoding," Chaos, Solitons & Fractals, Elsevier, vol. 177(C).
    13. Jacob Lohmer & Elias Ribeiro da Silva & Rainer Lasch, 2022. "Blockchain Technology in Operations & Supply Chain Management: A Content Analysis," Sustainability, MDPI, vol. 14(10), pages 1-88, May.

    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:eee:chsofr:v:143:y:2021:i:c:s0960077920309632. 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: Thayer, Thomas R. (email available below). General contact details of provider: https://www.journals.elsevier.com/chaos-solitons-and-fractals .

    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.