IDEAS home Printed from https://ideas.repec.org/a/eee/apmaco/v390y2021ics0096300320305579.html
   My bibliography  Save this article

Non-local telegrapher’s equation as a transmission line model

Author

Listed:
  • Cvetićanin, Stevan M.
  • Zorica, Dušan
  • Rapaić, Milan R.

Abstract

Transmission line displaying non-locality effects is modelled by considering the magnetic coupling of inductors in the series branch of Heaviside’s elementary circuit, so that the magnetic flux is obtained as a superposition of local and constitutively given non-local magnetic flux through the cross-inductivity kernel. Non-local telegrapher’s equations are derived as the continuum limit of corresponding Kirchhoff’s laws and solved for prescribed external excitation analytically by the means of integral transforms method and also numerically. Numerical examples of the mollified impulse responses illustrate the non-local behavior of signal propagation in case of power, exponential, and Gauss type cross-inductivity kernels.

Suggested Citation

  • Cvetićanin, Stevan M. & Zorica, Dušan & Rapaić, Milan R., 2021. "Non-local telegrapher’s equation as a transmission line model," Applied Mathematics and Computation, Elsevier, vol. 390(C).
    • Handle: RePEc:eee:apmaco:v:390:y:2021:i:c:s0096300320305579
    DOI: 10.1016/j.amc.2020.125602
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0096300320305579
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.amc.2020.125602?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. Weiss, George H, 2002. "Some applications of persistent random walks and the telegrapher's equation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 311(3), pages 381-410.
    2. J. Quintana-Murillo & S. B. Yuste, 2011. "An Explicit Numerical Method for the Fractional Cable Equation," International Journal of Differential Equations, Hindawi, vol. 2011, pages 1-12, September.
    3. Vitali, Silvia & Castellani, Gastone & Mainardi, Francesco, 2017. "Time fractional cable equation and applications in neurophysiology," Chaos, Solitons & Fractals, Elsevier, vol. 102(C), pages 467-472.
    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. Jonathan R. Potts, 2019. "Directionally Correlated Movement Can Drive Qualitative Changes in Emergent Population Distribution Patterns," Mathematics, MDPI, vol. 7(7), pages 1-11, July.
    2. Nikita Ratanov & Mikhail Turov, 2023. "On Local Time for Telegraph Processes," Mathematics, MDPI, vol. 11(4), pages 1-12, February.
    3. Awad, Emad, 2019. "On the time-fractional Cattaneo equation of distributed order," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 518(C), pages 210-233.
    4. Kolesnik, Alexander D., 2018. "Slow diffusion by Markov random flights," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 499(C), pages 186-197.
    5. Vallois, Pierre & Tapiero, Charles S., 2007. "Memory-based persistence in a counting random walk process," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 386(1), pages 303-317.
    6. Peggy Cénac & Arnaud Ny & Basile Loynes & Yoann Offret, 2018. "Persistent Random Walks. I. Recurrence Versus Transience," Journal of Theoretical Probability, Springer, vol. 31(1), pages 232-243, March.
    7. Bogachev, Leonid & Ratanov, Nikita, 2011. "Occupation time distributions for the telegraph process," Stochastic Processes and their Applications, Elsevier, vol. 121(8), pages 1816-1844, August.
    8. Nikita Ratanov, 2004. "Branching random motions, nonlinear hyperbolic systems and traveling waves," Borradores de Investigación 4331, Universidad del Rosario.
    9. Bohdan Datsko & Igor Podlubny & Yuriy Povstenko, 2019. "Time-Fractional Diffusion-Wave Equation with Mass Absorption in a Sphere under Harmonic Impact," Mathematics, MDPI, vol. 7(5), pages 1-11, May.
    10. García-Pelayo, Ricardo, 2007. "Solution of the persistent, biased random walk," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 384(2), pages 143-149.
    11. Vallois, Pierre & Tapiero, Charles S., 2009. "A claims persistence process and insurance," Insurance: Mathematics and Economics, Elsevier, vol. 44(3), pages 367-373, June.
    12. García-Pelayo, Ricardo, 2023. "New techniques to solve the 1-dimensional random flight," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 623(C).
    13. Maes, Christian & Meerts, Kasper & Struyve, Ward, 2022. "Diffraction and interference with run-and-tumble particles," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 598(C).
    14. Filliger, Roger & Hongler, Max-Olivier, 2004. "Supersymmetry in random two-velocity processes," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 332(C), pages 141-150.
    15. Van der Straeten, Erik & Naudts, Jan, 2008. "The 3-dimensional random walk with applications to overstretched DNA and the protein titin," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(27), pages 6790-6800.
    16. Nikita Ratanov, 2022. "Kac-Ornstein-Uhlenbeck Processes: Stationary Distributions and Exponential Functionals," Methodology and Computing in Applied Probability, Springer, vol. 24(4), pages 2703-2721, December.

    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:apmaco:v:390:y:2021:i:c:s0096300320305579. 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: Catherine Liu (email available below). General contact details of provider: https://www.journals.elsevier.com/applied-mathematics-and-computation .

    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.