IDEAS home Printed from https://ideas.repec.org/a/eee/phsmap/v377y2007i2p448-464.html
   My bibliography  Save this article

Monte Carlo investigation of anomalous transport in presence of a discontinuity and of an advection field

Author

Listed:
  • Marseguerra, M.
  • Zoia, A.

Abstract

Anomalous diffusion has recently turned out to be almost ubiquitous in transport problems. When the physical properties of the medium where the transport process takes place are stationary and constant at each spatial location, anomalous transport has been successfully analysed within the Continuous Time Random Walk (CTRW) model. In this paper, within a Monte Carlo approach to CTRW, we focus on the particle transport through two regions characterized by different physical properties, in presence of an external driving action constituted by an additional advective field, modelled within both the Galilei invariant and Galilei variant schemes. Particular attention is paid to the interplay between the distributions of space and time across the discontinuity. The resident concentration and the flux of the particles are finally evaluated and it is shown that at the interface between the two regions the flux is continuous as required by mass conservation, while the concentration may reveal a neat discontinuity. This result could open the route to the Monte Carlo investigation of the effectiveness of a physical discontinuity acting as a filter on particle concentration.

Suggested Citation

  • Marseguerra, M. & Zoia, A., 2007. "Monte Carlo investigation of anomalous transport in presence of a discontinuity and of an advection field," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 377(2), pages 448-464.
    • Handle: RePEc:eee:phsmap:v:377:y:2007:i:2:p:448-464
    DOI: 10.1016/j.physa.2006.11.083
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0378437106012490
    Download Restriction: Full text for ScienceDirect subscribers only. Journal offers the option of making the article available online on Science direct for a fee of $3,000
    File URL: https://libkey.io/10.1016/j.physa.2006.11.083?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. Gorenflo, Rudolf & Mainardi, Francesco & Moretti, Daniele & Pagnini, Gianni & Paradisi, Paolo, 2002. "Fractional diffusion: probability distributions and random walk models," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 305(1), pages 106-112.
    2. Scalas, Enrico & Gorenflo, Rudolf & Mainardi, Francesco, 2000. "Fractional calculus and continuous-time finance," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 284(1), pages 376-384.
    3. Mainardi, Francesco & Raberto, Marco & Gorenflo, Rudolf & Scalas, Enrico, 2000. "Fractional calculus and continuous-time finance II: the waiting-time distribution," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 287(3), pages 468-481.
    4. Margolin, Gennady & Berkowitz, Brian, 2004. "Continuous time random walks revisited: first passage time and spatial distributions," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 334(1), pages 46-66.
    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. Marseguerra, M. & Zoia, A., 2008. "Monte Carlo evaluation of FADE approach to anomalous kinetics," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 77(4), pages 345-357.
    2. Marseguerra, M. & Zoia, A., 2007. "Some insights in superdiffusive transport," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 377(1), pages 1-14.
    3. Marseguerra, Marzio & Zoia, Andrea, 2008. "Pre-asymptotic corrections to fractional diffusion equations," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(12), pages 2668-2674.
    4. Zheng, Guang-Hui & Zhang, Quan-Guo, 2018. "Solving the backward problem for space-fractional diffusion equation by a fractional Tikhonov regularization method," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 148(C), pages 37-47.
    5. Scalas, Enrico & Kaizoji, Taisei & Kirchler, Michael & Huber, Jürgen & Tedeschi, Alessandra, 2006. "Waiting times between orders and trades in double-auction markets," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 366(C), pages 463-471.
    6. Fan Yang & Ping Fan & Xiao-Xiao Li & Xin-Yi Ma, 2019. "Fourier Truncation Regularization Method for a Time-Fractional Backward Diffusion Problem with a Nonlinear Source," Mathematics, MDPI, vol. 7(9), pages 1-13, September.
    7. Ren, Fei & Gu, Gao-Feng & Zhou, Wei-Xing, 2009. "Scaling and memory in the return intervals of realized volatility," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 388(22), pages 4787-4796.
    8. Hajipour, Ahamad & Hajipour, Mojtaba & Baleanu, Dumitru, 2018. "On the adaptive sliding mode controller for a hyperchaotic fractional-order financial system," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 497(C), pages 139-153.
    9. Álvaro Cartea & Thilo Meyer-Brandis, 2010. "How Duration Between Trades of Underlying Securities Affects Option Prices," Review of Finance, European Finance Association, vol. 14(4), pages 749-785.
    10. Schumer, Rina & Baeumer, Boris & Meerschaert, Mark M., 2011. "Extremal behavior of a coupled continuous time random walk," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 390(3), pages 505-511.
    11. Saberi Zafarghandi, Fahimeh & Mohammadi, Maryam & Babolian, Esmail & Javadi, Shahnam, 2019. "Radial basis functions method for solving the fractional diffusion equations," Applied Mathematics and Computation, Elsevier, vol. 342(C), pages 224-246.
    12. Langlands, T.A.M., 2006. "Solution of a modified fractional diffusion equation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 367(C), pages 136-144.
    13. G. Fern'andez-Anaya & L. A. Quezada-T'ellez & B. Nu~nez-Zavala & D. Brun-Battistini, 2019. "Katugampola Generalized Conformal Derivative Approach to Inada Conditions and Solow-Swan Economic Growth Model," Papers 1907.00130, arXiv.org.
    14. Ya Qin & Adnan Khan & Izaz Ali & Maysaa Al Qurashi & Hassan Khan & Rasool Shah & Dumitru Baleanu, 2020. "An Efficient Analytical Approach for the Solution of Certain Fractional-Order Dynamical Systems," Energies, MDPI, vol. 13(11), pages 1-14, May.
    15. Marcin Wątorek & Jarosław Kwapień & Stanisław Drożdż, 2022. "Multifractal Cross-Correlations of Bitcoin and Ether Trading Characteristics in the Post-COVID-19 Time," Future Internet, MDPI, vol. 14(7), pages 1-15, July.
    16. Scalas, Enrico & Gallegati, Mauro & Guerci, Eric & Mas, David & Tedeschi, Alessandra, 2006. "Growth and allocation of resources in economics: The agent-based approach," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 370(1), pages 86-90.
    17. Foad Shokrollahi, 2016. "Subdiffusive fractional Brownian motion regime for pricing currency options under transaction costs," Papers 1612.06665, arXiv.org, revised Aug 2017.
    18. D’Amico, Guglielmo & Janssen, Jacques & Manca, Raimondo, 2009. "European and American options: The semi-Markov case," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 388(15), pages 3181-3194.
    19. Jorge E. Macías-Díaz, 2019. "Numerically Efficient Methods for Variational Fractional Wave Equations: An Explicit Four-Step Scheme," Mathematics, MDPI, vol. 7(11), pages 1-27, November.
    20. Boukhouima, Adnane & Hattaf, Khalid & Lotfi, El Mehdi & Mahrouf, Marouane & Torres, Delfim F.M. & Yousfi, Noura, 2020. "Lyapunov functions for fractional-order systems in biology: Methods and applications," Chaos, Solitons & Fractals, Elsevier, vol. 140(C).

    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:phsmap:v:377:y:2007:i:2:p:448-464. 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: http://www.journals.elsevier.com/physica-a-statistical-mechpplications/ .

    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.