IDEAS home Printed from https://ideas.repec.org/a/eee/chsofr/v187y2024ics0960077924008646.html
   My bibliography  Save this article

Incorporating memory effect into a fractional stochastic diffusion particle tracking model for suspended sediment using Malliavin-Calculus-based fractional Brownian Motion

Author

Listed:
  • Shen, Stanley W.
  • Tsai, Christina W.

Abstract

This study aims to develop a Fractional Stochastic Diffusion Particle Tracking Model (FSDPTM) to illustrate suspended sediment’s long-term dependence (LTD) trajectories immersed in fully developed turbulent flow. Carried by eddies in the open channel, individual suspended sediment behavior exhibits dependence on its past increments. The Fractional Brownian Motion (FBM) is incorporated into the FSDPTM to account for the randomness of turbulent flow and to include the time-dependent increments as a memory effect. Additionally, to enhance the capacity for differentiating FBM, this study introduces Malliavin Calculus, the stochastic calculus of variation, to construct the square -differentiable FBM. For the numerical realizations of square differentiable FBM, the integration of fractional Gaussian white noise and Wiener–Ito Chaos expansion with the Hermite sequence is employed. The FSDPTM offers probabilistic LTD trajectories as solutions to the Ito-type Langevin equation. It also provides particle velocity, acceleration, and ensemble statistics, collectively demonstrating the application of FBM to sediment transport modeling. In conclusion, the key feature of the FSDPTM is its ability to translate LTD derived from FBM into the trajectory of suspended sediment particles in fully developed turbulent flow. Additionally, it expands the solutions from non-differentiable to square-differentiable stochastic processes.

Suggested Citation

  • Shen, Stanley W. & Tsai, Christina W., 2024. "Incorporating memory effect into a fractional stochastic diffusion particle tracking model for suspended sediment using Malliavin-Calculus-based fractional Brownian Motion," Chaos, Solitons & Fractals, Elsevier, vol. 187(C).
    • Handle: RePEc:eee:chsofr:v:187:y:2024:i:c:s0960077924008646
    DOI: 10.1016/j.chaos.2024.115312
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0960077924008646
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.chaos.2024.115312?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. Djeutcha, Eric & Kamdem, Jules Sadefo, 2021. "Local and implied volatilities with the mixed-modified-fractional-Dupire model," Chaos, Solitons & Fractals, Elsevier, vol. 152(C).
    2. Choe, Hi Jun & Lee, Ji Min & Lee, Jung-Kyung, 2018. "Malliavin calculus for subordinated Lévy process," Chaos, Solitons & Fractals, Elsevier, vol. 116(C), pages 392-401.
    3. Zhang, Yong & Sun, HongGuang & Stowell, Harold H. & Zayernouri, Mohsen & Hansen, Samantha E., 2017. "A review of applications of fractional calculus in Earth system dynamics," Chaos, Solitons & Fractals, Elsevier, vol. 102(C), pages 29-46.
    4. Huang, Chi-Hsiang & Tsai, Christina W. & Wu, Kuan-Ting, 2020. "Estimation of near-bed sediment concentrations in turbulent flow beyond normality," Chaos, Solitons & Fractals, Elsevier, vol. 139(C).
    5. Iovane, G. & Chinnici, M. & Tortoriello, F.S., 2008. "Multifractals and El Naschie E-infinity Cantorian space–time," Chaos, Solitons & Fractals, Elsevier, vol. 35(4), pages 645-658.
    6. Olivera, Christian & Tudor, Ciprian A., 2021. "Absolute continuity of the solution to the stochastic Burgers equation," Chaos, Solitons & Fractals, Elsevier, vol. 153(P2).
    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. Sergeyev, Yaroslav D., 2009. "Evaluating the exact infinitesimal values of area of Sierpinski’s carpet and volume of Menger’s sponge," Chaos, Solitons & Fractals, Elsevier, vol. 42(5), pages 3042-3046.
    2. Kumbhakar, Manotosh & Tsai, Christina W., 2022. "A probabilistic model on streamwise velocity profile in open channels using Tsallis relative entropy theory," Chaos, Solitons & Fractals, Elsevier, vol. 165(P2).
    3. Hamid, Muhammad & Usman, Muhammad & Yan, Yaping & Tian, Zhenfu, 2023. "A computational numerical algorithm for thermal characterization of fractional unsteady free convection flow in an open cavity," Chaos, Solitons & Fractals, Elsevier, vol. 166(C).
    4. Silva, L.B.M. & Vermelho, M.V.D. & Lyra, M.L. & Viswanathan, G.M., 2009. "Multifractal detrended fluctuation analysis of analog random multiplicative processes," Chaos, Solitons & Fractals, Elsevier, vol. 41(5), pages 2806-2811.
    5. Goudarzi, M. & Vaezpour, S.M. & Saadati, R., 2009. "On the intuitionistic fuzzy inner product spaces," Chaos, Solitons & Fractals, Elsevier, vol. 41(3), pages 1105-1112.
    6. Hamid, Muhammad & Usman, Muhammad & Yan, Yaping & Tian, Zhenfu, 2022. "An efficient numerical scheme for fractional characterization of MHD fluid model," Chaos, Solitons & Fractals, Elsevier, vol. 162(C).
    7. Adán J. Serna-Reyes & Jorge E. Macías-Díaz & Nuria Reguera, 2021. "A Convergent Three-Step Numerical Method to Solve a Double-Fractional Two-Component Bose–Einstein Condensate," Mathematics, MDPI, vol. 9(12), pages 1-22, June.
    8. Prakash, Amit & Kumar, Manoj & Baleanu, Dumitru, 2018. "A new iterative technique for a fractional model of nonlinear Zakharov–Kuznetsov equations via Sumudu transform," Applied Mathematics and Computation, Elsevier, vol. 334(C), pages 30-40.
    9. Sabir, Zulqurnain & Raja, Muhammad Asif Zahoor & Guirao, Juan L.G. & Saeed, Tareq, 2021. "Meyer wavelet neural networks to solve a novel design of fractional order pantograph Lane-Emden differential model," Chaos, Solitons & Fractals, Elsevier, vol. 152(C).
    10. Kumbhakar, Manotosh & Tsai, Christina W., 2023. "Analytical modeling of vertical distribution of streamwise velocity in open channels using fractional entropy," Chaos, Solitons & Fractals, Elsevier, vol. 169(C).
    11. Bingqing Lu & Yong Zhang & Donald M. Reeves & HongGuang Sun & Chunmiao Zheng, 2018. "Application of Tempered-Stable Time Fractional-Derivative Model to Upscale Subdiffusion for Pollutant Transport in Field-Scale Discrete Fracture Networks," Mathematics, MDPI, vol. 6(1), pages 1-16, January.
    12. Huang, Chi-Hsiang & Tsai, Christina W. & Wu, Kuan-Ting, 2020. "Estimation of near-bed sediment concentrations in turbulent flow beyond normality," Chaos, Solitons & Fractals, Elsevier, vol. 139(C).
    13. Yong Zhang & Dongbao Zhou & Wei Wei & Jonathan M. Frame & Hongguang Sun & Alexander Y. Sun & Xingyuan Chen, 2021. "Hierarchical Fractional Advection-Dispersion Equation (FADE) to Quantify Anomalous Transport in River Corridor over a Broad Spectrum of Scales: Theory and Applications," Mathematics, MDPI, vol. 9(7), pages 1-15, April.

    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:187:y:2024:i:c:s0960077924008646. 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.