Ultrafast Diffusion Modeling via the Riemann–Liouville Nonlocal Structural Derivative and Its Application in Porous Media
Ultrafast diffusion disperses faster than super-diffusion, and this has been proven by several theoretical and experimental investigations. The mean square displacement of ultrafast diffusion grows exponentially, which provides a significant challenge for modeling. Due to the inhomogeneity, nonlinea...
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| Format: | Article |
| Language: | English |
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MDPI AG
2024-02-01
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| Series: | Fractal and Fractional |
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| Online Access: | https://www.mdpi.com/2504-3110/8/2/110 |
| _version_ | 1827343558120570880 |
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| author | Wei Xu Hui Liu Lijuan Chen Yongtao Zhou |
| author_facet | Wei Xu Hui Liu Lijuan Chen Yongtao Zhou |
| author_sort | Wei Xu |
| collection | DOAJ |
| description | Ultrafast diffusion disperses faster than super-diffusion, and this has been proven by several theoretical and experimental investigations. The mean square displacement of ultrafast diffusion grows exponentially, which provides a significant challenge for modeling. Due to the inhomogeneity, nonlinear interactions, and high porosity of cement materials, the motion of particles on their surfaces satisfies the conditions for ultrafast diffusion. The investigation of the diffusion behavior in cementitious materials is crucial for predicting the mechanical properties of cement. In this study, we first attempted to investigate the dynamic of ultrafast diffusion in cementitious materials underlying the Riemann–Liouville nonlocal structural derivative. We constructed a Riemann–Liouville nonlocal structural derivative ultrafast diffusion model with an exponential function and then extended the modeling strategy using the Mittag–Leffler function. The mean square displacement is analogous to the integral of the corresponding structural derivative, providing a reference standard for the selection of structural functions in practical applications. Based on experimental data on cement mortar, the accuracy of the Riemann–Liouville nonlocal structural derivative ultrafast diffusion model was verified. Compared to the power law diffusion and the exponential law diffusion, the mean square displacement with respect to the Mittag–Leffler law is closely tied to the actual data. The modeling approach based on the Riemann–Liouville nonlocal structural derivative provides an efficient tool for depicting ultrafast diffusion in porous media. |
| first_indexed | 2024-03-07T22:32:00Z |
| format | Article |
| id | doaj.art-c4e367346b5b40cf9e36b8f5087f7b09 |
| institution | Directory Open Access Journal |
| issn | 2504-3110 |
| language | English |
| last_indexed | 2024-03-07T22:32:00Z |
| publishDate | 2024-02-01 |
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| spelling | doaj.art-c4e367346b5b40cf9e36b8f5087f7b092024-02-23T15:17:14ZengMDPI AGFractal and Fractional2504-31102024-02-018211010.3390/fractalfract8020110Ultrafast Diffusion Modeling via the Riemann–Liouville Nonlocal Structural Derivative and Its Application in Porous MediaWei Xu0Hui Liu1Lijuan Chen2Yongtao Zhou3School of Science, Qingdao University of Technology, Qingdao 266520, ChinaSchool of Science, Qingdao University of Technology, Qingdao 266520, ChinaSchool of Science, Qingdao University of Technology, Qingdao 266520, ChinaSchool of Science, Qingdao University of Technology, Qingdao 266520, ChinaUltrafast diffusion disperses faster than super-diffusion, and this has been proven by several theoretical and experimental investigations. The mean square displacement of ultrafast diffusion grows exponentially, which provides a significant challenge for modeling. Due to the inhomogeneity, nonlinear interactions, and high porosity of cement materials, the motion of particles on their surfaces satisfies the conditions for ultrafast diffusion. The investigation of the diffusion behavior in cementitious materials is crucial for predicting the mechanical properties of cement. In this study, we first attempted to investigate the dynamic of ultrafast diffusion in cementitious materials underlying the Riemann–Liouville nonlocal structural derivative. We constructed a Riemann–Liouville nonlocal structural derivative ultrafast diffusion model with an exponential function and then extended the modeling strategy using the Mittag–Leffler function. The mean square displacement is analogous to the integral of the corresponding structural derivative, providing a reference standard for the selection of structural functions in practical applications. Based on experimental data on cement mortar, the accuracy of the Riemann–Liouville nonlocal structural derivative ultrafast diffusion model was verified. Compared to the power law diffusion and the exponential law diffusion, the mean square displacement with respect to the Mittag–Leffler law is closely tied to the actual data. The modeling approach based on the Riemann–Liouville nonlocal structural derivative provides an efficient tool for depicting ultrafast diffusion in porous media.https://www.mdpi.com/2504-3110/8/2/110ultrafast diffusionnonlocal structural derivativestructural functionmean square displacementporous media |
| spellingShingle | Wei Xu Hui Liu Lijuan Chen Yongtao Zhou Ultrafast Diffusion Modeling via the Riemann–Liouville Nonlocal Structural Derivative and Its Application in Porous Media Fractal and Fractional ultrafast diffusion nonlocal structural derivative structural function mean square displacement porous media |
| title | Ultrafast Diffusion Modeling via the Riemann–Liouville Nonlocal Structural Derivative and Its Application in Porous Media |
| title_full | Ultrafast Diffusion Modeling via the Riemann–Liouville Nonlocal Structural Derivative and Its Application in Porous Media |
| title_fullStr | Ultrafast Diffusion Modeling via the Riemann–Liouville Nonlocal Structural Derivative and Its Application in Porous Media |
| title_full_unstemmed | Ultrafast Diffusion Modeling via the Riemann–Liouville Nonlocal Structural Derivative and Its Application in Porous Media |
| title_short | Ultrafast Diffusion Modeling via the Riemann–Liouville Nonlocal Structural Derivative and Its Application in Porous Media |
| title_sort | ultrafast diffusion modeling via the riemann liouville nonlocal structural derivative and its application in porous media |
| topic | ultrafast diffusion nonlocal structural derivative structural function mean square displacement porous media |
| url | https://www.mdpi.com/2504-3110/8/2/110 |
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