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Radial anomalous diffusion in an annulus

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  • Wang, Shaowei
  • Zhao, Moli
  • Li, Xicheng

Abstract

In this study, time fractional radial diffusion has been modeled in cylindrical coordinates in order to analyze the anomalous diffusion in an annulus. By using an integral transform technique, the analytical solution of the concentration distribution formula is obtained. The establishing of the concentration distribution is found to be controlled by the fractional derivative α, and the influences of α on the concentration field, the total amount diffused and the quantity of mass passing through the inner wall are presented graphically and studied in detail. Asymptotic expressions for the exact solutions are developed in order to explain the numerical results at small and large time, respectively, and the physical mechanism explanation for the paradoxical behavior shown in the numerical results is given.

Suggested Citation

  • Wang, Shaowei & Zhao, Moli & Li, Xicheng, 2011. "Radial anomalous diffusion in an annulus," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 390(20), pages 3397-3403.
    • Handle: RePEc:eee:phsmap:v:390:y:2011:i:20:p:3397-3403
    DOI: 10.1016/j.physa.2011.05.022
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    References listed on IDEAS

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    1. Metzler, Ralf & Klafter, Joseph, 2000. "Boundary value problems for fractional diffusion equations," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 278(1), pages 107-125.
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