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Characterizing time dependent anomalous diffusion process: A survey on fractional derivative and nonlinear models

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  • Wei, Song
  • Chen, Wen
  • Hon, Y.C.

Abstract

This paper investigates the temporal effects in the modeling of flows through porous media and particles transport. Studies will be made among the time fractional diffusion model and two classical nonlinear diffusion models. The effects of the parameters upon the mentioned models have been studied. By simulating the sub-diffusion processes and comparing the numerical results of these models under different boundary conditions, we can conclude that the time fractional diffusion model is more suitable for simulating the sub-diffusion with steady diffusion rate; whereas the nonlinear models are more appropriate for depicting the sub-diffusion under changing diffusion rate.

Suggested Citation

  • Wei, Song & Chen, Wen & Hon, Y.C., 2016. "Characterizing time dependent anomalous diffusion process: A survey on fractional derivative and nonlinear models," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 462(C), pages 1244-1251.
    • Handle: RePEc:eee:phsmap:v:462:y:2016:i:c:p:1244-1251
    DOI: 10.1016/j.physa.2016.06.145
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    References listed on IDEAS

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    1. Baeumer, B. & Benson, D.A. & Meerschaert, M.M., 2005. "Advection and dispersion in time and space," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 350(2), pages 245-262.
    2. Valdes-Parada, Francisco J. & Alberto Ochoa-Tapia, J. & Alvarez-Ramirez, Jose, 2007. "Effective medium equations for fractional Fick's law in porous media," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 373(C), pages 339-353.
    3. Nigmatullin, R.R., 2006. "‘Fractional’ kinetic equations and ‘universal’ decoupling of a memory function in mesoscale region," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 363(2), pages 282-298.
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