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Anomalous transport in disordered systems under the influence of external fields

Author

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  • Metzler, Ralf
  • Barkai, Eli
  • Klafter, Joseph

Abstract

We discuss two models for the description of anomalous diffusion, these being the continuous time random walk scheme, and fractional diffusion equations. We show their interrelations, and combine both approaches for the description of anomalous transport in constant external velocity and force fields. For an arbitrary external force F(x), we introduce a fractional Fokker–Planck equation, which generalises the two Einstein relations.

Suggested Citation

  • Metzler, Ralf & Barkai, Eli & Klafter, Joseph, 1999. "Anomalous transport in disordered systems under the influence of external fields," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 266(1), pages 343-350.
    • Handle: RePEc:eee:phsmap:v:266:y:1999:i:1:p:343-350
    DOI: 10.1016/S0378-4371(98)00614-1
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    Cited by:

    1. Satin, Seema E. & Parvate, Abhay & Gangal, A.D., 2013. "Fokker–Planck equation on fractal curves," Chaos, Solitons & Fractals, Elsevier, vol. 52(C), pages 30-35.
    2. Caicedo, Alejandro & Cuevas, Claudio & Mateus, Éder & Viana, Arlúcio, 2021. "Global solutions for a strongly coupled fractional reaction-diffusion system in Marcinkiewicz spaces," Chaos, Solitons & Fractals, Elsevier, vol. 145(C).
    3. Halley Gomes & Arlúcio Viana, 2021. "Existence, symmetries, and asymptotic properties of global solutions for a fractional diffusion equation with gradient nonlinearity," Partial Differential Equations and Applications, Springer, vol. 2(1), pages 1-30, February.
    4. Lin, Guoxing, 2017. "Analyzing signal attenuation in PFG anomalous diffusion via a modified Gaussian phase distribution approximation based on fractal derivative model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 467(C), pages 277-288.

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